Electron beam RF amplifier and emitter

[0001] This application is a division of U.S. application Ser. No. 10/875,489 filed 23 Jun. 2004 now U.S. Pat. No. 7,446,601 which claims priority to U.S. provisional Application Ser. No. 60/482,106 filed 23 Jun. 2003, and hereby incorporated by reference.

[0002] The field of the invention is that of high-frequency electronic amplifiers intended for electromagnetic radio frequency reception and generation, both tuned and broadband. Applications also include digital signal processing and general purpose computing.

[0003] The twentieth century opened with the discovery of radio wave transmission by Marconi. World War II heralded the emergence of radar. The 1960's witnessed the launching of satellites. The 1990's saw the proliferation of commercial wireless data communications. These four events signaled epochal moments in history, opening up entirely new ranges of the electromagnetic spectrum for revolutionary applications such as radio, television, long-range surveillance, satellite communications and computer networking. The key components that made these advances possible were the development of electronic components capable of detecting, amplifying and re-transmitting high-frequency electrical signals: the point contact diode, the vacuum tube triode, the semiconductor transistor, the traveling wave tube, the integrated circuit. Each had—or is having—its moment and was superceded by a newer technology as demand for higher performance increased.

[0004] Today, RF communications, radar and other applications are pushing well into the high gigahertz region, as much as 200 GHz or more. Even home wireless networking and simple cordless telephones are operating at over 5 GHz, a domain once reserved to only the military a few short decades ago.

[0005] The key components that made these advances possible are high-frequency devices: transistors with current-gain-bandwidth products f_T>200 GHz, LNAs with high linearity (IIP3), emerging power transistors made of SiC and GaN, and the venerable traveling wave tube (TWT). Many applications such as digital radio and military surveillance today are limited by the power or bandwidth achievable in a conventional semiconductor, or by the size, weight, cost, power and distortion products of the TWT. Space electronics is also limited by the radiation hardness and reliability of semiconductors. Military applications also require greater bandwidth, with tuning ranges exceeding 10:1 at frequencies up to 100 GHz.

[0006] Semiconductor Amplifiers

[0007] Despite the ubiquity of modern semiconductors, they suffer several limitations for the highest frequency RF applications. First, transistor breakdown voltage must be reduced significantly to achieve the necessary bandwidth, often to a volt or two or less. This severely limits the power they can generate, especially when low distortion is required. More fundamentally, semiconductors have an upper bandwidth dictated by the physics of the semiconductors: the maximum carrier velocity, especially, the saturated electron velocity. Current art places a limitation of perhaps 400 GHz f_T on III-V compound devices such in InP, GaAs, InAs, and a theoretical limit of approximately 1 THz is dictated by the velocity of current-conducting carriers (electrons) in any semiconductor crystal. Practical applications such as an RF low-noise amplifier (LNA) usually can only operate at no more than 1/10 of the f_T. Furthermore, to operate at speeds of 100 GHz or more (as in an RF LNA) requires considerable power. At this time, there are almost no semiconductor power amplifiers capable of operating much above 10 GHz, leaving the entire field of high-power antennas to the field of vacuum electronic devices, such as the TWT, which are orders of magnitude more expensive and bulky. Semiconductor amplifiers are also extremely sensitive to radiation induced degradation and failure in space environments.

[0008] TWTs and Other Traditional Vacuum Electronic Devices

[0009] TWT's offer direct RF amplification with power gains exceeding 40 dB, frequency of amplification over 100 GHz, and bandwidth of more than 2 octaves in specialized devices. The drawback is they are large, very expensive, power consumptive, noisy and introduce significant signal distortion. Size can vary from 10 cubic inches in very high frequency devices (˜100 GHz). Cost can be $10,000 in a typical device to as much as $100 k in a space-rated device. Minimum power consumption can be hundreds of watts even in a low power device. Noise figures are typically 40 dB, compared to as little as 1 dB in a semiconductor LNA. Distortion products for wideband operation can be similarly oppressive, restricting their use to power amplification. TWTs can in principle operate at frequencies approaching or exceeding 1 THz, but become extremely inefficient at these frequencies (as little as a few percent), and very hard to build because of the micron-sized dimensions. Machining tolerances of a few nanometers become necessary, and waveguide losses become dominant, since a long waveguide (such as a helix, serpentine, or many coupled cavities) has unavoidable ohmic sidewall losses.

[0010] Many applications today are severely constrained by the lack of high-frequency performance in available amplifiers. For example, an emerging application is wireless networking in dense urban environments. The demand for communication bandwidth on network channels is already exceeding 1 Gbps, yet the limits of present-day carrier frequencies is only about 5-10 GHz. As is known in the art, the carrier frequency must normally be much higher than the data rate—100 times higher or more. For example, 2.4 Ghz carriers typically provide 10 Mbps data rates or less in the well-known “Bluetooth” system (sometimes called “802.11b”). 1 Gbps data rates imply a carrier of at least 100 GHz or more.

[0011] The problem is exacerbated in dense urban environments, especially around large office buildings. Current technology increases the spectrum capacity by limiting the range of a limited number of sub-channels (which may be spectrally broad in spread spectrum or Ultra Wideband (UWB) systems). No more than a few hundred low-bandwidth (10 Mbps) channels can typically be made available within a short geographic radius of a few hundred meters. In an urban environment with thousands of network connections within a single building and other buildings in close proximity, it can be seen that there is a hard limit, indeed, on the number of network connections and the aggregate data transfer rate that is possible per cubic mile.

[0012] Hard-wired networks traditionally overcome this density limitation, but they are difficult to install and very expensive to retrofit an existing structure. Wireless systems have recently proliferated (based on the 802.11b standard, among others) using higher carrier frequencies, but for higher bandwidths and link densities, few or no solutions exist today.

[0013] As mentioned, semiconductor amplifiers cannot operate much above 100 GHz with any gain at all, and are very power inefficient. TWT amplifiers also cannot operate efficiently much above 100 GHz (though they are much better), but are prohibitively expensive for most applications. What is needed is a solution that offers the size and economies of scale of semiconductors, and the gain and frequency performance of TWTs, with power efficiency and linearity greater than both. Thus, it can be appreciated that there is a real demand for a low cost, efficient millimeter wave to sub-millimeter wave RF technology.

[0014] Related Art

[0015] As will become apparent, the present invention relates to microminiature electron beam devices applied to RF amplification and signaling, particularly those that operate in the millimeter to sub-millimeter wave region (50 GHz to 2 THz). Similar inventions have claimed advances that might operate in this region. For example, Manohara et al (ref. [10]) have published work on sub-millimeter “nano-klystrons” based on many of the elements described herein for the present invention: semiconductor fabrication, MEMS and electron gun construction. An impressive development, it nonetheless suffers many deficiencies, including narrowband tuning, and relatively slow response to signal modulation, because of the resonant cavities inherent in the method. The nano-klystron also lacks integral phase and polarization control, which are highly desirable features of any RF power device intended for transmission purposes, yet expensive and bulky to provide as separate elements.

[0016] U.S. Pat. No. 5,497,053 issued to Tang, et al shows a deflection amplifier (or “deflectron”) that purports to offer wideband amplification, but suffers low gain, relative to the invention here, because the detrimental effects of space charge repulsion limit the maximum beam current. Furthermore, such beam current as Tang et al. can generate creates significant heating losses. Tang et al. also does not offer integral solutions to antenna coupling, phase and polarization control.

[0017] U.S. Pat. No. 3,725,803 issued to Yoder predates Tang et al., and teaches an electron beam driven P-N junction in a push-pull detector arrangement. Yoder does not suggest his method provides extra gain through the beam interaction with the semiconductor diodes, though it may be inferred. However, such extra gain as may be provided will be modest, and the apparatus does not lend itself well to microfabrication. Further, Yoder does not adequately elaborate on how his method will provide linear gain, and it may be inferred from the description that high linearity will not be achievable. For example, Yoder does not describe means for achieving a substantially uniform electron beam. Yoder does not indicate how the detection apparatus can be constructed so as to achieve a linear output from a uniform beam, and in fact, it achieves just the opposite. Thus, Yoder's arrangement is seriously deficient in regard to actual construction of a deflectron having linear response.

[0018] Chang, Muray, Lee, MacDonald (see references) have described “microcolumn arrays” of miniature electron guns and elements thereof for the purpose of improved electron beam lithography in semiconductor fabrication, yet they have not explored the potential of employing microcolumn arrays in amplifiers, RF generators or computing.

[0019] U.S. Pat. No. 3,922,616 issued to Weiner describes one way to provide gain from an electron beam, by means of an electron bombarded semiconductor. This is commonly called an “EBS” amplifier. The method is based on a p+-i-n+ diode with an intrinsic “i” layer. Kitamura et al (1993, ref [11]) explicitly describes an EBS amplifier based on a silicon Schottky diode, but do not employ deflection means. U.S. Pat. No. 4,410,903 issued to Weider describes a heterojunction EBS amplifier based on InGaAs and InP compounds to improve the speed and bandwidth, but these suffer from lack of compatibility with low-cost silicon microfabrication. All three disclosures provide means to improve the gain of an electron beam deflectron amplifier over that of Yoder or Tang et al.

[0020] U.S. Pat. No. 5,592,053 issued to Fox et al. describes a variation on the EBS amplifier that provides gain via an electron-beam activated diamond conductor. U.S. Pat. No. 5,355,380 issued to Lin describes a related e-beam excited diamond switch for millimeter wave generation that depends on modulating the current of an electron beam. The principle disadvantage in either is that high beam energies are required with a diamond detector material. This causes extra heating losses, reduced efficiency, and severely limits the deflection gain. Another disadvantage is that Fox does not employ a precision e-beam forming device, such as a microcolumn. Another disadvantage is the difficulty of fabricating high-quality diamond films. Again, beam deflection is not incorporated in the gain mechanism.

[0021] A principle disadvantage of following Tang et al., Yoder, or Weiner is that they rely on high current electron beams, which are difficult to focus in low-energy beam systems because of the space charge effect. Lack of focus reduces amplifier gain, decreases bandwidth and increases amplifier distortion. Fox overcomes this with a high energy beam. High current and high energy beams are antithetical to microfabricated electron beam systems. High current and high energy beams dissipate excess anode heating power. High voltage beam circuitry is susceptible to destructive arcing and requires high voltage power supplies, which are difficult to build, bulky and power consumptive, and not amenable to microfabrication.

[0022] U.S. Pat. No. 4,328,466 issued to Norris et al describes an EBS amplifier that operates with a sheet beam to disperse the space charge and permit higher beam current, but sheet beams still suffer substantial space charge effects, thereby limiting the beam current and amplifier gain. Norris' amplifier suffers from the complexity of a distributed architecture to achieve high frequency broadband and high power operation, making it unsuitable for low-cost microfabrication.

[0023] Low current beams are desirable, yet they reduce amplifier gain. It may be appreciated that there is a need for higher current, but low energy electron beam systems for microfabricated high speed amplifiers.

[0024] U.S. Pat. No. 5,041,069 issued to Seiler, U.S. Pat. No. 6,177,909 issued to Reid, and Froberg (ref. [07]) have constructed photoconductive antennas which employ semiconductor antenna excitation to generate THz radiation, yet they suffer from uncontrolled wideband transmission, no phase or polarization control, and require complex laser activation with slow pulse repetition rates. As will be seen, the present invention advances the art over all these examples of prior art, simultaneously providing, in different embodiments, controlled wideband modulation, high gain, RF transmission, phase and polarization control.

[0025] It will be appreciated in the following description and appended claims that the present invention combines many of the advantages of prior art while overcoming the deficiencies in a novel arrangement, to thereby achieve RF amplifier embodiments possessing higher gain, faster operation, less distortion and lower power consumption. These benefits accrue in almost any RF receiver or transmitter application including wireless networking and antenna beamforming, frequency multiplication, high-speed digital logic and computing.

[0026] The disclosure to follow provides method and apparatus for wideband RF amplification that solves the shortcomings of both semiconductor and conventional vacuum electronic amplifiers. It can simultaneously provide high frequency of operation (exceeding 1 THz), wide bandwidth (up to 10:1 frequency range or more), high power gain (60 dB or more), linear operation and low noise in a size comparable to an integrated circuit (several cubic millimeters) with similar cost and lower power consumption. What is disclosed is a hybrid of semiconductor and vacuum electronics. It can be constructed using standard semiconductor fabrication techniques. There are many embodiments of the same basic principle:

[0027] A first embodiment, amplifies a voltage signal and generates a highly linear current output by exciting a detector with a deflection modulated electron beam. The method includes a two-dimensional array of electron guns to generate beamlets, a distributed beam deflection apparatus in each electron gun array to provide high deflection gain to re-direct the electron beam in response to a voltage signal, and an electrostatic lens system to create a shaped electron beam spot where the beam strikes a current amplifying detector. The detector in one form comprises dual segments to differentially collect the beam in proportion to the deflection. Each segment converts a collected proportion of the beam to an electrical current, amplifies it, and couples it to an output network.

[0028] In the most linear configurations, the dual detector segments are triangular and oriented in opposition to respond to a narrow rectangular beam spot; for the highest linearity, the space separating the segments distorts the shape of the segments from pure triangularity. In the fastest configuration, the segments are rectangular and the beam spot is rectangular to give a configuration that has the smallest detector.

[0029] One construction is by semiconductor manufacturing processes including wafer bonding.

[0030] In another embodiment the detector is a Schottky diode made of a germanium-silicon heterostructure. In another, the detector is Schottky diode made from a low-ionization material such as InAs or InSb. In either case, the detector provides beam-generated cascade gain and avalanche multiplication by a sandwich of semiconductor between a beam contact and an output contact.

[0031] In another embodiment, the beam shaping is achieved with a shaped array of electron guns that are imaged on the detector by the electrostatic lens system.

[0032] In another embodiment, the lens system is a doublet of a retarding and accelerating lens constructed from planar electrodes in the drift cavity. One configuration comprises a circular disc electrode enclosing the electron gun array to generate the retarding lens, and a circular electrode enclosing the detector to generate the accelerating lens. The drift cavity is enclosed by a cylindrical drift can with the electron gun array centered in one end, and the detector centered in the other. Planar donut electrodes may enclose the first and second disc electrodes in their respective planes.

[0033] A variation achieves beam shaping with an astigmatic electron lens system comprising multiple shaping electrodes disposed around the exit plane of the electron gun array, and the electrodes are subject to different applied voltage potentials.

[0034] All embodiments employ electron gun construction comprising field emission cathodes, cathode gating, a plurality of focusing and aperture electrodes, and deflection plates. In one variation, the plurality of focusing and aperture electrodes is increased in number to reduce the diameter of the gun column (relative to the beam axis). In another a beam blanking deflector is incorporated for pulsed operation.

[0035] Another embodiment incorporates current control in every electron gun, comprising a ballast resistor to sense the cathode current and an amplifier to compare the ballast voltage against a reference, thereby generating an error signal that is applied to the cathode gate electrode.

[0036] In another embodiment, offset centering apparatus keeps the beam centered on the detector with a control loop comprising an integrator generating an offset correction signal in response to the beam offset as measured at the detector. A variation employs independent detector segments to measure the offset.

[0037] Another embodiment provides true time delay shifting by means of apparatus to adjust the energy of the electron beam and thereby the drift time through the drift cavity. One variation adjusts the potential of the detector plane, and in a configuration that improves the focusing, augments the cylindrical drift can electrode with a consecutive series of ring electrodes to approximate the fields potentials generated by a much larger drift cavity. In another variation the acceleration energy of the electron gun achieves the time delay control by augmenting the construction with a plurality of DACs coupled to deliver precise electrode focusing voltages for every time delay command. A further variation augments this arrangement with an analog-to-digital converter to couple a digitized measurement of the control gate with the time delay command, to generate electron gun focusing electrode potentials that are corrected for varying gate voltages in response to a current control loop.

[0038] Yet another embodiment achieves frequency multiplication. One configuration uses a multiplicity of detector segments in a linear array that provides programmable multiplication. Another configuration achieves lower inharmonicity by using a circular detector in a two-dimensional arrangement of segments similar to the slices of a pie, and uses horizontal and vertical electron gun deflection.

[0039] Another embodiment of frequency multiplication employs a single shaped detector segments and a shaped beam spot. The sweep of the shaped beam spot across the edge of the segment generates strong harmonics. The variations include triangular beam spots on rectangular detectors, rectangular beam spots on triangular detectors, rectangular beam spots on quadratically shaped detectors, and so forth, to generate second, third, fourth and so on harmonics.

[0040] Another embodiment, is a mixing device comprising a square detector made of four equal square segments arranged symmetrically around axes X and Y, a square beam spot disposed to sweep in X and Y directions in response to a first signal applied to an X deflection apparatus and a second signal applied to a Y deflection apparatus.

[0041] Another embodiment is a combinational logic device comprising a plurality of N deflectors X1, X2, . . . XN, a corresponding plurality of deflection signals V1, V2, . . . VN, and detectors D1, D2, . . . DM, each individually positioned to correspond to a logic state of the deflection vector V1 . . . VN. Some of the deflectors XN are oriented for horizontal beam deflection and some of the deflectors are oriented for vertical beam deflection to improve the degeneracy of states and the compaction of the system. A further extension of the concept employs deflectors of different geometries to achieve gray coding for a further reduction in the state degeneracy.

[0042] Another embodiment, is a method of exciting electromagnetic radiation by incorporating an antenna, such as a dipole, patch or horn. Some variations provide a selectable polarization dipole or patch by means of X and Y deflection, multiple detector segments and/or multiple addressable feedpoints.

[0043] Another radiating embodiment, excites a waveguide. The waveguide may be rectangular or circular. The excitation can be single or dual polarization to excite desired waveguide modes. The dual polarization device consists of four segments, with two opposing segments connected across a diameter of the waveguide, and the other two opposing segments connected across an orthogonal diameter of the waveguide. This may be augmented with a selectably shaped beam spot for selectable polarization, with a rectangular spot shape spanning two opposing detectors and a motion that sweeps between the two detectors. Any of the waveguide embodiments may be coupled to the feed of an antenna horn.

[0044] Another embodiment merges the detector and antenna in a single structure to make a novel radiator that can simultaneously generate harmonics and controlled phase and polarization. In a variation, multiple, independently steerable beams are employed to enhance the diversity of the output radiation.

[0045] Another embodiment, is constructed as an array of amplifiers according to any of the other embodiments, thereby achieving transmit antenna arrays, receive antenna arrays, T-R arrays and signal combining networks.

[0046] Another embodiment, is a crossbar matrix comprising a plurality of N independent electron guns, a plurality of M detectors and crossbar addressing means. Each electron gun includes independent X and Y deflectors, and receives N digital input signals and N X and Y offset control signals for addressably configuring the matrix. The crossbar addressing means comprises a plurality of DACs under the control of a processor or ROM.

[0047] An extension of the crossbar matrix further includes free-space photonic I/O comprising a photonic input array, an input lens system, a photodetector array, a laser diode array, an output lens system, and an output photonic coupling array. The lens system images the photonic input array on the photodiode array. The photodiode array electrically couples individual photodiodes to individual electron guns to transmit the signals to addressed detector outputs. The laser diode array electrically couples individual laser diodes to individual detectors. The photonic I/O can be provided by fiber optic bundles

[0048] Another embodiment, is a multiprocessing compute engine comprised of a crossbar matrix coupled to a plurality of processor elements.

[0171] Overview

[0172] FIG. 1 shows one embodiment of an electron-beam amplifier 10(1), including an array 100(1) of electron guns, an electrostatic deflection apparatus 130(1) driven by a voltage signal 140(1), a drift cavity 145(1) characterized by a length z_drift, two detector segments 150(1), 150(2) separated by a slot 160(1), and an output network 190(1). An X-Y plane in which detector segments 150(1), 150(2) are located is a detector plane 50; an X-Y plane at a nearest side of deflection apparatus 130(1) to the detector plane is an emission plane 20 (only small portions of emission plane 20 and detector plane 50 are shown, for clarity of illustration). Emission plane 20 and detector plane 50 are separated by a drift cavity length z_drift, as shown. A Z direction from detector plane 50 to emission plane 20 is a transmission axis 200; in this embodiment an X direction is a sweep direction 210. Detector segments 150(1), 150(2) may be semiconductor diodes or other beam-current amplifying detectors, as described below. Each of detector segments 150(1), 150(2) has a width X_D in sweep direction 210.

[0173] Amplifier 10(1) operates by (1) emitting a composite electron beam (“e-beam”) 110(1) (consisting of electron beams 120 emitted from individual electron guns that are not shown in this figure), (2) deflecting composite beam 110(1) by applying voltage signal 140(1) to deflector apparatus 130(1), (3) generating output currents I₁ 180(1) and I₂ 180(2) through the action of composite beam 110(1) impinging upon detector segments 150(1), 150(2) at beam spot 170(1), and (4) transmitting output currents 180(1), 180(2) into output network 190(1). By deflecting composite beam 110(1) with voltage signal 140(1), a physical change in position of beam spot 170(1) impinging upon segments 150(1), 150(2) generates changes in output currents 180(1), 180(2) that can be coupled to an output load such as a resistor, a transmission line, a waveguide, or an antenna.

[0174] The principle of operation may be understood as follows. Composite beam 110(1) sweeps back and forth in sweep direction 210 from detector segment 150(1) to detector segment 150(2) in response to voltage signal 140(1). Electron beams 120, and thus composite beam 110(1), carry an electrical current equal to the well-known electronic charge q times a number of electrons emitted per unit time. Voltage signal 140(1), applied across a gap within beam deflection apparatus 130(1) establishes an electric field E that subjects electrons in e-beams 120 to a transverse force F as they travel through the deflector. The force is described by the well-known law F=qE. At a maximum positive beam deflection, detector segment 150(1) may collect all of the impinging beam current; at a maximum negative deflection, detector segment 150(2) may collect all of the impinging beam current. Between these extremes of positive and negative deflection, each of detector segments 150(1) and 150(2) collects a proportionate amount of the beam current. For example, when composite beam 110 is centered, each of detector segments 150(1) and 150(2) may collect 50% of the beam current. If beam 110(1) is positioned to 70% of maximum deflection in the positive sweep direction (i.e., the X direction of FIG. 1), detector segment 150(1) may collect 30% of the beam current and detector segment 150(2) may collect 70% of the beam current. An absence of a voltage signal 140(1) applied to beam deflection apparatus 130(1), resulting in no deflection of e-beams 110(1) by deflection apparatus 130(1), is a quiescent state.

[0175] Other factors being equal (as explained below), a deflection of composite beam 110(1) may be proportional to voltage signal 140(1), and a beam current collected by either of detector segments 150(1), 150(2) may be linear in response to the change in position of beam 110(1). As shown in FIG. 1, beam 110(1) may approximate a sheet, made of a linear array of e-beams 120, and generating a line-shaped beam spot 170(1) (the terms “sheet” and “line spot” are not to be taken in the mathematical sense of having zero thickness or width respectively). When beam 110(1) is deflected across a rectangular detector segmented by a diagonal slot (e.g., detector segments 150(1), 150(2) and slot 160(1)) the collection of beam current by each of the detector segments 150(1), 150(2) may be proportional to a beam deflection and a resulting beam spot displacement on the detector.

[0176] FIG. 2 shows an amplifier transfer curve 182 for the electron-beam amplifier of FIG. 1. As explained above, each of output currents I₁ and I₂ (180(1) and 180(2) in FIG. 1) can vary according to the input voltage drive amplitude V_INPUT; at a given V_INPUT, a differential current ΔI_OUTPUT=I₂−I₁. ΔI_OUTPUT varies from a maximum negative amount to a maximum positive amount as input voltage V_INPUT varies, as shown in FIG. 2.

[0177] FIG. 3 shows an exemplary output network 190(1) for the electron-beam amplifier of FIG. 1. In this embodiment, a voltage source 192 is provided, and each of output currents 180(1) and 180(2) connect with voltage source 192 through loads 194(1) and 194(2) respectively. A differential current 182 forms in output network 190(1) such that output currents 180(1) and 180(2) convert to a voltage (FIG. 3). With sufficient deflector gain (as explained below), a large enough drift cavity length z_drift, and a small enough detector width X_D, the arrangement of FIG. 1 may have voltage gain.

[0178] Current Multiplying Detector

[0179] FIG. 4 shows a schematic cross section of one current multiplying Schottky e-beam detector 150 of electron-beam amplifier 10(1). Beam detector 150 consists of a thin beam contact 220 having a thickness t_bc, a cascade gain layer 230 having a thickness t₁, an avalanche multiplication layer 250 having a thickness t₂, and an output contact 270. Beam contact 220 and output contact 270 may be a diode anode and cathode, but which of the beam contact and output contact is anode or cathode will depend on the specific beam contact material and semiconductor being contacted.

[0180] A gain of electron-beam amplifier 10(1) may substantially increase when detector segments 150(1), 150(2) amplify collected beam currents so that output currents 180(1), 180(2) are much greater than the beam currents alone. For example, a gain of 1000 or more is possible with a Schottky diode detector. In the embodiment of FIG. 4, thin beam contact 220 mates to cascade gain layer 230 having a high cascade ionization gain. Beam contact thickness t_bc is thin enough to permit e-beam 120 to penetrate to cascade gain layer 230. In cascade gain layer 230, substantially all electrons in beam 120 excite hole-electron pairs in a cascade process that generates hole-electron pairs as beam energy dissipates within the diode (only exemplary electrons 240 are shown, for clarity of illustration). For example, germanium has a cascade ionization gain that generates one hole-electron pair per 2.8 electron-volts (eV) of beam energy. With, for example, a 280 eV beam exciting a germanium diode, the net cascade gain may be 100.

[0181] In certain semiconductor devices such as, for example, a Schottky diode, cascaded electrons can further multiply through the well-known avalanche multiplication effect. A key parameter for avalanche multiplication is thickness t₂ of avalanche multiplication layer 250. With an appropriate reverse bias voltage between cathode and anode contacts, a thickness t₂ of 250 to 1000 angstroms can create a sufficiently strong electric field within the diode to accelerate conduction electrons, generating even more hole-electron pairs (only exemplary electrons 260 are shown, for clarity of illustration). An avalanche gain of 10 or more is practical, and with a cascade gain of 100, an overall detector gain of 1000 is possible.

[0182] Alternative Detector Types

[0183] Many types of current multiplying detectors are possible, including Schottky diodes, junction diodes, photoconductors, and even micro-channel plates (MCPs, or micro-dynodes). Junction diodes operate similar to a Schottky diode, and may support higher voltage operation, but may have lower bandwidth. Photoconductors typically operate by generation of hole-electron pairs by photons to modulate the conductance of a resistor; a photoconductor can be designed to respond to electrons instead, generating conduction electrons by cascade excitation. A photoconductor may lack avalanche multiplication to supplement the cascade gain, and thus have lower gain than a diode; photoconductors also typically have a less linear response when coupled to a load. MCPs generate gain by a photomultiplier effect, but require high bias voltages (thousands of volts), complex construction, and have long response times.

[0184] It can be appreciated that a Schottky diode detector is preferred where high gain and fast response is desired.

[0185] Schottky Detector

[0186] The exemplary Schottky detector 150 of FIG. 4 has germanium and silicon epitaxial layers. A cascade gain layer 230 is n-type Ge and an avalanche layer 250 is n-type Si, where the cascade gain layer 230 and the avalanche layer 250 make up generally a semiconductor layer 255. A beam contact 220 is an anode made of gold (Au) forming a Schottky contact, and an output contact 270 is a cathode.

[0187] However, in other Schottky diode embodiments, other contact metals and semiconductor materials (such as, for example, InAs) may be used; in such embodiments a beam contact may be a cathode and an output contact may be an anode. A beam contact may connect with a bias voltage and the Schottky diode may be reverse biased to establish a field gradient between the beam contact and an output contact. The field gradient (1) accelerates carriers to generate avalanche multiplication of current, and (2) sweeps carriers rapidly out of the diode. The output contact is coupled to a load, for example a terminating resistor or a transmission line. When a beam contact is an anode, the bias voltage may be negative with respect to a load.

[0188] In detector 150 of FIG. 4, the electrons in e-beam 120 first impinge upon beam contact 220, which permits penetration of energetic electrons into cascade gain layer 230 with little absorption by the contact metal. Thus, detector 150 has a high beam current collection efficiency. If thickness t_bc of beam contact 220 is on the order of 10 angstroms, most electrons of e-beam 120 will enter cascade gain layer 230. Cascading starts when one high-energy beam electron (not shown) collides with an electron in a crystal lattice structure of cascade gain layer 230, leaving two electrons (and holes) with half the energy of the original. These two electrons in turn generate 4 electrons (and holes) of ¼ energy, and so on, until the energy of the pairs is comparable to typical thermal energies of electron and holes in Ge. The termination of the cascade process depends on a property called cascade ionization energy, which is the amount of energy in eV required for cascade-generation of a hole-electron pair.

[0189] Germanium is a desirable cascade layer material because it has a high cascade gain relative to other materials, such as silicon or diamond. In germanium, one cascade electron (and a corresponding hole) are generated for each 2.8 eV energy for each beam electron. The cascade energy of silicon is 3.5 eV; the cascade energy of diamond is 5.5 eV.

[0190] A cascade process generally occurs within approximately 50 angstroms of semiconductor depth for a beam energy of several hundred electron volts; for higher energy beams, the cascade may spread deeper. Because conduction electrons in germanium have lower saturation velocities than conduction electrons in silicon, thickness t₁ of cascade gain layer 230 is optimally thick enough to allow completion of the cascade process, but not thicker, so that a transit time of conduction electrons to avalanche layer 250 is minimized.

[0191] Avalanche layer 250 of detector 150 optimally achieves two goals: (1) it supports a high saturated electron velocity, for fast detector response, and (2) it produces efficient, low-noise avalanche multiplication. Avalanche multiplication occurs when conduction electrons accelerate in a high-field region of avalanche layer 250. Accelerated electrons may impinge upon electrons in a crystal lattice of avalanche layer 250, generating more hole-electron pairs. Electrons thus generated accelerate again, and the process repeats, generating an avalanche current. The electrons are collected by output contact 270; holes thus generated travel through cascade gain layer 230 and are collected by beam contact 220. Avalanche multiplication can easily provide current amplification of 5, 10, 20 or more. Practical limits to avalanche multiplication are set by leakage current across a Schottky junction, and electrical noise generated by the avalanche multiplication. Silicon is a desirable avalanche layer material because leakage currents in Si are lower than in many other materials. Ge—Si epitaxy is desirable because a large body of experience in reliably and inexpensively fabricating this material system exists.

[0192] Thus, a Ge—Si Schottky diode may provide high cascade gain, high avalanche gain, high speed response, and low leakage. With a 280 eV beam, a cascade gain may approach 100, avalanche gain may be 10, and a total detector gain may be 1000.

[0193] III-V Detectors

[0194] Fast, high gain detectors may also be constructed with epitaxial systems other than Ge—Si, and such detectors may offer suitable performance for some embodiments of electron-beam amplifier 10. For example, all of Ge, Si and diamond are indirect bandgap semiconductors; in each, the cascade ionization energy is approximately ⅓ of the bandgap. Materials with direct, small bandgaps may have lower ionization energies. For example, Indium Arsenide (InAs) has a direct bandgap of 0.35 eV. Indium Antimonide (InSb) has a direct bandgap of 0.17 eV. These bandgaps compare with 0.66 eV for Ge and 1.12 eV for silicon. Either of these materials from groups III and V of the periodic table (the “III-V” group), or a ternary compound (such as for example InAs_1-xSb_x) may have a cascade ionization energy of 1 eV or less, and provide a cascade gain of three times or more the cascade gain of Ge.

[0195] III-V materials have a zincblende crystal structure; epitaxial growth of this structure on a diamond lattice of silicon may be problematic or impossible. In order to overcome this difficulty, InAs or InSb layers could instead be mated with another III-V avalanche layer, such as Indium Phosphide (InP).

[0196] For example, one drawback of a Ge—Si detector 150 is that its breakdown voltage is limited by a Si layer thickness (e.g., thickness t₂ of FIG. 4). A diode with low breakdown voltage may limit output power since the diode cannot sustain a large reverse voltage; a Ge—Si detector that is a few hundred angstroms thick will be limited to an operating voltage of 2-3 volts. However, with an InP layer, an operating voltage of 6V or more may be possible while enabling the same detector response. This is partly because of high electron mobility in InP (about 4 times higher than in silicon) and partly because InP supports high saturated carrier velocity (almost 2.5 times higher than in Si), permitting a thicker avalanche region to be used while maintaining a given transit time. InP also has an inherently higher dielectric strength, so a thicker layer is required to achieve the same avalanche gain. Therefore, a useful embodiment of detector 150 may have an InAs/InP Schottky diode, or utilize other combinations of III-V materials that achieve high cascade and avalanche gain.

[0197] Detector Beam Contact

[0198] For electrons to penetrate a beam contact of a detector (e.g., beam contact 220 of detector 150) and enter an underlying semiconductor (i.e., Ge cascade gain layer 230, or another material), the contact metal must usually be thin. At beam energies of 100 eV to 300 eV, beam contact layer 220 may be around 10 angstroms, or thinner. However, a thin contact layer may have a high sheet resistance, for example about 10 ohms per square of metal. Contact layer 220 may conduct all of the detector current, which may be 100 mA or more, and an ohmic voltage drop across contact layer 220 may substantially de-bias a low-voltage detector 150. Such de-biasing may have consequences such as loss of detector gain, slower response, and signal distortion.

[0199] FIG. 5A and FIG. 5B show a schematic cross section of one e-beam detector 150(3) with a low resistance electrode 290. Detector 150(3) has gridded beam conductors 280 (only exemplary conductors 280 are labeled, for clarity of illustration) that are much thicker than beam contact 220, and connect with low resistance electrode 290 at each end. By fabricating gridded beam conductors 280 on top of beam contact 220, most electrons of beam 110 will still pass between conductors 280, and impinge upon and pass through beam contact 220. Conductors 280 ensure low electrical resistance between external connections (not shown) and all portions of beam contact 220, thus mitigating ohmic drops and power losses.

[0200] FIG. 6A and FIG. 6B show a schematic cross section of another e-beam detector 150(5) with a low resistance electrode 295. In detector 150(5), a rectangular grid of beam conductors 285 overlies beam contact 220, connecting beam contact 220 to low resistance electrode 295 from all sides.

[0201] A width of each of beam conductors 280 and 285 may be much less than a space between adjacent beam conductors. For example, if a space between beam conductors is 1 um, the beam conductors' width may be less than 0.1 um. Thus, in each of detectors 150(3), 150(4), 150(5) and 150(6), the proportion of area that beam 110 cannot penetrate the thick beam conductors may be less than 10%.

[0202] Amplifier Gain

[0203] An overall electron-beam amplifier gain depends on deflection and detection gain and an output coupling impedance. Beam deflector, drift cavity and detector geometries can generally be chosen to (1) provide a given level of gain and frequency response, and (2) achieve 100% differential beam collection at a maximum deflector input voltage. That is, in the example of FIG. 1, a maximum positive deflector input voltage will direct 100% of the beam current into detector segment 150(1) and zero beam current into segment 150(2); a maximum negative deflector input voltage will direct zero beam current into segment 150(1) and 100% beam current into segment 150(2). A differential transconductance gain g_m of electron-beam amplifier 10 is a ratio of a maximum output current swing 2I_BEAM to a maximum input voltage V_MAX, multiplied by a detector gain K_DET, or

[0204] $\begin{array}{cc}{g}_m=2\frac{I_{\mathrm{BEAM}}}{V_{\mathrm{MAX}}}{K}_{\mathrm{DET}}& \left(1.1\right)\end{array}$

[0205] The factor of 2 reflects the fact that the signaling is differential. For example, when a beam current is 100 μA, a maximum peak deflector voltage drive is 1V and a detector gain is 1000, the differential transconductance gain is 100 mA/volt. When output network 190 has a differential impedance Z₀=100 ohms, the amplifier voltage gain G_V=g_mZ₀ equals 10.

[0206] A power gain G_P is given by a ratio of an AC input power, V_IN²/2R_IN, to an AC output power,

[0207] $\begin{array}{cc}{V}_{\mathrm{OUT}}^2/2R_{\mathrm{OUT}}={\left(G_V{V}_{\mathrm{IN}}\right)}^2/2R_{\mathrm{OUT}}\text{:}& \left(1.2\right)\\ G_P=\frac{R_{\mathrm{IN}}}{R_{\mathrm{OUT}}}{\left(\frac{V_{\mathrm{OUT}}}{V_{\mathrm{IN}}}\right)}^2=\frac{R_{\mathrm{IN}}}{R_{\mathrm{OUT}}}{G}_V^2& \left(1.3\right)\end{array}$

[0208] where R_IN is an input impedance and R_OUT is an output impedance. With equal input and output impedances (e.g., 50 ohms), power gain G_P may be 20 db or more. For larger input impedances, the power gain will be larger. For instance, for an input impedance of 1 kohm, a differential output impedance of 100 ohm and a voltage gain of 10, G_P is 1000, or 60 db. High frequency systems typically do not utilize high input source impedances, but specialized systems may.

[0209] Other Detector Shapes and Beam Spots

[0210] FIG. 7A through FIG. 7B show various geometric embodiments of detector segments 150 and beam spots 170 that are drawn approximately to scale with one another for purposes of comparison. Diagonally segmented detectors 150(1), 150(2) and sheet beam spot 170(1) of FIG. 7A (and FIG. 1) illustrate a first embodiment that is characterized by very linear amplifier response, simple spot creation, and conceptual simplicity for purposes of illustration. The embodiment of FIG. 7A is also characterized by a large detector, slow response, and low gain. The low gain stems from a large beam deflection angle required for full scale detector output, and a low beam current of a sheet beam. The gain can be increased by decreasing detector segment width, as shown in detector segments 150(7) and 150(8) of FIG. 7B, but with some sacrifice in linearity, and the detector is still large.

[0211] High Speed Detector

[0212] FIG. 7C shows detector segments 150(9) and 150(10) separated by a vertical slot 160(2). The detector embodiment of FIG. 7C has a rectangular beam spot 170(2), and has a smaller size, a faster response and a higher beam current than the embodiments of FIG. 7A and FIG. 7B. Unlike a detector made of triangular segments and excited by a line spot, the detector embodiment of FIG. 7C has a much smaller detector, only about twice as large as beam spot 170(2). Detector segments 150(9) and 150(10) have lower parasitic junction capacitance and contact resistance than detector segments 150(1), 150(2), 150(7) and 150(8), and thus may support operation at higher frequencies.

[0213] Beam spot 170(2) permits high beam current by dispersing beam charge over an area, rather than a line. Detector segments 150(9) and 150(10) are small, with a height of segments 150(9) and 150(10) matching the height of beam spot 170(2), resulting in lower parasitic capacitance and wider bandwidth into an output impedance. Vertical slot 160(2) enables linear differential beam collection, with some sacrifice of linearity because of the small dimensions.

[0214] In a preferred embodiment, a height of a beam spot is slightly greater than a height of corresponding detector segments, placing current density variation substantially outside the detector segments. FIG. 8A and FIG. 8B show exemplary variation in beam current density in a rectangular e-beam 170(6) and a circular beam 170(7). Contour lines A, B, C and D of each of beams 170(6) and 170(7) represent regions of greatest to least current density, respectively; in particular, each contour line A encloses a region of maximum current density. Graphs below electron beams 170(6) and 170(7) show the beam current density as a function of position across each e-beam at a midpoint that is indicated by dashed lines M-M′ on each e-beam. Beam spots 170 (i.e., including beam spot 170(1), 170(2) and so on) shown in the accompanying drawings other than FIG. 8A and FIG. 8B correspond to maximum current density contour line A of FIG. 8A and FIG. 8B, and do not show variations in beam current density which may occur around edges of each beam spot.

[0215] When a beam spot 170 is larger than a corresponding detector segment 150, most of a beam current density variation may fall outside detector segment 150, where it has no effect. Thus, the region of the most uniform spot current density (i.e., an interior of a beam spot 170) sweeps across a vertical slot 160, enabling high linearity of differential beam collection. Any portion of an beam spot 170 that falls outside a detector segment 150 is collected by a passive metallic anode and returned to ground.

[0216] The linearity of the detector of FIG. 7C depends strongly on a uniform beam current density. FIG. 7D shows a version that is more linear in the presence of beam current density variation. Beam spot 170(3) is made somewhat larger than detector segments 150(9) and 150(10) so that beam current density variations fall outside the detector segments. This configuration incurs some loss of beam current and amplifier gain due to the portion of beam current that falls outside detector segments 150(9) and 150(10).

[0217] FIG. 7E shows a version that has both high speed and higher power. Detector segments 150(11) and 150(12) are stretched in height, and beam spot 170(4) is increased in area, so that more beam current can be delivered without incurring focusing distortions from space charge spreading, as explained below.

[0218] Unipolar Detector

[0219] In certain embodiments, a unipolar detector for driving only one output load may be preferred. Two versions are shown in FIG. 7F and FIG. 7G. Unipolar detectors 150(13) and 150(14) have only one of the two segments of the previously described differential detectors (e.g., FIG. 7A through FIG. 7E). The area surrounding detector segments 150(13) and 150(14) are ground or power planes (not shown), and a slot (not shown) exists between this ground plane and the detector segment. The unipolar detector configuration may drive a single output load, such as the unbalanced port of a balun.

[0220] Many detector configurations are possible for optimizing electron-beam amplifier operation and performance. Certain configurations will be described in the embodiments that follow, but others will be evident to those skilled in the art, as depending on the basic elements of a shaped e-beam spot and a high-gain detector consisting of one or more segments that are shaped.

[0221] Linearity Requirements

[0222] One attribute of many amplifiers is linearity of amplification. The linearity of RF amplifiers is characterized by a quantity known as a third order input intercept point (“IIP3”) that characterizes an input referred power of distortion products (i.e., an output distortion power divided by amplifier gain) in relation to an input signal power. IIP3 measures the most significant distortion product, a third harmonic, referred to an input of an amplifier. Fully differential operation of certain systems may eliminate the second and other even harmonics, or at least reduce them well below the third harmonic; thus the third harmonic is a useful measure of total non-linearity, including 5^th, 7^th, and higher orders, as well as intermodulation products.

[0223] IIP3 describes the concept that a ratio of third harmonic output power to signal output power may increase in direct proportion to a first harmonic input signal power (this ratio is the same when referred to the input). That is, small input signals may generate small distortion products, since the non-linearities present in an amplifier are less significant for the small input signals, while large input signals may generate proportionately larger distortion products. The output of an amplifier operating with large signals may “clip” peaks in an output waveform (i.e., the peaks of amplified signals may not achieve appropriate values, because such values would exceed the maximum voltages available). Generally, for a 3 dB increase in small-signal output power, third harmonic output power increases by 9 dB. Even if the third harmonic output power is much smaller than a linear output power under small-signal conditions, if the input increases sufficiently, the third harmonic output power may equal and even exceed it. The point where input signal power and the third harmonic output power are equal is called the third order intercept point. IIP3 is usually an extrapolated figure of merit since linear output power cannot usually reach this level of power because of gain compression (i.e., where amplifier gain starts to diminish at high signal levels).

[0224] FIG. 9 illustrates relationships among the fundamental output power, second harmonic output power, and third harmonic output power for an exemplary amplifier. Horizontal axis 300 is an input power axis and vertical axis 310 is an output power axis; both are logarithmically scaled. Curve 320 shows input referred output power at a fundamental (i.e., the input) harmonic (i.e., at an input frequency when the input is a single frequency tone); curve 330 shows input referred output power at the second harmonic; curve 340 shows input referred output power at the third harmonic. An intercept of curve 320 and curve 340 is IIP3.

[0225] IIP3 is a valid figure of merit for many amplifiers in a restricted range of actual operation. Higher IIP3 implies better amplifier performance in rejecting distortion, even if an amplifier cannot operate at an input signal level indicated by an IIP3 specification. A well-made low noise amplifier (“LNAs”) may achieve an IIP3 of +5 dbm. That is, 3 mW input signal power will generate 3 mW of distortion (referred back to the input). Certain amplifiers may achieve an IIP3 of +20 dbm or +40 dbm, but these performance figures may not be achieved at frequencies that exceed a few hundred MHz. Generally, the higher an operating frequency and the wider an operating bandwidth, the more difficult it is to achieve a high IIP3.

[0226] Electron-beam amplifier 10 may achieve an IIP3 as high or higher than typical solid-state amplifier, such as +40 dbm or better, at frequencies of many GHz, and potentially up to K band (40 GHz) or higher. This may be shown by considering an input-referred effect of third harmonic distortion as described by a transfer function of the form y=x+a₃x³:
V_in=V₁+a₃V₁³=V₁(1+a₃2Z₀P₁)  (1.4)

[0227] where V_in is an input voltage, V₁ is an input deflection voltage corresponding to a maximum beam deflection (e.g., a peak sinusoidal input cos(ωt)), a₃ is a third harmonic distortion coefficient, Z₀ is an input impedance, and P₁ is an extrapolated input power. At a very high IIP3 of +50 dbm, P₁ is 100 W from a 50 ohm source Z₀. At an IIP3 intercept point, third harmonic power is the same as input power, so solving the above equation, the third harmonic distortion coefficient is

[0228] $\begin{array}{cc}{a}_3=\frac{1}{2Z_0·\mathrm{IIP}3\left(\mathrm{watts}\right)}=1\times {10}^{-4},& \left(1.5\right)\end{array}$

[0229] or 0.01%. This harmonic distortion coefficient is of the same order of magnitude as the manufacturing tolerances that may be achieved in a microfabricated embodiment of the electron-beam amplifier (for example, the reproducibility that may be achieved in the beam spot and the detector and slot geometries). For example, a detector of 10 um width may be made with segment tolerances of about 1 nm, about 10,000 times smaller than the width. Given the wide bandwidth of the electron-beam amplifier, it is possible to achieve high IIP3, and by the wideband nature of the amplifier, can achieve such high IIP3 at extremely high frequencies.

[0230] Distortion Compensation

[0231] Solid-state amplifiers have little flexibility in eliminating distortion. For example, low distortion requires high bias levels and amplifier bandwidth much wider than a signal bandwidth; reducing output signal level as a fraction of total bias level, in turn reducing the range and effect of non-linearities. The high bias levels lead to excessive power consumption in exchange for minor linearity improvement.

[0232] Non-linearity of electron-beam amplifier 10 is primarily related to non-ideal deflector apparatus 130, a shape and a current density of beam spot 170 and a shape of detector segment(s) 150. The most difficult linearity parameters to control are deflector apparatus 130 and beam current density. Though deflector apparatus 130 inherently has a linear response, fringing fields are unavoidable and difficult to compensate in a compact electron-beam amplifier 10. Beam current density is also difficult to control because of space-charge spreading effects and variations in currents among individual e-beams 120.

[0233] High linearity in electron-beam amplifier 10 can be achieved by optimizing the geometry of apparatus 130 and regulating beam currents of individual e-beams 120 with control loops to assure a uniform, controlled beam spot current density. Residual beam spot and deflection distortion can be compensated by appropriately shaping a geometry of beam spot(s) 170, and slot(s) 160 separating detector segment(s) 150.

[0234] As discussed above, beam spot 170 is an outline of a cross-sectional current density of e-beam 110 where it impinges upon detector(s) 150. This current density may be non-uniform, and a “spot shape” is simply a contour of some value of current density. For many configurations of electron-beam amplifier 10, it may be convenient to assume that this current density is essentially uniform within the spot, and zero outside. It can be appreciated that simply referring to the “beam spot” may facilitate understanding of the basic principles of electron-beam amplifier 10.

[0235] Non-uniform beam spots 170 may occur for many reasons, including imperfect electron gun focusing, thermal agitation of electrons, space charge spreading, imperfect focusing of multiple e-beams 120 into a single beam spot 170, and quantum effects. In electron-beam amplifier 10, the beam spot 170 and detector segments 150 may be shaped to effectively eliminate many distortion effects, substantially extending the linearity and utility of the amplifier.

[0236] Slot Deformation Linearity Correction

[0237] FIG. 1 shows a simple arrangement of electron-beam amplifier 10(1) for conceptual purposes, with a pair of complementary triangular detector segments 150(1) and 150(2) and a narrow sheet beam 110 that generates a line spot 170. It can be seen that when beam 110 is centered with zero deflection, both of segments 150(1) and 150(2) collect equal amounts of beam current. As beam 110 is displaced left or right, output currents I₁ and I₂ (180(1) and 180(2) in FIG. 1) change in proportion to the deflection. Ideally, this arrangement generates no distortion at all; for example, as long as line spot 170 is straight and has a uniform current density from top to bottom.

[0238] FIG. 10 shows a distorted amplifier transfer curve and a corrected amplifier transfer curve. When a shape of beam spot 170 is distorted but is otherwise uniform in current density, a transfer curve of the amplifier may become distorted; curve 360 is an example of a distorted transfer curve.

[0239] FIG. 11 shows three embodiments of detectors shaped to adjust amplifier transfer function characteristics. Detector segments 150(15) and 150(16), separated by slot 160(3), may compensate for a distorted beam spot 170(6) and a corresponding transfer function distortion illustrated in curve 360 of FIG. 10. Slot 160(3) has a geometry that makes a differential increase in collected current constant as a function of spot displacement X; that is, slot 160(3) keeps d(ΔI_OUTPUT)/dX constant until the maximum value of ΔI_OUTPUT is reached. Curve 370 in FIG. 10 shows an amplifier transfer curve that may be generated by the use of detector segments 150(1-5) and 150(16).

[0240] The principle of slot deformation can extend to other shapes of beam spots 170 and detector geometries 150. For example, in some configurations it may be convenient to utilize a circular spot shape rather than a line spot; others might employ a triangular shape. Other embodiments may unavoidably have beam spots 170 with non-uniform current density.

[0241] Detector Shaping Linearity Correction

[0242] Because slot 160(2) between high speed detector segments 150(9) and 150(10) of FIG. 7C is always covered by beam spot 170(2), it cannot be deformed to correct for a non-linearities caused by beam spot current density variation or an imperfect rectangular spot shape. Instead, distortion may be corrected by shaping the geometry of the detector without altering the spot. This is illustrated in detector segments 150(17), 150(18), 150(19), and 150(20) of FIG. 11. A shape of beam spot 170(7), of course, may also be altered, but precise distortion correction is generally more easily achieved by shaping detector segments 150. When a beam spot 170 is larger than corresponding detector segments 150, a proportion of beam current collected by the detector segments and collected by a surrounding ground plane changes as the spot is swept. Thus, with appropriate shaping, a linearity of differential collection can be improved.

[0243] Beam Centering

[0244] Proper operation of electron-beam amplifier 10 requires centering of e-beam 110 on detector segments 150, since a displacement of the beam with respect to a center position generates an amplifier output signal. Because of manufacturing tolerances in mechanical construction of the amplifier (including for example tolerances in geometries within beam deflection apparatus 130(1), and in axial alignment of deflection apparatus 130(1) to detector segments 150) the beam may be displaced from the center position when the voltage signal 140 is zero. For this reason, a feedback amplifier may be incorporated to center e-beam 110 through use of an offset control loop.

[0245] FIG. 12A and FIG. 12B show two embodiments of a beam offset control loop. FIG. 12A shows a beam offset control loop 375 with an integrator 380 coupled to receive a differential detector output 382(1) and 382(2), and coupling (as explained below) from an integrator output 384 to a deflection apparatus 130(2). Deflection apparatus 130(2) can be a distributed structure, but FIG. 12B shows a single deflection apparatus for purposes of illustration.

[0246] In beam offset control loop 375, a differential voltage ΔV develops when currents from detector segments 150 are applied to a load. Integrator 380 filters and amplifies ΔV over time to generate a correction signal V_OS, which is a measure of a misalignment of beam 120 with respect to a center position 390 between detector segments 150. V_OS is applied to deflection apparatus 130(2) as described below. Correction signal V_OS acts to restore an average beam position so that it stays centered between detector segments 150. A static gain of electron-beam amplifier 10 may be high enough that a residual offset is negligible.

[0247] In beam offset control loop 375, the coupling from integrator output 384 to deflection apparatus 130(2) includes a summing circuit 400. Correction signal V_OS is summed with an RF voltage input V_IN being amplified, and the sum of these signals is applied to a single deflection apparatus 130(2). In a beam offset control loop 376 shown in FIG. 12B, V_IN is applied to one deflection apparatus 130(3) and the correction signal is applied to a separate deflection apparatus 130(4).

[0248] FIG. 13A and FIG. 13B show two circuit embodiments of integrators for beam centering. FIG. 13A shows an integrator embodiment 410 made from transistors in a standard cascaded differential pair with a current mirror load. Detector output voltages V₁ and V₂ are generated by currents, from detector segments 150(21) and 150(22) that are shown schematically here as diodes, driving output loads 420(1) and 420(2). A voltage difference V₁−V₂ corresponds with an instantaneous beam offset. Transistors 430(1) and 430(2) respond to V₁−V₂ by generating currents I_a and I_b, while rejecting common-mode voltage of V₁ and V₂. The current mirror copies and reflects I_a to generate I_c, which in turn generates filter current I_F=I_a−I_b feeding capacitor C_F. When a composite beam (not shown) is offset towards detector segment 150(21), V₁<V₂ and I_F causes V_OS to increase, forcing the beam away from detector segment 150(21). Conversely, if the beam is offset towards detector segment 150(22), V₁>V₂ and I_F causes V_OS to decrease, forcing the beam away from detector segment 150(22). A filtering action of C_F makes the circuit of FIG. 13A responsive to the average beam position, and non-responsive to the input signal. High impedance of current sources I_c and I_b into the high DC impedance of the capacitive deflector load generates a high gain response at low frequencies. Thus, an average position of the beam is centered.

[0249] FIG. 13B shows another integrator embodiment 450 employing an operational amplifier (“opamp”) 460. Again, detector output voltages V₁ and V₂ are generated by currents from detector segments (not shown) driving output loads 470(1) and 470(2) with values of R₁ and R₂ respectively. The circuit of FIG. 13B also includes capacitors 480 and 490, with values of C₁ and C₂ respectively. By utilizing a nodal analysis, the output V_OS is seen to respond to the average of V₁ and V₂ according to

[0250] $\begin{array}{cc}{V}_{\mathrm{OS}}=\frac{-1}{{\mathrm{sR}}_1{C}_1}\left(V_1-V_2\right)+\frac{V_2}{1+{\mathrm{sR}}_2{C}_2}& \left(1.6\right)\end{array}$
for frequencies f>>½πR₂C₂, where s is a Laplace frequency variable equal to j2πf. At high frequencies, the second term is near zero, and the device acts as an integrator with a time constant τ₁=R₁C₁. At low frequency, the first term still dominates because

[0251] $\begin{array}{cc}\frac{V_1-V_2}{{\mathrm{sR}}_1{C}_1}>>V_2.& \left(1.7\right)\end{array}$

[0252] Thus, integrator 450 has feedback loop characteristics similar to those of integrator 410; both are suitable for beam centering in certain embodiments of electron-beam amplifier 10. In certain other embodiments of electron-beam amplifier 10, it may be advantageous to have dedicated detector segments, called “offset sense segments,” for measuring beam offset.

[0253] FIG. 14A and FIG. 14B show a control loop configuration, an integrator circuit, and several offset sense segment configurations for implementing beam offset control. FIG. 14A shows a beam offset control loop 377 with construction similar to beam offset control loop 376 of FIG. 12B. A portion of a beam 120 strikes offset sense segments 150(23) and 150(24), generating currents I₁ and I₂ that are fed into inputs 510(1) and 510(2) of an integrator 500. An output 520 of integrator 500 connects with beam deflection apparatus 130(5) to apply a correction to beam 120. FIG. 14B shows an integrator 530 which is simpler than integrator 410 (i.e., the amplifier need not decouple an input RF signal).

[0254] FIG. 15A through FIG. 15. D show several offset sense segment configurations. FIG. 15A shows arrangement 551 which includes detector segments 150(25) and 150(26) with offset sense segments 540(1) and 540(2), a simple arrangement that provides a signal for controlling beam offset in one direction for one pair of detector segments. FIG. 15B shows arrangement 552 which includes detector segments 150(27), 150(28), 150(29) and 150(30) with offset sense segments 540(3) and 540(4); this arrangement supports two pair of detector segments but still provides a signal for controlling beam offset in only one direction. FIG. 15C shows arrangement 553 which includes detector segments 150(31) and 150(32) with offset sense segments 540(5), 540(6), 540(7) and 540(8). Arrangement 553 may provide more balanced offset signals if there is current density gradation around the edge of beam spot, and a suitable pair of integrators (not shown) may derive offset control signals in a sweep direction (horizontal in this view) and an orthogonal direction (vertical in this view). FIG. 15D shows arrangement 554 which includes detector segments 150(31) and 150(32) with offset sense segments 540(5), 540(6), 540(7) and 540(8). Arrangement 554 may also be used to derive control signals in a two directions, and a pair of integrators corresponding to arrangement 554 may be simpler than the pair of integrators corresponding to arrangement 553, there being a dedicated set of offset sense segments in each axis. However, arrangement 554 requires a larger beam spot to overlap around detector segments 150(33) and 150(34), resulting in lower amplifier gain due to lost beam current; offset sense segments are also more susceptible to current density variations in arrangement 554 than in arrangement 553.

[0255] Microminiaturized Fabrication

[0256] Electron-beam amplifier 10 may be made with microminiaturized construction using wafer-based semiconductor fabrication technology. Microminiaturized deflectors may be as little as 1 μm long and may produce a frequency response greater than 1 THz. Single electron guns may have a cross-section of a few microns, and entire arrays of hundreds of guns may generate a precise beam with a diameter of 100 μm or less. Electron-beam detectors may be as small as a few microns, with femto-farad parasitic capacitance and THz bandwidth. An entire amplifier may have dimensions of only a few millimeters and thousands of amplifiers may be batch produced simultaneously with low cost, high yield and reliability characteristic of conventional integrated circuits.

[0257] FIG. 16A shows a dimension of one microfabricated electron-beam amplifier 10(2). Outer dimensions of the amplifier A_X, A_Y, and A_Z may be, for example, 5 mm. FIG. 16B shows another dimension of electron-beam amplifier 10(2). A height h_ega of electron gun array 100(2) may be in the range of 50 μm to 200 μm. A diameter d_drift of drift cavity 560 may be, for example, 3 mm, and a drift cavity length z_drift may be 2 mm.

[0258] Manufacturing of a microminiaturized electron-beam amplifier may include fabrication, alignment, and bonding of individual elements such as field emission cathodes, beam focusing electrodes, deflector plates and other components into electron gun assemblies called “microcolumns” or “electron gun microcolumns” herein. Techniques such as photolithography, etching, deposition, implantation, plating, multi-level metallization, wafer bonding, and possibly other methods may be used to assemble components such as microcolumns, drift cavities, detectors, output coupling networks and bias circuitry into a monolithic device.

[0259] Entire wafers may be constructed as arrays of amplifiers, for individual use or to work in concert. Silicon wafers are useful substrates for forming certain components because of silicon's low cost and because diverse fabrication techniques are available. For example, field emission cathodes on silicon wafers, including the molybdenum tips called Spindt cathodes disclosed in U.S. Pat. No. 3,665,241, have been especially successful. Wet etching may be employed for large drift cavities, and dry etching methods such as deep reactive ion etching can cut very small, precise, high-aspect ratio features such as the beam contact grid of the detector. Critical holes in electron guns can be fabricated with even more precise focused ion-beam and laser drilling. Multi-level planarized metallization processes using chemical and mechanical polishing (“CMP”) may form many of the electrodes, especially those in the microcolumn electron guns. Aluminum, gold, copper, nickel, tungsten and other metals are widely applied with both sputtering, vacuum deposition and plating techniques. Semiconductor devices (for example, bias circuits, output networks and other circuitry for use with electron-beam amplifier 10) may be formed concurrently with other electron-beam amplifier components on a silicon substrate, using similar, compatible techniques.

[0260] High aspect ratio etching technologies and waferbonding are characteristic of what is called “micromachining” or micro-electrical mechanical systems (“MEMS”) technology. Because of the complex three-dimensional geometries, different elements of the device may be constructed on separate substrates, and these substrates can be assembled into a single unit. Many methods of bonding wafers exist today, such as, for example, eutectic or fusion bonding. Techniques for wafer bonding have also been developed to create vacuum-encapsulated cavities, which are useful for electron beam devices, e.g., as shown in U.S. Pat. No. 5,842,680 issued to Davis and U.S. Pat. No. 6,479,320B1 issued to Gooch. Furthermore, SiO₂ gettering materials are compatible with silicon semiconductor processing and have been demonstrated to sustain ultra-high vacuum and enhance cathode lifetime in electron guns, e.g., as shown in U.S. Pat. No. 4,771,214 issued to Takenaka et al.

[0261] Space Charge Spreading

[0262] A primary reason for limited beam current in any e-beam amplifier is an inherent, electric-field induced repulsion between beam electrons, which forces apart electrons in a focused beam, and is called “space charge spreading”. In high current beams, the forces are substantial, and as electrons travel through a drift cavity, these forces can spoil an initial focus that may exist just after a beam exits from an electron gun.

[0263] FIG. 17 illustrates a space charge spreading effect in a high current electron beam. Electron-beam 110′ traveling in a direction shown by arrow Z spreads as it travels.

[0264] Coulomb's Law describes a force between two electrons:
F∝1/R²,  (1.8)

[0265] where R is a distance between adjacent electrons. Since, for any two electrons at random positions within a beam, R is proportional to the radius r of the beam, so an average repulsive force between electrons decreases (to first order) quadratically with the total radius of a beam, for the same total beam current. Thus, a beam of 10 um diameter will have 100 times less repulsive force than a beam of 1 um diameter.

[0266] Electron Gun Arrays

[0267] An embodiment of an electron-beam amplifier minimizes space charge spreading by using a two-dimensional (“2-D”) array of electron guns. Like a linear (i.e., one-dimensional) array, a 2-D array of electron guns generates individual electron beams that are emitted as parallel beams from an emission plane (e.g., emission plane 20).

[0268] FIG. 18 shows one embodiment of a two-dimensional microcolumn array, and an associated electron beam and detector. Microcolumn array 570 emits e-beam 110(2) towards detectors 150(1) and 150(2). As described below, electron optics consisting of a first electrode 580(1) and a third electrode 590(1) focus composite e-beam 110(2) consisting of individual e-beams 120 to a beam spot 170(8). Each e-beam 120 has a current that is low enough that space charge spreading within the e-beams is negligible over the length z_drift of a drift cavity, (e.g., drift cavity 145). The electron gun array spaces the e-beams sufficiently far apart so that the space charge repulsion between adjacent beamlets is also negligible over the length of the drift cavity.

[0269] The aggregate sum of the individual e-beams is termed here the composite electron beam. The low Coulomb force interactions within individual e-beams reduces beam spreading in proportion to a cross-sectional area of the beam, permitting higher total beam current for a given amount of spreading force. For example, a linear array of electron guns emitting N e-beams of current I will have approximately the same spreading force as a circular two-dimensional electron gun array emitting N² e-beams of current I. The circular array will have N times higher current for the same spreading force.

[0270] From this example, it may be appreciated that a 2-D arrays of electron guns provides a significant reduction in space charge spreading forces in a microminiaturized electron-beam amplifier 10. In combination with beam current amplification from an active detector 150, and optical focusing techniques described below, electron-beam amplifier 10 achieves higher gain and power, and requires no (large, heavy and costly) magnets. Thus, microminiaturized amplifier construction is possible, with attendant advantages including, for example, high bandwidth and low cost.

[0271] Distributed Deflector Array

[0272] To achieve high-gain deflection performance with a two-dimensional array of beams, it is not possible to simply pass all electron beams through a single large pair of deflection plates. A beam originating at an emission plane (e.g., emission plane 20) with a diameter corresponding to a 2-D electron gun array would require a deflector with a plate spacing that is too large to generate sufficient beam deflection at reasonable voltage drives. This reduces amplifier gain unacceptably, unless the plate lengths were made correspondingly longer; however, longer plates reduce bandwidth performance proportionately.

[0273] For example, if an electron gun array has a diameter of 100 μm at an emission plane, a deflector with 100 μm plate spacing would have 100 times less deflection force than a deflector with a plate spacing of only 1 μm. To get the same beam deflection as the deflector with 1 μm plate spacing, the deflector with 100 μm plate spacing would have to be 100 times longer.

[0274] Disadvantages of large deflectors include low bandwidth, and a physical size that is incompatible with microminiaturized construction. In the above example, bandwidth of the 100 μm long deflector is 100 times lower than bandwidth of a 1 μm deflector for a single e-beam. Large deflectors may also have uneven electric field gradients between deflector plates. For a large diameter beam, this causes uneven deflection for different parts of the beam; in an array of individual e-beams, it causes different deflections for different e-beams. In either case, beam misfocusing results, causing amplifier gain distortion.

[0275] One advantage of the instrumentalities described herein is the incorporation of independent, matched deflectors at the output of each individual electron gun in an array of electron guns. Each electron gun and a corresponding deflector is part of a single microcolumn.

[0276] FIG. 19 shows a set of independent matched deflectors 130 corresponding to individual electron beams 120. Each deflector 130 has two plates (e.g., plates 600(1), 600(2)) spaced only slightly further apart than a diameter of each electron beam 120, thereby providing a strong deflection force with a short deflector, for high bandwidth. The electric field gradients of a small deflector may be more uniform across the region where a single beamlet passes through.

[0277] In a microfabricated device, plate spacing and length may be less than 1 μm. Microfabricated plate tolerances may be controlled to under 1 nm, so that deflectors of all microcolumns are matched to 0.1% or better, so that all e-beams are deflected the same amount for the same drive signal. A set of deflectors (“ganged deflectors”) driven in this manner constitutes a distributed deflector structure that provides uniform deflection to an array of e-beams, with high gain and fast, wideband response.

[0278] FIG. 20A shows a three-dimensional cutaway view and FIG. 20B shows an end view of a microcolumn or electron gun 610(1) of an electron-beam amplifier 10. Visible in FIG. 20A are a Spindt cathode 620(1), focusing electrodes 630, an aperture plate 640(1), X deflector plates 600(3), 600(4) and a shield plate 650(1) with a hole 655(1). In FIG. 20B, deflector plates 600(3), 600(4) are partially hidden by shield plate 650(1); shield plate 650(1), deflector plates 600(3), 600(4) and aperture plate 640(1) completely hide focusing electrodes 630. Microcolumn 610(1) emits electron beam 120 (not shown in the end view). It can be appreciated in these pictures that the mechanical complexity of the device makes microfabrication of microcolumn 610(1) essential, as construction by conventional machining at the required size would be difficult or impossible.

[0279] Microcolumn with X-Y Deflectors.

[0280] X-Y deflection is required for certain embodiments of electron-beam amplifier 10. This is enabled by adding a second beam deflector to each electron gun. It will be appreciated that the use of “X” and “Y” is for reference only; actual beam sweep directions in an electron-beam amplifier 10 are a matter of design choice, but X and Y are meant to convey two orthogonal directions in which an electron beam may be swept.

[0281] FIG. 21A shows a three-dimensional cutaway view and FIG. 21B shows an end view of a microcolumn or electron gun 610(2) configured for X-Y deflection. A pair of X deflection plates 600(3) and 600(4) and a pair of Y deflection plates 600(5) and 600(6) are positioned in close proximity to shield plate 650(2). Deflection plates 600(3) and 600(4) are orthogonal to plates 600(5) and 600(6), as shown; each pair of plates is separated from the other pair by an aperture plate 651(1). A width (but not plate spacing) of plates 600(5) and 600(6) may be increased relative to a height of deflection plates 600(3) and 600(4) to accommodate the deflection generated by plates 600(3) and 600(4). Cathode 620(1), focusing electrodes 630, and aperture plate 640(1) are the same as in microcolumn 610(1) of FIG. 20A. Microcolumn 610(2) emits beam 120 through opening 655(2) in shield plate 650(2). In the end view of microcolumn 610(2), deflector plates 600(5), 600(6) are partially hidden by shield plate 650(2), deflector plates 600(3), 600(4) are partially hidden by shield plate 650(2) and deflector plates 600(5), 600(6), and deflector plates 600(3), 600(4) and aperture plate 640(1) completely hide focusing electrodes 630. Again, the deflector geometries, shield plates and apertures are created through microfabrication. As discussed below, X-Y deflection makes possible other embodiments of electron-beam amplifier 10 such as, for example, combinational logic, certain frequency multipliers, and certain radiating amplifiers that require polarization of an RF output.

[0282] Deflector Loading

[0283] Loading of an array of ganged deflectors is low. For example, if each deflector consists of two 1 um×1 um deflector plates with a spacing of 1 um between plates, a capacitance per deflector is only 8.85 aF (10⁻¹⁸ F). 100 deflectors in an array of 100 electron guns will have a total capacitance of only 0.9 fF. (10⁻¹⁵ F). A 3 dB bandwidth (=½πZ₀C_LOAD) of a 50 ohm source driving the deflector array capacitance is 3.6 THz. The loading of an array of deflectors thus has little effect on the device performance, and enables a wide bandwidth that is compatible with that of the other system elements.

[0284] Electron Gun

[0285] FIG. 22 is a schematic cross-sectional view of a microcolumn or electron gun 610(3). Microcolumn 610(3) includes a cathode 620(2), a control gate 625, focusing electrodes 630, an aperture plate 640(2), a drift region 645, voltage signal 140(2), deflection plates 600(7), 600(8) and a shield plate 650(3). Cathode 620(2) may be a field emitter (“FE”) and may be a molybdenum tip (e.g., a Spindt cathode) because of its high gain, emission efficiency, low power, maturity and compatibility with microfabrication technology; however, other field emitter types may be employed, including Schottky, diamond, etched silicon tip, and carbon nanotube. Advantages of a field emission cathode include no requirement of a heating element, instantaneous start-up, low-voltage (10V-50V) operation, and low energy electron emittance (with an energy spread <0.3V), leading to low chromatic dispersion in the electron beam focusing, as discussed below.

[0286] The basic operation of the electron gun is as follows. A strong voltage between control gate 625 and cathode 620(2) (typically in the range of +10 to +50V) creates a strong electric field around cathode 620(2) that causes a release of electrons into free space. A current transported by the electrons may be described by the Fowler-Nordheim theory of electron flux over an energy barrier. Electrons may be released in the direction of the gate, with an angular distribution and an energy approximately equal to the potential difference between control gate 625 and cathode 620(2). By appropriate design, most of the electrons pass through the center of the gate electrode, and from there, they are focused within the electron microcolumn, as explained below.

[0287] Many electron gun microcolumn designs may be conceived as variations on the teachings herein to collimate electrons from a field emission tip into a narrow parallel beam.

[0288] Electron Gun Current

[0289] An electron gun 610 may be designed with a low enough beam current so that individual beam electrons are separated, on average, by a distance greater than the beam diameter. As a result, the electrons are far enough apart that mutual repulsion is minimized, so that space charge effects do not materially affect focusing.

[0290] Electron gun beams may have a diameter <1 μm and a maximum current of approximately 1 μA. This low current is consistent with negligible beam spreading because of a low density of electrons at beam energies typically used (around 100 eV to 300 eV). Generally, a lineal density λ that is a number n of electrons per unit beam length x, is given by

[0291] $\begin{array}{cc}\lambda =\frac{dn}{dx}=\frac{I_{\mathrm{BEAM}}}{{\mathrm{qv}}_{\mathrm{BEAM}}}& \left(1.9\right)\end{array}$

[0292] where I_BEAM is a beam current, q is the electron charge, and ν_BEAM is a velocity of the electrons, given by
ν_BEAM=√{square root over (2qV_BEAM/m_e)}.  (1.9.1)

[0293] Here, V_BEAM is a beam energy in volts, and m_e is the mass of an electron (9.11×10⁻³¹ kg). At 200V, ν_BEAM is 8.4×10⁶ m/s, and at I_BEAM=1 μA, the lineal electron density λ is 0.75 electrons per micron. A 1 μA beam current spaces the electrons apart by approximately the beam diameter, so that the electrons experience no significant lateral Coulomb force interactions or beam spreading.

[0294] Electron Optics

[0295] Focusing of electron beams 120 by electron optics can be understood by analogy to geometrical light optics. The advantage of the optical analogy is that it clearly predicts how focusing works for electron beams 120 from any direction, and provides insight into design of focusing fields.

[0296] If electron beams 120 exiting an emission plane (e.g., emission plane 20) are collimated into parallel beams they may be considered, by analogy, like light rays emitted from an object at an infinite distance from a lens. The lens is analogous to the electron optics. In geometrical optics, parallel rays can be focused to a point on an image plane on another other side of a lens, one focal length away.

[0297] FIG. 23 shows an optical lens 660 imaging an object 710 into an image 720. Light rays 670 travel from object 710 in an object plane 680 through lens 660 and form image 720 in an image plane 690. The basic Gaussian relation of geometrical optics is

[0298] $\begin{array}{cc}\frac{1}{f}=\frac{1}{o}+\frac{1}{i},& \left(1.10\right)\end{array}$

[0299] where f=focal length, o=distance from object plane to lens, and i=distance from lens to image plane. (As in light optics, the lens “position” in this case is described in terms of “principal planes” 700(1) and 700(2), which are generally different for the object and image sides of a thick lens, but for purposes of this analogy the principal planes can be assumed coincident in position, which is the “thin lens” approximation from light optics.)

[0300] In electron optics, a “lens” consists of electrodes of appropriate sizes, shapes, and voltage potentials. FIG. 24A and FIG. 24B show a front and a side view of one electron optics focusing electrode 630. Focusing electrode 630 may be, for example, a conductive plate with a circular hole to allow electrons to pass through. Hole 730 may be centered about an axis 740 which is a transmission axis of electrons through an electron gun. The positional relationship of focusing electrodes 630 to each other, the sizes of holes 730 in each electrode 630, and the voltage potential differences among electrodes 630 create electric fields that may focus moving electrons. The concepts of focal length, object plane and image plane from geometrical light optics apply substantially to electron optics.

[0301] FIG. 25 shows a schematic cross-sectional view of one accelerating electron lens 750(1). Electrodes 630(1), 630(2) and 630(3) in this idealized case extend much further away from a transmission axis 740 than shown in the drawing. Electrons accelerate in the direction indicated by arrow x. The essence of lens 750(1) is that an electric field gradient (indicated by the spacing of equipotential lines 760) between electrodes 630(1) and 630(2) is greater than the electric field gradient between electrodes 630(2) and 630(3), measured far from transmission axis 740. This can be achieved by selecting appropriate electrode potentials and plate spacing, since an electric field gradient E is given by the formula E=dV/dx from electromagnetic theory. In electron lens 750, electrodes 630(1), 630(2) and 630(3) have potentials V₁, V₂, and V₃ respectively; thus the field gradient between electrodes 630(1) and 630(2) is E₁₂=(V₂−V₁)/x₁₂ and the gradient between electrodes 2 and 3 is E₃₂=(V₃−V₂)/x₂₃. For example, if a potential difference (V₂−V₁) is the same as a potential difference (V₃−V₂), then a plate spacing x₁₂>x₂₃ will create a stronger gradient between electrodes 2 and 3, and the electrodes will generate a convex lens action by means of an accelerating field. An electrostatic force on an electron will be perpendicular to equipotential lines 760 at each point; accordingly, force vectors exemplified by arrows 770 act to focus electron beams 120 as shown.

[0302] FIG. 26 shows a schematic cross-sectional view of one decelerating electron lens 750(2). Electrodes 630(4), 630(5) and 630(6) in this idealized case extend much further away from transmission axis 740. An electric field gradient (indicated by the spacing of equipotential lines 760) between electrodes 630(4) and 630(5) is less than the electric field gradient between electrodes 630(5) and 630(6), measured far from transmission axis 740. In this case, if potential difference (V₅−V₄) is the same as potential difference (V₆−V₅), plate spacing x₄₅<x₅₆ gives a stronger gradient between electrodes 630(4) and 630(5). Force vectors exemplified by arrows 770 act to focus electron beams 120 as shown (note that arrows 770 point in the negative x direction in lens 750(2) because potentials are decreasing in the positive x direction).

[0303] It can be understood from electron lenses 750(1) (FIG. 25) and 750(2) (FIG. 26) that an electron lens with “convex action” (in analogy to light optics) may be made from either accelerating or retarding fields; similarly, either accelerating or retarding fields may be used to create an electron lens with “concave action”. A concave lens essentially works with a “negative” focal length, and causes parallel rays to diverge, or converging rays to converge less.

[0304] Election Gun Focusing

[0305] FIG. 27A shows a schematic cross-sectional view of a two-lens light optics system and FIG. 27B shows a schematic cross-sectional view of a two-lens electron optics system in an electron gun. Each of focusing electrodes 630 is connected to a potential voltage shown above the electrode. The regions marked 750(3) and 750(4) correspond to electron lenses acting on an electron beam 120 which function like corresponding glass lenses 660(2) and 660(3) acting on light rays 670. Lens 750(3) acts like convex lens 660(2), focusing a radial distribution of electron beams 120 from cathode 620 on the other side of the lens. Lens 750(4) acts like concave lens 660(3), converting converging electron beams 120 to a parallel bundle of beams having a very small angular distribution (for example, a fraction of a degree). When a concave lens power of lens 750(4) is matched to a convex lens power of lens 750(3), the converging beams can be made parallel. An aperture plate 640(2) masks stray electrons caused by focusing aberrations to ensure perfect parallelism of electron movement within beam 120, and to ensure that the diameter of beam 120 at an exit aperture 790 is under 1 μM.

[0306] In electron optics of an electron gun microcolumn, the “lens” may be constructed as a stack of electrodes perforated by circular holes (e.g., focusing electrodes 630). In the microcolumn, electrodes 630 may be metal layers (such as Al) separated by insulating layers (such as SiO₂). Potential voltages applied to the electrodes create electric fields in the microcolumn that act on the emitted electrons to produce focusing action. In this way, electrons can be either accelerated or retarded in velocity.

[0307] Optical Aberrations

[0308] A limitation of optics, whether for light rays or electron beams, is focusing aberration. Two common aberrations that are relevant to electron-beam amplifiers are spherical and chromatic aberrations.

[0309] Spherical aberrations are characteristic of off-axis rays that meet the lens at a large angle. These rays are focused closer to the lens than rays that travel at angles close to the lens axis (called “paraxial” rays in optics). Correction of spherical aberrations can be accomplished in light optics through certain deviations of a lens shape from a spherical surface (“aspheric” lenses). In electron optics, analogous corrections can be made by shaping the electric fields via electrode sizes, shapes, spacings and potentials, although no “spherical” surface per se is being corrected.

[0310] Chromatic aberration is caused in light optics by different wavelengths being bent by different amounts within lenses. Chromatic aberration produces, in a given lens system, longer focal lengths for short wavelengths, and shorter focal lengths for long wavelengths. Correcting chromatic aberration in light optics can be done through certain combinations of lenses made from materials having different indices of refraction (for example, crown glass and flint glass), a combination referred to as an “achromat.” With the right combination of lens materials and curvatures, a lens system can balance chromatic variations in focal length for different lenses and can achieve approximately the same focal length for over a range of wavelengths.

[0311] In an electron optical system, chromatic effects arise from electrons of different energies. In an electron-beam amplifier, this may occur primarily at the point of emission from the field cathode. The general principle of correction through an achromat combination is analogous to an achromat in light optics; an electron achromat uses lenses of different field gradient densities to achieve the effect of different indices of refraction. However, it is difficult to combine separate lenses of different field densities because of the electrode structures required. An alternative to use of an achromat is to filter electrons of different energies with an aperture stop. This solution operates somewhat like a pinhole camera.

[0312] FIG. 28A shows a schematic cross-sectional view of a three-lens light optics system with an aperture stop, and FIG. 28B shows a schematic cross-sectional view of a three-lens electron optics system with an aperture stop in an electron gun. In FIG. 28B, each of focusing electrodes 630 is connected to a potential voltage shown above the electrode. The regions marked 750(5), 750(6) and 750(7) correspond to electron lenses acting on an electron beam 120, which function like corresponding glass lenses 660(4), 660(5) and 660(6) acting on light rays 670 in FIG. 28A. Lens 750(5) acts like convex lens 660(4), focusing a radial distribution of electron beams 120 from cathode 620 on the other side of the lens. However, lens 750(5) and lens 660(4) are optimized for electrons of a certain energy, and light of a certain wavelength, respectively. High energy electrons 121 and high energy (low wavelength) light ray 671 have longer focal lengths than electron beam 120 and light ray 670 respectively; low energy electrons 122 and low energy (long wavelength) light ray 672 have shorter focal lengths. Electron aperture stop 640(3) and optical aperture stop 665 block these high and low energy electrons and light rays respectively. Lens 750(6) and 660(5) refocus the remaining electrons and light rays respectively. Lens 750(7) and concave lens 660(6), convert the converging electron beams 120 and light rays 670, respectively, to parallel bundles.

[0313] A disadvantage of filtering electron beams with apertures, as opposed to use of an electron achromat, is that some portion of beam current is blocked, reducing efficiency of an electron gun. An advantage is that a beam emerging from an aperture may be well focused and collimated. Spherical and chromatic aberrations may be corrected to produce an electron beam diameter of a few nanometers in a microcolumn that is several millimeters in length, at beam energies of 1 keV and currents up to 50 nA. Generally, higher energies, lower currents, longer columns and short drift distances achieve better focusing.

[0314] An electron-beam amplifier may require beam focusing on the order of a micron to ensure proper focusing across a drift cavity. Another way of looking at the beam focus requirement is that all e-beams emitted from a microcolumn array should act as if emitted from a single point source at infinite distance.

[0315] Electron Gun Fabrication

[0316] The components of an exemplary electron gun microcolumn include an FE tip cathode, a control gate (called a “wehnelt” in some literature), electrodes forming a first lens element, a first aperture plate, electrodes forming a second lens element, a second aperture plate, deflection plates, and a shield plate. The cathode may be a single field emitter tip; alternatively, a heated Schottky or other thermionic emitter may be used.

[0317] The microfabricated construction of an electron gun in an electron-beam amplifier may follow a sequence of fabricating components on individual silicon wafers, followed by alignment and wafer bonding of the wafers into a stack.

[0318] FIG. 29 shows an exploded, cross-sectional view of one electron-beam amplifier 10(3) assembled by bonding multiple wafers 800, 810, 820, 840 and 850. Cathodes 620 and control gates 625 are constructed on first silicon or glass wafer 800. Electrodes 630, forming a first lens, and a first aperture plate 640 may be formed on a first side 811 of second wafer 810; one or more lens electrodes 630 and aperture plates 640 may be formed on a second side 812 of wafer 810. More lens electrodes and aperture plates may be formed on a first side 821 of third wafer 820; deflectors 600 and shield plates 650 may be formed on a second side 822 of wafer 821. Wafers 800, 810, and 820 may then be aligned to each other and bonded together; holes 830 may be drilled through these wafers to provide paths for electron passage. Several drift cavity wafers (shown in FIG. 30 as a single wafer 840) and a detector wafer 850 (including detectors 150 and detector connections 155) may be aligned to wafers 800, 810 and 820 and all of the wafers may be bonded together, forming electron-beam amplifier 10(3).

[0319] FIG. 30 shows an exploded view of wafers 800, 810, 820, 840 and 850 of FIG. 29 in alignment for bonding. In a bonding operation, one wafer may be selected as a reference wafer; the other wafers may be aligned to the reference wafer in a rotational direction θ and translational directions X and Y, before bringing the wafers together in the Z direction and bonding them.

[0320] The wafers and assembly illustrated in FIG. 29 and FIG. 30 are by way of example only; it may be appreciated that many variations are possible. For example, more or fewer wafers may be used depending on the complexity of the electrode structures and the length of the gun column, and components may be fabricated on either side of any of the wafers. Additional structures such as optical elements and integrated circuits may be fabricated in wafers and bonded into the wafer stack. Wafer bonding technology may provide for electrical conduction, selective interconnection, or insulation between adjacent wafers. Holes of different diameters may be drilled through individual wafers or groups of wafers bonded together (i.e., to produce focusing electrodes with large holes in certain wafers, and aperture stops with small holes in others) before a final bonding step completes a wafer stack.

[0321] Multiple Focusing Electrodes

[0322] In electron-beam amplifier 10, multiple microcolumns are advantageously constructed concurrently in a compact array. Making a gun array as small as possible helps create high beam current density with good spot formation. For example, a single microcolumn may have a diameter of 5 μm or less to allow several hundred or more microcolumns to be fabricated in an array having a diameter of approximately 100 μm.

[0323] It is possible to use large electron lens electrodes achieve aberration-free focusing, as in light optics, in which large lenses improve image quality. In electron optics, as discussed above, perforated electrodes may act as lens elements (see FIG. 25). Circular perforations make spherically symmetrical lenses (called “stigmatic”), and large perforations help electron optics achieve low spherical focusing aberrations that characterize a paraxial (ideal) lens system. Put another way, high performance may result when an electron lens is much larger than a beam diameter. For example, a 1 μm beam may be advantageously focused by a 20 μm lens perforation. These numbers are very approximate, since any properly designed system requires precise specification of plate spacings, number of plates, perforation sizes, plate potentials and mechanical tolerances (since larger perforations are less sensitive to size irregularities).

[0324] It can be appreciated that large lenses are not compatible with a small diameter microcolumn and a dense gun array. In an improved embodiment of an electron-beam amplifier, small microcolumns having a plurality of small electrodes approximate the focusing of a single large electrode.

[0325] FIG. 31 shows an electron lens 750(8) constructed from three large electrodes 630(7), 630(8) and 630(9), and a corresponding lens 750(9) constructed from ten small electrodes 630(10) through 630(19). Electrodes 630(7) and 630(10) are at a reference potential within lenses 750(8) and 750(9) respectively. Each equipotential line 760 is identified by a numeral and indicates positions of a potential, and each successive equipotential line 760 indicates a uniform change in potential from the corresponding reference potential (for example, successive lines may indicate 10V, 20V, 30V, and so on). A “bulge” in equipotential lines 760 arises from the stronger field gradient between certain adjacent electrodes as opposed to the field gradient between other adjacent electrodes.

[0326] Where the potential lines coincide with electrode surfaces, they have the same potential as the corresponding electrode. This is the principle of an improvement to electron-beam amplifier 10. The potential gradients near the centerline of the lens, within the radius of the perforation, can be preserved without a wide diameter lens by using a series of thin, small diameter electrodes. For example, each equipotential line 760 in lens 750(9) has the same spacing and shape as a corresponding equipotential line 760 in the small region between dashed lines 860, 860′ within lens 750(8). Thus, lens 750(9) may provide similar focusing action, within a smaller physical size, as lens 750(8). In the case of an infinite number of differential electrodes, the lens 750(9) performs exactly as lens 750(8). In practice, only a few extra electrodes are required to substantially approximate a large three electrode lens with a small, multi-electrode lens.

[0327] Beam Current Control

[0328] Formation of a useful beam spot 170 requires substantially uniform beam current from all electron guns that supply individual beams for the composite beam. Field emission cathode tips (“FE tips”) may have nonuniform current-voltage characteristics (“I-V characteristics”); applying a single potential to a gate electrode 625 of each gun in an electron gun array 100 may result in a beam spot 170 with large current density variations. For this reason, beam current from each electron gun may be individually regulated by a control loop so that each electron gun produces substantially equal current.

[0329] The gate electrode potential has a significant effect on the electron optical focusing of the microcolumn, and changes in gate potential may significantly defocus the electron gun beam unless compensated by changes in potentials of other electrodes. For this reason, an improved electron-beam amplifier 10 may include circuitry which adjusts certain electron gun focusing electrodes at the same time as the potential of a gate electrode is changed, to maintain constant focusing characteristics.

[0330] Focusing potentials are generally difficult to determine except by computer analysis. One method of adjusting electron gun focusing potentials in the presence of a current-regulated gate potential consists of an analog-to-digital converter (“ADC”), a digital-to-analog converter (“DAC”) and a read-only memory (“ROM”) that is programmable with digital values. The ADC may be coupled to the gate electrode, to develop a digital word representative of the gate potential. This word is transmitted to the ROM as an address. The ROM functions as a look-up table, and stores DAC codes representative of optimized electrode potentials for any given gate potential measured by the ADC. The DAC responds to the output of the ROM by generating a focusing potential, which may be applied to an electrode. Thus, one or more electrode potentials may be arranged to correlate directly to the gate potential. In alternative embodiments, it may be appreciated that the ROM can be replaced with other means of generating digital values, such as a processor element.

[0331] FIG. 32 shows one arrangement for controlling beam current and focusing electrode potentials. Beam current control operates by regulating a potential difference between a gate electrode 625(2) and a corresponding cathode 620(3). A current control loop 865(1) includes a current sensing ballast resistor 870 having a value R_BALLAST, and an opamp 880. A positive terminal 882 of opamp 880 is connected with a reference potential 890. A beam current 900 with a value I_BEAM flowing through cathode 620(3) develops a ballast potential across ballast resistor 870; this potential may be applied to a second resistor 910 having a value R₁, which connects with a negative input 884 of opamp 880, as shown. The voltage difference between the ballast potential and reference potential 890 is an error voltage representative of the difference between a desired current and the actual beam current 900. This error voltage difference is filtered by a capacitor 920 having a value C₁ to eliminate noise fluctuations, amplified by opamp 880, and applied to gate electrode 625(2). Changes in potential of gate electrode 625(2) driven by opamp 880 thus make the ballast potential equal to reference potential 890, assuming gain of opamp 880 is high enough to reduce the error voltage difference to a small level. In this manner, reference potential 890 commands a desired current I_BEAM.

[0332] Focusing electrode controller 930 controls potentials of focusing electrodes 630(20), 630(21), 630(22) and 630(23) as follows. An ADC 940 connects with gate electrode 625(2) and generates a digital gate word 950 which is transmitted to a ROM 960. ROM 960 accepts digital gate word 950 as input and generates electron gun focusing words 970(1), 970(2), 970(3) and 970(4) as output; the electron gun focusing words are transmitted to corresponding DACs 980(1), 980(2), 980(3) and 980(4) which generate gun focusing potentials corresponding to each electron gun focusing word, and transmit the gun focusing potentials to focusing electrodes 630(20), 630(21), 630(22) and 630(23).

[0333] In a focusing electrode controller (e.g., controller 930) each electrode driven by a ROM (e.g., ROM 960) increases a storage capacity required in the ROM by a number of input levels values resolved by a corresponding ADC (e.g., ADC 940), times the number of DACs, times the number bits of resolution required as input by the corresponding DACs. For example, in the case shown in FIG. 32, if ADC 940 measures gate potential to 6 bit accuracy, the number of input levels resolved is 64; if each of DACs 980(1-4) requires a 7 bit word (e.g., electron gun focusing words 970(1-4)) as input, then the required ROM storage capacity is 64×4×7 bits (1792 bits).

[0334] The technique used in focusing electrode controller 930 may be extended to control all electrodes of an electron gun that are affected by a gate potential. Each electrode (e.g., electrodes 630) requires one DAC, and the required ROM storage capacity grows proportionately. There is no restriction on the number of bits in the electron gun focusing word supplied to a given DAC. Different DACs may resolve gun focusing potentials to different accuracy levels and may require correspondingly more or fewer bits per electron gun focusing word. For example, electrodes closest to the cathode may require high DAC accuracy and thus more ROM bits. Electrodes further from the cathode (in the microcolumn) may require less DAC accuracy and fewer ROM code bits. Generally, a first aperture plate of the electron gun (e.g., aperture plate 640(1) of FIG. 20A) will block defocusing effects of changes in control gate potential from propagating farther down a microcolumn, and focusing adjustments may be needed for only the first one or two lenses of the microcolumn

[0335] Typical Mechanical Parameters

[0336] Electron beam amplifier 10 may be designed or optimized for a parameter space of operation that may include gain, frequency response, bandwidth, power output, efficiency, noise, and drift time. Variables which may be manipulated as matters of design choice include electron gun energy, beam current, number of guns, number of deflection plates per electron gun (horizontal, vertical, cross-axis, blanking, offset centering), drift cavity acceleration, cavity length, detector size, shape and configuration, cascade and avalanche gain, diode material, voltage rating, bias, and output coupling method. Certain combinations of these parameters will result in amplifiers that may have vastly different mechanical dimensions and electrical specifications. For example, the mechanical dimensions shown in FIG. 16A and FIG. 166B for a microminiaturized electron-beam amplifier 10(2) include overall packaging dimensions A_X and A_Y of 5 mm. At this size, height h_ega of electron gun array 100 may be in the range of 50 μm to 200 μm, and a drift cavity length z_drift may be 2 mm. These numbers are merely representative and can vary significantly by application. For example, with a lower power output requirement a lower beam current may be used. With a higher tolerable noise figure, a smaller electron gun array may be used. With lower gain or linearity requirements, drift cavity length z_drift may be shorter and this, in turn, may reduce the length of microcolumns. Smaller gun arrays in turn create smaller beams, so the drift cavity diameter (e.g., d_drift in FIG. 16B) can also be smaller. Thus, a small change in one or two parameters (e.g., power gain and noise figure), may allow a much smaller electron-beam amplifier to meet all requirements.

[0337] Wideband Feedback

[0338] Certain systems require an amplifier with almost perfectly linear response such as, for example, a low noise amplifier (“LNA”) which may be used at the front-end of an RF receiver. High gain may not be required of an LNA, but distortion free response may be required to help detect small signals when a large interfering signal is present. For example, an interfering signal may have 1V peak-to-peak (“p-p”) amplitude, and a signal of interest may be 0.1 mV p-p (for example, when a jamming signal is present, or when a high-power transmitter is close to a receiver attempting to detect a distant signal).

[0339] In such applications, dynamic wideband feedback is often applied to a transistor amplifier to provide controlled gain with very low distortion. The transistor amplifier must be very wideband to operate with the feedback, since as is well known, this may be essential to achieving stable operation with the feedback. The wideband characteristic translates to a short delay through the amplifier; specifically, it is known that for feedback to be applied, the delay through the amplifier should normally be less than ½ cycle of a highest signal frequency for which the amplifier gain exceeds unity, or the feedback will be unstable and the amplifier will oscillate uncontrollably.

[0340] A delay time of an electron-beam amplifier may depend in part on a drift cavity length z_drift. For example, a 200 eV beam has a beam velocity of 8.4×10⁶ m/s. With a 1 mm cavity, drift time is 119 ps. This is a short interval, but not short enough to use the amplifier with wideband feedback at frequencies for which it has useable gain. Since an electron-beam amplifier may offer significant gain at frequencies of 100 GHz or more (as described below), some embodiments may require a drift time of 5 ps or less. Based on this criterion, if stable feedback is to be applied at 100 GHz, a maximum drift cavity length z_drift is 40 um for a 200 eV beam.

[0341] A short drift cavity length z_drift, has significant impact on parameters of an electron-beam amplifier. Short z_drift may mean that a smaller array of fewer electron guns may be used, since there is less distance over which to focus beams on a detector; but conversely, since less beam spreading occurs over the short z_drift, the guns may operate at a correspondingly higher current. For example, with z_drift, of 40 μm, a gun array may have a diameter of 20 μm and may include only 16 guns. Individual beam currents may be on the order of 10 μA, since there will be less beam spreading over a short drift time, while a greater drift cavity length z_drift might only be compatible with beam currents on the order of 1 μA. Total beam current could therefore be 160 μA; not much different than in a long cavity, but higher beam energy may be used to reduce drift time and increase output current with higher cascade gain. For example, an 800 eV beam may provide a drift time of 2.4 ps. This is one-half the time of a 200 eV beam. Thus, feedback can be applied over 200 GHz bandwidth. With a 20 μm drift length, feedback bandwidth may be over 400 GHz.

[0342] Thus, it can be appreciated that many matters of design choice may be used to optimize an electron-beam amplifier 10 for a particular application, and that feedback may be applied to some electron-beam amplifier configurations to enable very low-distortion performance at high frequencies.

[0343] Typical Electrical Parameters

[0344] In typical configurations of an electron-beam amplifier 10, with or without feedback, beam energy may be 200-300 eV, individual electron beam currents may be on the order of 1 μA, detector gain may be 1000, and maximum deflector voltage drive may be 100 mV to 1 V.

[0345] Like mechanical parameters, electrical parameters may range widely according to an intended application. Some parameters are related to mechanical dimensions, while others are more constrained by physics. For example, in most applications, one design objective is to generate an electron beam of maximum current without large spreading forces. At 300 eV energy, this translates to a maximum electron beam current of about 1 μA, based on electron density in the beam (though a shorter or longer drift cavity may increase or decrease the maximum electron beam current somewhat).

[0346] Another physical limitation is maximum beam energy. High beam energies at higher beam currents can cause excessive heating of a detector. High voltages (thousands of volts) which may be used to generate high beam energies can also cause arcing in a microminiature device, even at low beam currents. High energy also is not compatible with most integrated bias circuitry, which may withstand only a few hundred volts. Thus, a maximum beam energy in a range of 300 eV to 1000 eV is currently preferred.

[0347] Minimum beam energy is another limitation. If a beam energy is too low, cascade gain of a detector may be inadequate. As discussed above, low cascade gain cannot always be compensated by larger avalanche gain, since avalanche gain is limited by detector junction leakage and radiation sensitivity.

[0348] Another physical limitation is a minimum beam current which can produce a desired noise figure. Even with an ideal detector, electron beam shot noise (the effect of discrete electrons, rather than a smooth stream of current, striking a detector) is still amplified.

[0349] Many factors may drive deflector voltage drive range, including individual electron beam diameter, minimum plate spacing that can be manufactured reliably, drift cavity length z_drift, detector size, amplifier gain and input signal range. Since one application of an electron-beam amplifier 10 is as an antenna coupled LNA, its input signal may vary from microvolts to more than 1V. A maximum tolerable deflector voltage is set by the arc-limit of the plates, and may be around 10V per micron of space; if electron-beam amplifier 10 is fed from a solid-state amplifier, a lower limit of about 1V may be set by a voltage breakdown of high-frequency (GHz bandwidth) solid-state transistors.

[0350] These are not the only factors that constrain the electrical parameters, but illustrate some of the principles underlying the electrical parameter limitations.

[0351] Deflection Gain

[0352] Microminiaturization of e-beam dimensions and deflector plate spacing to micron or even submicron dimensions provides two benefits: high deflection gain and fast response. Thus, if plate spacing (e.g., spacing of deflector plates 600) is small, small signal voltages may generate strong electric fields for beam deflection, in turn creating large transverse beam displacement over very short transit times (of a beam through the deflector plates), permitting deflectors with short plate length L_P. In practice, deflectors can be shorter than 1 μm, with transit times of much less than 1 ps.

[0353] A general relation for deflection force F is F=qE, where q is the electron charge and E is the electric field between two deflector plates, approximately
E=V_sig/W_P,  (1.11)

[0354] where V_sig is an instantaneous signal voltage applied across the plates separated by a spacing W_P.

[0355] FIG. 33 shows how a deflection angle θ relates to a drift cavity length z_drift and a beam displacement ΔX across the drift cavity. A voltage applied across deflector plates 600(9) and 600(10) deflects beam 120 by deflection angle θ, resulting in a displacement ΔX as the beam passes through a drift cavity with length z_drift.

[0356] Deflector plates only approximate parallel plates, both in physical construction and in transfer function, but the parallel plate approximation may be used for most calculations. The essence of the approximation is that a one-dimensional, uniform electric field exists between two plates; from this, a basic relation may be derived for the deflection angle θ in response to an input signal ΔV. For a parallel plate deflector of plate spacing W_P and plate length L_P, a ratio of lateral transverse beam velocity ν_x (imparted by the deflection process) to a longitudinal beam velocity ν_z is

[0357] $\begin{array}{cc}\frac{v_x}{v_z}=\sqrt{\frac{\Delta V}{2V_{\mathrm{BEAM}}}}=\tan \Theta =\frac{W_P}{L_P}\frac{\Delta X}{z_{\mathrm{drift}}}& \left(1.12\right)\end{array}$

[0358] where beam energy is V_BEAM (in volts). ΔX is lateral displacement of a beam after propagating across a drift region of length z_drift between the deflector and the detector plane.

[0359] Within an electron-beam amplifier, a ratio G_BEAM of lateral beam displacement to a corresponding change in a deflection signal is

[0360] $\begin{array}{cc}{G}_{\mathrm{BEAM}}=\frac{\Delta X}{\Delta V_{\mathrm{SIG}}}=z_{\mathrm{drift}}\frac{L_P}{W_P}\frac{1}{2V_{\mathrm{BEAM}}}& \left(1.13\right)\end{array}$

[0361] For example, with appropriate choice of W_P and L_P, a spot of a 100 eV beam may be deflected 71 μm per volt of signal at the detector when drift length z_drift is 1 mm. Longer drift lengths, longer deflectors and smaller plate spacings increase G_BEAM; higher beam energies reduce G_BEAM.

[0362] A collection gain G_coll is a differential current collected by the detector with respect to a change ΔX in beam spot position. G_coll may depend on width and geometry of a detector. As discussed above, an electron-beam amplifier may be constructed so that its detectors collect substantially all available beam current when a beam is fully deflected across a detector width X_D:
G_coll=I_BEAM/X_D.  (1.14)

[0363] With k_C and k_A representing detector cascade and avalanche gain factors respectively, and k_D=k_Ck_A representing total detector gain, the above formula for G_coll may be multiplied by k_D to give the total amplifier transconductance gain g_m, the change in differential output current between the detector segments, with respect to a change of input signal:

[0364] $\begin{array}{cc}{g}_m=\frac{\Delta I_{\mathrm{out}}}{\Delta V_{\mathrm{in}}}=G_{\mathrm{BEAM}}{G}_{\mathrm{coll}}{k}_C{k}_A=z_{\mathrm{drift}}\frac{L_P}{W_P}\frac{1}{2V_{\mathrm{BEAM}}}\frac{I_{\mathrm{BEAM}}}{X_D}{k}_D& \left(1.15\right)\end{array}$

[0365] Parameters W_P, L_P, z_drift and V_BEAM can be selected so that:

[0366] $\begin{array}{cc}{g}_m=\frac{I_{\mathrm{BEAM}}}{\Delta V_{\mathrm{in}(\max })}{k}_D& \left(1.16\right)\end{array}$

[0367] For example, if I_BEAM=100 μA, ΔV_in=1V p-p (i.e., +/−0.5V) and k_D=1000, the transconductance gain is 100 mS (A/V). However, longer drift regions, smaller detectors and other parametric variations may allow an electron-beam amplifier to provide substantially higher gain from the amplifier, and ganging electron-beam amplifiers can provide even higher gain. Moreover, amplification may be very linear, so an electron-beam amplifier 10 may provide more usable gain than known amplifiers.

[0368] Deflector Frequency Response

[0369] Microfabrication also offers an advantage in terms of high frequency performance. When deflector plates (e.g., deflector plates 600) are shrunk to micron-scale dimensions, frequency response between input and output increases dramatically. Physically, the finite bandwidth of a deflector (e.g., deflector 130(1) consisting of matched deflector plates 600) can be understood as the time it takes a single electron to pass through the deflectors, since dynamic changes in deflector drive voltage will filter and average the deflection. For example, first define a transit time τ as the time it takes an electron to traverse the region between deflector plates. If a drive voltage is positive for half of τ and equally negative for the other half of τ, it can be appreciated that the net deflection will be zero. Thus, transit time τ should be designed as much less than a period of a maximum signal frequency. In a parallel plate deflector, a relation of 3 dB bandwidth to τ, or to beam velocity ν_z and plate length L_P, may be derived as

[0370] $\begin{array}{cc}{f}_{3\mathrm{DB}}=\frac{\mathrm{.442}}{\tau }=0.442\frac{v_Z}{L_P}& \left(1.17\right)\end{array}$

[0371] When beam velocity is expressed in terms of the total electron gun accelerating potential V_BEAM, the response is

[0372] $\begin{array}{cc}{f}_{3\mathrm{DB}}=\frac{{262.10}^3}{L_P}\sqrt{V_{\mathrm{BEAM}}}& \left(1.18\right)\end{array}$

[0373] where f_3DB is the frequency at which the deflection gain is reduced to 0.707 (3 db) of the low frequency response.

[0374] Table 1 shows electron-beam amplifier physical and electrical parameters for selected values of V_BEAM, V_in and L_P. All entries in Table 1 assume W_P is 1 μm and z_drift is 1000 μm. As shown in Table 1, frequency response of the deflector may exceed 1 THz. X_DET The calculated values of f_3DB, tan Θ, and Table 1.

[0375]

VBEAM	Vin	LP	f3DB		XD
(volts)	(mv)	(μm)	(GHz)	tanΘ	(μm)
10 v	30 mv	25.8	32	.0387	154.8
10 v	300 mv	8.2	101	.123	492
50 v	30 mv	57.7	32	.0173	31
50 v	300 mv	18.25	101	.055	98.4
200 v	30 mv	115	32	.0087	7.7
200 v	300 mv	36.5	101	.0274	24.6
1000 v	30 mv	10	828	.0274	0.6
1000 v	300 mv	3	2760	.0274	1.8

[0376] Dimensions and construction of detectors permit similar bandwidth, for example, where these bandwidths are where the gain is only down by 3 db compared to a low frequency response. Unity gain frequency response, or gain-bandwidth product, is another common measure of amplifier performance. With a voltage gain of 10, the gain-bandwidth product of an electron-beam amplifier may be 10 THz. Though an electron-beam amplifier has the potential for THz performance, gain-bandwidth product can be used as a figure of merit to assess usable gain at any frequency, or to determine the ultimate performance potential, or to make comparisons to other technologies. By way of comparison, a single-stage HEMT amplifiers may have gain-bandwidth products of about 400 GHz.

[0377] High Power Output.

[0378] Power output may be increased substantially by ganging amplifiers. A 100 gun array may have only 0.9 fF loading capacitance, so small that many amplifiers can be ganged and driven in parallel with little loss of bandwidth. For example, one electron-beam amplifier driven by a 50 ohm source may have an input bandwidth of 3.6 THz. Ten electron-beam amplifiers driven in parallel by a common 50 ohm source impedance may have an input bandwidth of 360 GHz, still high enough to pass most input frequencies, and the parallel gang provides 10 times the power output of a single amplifier. Similarly, a gang of 100 electron-beam amplifiers may have 100 times the power output, at 36 GHz.

[0379] With a hierarchical or “corporate” power input distribution system (see FIG. 64) amplifiers may “fan out” to drive progressively more and more amplifiers. By this means, a microfabricated electron-beam amplifier array may include as many as millions of amplifiers on a single silicon wafer, and the entire amplifier array may be driven from a single source. The total coherent power output of the amplifier array may exceed 10 kW, while preserving the wide bandwidth of individual amplifier elements. It can be appreciated that the ability to gang many amplifiers is one characteristic of electron-beam amplifiers for applications that require very high, wideband power output.

[0380] Efficiency

[0381] Another benefit is power-added efficiency (“PAE”). This is the RF power that is added to the output of an amplifier (i.e., P_OUT−P_IN) as a percentage of total amplifier power P_IN, including thermal losses:

[0382] $\begin{array}{cc}\mathrm{PAE}=100\%\times \frac{P_{\mathrm{OUT}}-P_{\mathrm{IN}}}{P_{\mathrm{TOT}}}& \left(1.19\right)\end{array}$

[0383] Conventional semiconductor amplifiers can provide high power gain, but often have low efficiency, or somewhat higher efficiency over a narrow band of operation at relatively low frequencies (up to around 10 GHz). TWTs can provide much higher power output over an octave or more of bandwidth, with PAE approaching 50% in the best devices, but with a significant power overhead required to heat thermionic cathodes and generate a high-voltage collector bias (10 kV or more). For this reason, TWTs rarely operate with less than 100 watts of power, which is undesirable in many applications.

[0384] In contrast, an electron-beam amplifier 10 may provide high power gain (60 dB or more) in a miniature device dissipating as little as milliwatts of total power, or as much as many watts, at a PAE exceeding 50%.

[0385] A total amplifier power is approximately P_TOT=P_BEAM+P_supp, where P_BEAM is the beam power and P_supp is the total detector power into the output power supply, V_supp. The total beam power is P_BEAM=I_BEAMV_BEAM., where V_BEAM is the beam energy in electron-volts (i.e., the acceleration potential) and I_BEAM is the beam current.

[0386] The supply power due to detector current is P_supp=I₀V_supp when a constant power supply absorbs a constant total current I₀=k_DETI_BEAM from two detector segments (i.e., nearly 100% of the beam is over one detector segment or the other). If each detector segment terminates in a load resistor of value R, the optimum amplifier efficiency occurs for the largest output voltage swing within V_supp. That is, if the signal is sinusoidal, the current output waveform from a single detector is

[0387] $\begin{array}{cc}i\left(t\right)=\frac{I_0}{2}\left(1+\cos \mathrm{\varpi t}\right)& \left(1.20\right)\end{array}$

[0388] and the maximum voltage across the load resistor is V_supp=I₀R. Detector current causes an output voltage to swing between 0 to V_supp across the load R (ignoring certain factors such as a minimum detector bias for generating detector gain k_DET, but this is a reasonable approximation). Given these assumptions, supply power is
P_supp=I₀V_supp=I₀²R  (1.21)

[0389] If all of the RF power from one detector segment is dissipated in the load, the RF power output is

[0390] $\begin{array}{cc}{P}_1=\frac{1}{T}{\int }_0^T{i}^{2}Rdt,& \left(1.22\right)\end{array}$
averaged over one period T of the RF. Normalizing over an angle θ from 0 to 2π,

[0391] $\begin{array}{cc}\begin{array}{c}{P}_1=\frac{1}{2\pi }{\int }_0^{2\pi }(\frac{I_0}{2}{\left(1+\cos \left(\theta \right)\right)}^{2}Rd\theta =\frac{I_0^{2}R}{4}\frac{1}{2\pi }{\int }_0^{2\pi }{\left(1+\cos \left(\theta \right)\right)}^{2}d\theta \\ =\frac{I_0^{2}R}{4}\frac{1}{2\pi }{\int }_0^{2\pi }\left(1+2\cos \left(\theta \right)+{\cos }^2\left(\theta \right)\right)d\theta \\ =\frac{I_0^{2}R}{4}\frac{1}{2\pi }{\int }_0^{2\pi }\left\{1+2\cos \left(\theta \right)+0.5\left(1+\cos \left(2\theta \right)\right)\right\}d\theta =\\ =\frac{I_0^{2}R}{4}\frac{1}{2\pi }{\left\{\theta +2\sin \left(\theta \right)+0.5\left(\theta +\frac{1}{2}\sin \left(2\theta \right)\right)\right\}}_0^{2\pi }=\frac{I_0^{2}R}{4}\frac{1}{2\pi }\left\{2\pi +\pi \right\}\end{array}& \left(1.23\right)\end{array}$
and finally the RF output power from one detector segment is

[0392] $\begin{array}{cc}{P}_1=\frac{3}{8}{I}_0^{2}R,& \left(1.24\right)\end{array}$

[0393] The total RF output load power P_LOAD from both detector segments is twice P₁, or

[0394] $\begin{array}{cc}{P}_{\mathrm{LOAD}}=2P_1=\frac{3}{4}{I}_0^{2}R& \left(1.25\right)\end{array}$

[0395] While certain RF amplifiers do not have a simple resistive load from which to calculate a transmitted P_OUT, a good first approximation is to use P_OUT=P_LOAD.

[0396] Assuming an e-beam of 50 μA accelerated to a 200V potential, beam power P_BEAM is 10 mW. If a detector has a gain of 2000, I₀=100 mA. If an output load is 20 ohms, P_LOAD=200 mW and P_OUT=150 mW. Using these assumptions, P_TOT=110 mW. If the input is from a 50 ohm source with an amplitude of V_IN=0.1V (peak), then

[0397] $P_{\mathrm{IN}}=V_{\mathrm{IN}}^2/\left(2\times 50\right)=0.1\mathrm{mW}.\mathrm{From}\mathrm{these}\mathrm{numbers},\mathrm{PAE}=100\%.\frac{150\mathrm{mW}-0.1\mathrm{mW}}{210\mathrm{mW}}=71.4\%$
This PAE compares favorably with solid-state or TWT amplifiers, but at higher frequencies and wider bandwidth.

[0398] Even higher PAE can be achieved in a specialized device that excites a resonant load with a non-sinusoidal pulsed current drive. If a detector is overdriven to operate as a photoconductive switch in such a case, the efficiency can approach 90% or more. Thus, it can be appreciated that electron-beam amplifier 10 may provide performance comparable to, or exceeding, that of known devices.

[0399] If amplifier power gain G_P is high, the input power P_IN is small with respect to the output power P_OUT. An electron-beam amplifier 10 may can achieve values of G_P>10⁶, so

[0400] $\begin{array}{cc}\begin{array}{c}\mathrm{PAE}=100\%\times \frac{P_{\mathrm{OUT}}-P_{\mathrm{IN}}}{P_{\mathrm{TOT}}}\\ =100\%\times \frac{P_{\mathrm{OUT}}}{P_{\mathrm{TOT}}}\left(1-\frac{1}{G_P}\right)\\ \approx 100\%\times \frac{P_{\mathrm{OUT}}}{P_{\mathrm{TOT}}}\\ =100\%\times \frac{\frac{3}{4}{I}_0^{2}R}{I_0^{2}R+P_{\mathrm{BEAM}}}\\ =100\%\times \frac{0.75}{1+\frac{P_{\mathrm{BEAM}}}{I_0^{2}R}}\\ \mathrm{PAE}=\frac{75\%}{1+\frac{P_{\mathrm{BEAM}}R}{{V_{\mathrm{supp}}}^2}}\end{array}& \left(1.26\right)\end{array}$

[0401] This brings out the useful result that increasing output power supply voltage increases the efficiency (for example, by using a high breakdown strength detector material with high detector current), and decreasing the load resistance or the beam energy increases the efficiency, but the maximum efficiency can never be greater than 75%.

[0402] To understand the relation between detector gain, detector breakdown V_BV and beam energy, let
V_supp=V_BV=I₀R=k_DETI_BEAMR.  (1.27)

[0403] As discussed above, detector gain is the product of the cascade and avalanche gain, k_DET=k_Ck_A, and the cascade gain k_C is given approximately by k_C=V_BEAM/V_CI, where V_CI is the cascade ionization energy of the detector material. Solving for I_BEAM,

[0404] $\begin{array}{cc}{I}_{\mathrm{BEAM}}=\frac{V_{\mathrm{BV}}}{k_{\mathrm{DET}}R}=\frac{V_{\mathrm{BV}}{V}_{\mathrm{Cl}}}{k_A{V}_{\mathrm{BEAM}}R}.& \left(1.28\right)\end{array}$

[0405] Substituting into P_BEAM=I_BEAMV_BEAM, the power added efficiency is

[0406] $\begin{array}{cc}PAE=\frac{75\%}{1+\frac{V_{\mathrm{BEAM}}R}{V_{\mathrm{BV}}^2}\frac{V_{\mathrm{BV}}{V}_{\mathrm{Cl}}}{k_A{V}_{\mathrm{BEAM}}R}}=\frac{75\%}{1+\frac{V_{\mathrm{Cl}}}{V_{\mathrm{BV}}{k}_A}}.& \left(1.29\right)\end{array}$

[0407] Notably, the beam energy and load resistance does not affect PAE. PAE is highest with a detector material that has the highest ratio of V_BV/V_CI, and a detector structure with a high avalanche gain. Table 2 gives material parameters V_CI, E_BV, and V_BV for certain materials.

[0408]

TABLE 2
VCI, EBV, and VBV for various materials and heterostructures
	Cascade	Breakdown	Breakdown
	Ionization	Field, EBV	voltage, VBV (V)	VBV/
Material	Energy, VCI (V)	(×107 V/m)	@ tDET = 1000 Å	VCI
InAs	1.8 (est)	<1	<1	<0.55
Ge	2.8	1	1	0.36
Si	3.6	3	3	0.83
GaAs	4.3	4	4	0.93
InP	4.2	5	5	1.2
3CSiC	7.2	10	10	1.4
4HSiC	9.5	40	40	4.2
GaN	8.9	50	50	5.6
heterostructures
Ge—Si	2.8	3	3	1.07
Ge—GaAs	2.8	4	4	1.43
InAs—GaAs	1.8	4	4	2.22
InAs—InP	1.8	5	5	2.78

[0409] Thermal Heating

[0410] High PAE corresponds to high thermal efficiency, which may be another benefit of electron-beam amplifier 10. With high detector gain and low beam current, little joule heating of the detector by a high energy beam occurs, so little power is wasted. For example, a 280 eV beam of 100 μA dissipates only 28 mW of power in detector heating, while generating 100 mA of diode current. Actual temperature rise of a detector is insignificant, on the order of a few degrees for typical semiconductor coefficients of thermal conductivity (eg, 100 degrees C. per watt).

[0411] Power Transformation

[0412] Electron-beam amplifier 10 is also an efficient power transformer, insofar as it converts a high-impedance, low-power input signal (a deflection voltage) to a low-impedance, high-power output signal (a detector current into a load network). This is another benefit of a high gain detector. A power-transforming advantage provided by electron-beam amplifier 10 is evident in radiating embodiments, as explained below.

[0413] Noise Figure

[0414] Noise in electron-beam amplifier 10 is predominantly shot noise. In an electron beam (e.g., composite electron beam 110), shot noise current i_NB for a bandwidth Δf is spectrally white and is described by
i_NB=√{square root over (2qI_BEAMΔf)}(RMS,Amps/√{square root over (Hz)})  (1.30)

[0415] This is true because field emission obeys Poisson statistics, which are characteristic of current across a barrier potential. The detector introduces noise primarily through the avalanche gain. The cascade gain is essentially noise free, but the beam noise is amplified by the total detector gain. It can be shown that with sufficient cascade gain, the noise introduced by an avalanche process is negligible.

[0416] Shot noise is characteristic of a quantized current flow. The quantization in normal semiconductors arises from discrete charge quantities of electrons moving across a potential barrier, such as a P-N or Schottky junction. Shot noise in an e-beam is similar, since the charge quantities are still electrons. The effect of cascade gain on detector noise can be inferred from this. Each beam electron that penetrates the detector generates a cascade of k_C electrons in only a few femtoseconds. The time frame of the cascade is so short that the effect is equivalent to a single particle of charge k_Cq (where k_C is as defined above) striking a detector which has no cascade gain. Thus, the cascade-amplified beam current has a noise power i_ND that is still described by shot noise power:

[0417] $\begin{array}{cc}{i}_{\mathrm{ND}}^2=2\left(k_{C}q\right)I_{\mathrm{BEAM}}\Delta f=2\left(k_{C}q\right)\frac{d{Q}_{\mathrm{BEAM}}}{dt}\Delta f=2\left(k_{C}q\right)\left(k_{C}q\right)\frac{d{n}_{\mathrm{BEAM}}}{dt}\Delta f& \left(1.31\right)\end{array}$
where I_BEAM is first rewritten as dQ_BEAM/dt and then as qdn_BEAM/dt, with n being a number of electrons. In effect this can be rearranged as
i_ND²=2q(k_C²I_BEAM)Δf.  (1.32)

[0418] This is exactly the noise of an ideal amplifier, showing that the cascade process introduces no excess noise. If a Noise figure NF is defined as
NF=10 log(1+N_ADDED/N_IN)  (1.33)

[0419] where N_IN is an ideal minimum input noise and N_ADDED is the noise added by an amplifier, referred to the input, the cascade process is seen to have a noise figure near 0 dB. This can be understood by considering the noise added to a single beam electron—there is none, since the assumption is that each is exactly multiplied by the cascade factor k_C. The total noise power, however, increases as the square of the gain because gain refers to current amplification, not power; hence the factor k_C². This is characteristic of any kind of amplifier.

[0420] By contrast, avalanche multiplication introduces noise through two mechanisms: multiplication of diode leakage current, and excess noise factor, which describes the statistical fluctuations in the multiplication arising from the sequence of hole or electron impact ionization events. Neglecting leakage, avalanche noise is given by
i_NA²=2qFk_A²I_CΔf  (1.34)

[0421] where I_C is the beam current after multiplication by the cascade, k_A is the avalanche gain, and F is the avalanche excess noise factor. F is a device specific parameter that is typically greater than 2, varying from 3 in silicon to 9 for germanium. The total noise at the output of the detector is
i_ND²=2qk_A²k_CI_BEAM(k_C+F)Δf.  (1.35)

[0422] If k_C>>F, this simplifies to
i_ND²=2qk_D²I_BEAMΔf  (1.36)

[0423] where k_D=k_Ak_C, the total detector gain. Thus, a requirement for low noise detector operation is a cascade gain much higher than the excess avalanche noise. In one embodiment of the detector, the cascade occurs in a thin germanium layer and the avalanche takes place in a silicon layer. For example, a 280eV beam will have a cascade gain of approximately 100 in germanium. A silicon avalanche diode can be optimized for F=3. Thus, it can be seen that the effect of avalanche excess noise is small, and for certain embodiments, the detector essentially operates as a noiseless amplifier (noise figure=0dB). This is a key benefit of electron-beam amplifier 10.

[0424] Radiation Tolerance

[0425] Another benefit of electron-beam amplifier 10 is high radiation tolerance. An e-beam itself is inherently immune to radiation levels, and an energy flux of e-beams in electron-beam amplifier 10 is much greater than an energy flux of natural radiation (even in a low earth orbit of 700 km, where radiation is high). The primary effect of radiation on electron-beam amplifier 10 is leakage across diode junctions because of hole-electron pairs generated when high energy particles pass through semiconductors. High-energy electrons and protons are both significant, but the effect is similar. Under most natural conditions an effect of radiation may be a small increase in detector noise.

[0426] Beam Focusing in a Microminiaturized Amplifier

[0427] As discussed above, space charge induced beam spreading is mitigated by several means, including high detector gain to reduce beam current requirements, and by using electron gun arrays 100 to increase beam diameter. In a microminiaturized high-speed electron-beam amplifier 10 beam spreading may be significant, because small detector(s) 150 are necessary to achieve the high speed, and a beam spot 170 may be small, to match the detector. For operation above 100 GHz, a detector size of less then 10 μm is preferred. If a 100 μm diameter electron gun array is used, this means a 10:1 reduction in a diameter of a resulting composite beam 110 may be achieved by focusing action in a drift cavity 145. It can be appreciated that a means of overcoming space charge spreading forces to compress a composite beam diameter from approximately 100 um at an emission plane 20 (in a microminiaturized device) to a spot diameter that may be at least 10 times smaller at a detector plane 50 improves performance of an e-beam amplifier 10.

[0428] Improved Embodiment for Small Beam Spot

[0429] An improved electron beam amplifier 10 includes electron beam focusing in a drift cavity 145, providing higher beam current, higher power output, lower thermal heating, lower noise and higher efficiency.

[0430] FIG. 34 shows a schematic cross-section of an electron-beam amplifier 10(4) including array beam focusing. An array of parallel electron beams 120 forming composite beam 110(3) exits an electron gun array 100(3) at emission plane 20, into drift cavity 145(4). In drift cavity 145(4) composite beam 110(3) is subjected to focusing fields of an electron lens 1000 generated by a potential difference between two electrodes 1020 and 1030, as shown. The dashed rectangle indicating electron lens 1000 is an abstraction of its general position, and does not mean the lens acts only within the region of the rectangle. Equipotential lines 1005 show the action of a decelerating field in electron lens 1000 in the same manner as equipotential lines 760 of FIG. 26. These focusing fields impart an inwardly directed radial momentum to composite electron beam 110(3) so that the outer electrons arrive at a desired spot diameter when they reach detectors 150. The imparted momentum may also compensate for space charge repulsion effect as beam 110(3) compresses. Thus, electron lens 1000 focuses beam 110(3) via a constricting force that decreases the large diameter of beam 110(3) as it leaves emission plane 20 to a smaller diameter, rendering a small beam spot at detectors 150.

[0431] Doublet Lens System

[0432] A second electron lens 1010, using an accelerating potential at the detector plane, creates a doublet lens arrangement of electrodes 1020, 1030 and 1040 to provide improved beam compression, cascade gain, and aberration correction. As also shown in FIG. 34, electrodes 1030 and 1040 comprise electrodes of second lens 1010 (shown in an abstract sense by a dashed rectangle). A higher potential of electrode 1030 relative to electrode 1040 generates an accelerating field, and the relationship of electrodes 1030 and 1040 generates field gradients that create an inward radial force, compressing beam 110. Equipotential lines 1015 show the action of a accelerating field in electron lens 1000 in the same manner as equipotential lines 760 of FIG. 25. Additional energy imparted to beam 110 by the accelerating field contributes to detector cascade gain.

[0433] In electron-beam amplifier 10(4), electrodes 1020 and 1040 are circular discs surrounding the electron gun array and the detectors respectively. Electrode 1030 is an annular can or “drift can” partially closed at both ends by endplates, as shown in FIG. 34.

[0434] FIG. 35 shows a midsectional plan view of drift cavity 145(4) within electron-beam amplifier 10(4) along lines F35-F35′ of FIG. 34. Electrode 1020 is centered in a perforation of electrode 1030 in emission plane 20. A small gap separates electrode 1020 from electrode 1030, as shown. Electrode 1020 completely surrounds electron gun array 100(3) in emission plane 20.

[0435] Similarly to FIG. 35, and as shown cross-sectionally in FIG. 34, electrode 1040 is centered in a perforation of electrode 1030 in detector plane 50, and electrode 1040 completely surrounds detectors 150 in detector plane 50.

[0436] In electron-beam amplifier 10(4), electrode 1030 may be at ground potential. Electron lenses 1000 and 1010 achieve focusing action through positive potentials on electrodes 1020 and 1040; the potential of electrode 1040 being substantially greater than the potential of electrode 1020, to provide acceleration through the drift cavity. For example, electrode 1020 might be at 50V and electrode 1040 might be at 300V.

[0437] The structure may be considered a doublet of two lenses. Both electron lenses 1000 and 1010 achieve lens action by the geometrical relationships of the sizes and the potential differences among electrodes 1020, 1030 and 1040, in a manner similar to that described above with respect to electron optics electron guns. The effect of using discs for electrodes 1020 and 1040, each in a common plane with electrode 1030, may be seen as making one of distances x₁₃ or x₂₃ in FIG. 25 equal to zero.

[0438] According to the electromagnetic theory of superposition, the fields of electron lenses 1000 and 1010 may overlap, but the lenses may be treated as if they act independently. Both lenses 1000 and 1010 may be considered “immersion lenses,” since electron gun emission occurs inside lens 1000 and beam detection occurs inside lens 1010.

[0439] Since electron beam emission consists of parallel rays at emission plane 20, an optical “object” for the emission is virtually located at infinity behind the emission plane. The “image” of this “object” is a focal length away from a principal plane on an image side of a two lens system. The term “principal plane” from geometrical optics describes a point from which a focal length is measured in an optical system that has a non-zero thickness; there are two principal planes, one on an object side, and one on an image side (which in e-beam amplifier 10(4) is a region of drift cavity 145(4) towards detector plane 50).

[0440] An advantage of a doublet lens is that focusing and acceleration occur simultaneously. If only lens 1010 were used, the focusing action is not as strong because the short distance to detector 150 and the accelerating field reduce a transit time over which radial forces can act. If only lens 1 is used, the focusing action is strong because an inward momentum is imparted just past the emission plane, but a retarding field slows the beam, increasing transit time and reducing beam energy and detector cascade gain. A doublet lens provides the benefits of strong focusing and acceleration. Furthermore, a doublet lens provides extra degrees of freedom to correct for other well known optical phenomena such as spherical aberration, coma and field curvature.

[0441] Certain embodiments of an electron-beam amplifier may use only one electron lens. For example, in embodiments using single electron guns that are independently deflected by multiple signals, an electron lens like lens 1000 may be undesirable. In embodiments using multiple beams, an electron lens like lens 1010 may be undesirable. Several electron-beam amplifiers in which these considerations apply will be discussed below.

[0442] Parallel Beam Deflection and Focusing

[0443] In FIG. 34, electron gun array 100(3) delivers an essentially parallel array of electron beams 120 to lens 1000 within drift cavity 145(4). A distributed deflection apparatus (not shown) may deflect each electron beam 120 in response to a signal, but beams 120 remain parallel at emission plane 20. From the foregoing theory, beams 120 appear to come from a virtual object point at an infinite distance behind emission plane 20, at an angle determined by a deflection apparatus. Parallel beams are preferred because they are easily generated from an array of electron guns. Furthermore, the parallelism makes it possible to focus the rays at any deflection angle, since they all appear to come from an object at infinity.

[0444] FIG. 36 shows a schematic cross section of a virtual lens 1050 focusing a composite electron beam 110(4) in a drift cavity 145(5). Deflectors (not shown) within electron gun array 100(4) deflect each electron beam 120 through an angle Θ at emission plane 20. Virtual lens 1050 illustrates the focusing action of an electron lens, and focuses parallel electron beams 120 on an image plane which is detector plane 50, a focal length f away from the virtual lens. According to geometrical optics, an angle of deflection is preserved across the principal plane, so a displacement ΔX of a focal point from an optical axis 1060, at detector plane 50 is related to the deflection angle Θ as
ΔX=f sin Θ.  (1.37)

[0445] For example, if Θ is 10 degrees and f is 1 mm, ΔX will be 174 μm.

[0446] Spot Formation

[0447] In a first method of spot formation, an electron gun array is arranged with an outline that is the same as an outline of an intended spot, and drift cavity optics image and demagnify electron beams from the array onto a detector. In a second method of spot formation, an array shape and astigmatic focusing optics are chosen to create a desired spot image.

[0448] Many spot shapes are possible, ranging from simple points, line spots and rectangles to circles, triangles and more complex shapes.

[0449] FIG. 37A through FIG. 37H shows representative electron gun array shapes 101(1-4) and corresponding electron beam spots 170(9-12). Space charge spreading forces are highest for beams corresponding to array shape 101(1); lower forces apply to array shapes 101(2) and 101(3), and the lowest space charge spreading forces apply to array shape 101(4).

[0450] Placement of a detector at a focal point of a composite electron beam is undesirable in embodiments of an electron beam amplifier 10 wherein correct operation of the amplifier uses a shaped beam spot by design. To create a shaped spot, a detector may be placed ahead of, or behind, an image plane.

[0451] FIG. 38A, FIG. 38B and FIG. 38C show several views of an electron gun array 100(5), a corresponding electron gun array shape 101(5) and corresponding electron beams 120 being imaged on detectors 150. In FIG. 38A, electron gun array 100(5) emits electron beams 120 at emission plane 20. In FIG. 38B, electron gun array shape 101(5) is a midsectional view of electron guns of electron gun array 100(5) along lines 38B-38B′ in FIG. 38A. Electron beams 120 are focused by electron lenses (not shown), aiming the beams so that they converge towards a point on an image plane 1070 in FIG. 38A. However, detector plane 50 and detector 150 are located in front of image plane 1070, causing detector 150 to intercept electron beams 120 before they fully converge. Detector 150 is shown in cross section in detector plane 50 of FIG. 38A, and again in FIG. 38C, in a midsectional view along lines 38C-38C′. Because electron beams 120 are initially parallel, an image of electron gun array 100(5) is preserved in a beam spot 170(13) that has a width Ws on detector 150.

[0452] In FIG. 38B, the electron gun array shape 101(5) has an aspect ratio that is the same as an aspect ratio of beam spot 170(13) in FIG. 38C. However, an array shape can be rectangular, circular, oval or other shapes as necessary to match a desired spot shape. A non-uniform spot density can also be generated by selective placement of electron guns within an array.

[0453] Astigmatic Optics

[0454] An electron beam amplifier 10 may generate a desired focused beam spot 170 with an electron gun array shape 101 that differs from the shape of the beam spot through use of astigmatic focusing optics. Astigmatic focusing optics are asymmetrical about an axis, and have different focal lengths in different axial planes.

[0455] FIG. 39 shows an example of astigmatic focusing electron optics. A square electron gun array 100(6) (in midsectional view) emits electron beams through openings in a square first electrode 1080. Electrode 1080 is surrounded by four trapezoidal electrodes 1090(1-4), of which, electrodes 1090(1) and 1090(3) are oriented along the X-axis, and electrodes 1090(2) and 1090(4) are oriented along the Y-axis. Electrode 1080 is connected with a first potential V₁. Each opposing pair of trapezoidal electrodes 1090 (e.g., 1090(1) and 1090(3), or 1090(2) and 1090(4)) have the same potential, but orthogonal pairs have potentials that differ by a potential ΔV about an average second potential V₂. The effect of a potential difference V₂−V₁ is to focus electron beams as they move across a drift cavity; the effect of ΔV is to create a focusing difference along the two axes that gives rise to two different focal lengths. When ΔV is positive, beam spot 170(14) will be present on a detector plane (not shown); when ΔV is negative, beam spot 170(15) will be present. When ΔV is zero, that is, each of electrodes 1090(1-4) are all at the same potential, a square beam spot (not shown) will be present.

[0456] Dynamic alteration of beam spot shape by electrical control of astigmatic electrodes is useful in other embodiments of an electron-beam amplifier, as explained below.

[0457] EBRX

[0458] From the foregoing, it can be appreciated that an electron-beam amplifier may include various combinations of the following elements: a two-dimensional electron gun array, low-current electron beams, composite electron beams, single or distributed beam deflectors, a drift cavity, drift cavity electron optics that provide focusing and/or beam acceleration, one or more high gain detectors, and one or more output networks; any of these elements may be made through microfabricated construction. Combinations of these elements may be termed here an “EBRX” for Electron Beam RF Amplifier (“X” being a common abbreviation for “amplifier”). As discussed below, certain of these elements are common to many embodiments of an electron-beam amplifier.

[0459] Time Delay Control

[0460] One embodiment of electron-beam amplifier 10 provides time delay control. Variable time delay is a feature of many RF systems such as, for example, phased array antennas and wideband electronic beam steering. In such systems, radio waves radiated by antenna(s) are timed to adjust a directionality and gain of receiving or transmitting antenna(s). True time delay shifting (“TTDS”) has an advantage over simple phase shifting (“PS”) in that control is broadband, rather than narrowband. Therefore TTDS is preferred, but traditionally both TTDS and PS have been expensive and complex to implement. Thus, a low cost time delay control of electron-beam amplifier 10 may provide a useful means of antenna beamforming.

[0461] In one embodiment, an output signal (e.g., output currents 180) from electron-beam amplifier 10 is variably time delayed by adjusting electron beam energy, thus adjusting electron velocity and transit time of electrons across a drift cavity to a detector. Variable time delay control is an almost free feature of electron-beam amplifier 10, since little extra power is required and physical elements of the amplifier (i.e., electron guns, drift cavity, focusing electrodes, detectors and so on) are not altered. A microfabricated electron-beam amplifier 10 may implement time delay control over a usable range of hundreds of picoseconds, which may support electronically steered antennas for narrow steering angles at millimeter and submillimeter wavelengths. For larger antennas or longer wavelengths, which may require total time delay control on the order of nanoseconds, specialized electron-beam amplifiers 10 may be used. For the largest antennas, multiple electron-beam amplifiers 10 may be cascaded for a control range of tens of nanoseconds, or an electron-beam amplifier 10 may be used as a delay fine-tuning mechanism in a hybrid arrangement, with large delays provided by other means, such as switchable delay lines.

[0462] Generally, the velocity of electrons in a beam is given by
ν_e=√{square root over (2qV_b/m_e)},  (1.38)
where q is the electronic charge (8.85×10⁻¹⁹ C), V_b is a beam accelerating potential, and m_e is mass of an electron (9.11×10⁻³¹ kg). Transit time of a beam through a drift cavity of length z_drift is simply t_DELAY=z_drift/ν_e) and a change in delay is

[0463] $\begin{array}{cc}\Delta t_{\mathrm{DELAY}}\approx \frac{\Delta V_{\mathrm{BEAM}}}{V_{\mathrm{BEAM}}}{t}_{\mathrm{DELAY}}.& \left(1.39\right)\end{array}$

[0464] Thus, by adjusting a beam accelerating potential V_BEAM, the transit time may be adjusted, and a signal at an output of a detector may be delayed. For example, if Z_drift=10 mm, V_BEAM=50v, and ΔV_BEAM=+/−10v,
t_DELAY(min)=2.67 ns
t_DELAY(max)=2.18 ns
Δt_DELAY=490 ps.

[0465] A Δt_DELAY of 490 ps may be expressed as a phase shift Δφ of a period T of certain RF frequencies:
Δφ=49 T@100 GHz
Δφ=4.9 T@10 GHz
Δφ=0.49 T@1 GHz.

[0466] Typical phase shifting applications delay a signal for a significant fraction of a period of an RF frequency. It can be seen that the time delay mechanism is suitable for the RF applications that operate above 1 GHz. Furthermore, electron-beam amplifier 10 introduces no dispersion (filtering) effects when a broadband signal is amplified, since electron-beam amplifier 10 is broadband, so all frequency components are delayed by the same amount. Thus, it can be appreciated that electron-beam amplifier 10 achieves true time delay control.

[0467] Detector Plane Adjustments for Time Delay Control

[0468] FIG. 40 shows an electron-beam amplifier 10(5) that implements true time delay control. A potential V₂ of an electrode 1110 in detector plane 50 may be adjusted to change a transit time t_DELAY of electron beam 120 moving across drift cavity length z_drift. Higher V₂ on electrode 1110 (relative to an electrode 1100 in emission plane 20) accelerates electron beam 120 and decreases t_DELAY according to the above formula; decreasing V₂ increases t_DELAY.

[0469] One effect of changing a potential in detector plane 50 is to alter the focusing properties of electron focusing optics. For example, in electron-beam amplifier 10(4) of FIG. 35, if the potentials of electrodes 1020 and 1030 are held constant, the effect of changes to the potential of electrode 1040 is to change the focal length of the system. One method of correcting for such focal length changes is to simultaneously increase the potential of electrode 1030 as the potential of electrode 1040 increases.

[0470] This can be understood by recalling that electron-beam amplifier 10(4) has a retarding lens 1000 and an accelerating lens 1010. The retarding effect of lens 1000 occurs because electrode 1020 is more positive than electrode 1030; the accelerating effect of lens 1010 occurs because electrode 1040 is more positive than electrode 1030. Thus, if the potential of electrode 1030 is constant, making the potential of electrode 1040 more positive increases the focusing power of lens 1010. By increasing the potential of electrode 1030 as some fraction of the change in potential of electrode 1040, the focusing power of both lenses 1000 and 1010 can be decreased, offsetting the increased power of lens 1010 in the absence of a potential change on electrode 1040.

[0471] FIG. 41 shows true time delay control implemented using a ROM 1120 and two DACs 1140(1), 1140(2). An electron gun array 100 transmits electron beams 120 through perforations in an electrode 1160 that is maintained at a potential V₁. ROM 1120 receives a time delay control command 1130 and transmits digital word values 1150(1), 1150(2) to each of DACs 1140(1), 1140(2). As a matter of design choice, ROM 1120 may be, for example, one device with enough output bits to drive the inputs of DACs 1140(1) and 1140(2) simultaneously, or ROM 1120 may be two devices, one connected with DAC 1140(1) and the other connected with DAC 1140(2). Digital word value 1150(1) causes DAC 1140(1) to set a potential V₂ on an electrode 1180 to produce a desired time delay; digital word value 1150(1) causes DAC 1150(2) to set a potential V₃ on a drift can electrode 1170. Potentials V₂ and V₃ are potentials which preserve the collective focusing characteristics of electron lenses 1190 and 1200; digital word values 1150(1) and 1150(2) are previously determined optimum focusing potentials, which may be derived through testing or simulation of electron lenses 1190 and 1200 for certain potentials V₂.

[0472] Because changes in electron acceleration accompany adjustments of time delay, changes in deflection gain may also occur, even when a lens system is adjusted to maintain focal length. Even when transverse momentum imparted to beam electrons by a signal deflector is constant (since as-emitted beam energy of electron beams 120 remains constant), when transit time is reduced by increasing acceleration, lateral displacement less time to accumulate. Accordingly, deflection of electron beams 120 is reduced by increased acceleration.

[0473] FIG. 42A and FIG. 42B show the effect of acceleration on beam displacement. Initial deflection of electron beam 120(1) and 120(2) by deflectors 130(6) and 130(7) in response to an identical voltage signal 140(3) are an equivalent amount Θ from respective axes 1210(1) and 1210(2). However, accelerating field 1220 accelerates electron beam 120(2), reducing lateral displacement from axis 1210(2) within accelerating field 1220 (relative to the lateral displacement of electron beam 120(1) from axis 1210(1)).

[0474] A change in deflection gain caused by acceleration is independent of lensing action of a detector plane electrode (e.g., electrode 1180 of FIG. 41). The focal length of an accelerating lens alone is infinite. When electrodes 1170 and 1180 of FIG. 41 are constructed to generate lensing action with a finite focal length (through a doublet arrangement as discussed above), a change in deflection gain is more pronounced. Thus for time delay adjustments, it is useful to minimize lensing action of a detector plane electrode.

[0475] FIG. 43 shows a schematic cross section of electrodes 1230, 1240 and 1250 within an electron-beam amplifier 10 configured for time delay adjustment. Electrode 1250 is wide in diameter, relative to a diameter of a drift cavity 145(6); accordingly, equipotential lines 1260 (formed through an interaction of potentials of electrodes 1240 and 1250) are nearly parallel with electrode 1250. In this configuration, changes in the potential of electrode 1250 have little effect on beam focusing. No substantial inward radial momentum is imparted to beam electrons; changes in the potential applied to electrode 1250 increase only a field gradient and thus acceleration of electrons (not shown).

[0476] FIG. 44 shows a schematic cross section of electrodes 1270, 1280, 1290(1-4) and 1300 around a drift cavity 145(7), and a bias circuit for the electrodes. Electrode 1270 is in an emission plane 20 and electrode 1300 is in a detector plane 50. Drift cavity 145(7) is surrounded by a partial drift can electrode 1280 and ring electrodes 1290(1-4). Dashed lines across drift cavity 145(7) show electrical continuity of each ring electrode 1290(1-4) from a portion seen on one side of the drift cavity to a portion seen on the other side of the drift cavity. Ring electrodes 1290(1-4) have progressively greater potentials applied to them, in the manner previously described with respect to electron gun focusing electrodes (see FIG. 31), to shape electric fields (not shown) within drift cavity 146(7). Field lines (not shown) within drift cavity 145(7) may be shaped substantially the same as field lines in the center of drift cavity 145(6) of FIG. 43; further, the size of drift cavity 145(7) (and the overall dimensions of an electron-beam amplifier 10 incorporating drift cavity 145(7)) may be reduced. It is understood that the number of electrodes indicated in FIG. 44 is representative, and more or fewer electrodes may be employed.

[0477] One means of biasing ring electrodes 1290(1-4) includes potentials derived from a set of resistors 1330(1-5) with respective values R_A, R_B, R_C, R_D and R_E, connected in series. As shown in FIG. 44, a power supply 1310 connects a potential V₃. with partial drift can electrode 1280 and with one end of resistor 1330(1). Connections between successive resistors 1330(1-5) also connect with successive ring electrodes 1290(1-4), and an end of resistor 1330(5) connects with electrode 1300 and with another power supply 1320 at an acceleration potential V₂. Certain resistor values R_A, R_B, R_C, R_D and R_E (which may be determined through simulation or experimentation) adjust the potentials on ring electrodes 1290(1-4) to produce approximately planar accelerating fields near electrode 1300 for different values of V₂. Resistors 1330(1-5) may also be variable resistance devices (e.g., potentiometers) so that resistor values R_A, R_B, R_C, R_D, R_E may be modified if necessary. By this means, a planar acceleration field can be established.

[0478] FIG. 45 shows a schematic cross section of electrodes 1270, 1280, 1290(1-4) and 1300 around drift cavity 145(7), with a different bias circuit for the electrodes. With electrode 1270 set at a reference potential (not shown), each of electrodes 1280, 1290(1-4) and 1300 are driven by a corresponding DAC 1360(1-6) under control of a ROM 1340. In similar manner to the arrangement of FIG. 32, control words are provided to the ROM, which provides a digital control word to each DAC; each DAC then drives a corresponding potential for an electrode. In the arrangement of FIG. 45, each control word is a time delay control command word 1330 and each digital control word is a ring-electrode voltage word 1350(1-6). The digital control words may be determined by simulation or experimentation and stored in ROM 1340 to provide optimum electrode potentials for a desired range of time delays.

[0479] Electron Gun Adjustments for Time Delay Control

[0480] Adjusting potential of an electrode in detector plane 50 has advantages over adjusting an electron gun acceleration potential; adjusting potentials in an electron gun may affect deflection gain, and beam energy adjustments to a electron gun may be difficult due to complex electron gun electrode structure. Thus it is preferred, for most applications, to keep electron gun beam energy constant. Nonetheless, some applications of electron-beam amplifier 10 may benefit from a constant detector plane potential, such as for example applications which employ multiple independent e-beams, as discussed below. In these applications, time delay control may be achieved by adjusting electron gun acceleration potential.

[0481] FIG. 46 is a schematic cross-sectional drawing of an electron gun 610(4) and circuitry for beam energy and current control. A cathode 620(4) emits electrons that are focused into electron beam 120(3). A current control loop 865(2) (e.g., as shown in FIG. 32) adjusts the beam current of beam 120(3) through adjustments to a potential of a gate electrode 625(3). The potential of gate electrode 625(3) connects with ADC 1380, which transmits a digital gate word as input to a ROM 1400. ROM 1400 also receives a time delay control command word 1370 as input, and transmits a digital focusing command word 1410(1-7), corresponding to the combination of the digital gate word and the time delay control command word received, to each of DACs 1420(1-7) respectively. Each of DACs 1420(1-7) drives a potential that corresponds to the digital focusing command word received to a focusing electrode 630(24-30). A shield plate 650(4) on an exit plane of electron gun 610(4) is held at the same potential as final focusing electrode 630(30), so that potential differences do not exist around two deflector plates 600(11) and 600(12). Shield plate 650(4) may be, for example, electrode 1160 in the doublet lens system of FIG. 41. As in the circuits discussed above that use a ROM and DACs to control potentials, the optimum potentials applied to focusing electrodes 630(24-30) can be determined by simulation or experimentation; the number of focusing electrodes may be varied; ROM 1400 may be replaced by a plurality of ROMs, or may be replaced by other means for generating digital focusing command words, such as a processor.

[0482] Once electron beams 120 exit electron guns at an emission plane and enter a drift cavity, changes in beam energy affect beam focusing in this method, unless otherwise compensated. The reason is that the potentials of electrodes in a doublet lens system (e.g., electrodes 1160, 1170 and 1180 forming lenses 1190 and 1200 in FIG. 41) are optimized for a particular beam energy. The effect of beam energy on beam focusing can be compensated by an arrangement that adjusts a potential difference of the emission plane optics consisting of electrodes on each side of the drift cavity. For minor focusing adjustments, potential of a detector plane electrode may be adjusted. Again, a DAC responding to a ROM can set the potential of the detector plane electrode. For larger focusing adjustments caused by larger beam energy adjustments, potentials of a drift can electrode and a detector plane electrode may be adjusted.

[0483] Gain Stabilized Time Delay Control

[0484] Time delay changes effected by altering the beam energy, either by electron gun adjustments or detector plane acceleration adjustments, may be accompanied by changes in both deflection gain of the beam and cascade gain of the detector. Thus, the overall amplifier gain is changed. As described earlier, amplifier transconductance is given by

[0485] $\begin{array}{cc}{g}_m=\frac{\Delta I_{\mathrm{out}}}{\Delta V_{\mathrm{in}}}=G_{\mathrm{BEAM}}{G}_{\mathrm{coll}}{k}_C{k}_A=z_{\mathrm{drift}}\frac{L_P}{W_P}\frac{1}{2V_{\mathrm{BEAM}}}\frac{I_{\mathrm{BEAM}}}{X_D}{k}_D.& \left(1.40\right)\end{array}$

[0486] This calculation assumes that one detector segment receives all available beam current at a maximum deflection signal voltage. Altering deflection gain is effectively the same as changing detector width X_D. For example, increasing beam energy reduces transit time of beams through a cavity; X_D decreases correspondingly. At the same time, increasing beam energy increases detector gain k_D. The changes in X_D and k_D both increase g_m when beam energy increases Likewise, decreasing beam energy decreases g_m.

[0487] For this reason, amplifier gain may be stabilized by adjusting e-beam current. From the preceding equation, it is clear that changes in X_D and k_D can be compensated by changing the beam current. As beam energy is increased, beam current is decreased, and vice versa. For each change in detector plane potential, the electron gun currents are adjusted to maintain constant average output current.

[0488] FIG. 47 shows a circuit for gain-stabilized time delay control. A ROM 1430 stores codes 1440 corresponding to current reference values for every beam energy. In response to a time delay command 1370(2), a ROM code 1440 is transmitted to a DAC 1450, which generates a voltage reference for the electron gun current control loop consisting of the opamp 880, resistors 870 and 910, and capacitor 920 of FIG. 32. Opamp 880 drives the potential of gate electrode 625(2), regulating the flow of electrons emitted by cathode 620(3) that form electron beam 120(4).

[0489] Gain Controlled Amplifier

[0490] From the preceding, it can be appreciated that an electron-beam amplifier 10 may use a gain controlled amplifier. One method by which this can be accomplished is by implementing any of the methods of time delay control, but without current controlled gain stabilization. Another method is by a current controlled beam without beam energy adjustments. Finally, amplifier gain can be adjusted via beam energy adjustments working in concert with a current controlled beam, a difference being that current control works in the opposite sense of gain stabilization, so that it enhances the gain variation induced by the time delay control.

[0491] Pulsed Operation

[0492] Electron gun beam blanking is easily implemented in an electron beam amplifier 10. One application of electron gun beam blanking is an RF transmit amplifier that generates pulsed beams. This is beneficial for applications like radar and Ultra-Wideband (UWB) communications. With beam blanking, a continuous RF signal can be applied to deflection plates, and the amplifier output can be turned rapidly on and off with pulse widths as short as 10 picoseconds, without interrupting the RF signal.

[0493] Pulsing can be achieved by various means, for example, through gate electrode control, and through the inclusion of an extra deflector in each electron gun, called here a “blanking deflector.” Cathode control may involve a high loading capacitance and a slow response time. In many applications, such as radar and UWB, sub-nanosecond switching is desirable and cathode controlled gating is too slow. A blanking deflector has high-speed characteristics like other deflectors described above (e.g., deflector 130(1)) including very low loading of a driving source.

[0494] FIG. 48 shows an electron gun configured for beam blanking. An electron gun is shown schematically that includes a cathode 620(5), a gate electrode 625(4), focusing electrodes 630, a shield plate 650(5), a blanking deflector driven by a blanking signal 1470, a shield plate 650(6), an aperture plate 1480, a signal deflector 130(8) driven by a voltage signal 140, an emission plane shield plate 650(7) and an e-beam 120. E-beam 120(5) is emitted by cathode 620(5) through gate electrode 625(4), focused by focusing electrodes 630, and propagates through shield plate 650(5). the blanking deflector, aperture plate, and signal deflectors. When blanking signal 1470 is in an “off” state, a zero bias is applied across blanking deflector 1460. When blanking signal 1470 is in an “on” state, a positive or negative bias is applied across blanking deflector 1460, causing beam 120(5) to be deflected away from a hole in aperture plate 1480, so that beam 120(5) is stopped by the aperture plate. This blocks (“blanks”) beam 120(5) from propagating through the signal deflectors, thus “turning off” the beam. With no beam current, there is no detector excitation and no amplifier output.

[0495] As in other electron beam amplifiers 10, electron guns with blanking capability can be arrayed to create a composite e-beam from many individual beams, and all such blanking deflectors may be coupled together under control of a single blanking signal.

[0496] Frequency Multiplication

[0497] Some high frequency applications utilize both frequency multiplication and amplification; for example, high-frequency oscillators, high-frequency references for TWTs and other high-power amplifiers, and RF carriers for radar transmitters and communications systems.

[0498] Frequency multiplication at RF frequencies is sometimes achieved by driving a non-linear element with a sinusoidal signal and filtering a resulting waveform with a tuned filter to extract a higher order harmonic. The principle can easily be grasped by considering simple second order non-linearity, y=x². If the value x=cos ωt, the value y=(1+cos 2 ωt)/2, so the frequency has been doubled. Higher order non-linearities can generate higher frequency multiples. However, extra filtering is required to extract the desired harmonic, and the process may be inefficient, since harmonics have energy that diminishes roughly in proportion to the order of the harmonic. For example, a 5^th harmonic normally has much less energy than the 3^rd harmonic.

[0499] A frequency multiplying electron beam amplifier 10 may provides efficient harmonic generation, even for higher orders. The method employs a detector with a multiplicity of segments greater than two, and may use one or two deflectors arranged for deflection in two orthogonal directions (e.g., directions X and Y of FIG. 1).

[0500] FIG. 49 shows a detector arrangement configured for frequency doubling. Electron beams 120 pass through ganged deflectors 130 configured to deflect the individual beams in a common direction in response to a common voltage signal 140(4); beams 120 are focused to form a beam spot 170(15). Detector segments 150(35), 150(36), 150(37) and 150(38) are arranged in a linear row and connected to an output load in an alternating arrangement, whereby segments 150(35) and 150(37) are connected to a positive (+) output 1490(1), and segments 150(36) and 150(38) are connected to a negative (−) output 1490(2). Detector segments 150(35-38) are separated by diagonal slots, as described above, with diagonal slots indicated in FIG. 49 by way of illustration only. Voltage signal 140(4) having frequency f₁ and amplitude V₀ is applied to deflectors 130 to scan beam spot 170(15) across detector segments 150(35-38). Each cycle of voltage signal 140(4) passes across all four detector segments 150(35-38) in each direction, and the coupling of four segments to two output nodes, as shown, generates two cycles of output current for each input cycle. Current 180(3) on output 1490(1) is illustrated for comparison with input voltage 140(4); current 180(4) on output 1490(2) is of identical frequency but 180 degrees out of phase with respect to current 180(3). Proper shaping of beam spot 170(15) and detectors 150(35-38), may be used to ensures an output of frequency 2f₁ with tonal purity, low residual harmonics, and small DC component.

[0501] By increasing a number of detector segments, higher order frequency multiplication may also be achieved. With a linear row arrangement, 6 segments achieves frequency tripling, 8 segments achieves quadrupling, and so forth; furthermore, frequency multiplication can be controlled by controlling the amplitude of an input voltage.

[0502] FIG. 50 shows an arrangement of detector segments configured to provide frequency multiplication factors of 1, 2, 3 or 4 with high tone purity. For small beam deflection amplitudes, only detector segments 150(42) and 150(43) will be excited by a beam spot, and the output frequency will be the same as the input frequency driving the deflection. The multiplication factor for this case will be 1. If the signal amplitude is increased to scan the beam across segments 150(41), 150(42), 150(43) and 150(44), the frequency multiplication factor will be 2. If the deflection amplitude is increased to scan across segments 150(40), 150(41), 150(42), 150(43), 150(44) and 150(45), the frequency multiplication factor will be 3, and so forth.

[0503] There are two limitations of the simple linear array. First, high orders of multiplication may require a wide layout of detector segments, and require a correspondingly large scan angle which may exceed the range of a deflector and voltage signal. Second, it may be difficult to achieve exactly periodic spacing of zero-crossings of a multiplied frequency output with a linear array of segments. The effect of aperiodic zero-crossings may depend on an application. In an RF mixer, spurious tones may be generated that can limit the sensitivity of a receiver. If an application is as a frequency reference for an analog-digital-converter (ADC), the aperiodic crossings may create sampling errors and limit conversion accuracy.

[0504] FIG. 51 illustrates time statistics of a sinusoid, and an arrangement of detector segments arranged to compensate for the time statistics. Axis 1500 is a distance axis. Position 1501 indicates one end of a sinusoidal sweep (i.e., the path traced by a beam spot 170 being driven by deflectors 130 in response to a sinusoidal voltage signal 140). Position 1503 indicates the other end of the sweep, and position 1502 indicates the midpoint of the sweep. Thus, a single cycle of a sinusoidal input voltage may sweep a beam spot 170 from position 1501 at a time 0, past position 1502 at a time T/4, to position 1503 at time T/2, past position 1502 again at a time 3T/4, and back to position 1501 at time T that is the period of the sinusoid, as indicated by arrows 1520(1) and 1520(2). Axis 1510 is a time axis, and curve 1530 shows the relative time spent at a given position along time axis 1500 by a sinusoidal sweep. As shown, when all detector segments in a linear row are uniform in size, a beam spot may spend more time dwelling on outermost detector segments and less time on inner segments.

[0505] One method of achieving periodic zero-crossings is to adjust detector segment geometry to balance dwell times of a beam over all segments to lower the undesired harmonic content in the output. Detector segments 150(47-54) are arranged to compensate for the effect of a sinusoidal sweep pattern that spends more time on outermost regions of a sweep and less time on inner regions of the sweep. A beam spot (not shown) may scan all of segments 150(47-54), but the beam spot will spend more time on wider segments 150(50) and 150(51) due to their width, will spend less time on narrower segments 150(49) and 150(51), and so on.

[0506] Circular Frequency Multiplier

[0507] Another method of achieving periodic zero-crossings employs a circular detector with “pie-slice” segmentation and two-dimensional scanning that sweeps a beam in a circular pattern (for example, forming traces known as “lissajous figures” in the field of electron beam oscilloscopes).

[0508] FIG. 52A and FIG. 52B show two circular detector configurations 151(10) and 151(11) configured for frequency multiplication. Configuration 151(10) includes detector segments 150(56), 150(57), 150(58) and 150(59) as shown. A beam spot 170(17) travels in a circular path around detector segments 150(56-59). Beam spot 170(17) is created by electron guns (not shown) including deflectors driven by a pair of sinusoidal voltage signals V_x and V_y that have identical amplitude and frequency, but differ in phase by 90 degrees. As in electron-beam amplifiers 10 with linear arrays of detectors configured for frequency multiplication, segments 150(56-59) are coupled in alternating fashion to output lines 183(1) and 183(2), as shown. An output waveform of output lines 183(1) and 183(2) will have twice the frequency of voltage signals V_x and V_y. The four segments in detector configuration 151(10) is again equal to twice the frequency multiplication factor.

[0509] A circular detector used with a beam swept in a lissajous pattern has an inherent tolerance with respect to variations in input signal amplitude. As long as a lissajous pattern formed by beam spot 170(17) stays centered on and within segments 150(56-59), the amplitude of V_x and V_y may vary without affecting an amplitude or duty cycle of an output waveform on output lines 183(1) and 183(2). Centering of the lissajous pattern on the detector may be ensured by means of beam centering arrangements, as described above. Nonetheless, there may be an optimum amplitude of V_x and V_y for a given beam spot shape that will minimize harmonic distortion in the output waveform.

[0510] The phase offset between voltage signals V_x and V_y, may also be useful where phase offsets other than 90 degrees may lead to aperiodic zero crossings, which are equivalent to skews in duty cycle from the 50% duty cycle characterizing a sinusoidal output centered about a value of zero. Altering a phase offset between voltage signals V_x and V_y may be used to tune the duty cycle of an output waveform.

[0511] Detector 151(11) includes six output segments 150(61) through 150(66), with alternating segments connected to positive and negative output terminals as shown by the + or − sign within each segment. Detector 151(11) generates an output waveform with a frequency that is triple an input frequency applied to X and Y deflectors used to steer beam spot 170(18).

[0512] Other embodiments of an electron-beam amplifier 10 using X-Y deflection may optimize detector shape for low distortion or high frequency operation, such as, for example through use of an elliptical detector, or a segmented ring detector.

[0513] Other Frequency Multipliers

[0514] A multiply segmented detector is only one means of achieving frequency doubling. For example, in another electron-beam amplifier 10, frequency multiplication is achieved with a single detector segment. By appropriately shaping a detector and/or a beam spot, harmonic components may be emphasized as the beam spot sweeps across an edge of the detector. Emphasis of harmonic components results from a non-linear change in beam current collection with respect to beam spot position. An electron-beam amplifier 10 that multiplies an input frequency through shaped, single beam spots and detectors may generate output frequency tones that are not as pure (i.e., free of harmonics) as in multiple segment embodiments, but smaller, faster detectors and simpler microcolumns (i.e., with only one deflector instead of two) may be used.

[0515] FIG. 53A and FIG. 53B show two beam spot and detector configurations for frequency multiplication. Beam spot and detector configuration 151(13) includes a rectangular beam spot 170(20) and a triangular detector segment 150(67). Beam spot 170(2) sweeps through a position ΔX corresponding to an angle θ (measured with respect to an undeflected beam from a microcolumn array, not shown). Beam current collected by detector segment 150(67) thus changes quadratically, as I=aθ² (where a is a proportionality constant representing variables including beam current and detector size). From trigonometry, if θ changes in response to a deflector voltage V₀ which varies sinusoidally with a frequency ω, then θ=V₀ sin(ωt), and the collected current will have a frequency component 2ω according to

[0516] $\begin{array}{cc}{\sin }^2\mathrm{\varpi t}=\frac{1}{2}\left(1-\cos 2\varpi t\right)& \left(1.41\right)\end{array}$

[0517] It is also possible to make a beam spot 170(21) triangular and a detector segment 150(68) rectangular, as shown in configuration 151(14). Again, collected current changes quadratically in relation to a sinusoidal beam sweep. The triangular shape of beam spot 170(21) may be generated by the methods discussed above, including use of a triangular shaped microcolumn array imaged onto a detector plane. Configuration 151(14) may offer a somewhat smaller, faster detector, and illustrates the principle that it is the relation of beam spot to detector shape that is useful in generating a desired output.

[0518] Other shapes may be used to generate even higher frequency multiplication factors. FIG. 54A and FIG. 54B show, by way of example, two configurations that produce third harmonics of an input frequency. Configuration 151(15) has a rectangular spot and a detector 150(69) with a quadratic shape; configuration 151(16) has a triangular spot and a triangular detector 150(70), as shown. Fourth harmonics may be generated by quadratic spot shaping in relation to a triangular detector, fifth harmonics may be generated by a quadratic spot in relation to a quadratic detector shape, and so on.

[0519] Mixer

[0520] RF mixing is another application of an electron-beam amplifier 10 that may multiply a frequency and generate intermodulation products of two frequencies. FIG. 55 shows a detector and beam spot configuration 151(17) configured for use as an RF mixing device. A microcolumn array (not shown) with X-Y deflection apparatus driven by voltage signals V_x and V_y scans a square beam spot 170(23) across a two-dimensional array of four equal, square detector segments 150(71-74), as shown. RF signals V_x and V_y are coherently demodulated, as discussed below. Detector segments 150(71-74) are cross-connected to detector outputs 183(3) and 183(4), as shown. V_x has frequency f₁ and is the voltage signal applied to an X deflector; V_Y has frequency f₂ and is the voltage signal applied to a Y deflector.

[0521] Beam spot 170(23) will move in the X and Y directions across detector segments 150(71-74) so as to cause a differential current ΔI_out across detector outputs 183(3) and 183(4) to have a fundamental frequency component at a frequency difference f₁−f₂. Harmonics that may exist in ΔI_out may be filtered according to means known in the art.

[0522] In configuration 151(17), detector segments 150(71-74) each have a width and height of 2 W; square beam spot 170(23) is also of width and height 2 W, and has a uniform cross-sectional current density J. Beam spot 170(23) is deflected in an X direction in response to V_x and in a Y direction in response to V_y, instantaneous deflections in these directions are called Δx and Δy respectively, and Δx and Δy are linearly proportional to signals V_x and V_y. Currents generated from each of detector segments 150(71-74) are I₁, I₂, I₃ and I₄, respectively. These currents vary in response to beam spot deflections Δx and Δy, as shown below
I₁=J(W+Δx)(W+Δy)
I₂=J(W−Δx)(W−Δy)
I₃=J(W−Δx)(W+Δy)
I₄=J(W+Δx)(W−Δy)  (1.42)
When the beam spot is centered, each segment receives a current J·W². Currents I₁ and I₂ are coupled to drive terminal 183(3) to form current I_B and segment currents I₃ and I₄ are coupled to drive terminal 184(4) to form current I_A. Net output currents I_B and I_A to terminals 183(3) and 184(4), respectively, are
I_B=I₁+I₂=2J(W²+ΔxΔy)
I_A=I₃+I₄=2J(W²−ΔxΔy)  (1.43)

[0523] Differential output current ΔI_out is given by
ΔI_out=I_B−I_A=4JΔxΔy  (1.44)

[0524] Thus, the action is that of a multiplier.

[0525] As known in the art of RF receivers, a multiplier is a basic element of many mixers. This may be seen when Δx and Δy are proportional, respectively, to sinusoids of amplitudes X₀ and Y₀, and frequencies f₁ and f₂:
Δx=X₀ sin(2πf₁t)
Δy=Y₀ sin(2πf₂t)  (1.44)

[0526] As may be derived using the Law of Cosines,

[0527] $\begin{array}{cc}\begin{array}{c}\Delta I_{\mathrm{out}}=4J\Delta x\Delta y=4J·X_0\sin \left(2\pi f_{1}t\right)Y_0\sin \left(2\pi f_{2}t\right)\\ =2{\mathrm{JX}}_0{Y}_0\left\{\sin \left[2\pi \left(f_1+f_2\right)t\right]+\sin \left[2\pi \left(f_1-f_2\right)t\right]\right\}\end{array}& \left(1.45\right)\end{array}$

[0528] This shows the sum and difference frequencies characteristic of a mixer. In certain RF applications, the sum frequency is removed by filtering, leaving a difference frequency (f₁−f₂) representative of an intermediate (IF) or modulation frequency.

[0529] It may be appreciated that e-beam spot deflections Δx and Δy are generated according to the basic principles of electron-beam amplifier 10. When scan deflections Δx and Δy are small with respect to the dimensions 2 W of the spot, a linear multiplication is effected. When the scan deflections are large such that Δx and Δy approach or exceed the spot half dimension W, then a “bang-bang” rectifying type mixer is achieved, operating similar to known circuits which employ active switches, such as MOS transistors, or diodes.

[0530] Combinational Logic

[0531] Combinational logic is an application for an electron-beam amplifier 10 that resembles the mixing and frequency multiplying embodiments discussed above, but which operates in a different parameter space and for a different purpose. A combinational logic embodiment may include a short drift cavity and multiple deflectors, and may have only one electron gun per logic element. Detectors in combinational logic embodiments may have two or more segments. Voltage signals for Deflectors may be logic signals of binary or multiple quantized voltage levels. Combinations of quantized voltage input states correspond to quantized beam deflections, each quantized beam deflection being representative of a logic state formed by the combination of input states. By positioning detector segments at locations corresponding to quantized beam positions, the detector outputs may be representative of respective logic states. By this means, logic operations, such as AND, OR, XOR, and even complete functions (such as, for example, a full adder) may be constructed. With the inherent advantages, including high-frequency operation and microfabrication, it can be appreciated that combinations of logic elements can be incorporated as complex arithmetic units, digital multipliers or memory elements that operate at picosecond speeds.

[0532] The basic principle of a combinational logic embodiment is that if a signal representing a quantized logic value, for example a signal that may be −1V or +1V, is applied to an e-beam deflector, then the corresponding beam may be deflected to one of two states, corresponding to deflection angles, for example θ₁ or θ₂. If a second deflector that is likewise responsive to a signal representing a quantized logic value is incorporated, the number of possible states increases to four, such as beam angles θ₁, θ₂, θ₃, θ₄. With three deflectors, the number of possible states is 8, and so on. The principle may also be extended to multi-valued logic; for example, if 4-level logic signals are applied to two deflectors, the beam angle may have 16 states.

[0533] FIG. 56 shows a two-deflector combinatorial e-beam logic system with three linearly arranged detector segments 150(75), 150(76) and 150(77). Signalling in FIG. 56 is binary; two inputs A and B are applied to a deflector 130(9) and a deflector 130(10) respectively. In FIG. 56, four possible deflection states of an electron beam 120(6) exhibit a degeneracy when input A is the inverse of input B. This can be understood with a truth table where A and B take on binary voltage values of +1V and −1V that correspond to deflections +θ and −θ as logic 0 and logic 1 states:

[0534]

TABLE 3
Two-input logic gate
	State	A	B	Θ
	1	−1	−1	~2θ
	2	−1	+1	0
	3	+1	−1	0
	4	+1	+1	2θ

[0535] Only one detector is activated for each state, but this shows that two of the binary states have the same deflection angle (0). This is reflected in FIG. 56 by the fact that there are only three detector segments. FIG. 56 shows the logic value of each detector segment, the value of the middle detector being an exclusive-or (⊕) of inputs A and B.

[0536] A linear arrangement of deflectors and detectors may require a large deflection range when multiple inputs are used. For example, a binary deflection state corresponding to identical deflection angles applied to three successive deflectors may involve three times the deflection angle of a state in which only one deflector is active. Accommodating the deflection range necessary for all logic states may be difficult; this can be mitigated by use of a long drift region, but this increases the drift time of the beam, thus slowing the maximum switching speed and the latency of associated logic operations.

[0537] FIG. 57 shows a two-deflector combinatorial e-beam logic system with four detector segments 150(78), 150(79), 150(80) and 150(81) arranged in a two-dimensional array. In FIG. 57, a deflector 130(11) provides X deflection, and a deflector 130(12) provides Y deflection, for electron beam 120(7). The separation of A and B inputs into orthogonal directions removes the degeneracy of states 2 and 3 shown in Table 3.

[0538] An electron gun microcolumn 610 may have multiple X and Y deflectors for logic involving more than two inputs. For example, for three logic inputs, a microcolumn may have two X deflectors and one Y deflector. For four logic inputs, a microcolumn may have two X deflectors and two Y deflectors. With X and Y deflection, the logic states are described by a two-dimensional set of beam states, detected with a two dimensional array of detector segments. The result is similar to creating a physical Carnaugh map, as known in the art of logic devices.

[0539] For the case of four logic inputs described above, the corresponding 16 logic output states are detected with a matrix of three rows and three columns of detector segments. FIG. 58 shows a two-deflector combinatorial e-beam logic system with nine detector segments 150(82-90) arranged in a two-dimensional array, with a corresponding diagram of input states mapped to the detector segments. Signalling in FIG. 58 is binary; each of inputs A, B, C and D is applied to a corresponding deflector 130(13), 130(14), 130(15) or 130(16) for deflecting electron beam 120(8). Again, there are fewer segments than states, because degeneracies exist with 2 or more deflectors in either of the X and Y directions. However, it can be seen that the number of degenerate states created by deflectors in two directions is less than if all deflectors acted in the same direction.

[0540]

TABLE 4
Four-input logic states
								Detector
	State	A	B	C	D	ΘX	ΘY	segment
	1	−1	−1	−1	−1	2θ	2θ	150(88)
	2	−1	−1	−1	1	2θ		150(85)
	3	−1	−1	1	−1	~	2θ	150(89)
	4	−1	−1	1	1	~	~	150(86)
	5	−1	1	−1	−1	2θ	~	150(85)
	6	−1	+1	−1	+1	−2θ	2θ	150(82)
	7	−1	+1	+1	−1	~	~	150(86)
	8	−1	+1	+1	+1	~	2θ	150(83)
	9	+1	−1	−1	−1	~	2θ	150(89)
	10	+1	−1	−1	+1	~	~	150(86)
	11	+1	−1	+1	−1	2θ	2θ	150(90)
	12	+1	−1	+1	+1	2θ	~	150(87)
	13	+1	+1	−1	−1	~	~	150(86)
	14	+1	+1	−1	+1	~	2θ	150(83)
	15	+1	+1	+1	−1	+2θ	~	150(87)
	16	+1	+1	+1	+1	+2θ	2θ	150(84)

[0541] An examination of this table for particular detectors segments shows that degenerate states correspond to some form of exclusive-or combination; for example, detector segments 150(83), 150(86) and 150(89) correspond to A⊕C, while detector segments 150(85), 150(86) and 150(87) correspond to B⊕D.

[0542] Despite the degeneracy observed, orthogonal deflection drive is a preferred construction; it still minimizes degeneracy as compared to a linear array configuration, and a deflection required in each of the X and Y directions is smaller than would be required in a linear detector array configuration. Smaller deflection allows a proportionately shorter drift region, shorter drift time and smaller deflection drive voltages. For example, with only two deflectors, one in X and the other in Y, drift distance and time may be reduced by one-half when compared to a pair of X deflectors; correspondingly, logic switching operations occur twice as fast. Alternatively, for a given drift distance, a deflection voltage may be smaller (for example, 0.5V versus 1V) so that power consumption may be reduced or switching speed may be increased.

[0543] It may be appreciated that degenerate states are not the only way to combine logic states. In the case of FIG. 57, the logic functions AND (A·B), OR (A+B), NAND ( A·B), NOR, XOR (exclusive-or, ⊕) and XNOR (inversion of exclusive-or) can be created with nothing more than one or two wires to connect appropriate detectors to a load. With a single deflector and detector, inversion may also be achieved. With two deflectors, any of four possible boolean states may be represented. With three deflectors, more complex functions may be achieved. Furthemore, a logic input state may be inverted by simply reversing the coupling of signals to a deflector.

[0544] By “wire-oring” (as it is termed) deflector inputs and/or detector outputs using electrical connections, other logic functions may be implemented, providing great flexibility in a simple structure, since any of these means may switch almost as fast as any other. This is unlike conventional logic gates made from transistors, where certain gate types are much slower than others. For example, a CMOS NOR gate is slower than a CMOS NAND gate; also, conventional static CMOS logic lacks an inherent complement output, which must be generated with a second inversion gate, adding to switching delays. An ECL or current mode gate suffers loss in performance because multiple transistors are required for complex functions, and due to having a limited power supply range. In contrast, logic embodiments of e-beam amplifier 10 may be fast in almost any logic combination, because the logic function is encoded as a beam position (or state), rather than as a combination of switches.

[0545] FIG. 59 shows schematically a logic device with two electron beams 120(9) and 120(10) and their associated detector segments 150(91) and 150(92) acting collectively as a signal source for a deflector of a third electron beam 120(11). In the embodiment of FIG. 59, if electron beams 120(9) and 120(10) are respectively steered by deflectors according to logic inputs A and B, then electron beam 120(11) corresponding to a logic output C will be steered according to an AND function of A and B.

[0546] Other combinations are possible. For example, deflectors may be physically designed to achieve more or less deflection for a given input voltage (“deflection gain”). One deflector might have a deflection gain of 10 degrees beam deflection per volt of deflection drive, while another deflector might have a deflection gain of 5 degrees per volt. As described above, longer or shorter deflector plates will alternately increase or decrease deflector gain; spacing deflector plates more closely or further apart will also increase or decrease deflector gain, respectively. By using deflectors with varying amounts of deflection gain, beam deflection states may be gray-coded to eliminate degeneracies and make detection more resistant to errors. These two goals follow directly from use of multiple deflection gains.

[0547] Gray coding is a well-known method of digital word encoding whereby single bit errors in the word cause only one bit of error in a digital count represented by a word. Gray-coded operation is useful for specialized functions often found in communication systems, where robust signaling that is tolerant of small errors is necessary. In electron-beam amplifiers 10, gray-coded beam states make detection resistant to single bit errors in beam displacement.

[0548] FIG. 60 shows a two-input gray-coded logic gate with four detector segments in a linear array, and a corresponding map of input states mapped to the detector segments. A deflector 130(17) produces a deflection angle of +θ or −θ in response to values of an input logic state B. Deflector 130(17) has twice the plate spacing as a deflector 130(18) that produces a deflection angle of +2θ or −2θ in response to values of an input logic state A. (Alternatively, and not shown, deflector 130(17) could have half the plate length of deflector 130(18) but with identical plate spacing, to produce the same difference in deflection gain). Detector segments 150(93-96) are arranged such that deflection angle changes of 2θ move electron beam 120(12) to each succeeding segment, as shown. The deflection angle coding is as shown in Table 3 and FIG. 60.

[0549]

TABLE 5
Gray-coded Deflections
State	A	B	θ	Detector segment
1	−1	−1	+3θ	150 (93)
2	−1	+1	+θ	150 (94)
3	+1	−1	−θ	150 (95)
4	+1	+1	−3θ	150 (96)

[0550] For example, if logic states A and B represent a binary number with A the most significant bit (“MSB”) and B the least significant bit (“LSB”), it can be seen that a maximum error in the output generated by a single logic state error (perhaps due to a noise glitch at an earlier stage of digital processing) may be 1 LSB. In contrast, the previous 2-input gate could exhibit a 1 MSB error. Gray-coding may be extended to more bits, as is known in the art.

[0551] One aspect of a logic gate may be that logic levels are compatible between gate inputs and outputs. In certain embodiments of an electron-beam amplifier, a difference in potential between detectors and deflectors may be up to several hundred volts. If the logic switching is dynamic enough, this potential difference may be accommodated with capacitive coupling.

[0552] Another means of logic level compatibility is to ensure that detector output levels are the same as deflector input levels. One method of keeping these potentials compatible is to use a zero bias drift cavity in which an exit plane of an electron gun is at the same potential as a beam contact and a detector plane (i.e., allowing electrons to drift from deflector to detector through a field-free region). Since a deflector is inherently a differential input device, a common mode level can be rejected to some degree, and detector output can be directly coupled to the deflector.

[0553] For logic operation, a suitable detector bias is less than 1V. This is consistent with an extremely high-speed device. Logic devices may use faster, lower bias detectors than amplifiers, since power is not required or desired. Operation at less than 0.5V is possible when detectors are Schottky diodes with turn-on potentials of around 0.2 to 0.3V.

[0554] A detector may be terminated in either a resistor or an active load, such as a resonant tunnel diode (RTD). When a resistor is used, beam current may pull down the output potential of the detector to the beam contact potential; this is a logic “0.” Without beam current, the resistor acts to pull up the output potential to the power supply voltage, representing a logic “1.” An RTD load behaves similarly, except that an RTD has a negative differential resistance, so the pull-up and pull-down are speeded up for faster operation.

[0555] As mentioned previously, it is desirable to operate e-beam logic elements with a single electron gun per gate. Because a very short drift region is required for low gate delay (a few microns), a single gun can tolerate higher beam current without space charge spreading causing beam defocusing during the drift time.

[0556] Nonetheless, a low beam current is still preferred to reduce detector heating. For this reason, detector gain should be as high as possible, but this conflicts somewhat with the requirement of high deflection gain. On one hand, high deflection gain is achieved with a low-energy electron gun; on the other hand, high detector gain is achieved with a drift cavity field that accelerates beam electrons to achieve high cascade gain. If the drift cavity is field free, all the cascade gain may come from the electron gun acceleration. One solution is to accept the lower cascade gain and compensate with higher avalanche gain in the detector. For example, photonic detectors with avalanche gains exceeding 1000 are relatively common. The downside is less radiation tolerance, which might be acceptable for many applications, and might be offset by a slightly higher beam current. For example, an electron-beam amplifier 10′ for an amplifying application might have a beam current of 1 μA, a cascade gain of 100, an avalanche gain of 10 and an overall detector gain of 1000; an electron-beam amplifier 10″ for a logic application might have a beam current of 2 μA, a cascade gain of 20, an avalanche gain of 25 and an overall detector gain of 500. The higher beam current of electron-beam amplifier 10″ provides the same detector output current, and almost entirely compensates for an increased radiation sensitivity due to the 2.5× higher avalanche gain.

[0557] In electron-beam amplifiers 10′ and 10″ above, the detector current is 1 mA; this may be inadequate for the highest speed operation, so even higher beam current and avalanche gain may be required. For example, a 50 ohm load, 500 mV switching application may require at least 10 mA detector current; avalanche gain may be increased by a factor of 10, or beam current may be somewhat (which may be tolerated because of a very short drift cavity). Beam current might be increased to 4 μA and avalanche gain increased by a factor of 5, or the beam current increased by a factor of 3× and the avalanche gain increased by a factor of 3.3. An advantage of sharing the gain increase between beam and detector is, again, to reduce radiation sensitivity.

[0558] As mentioned, a drift cavity of an e-beam amplifier 10 in a logic application may be very short, to minimize transit time of a beam. Beam delay directly affects a maximum cycle time that the logic can operate at. For example, if two deflectors are 1 μm long each, with a 1 μm drift cavity, the total drift distance is approximately 3 μm. For a 50V beam (with a velocity of 4×10⁶ m/s), transit time from the input of a first deflector to a detector is 750 femtoseconds (10⁻¹⁵). This suggests an upper switching rate limit of around 1 THz.

[0559] Gate loading delays can also be estimated, by way of example. With a 1 um drift cavity, detectors may be on the order of 0.25 μm×0.25 μm in size. Junction devices such as Schottky diodes typically have capacitances on the order of 1 fF/μm². Thus, a detector capacitance may be approximately 0.125 fF. The loading of a single deflector with plate spacing of 1 μm, a plate length of 1 μm and a plate height of 1 μm is 0.009 fF. For a 50 ohm load, capacitance is very dependent on construction, but may be well under 1 fF, so a value of 0.5 fF will be conservatively assumed here. Thus, a total loading capacitance may be 0.125 fF+0.009 fF+0.5 fF, or approximately 0.75 fF. The fall time when a detector turns on is dominated by pull-down current times into the total loading capacitance, given by dv/dt=I/C. With a 500 mV power supply and a 1 mA beam current, a fall time may be 375 fs. A rise time when the detector turns off is approximately the RC time constant of the load resistor and capacitance, or, 50 ohms×0.75 fF=37.5 fs. These figures are approximate and will depend strongly on the application, but they demonstrate rise/fall times on the same order as the gate delay, thus an e-beam amplifier 10 used in a logic application may have switching speeds on the order of 1 THz.

[0560] As with other embodiments of an electron-beam amplifier 10, detectors provide gain with respect to collected beam current. This gain is essential if a single electron gun is to be used, which may be a preferred construction when many logic elements are combined in an integrated processor or other complex logic system. Since detector gain is not precise, diode means may be used to limit detector output voltage to controlled binary logic levels. Schottky diodes are preferred, since they are readily available from the detector construction, and they are among the fastest clamping devices known.

[0561] FIG. 61 schematically shows an output network 190(2) using clamping diodes 1540(1) and 1540(2). Output network 190(2) is connected to two power supplies 1550(1) and 1550(2) and is configured to provide differential outputs 1560(1) and 1560(2) that are complementary logic states, as shown. Power supply 1550(1) is a reference potential that corresponds to an appropriate level for one of the complementary logic states; power supply 1550(2) is a potential that may be different from the reference potential by an amount that exceeds a desired difference between the complementary logic states. Each side of output network 190(2) includes a detector segment 150(97) or 150(98), a resistor 1570(1) or 1570(2), and a clamping diode 1540(1) or 1540(2), as shown.

[0562] A beam 120 is configured by an electron gun and focusing optics (not shown) to strike detector segment 150(97) or 150(98). A detector 150 that is not struck by beam 120 isolates a corresponding output 1560 from power supply 1550(2), allowing the corresponding resistor 1570 to pass a current I_R so that the corresponding output 1560 reaches the potential of power supply 1550(1). In this illustration, detector 150(97) is not struck by beam 120, current I_R passes through resistor 1570(1), and output 1560(1) reaches the potential of power supply 1550(1), but it will be appreciated that the circuit symmetry is designed to produce an equal effect on detector 150(98), resistor 1570(2) and output 1570(2) if the beam strikes detector 150(97).

[0563] A detector 150 that is struck by beam 120 emits an output current I_D that drives the potential of a corresponding output 1560 until the corresponding output 1560 reaches a clamp potential of the corresponding clamping diode 1540. When current I_D changes the potential of output 1560 to exceed the clamp potential V_clamp, clamping diode 1540 passes a current I_C that prevents any further change to the potential of output 1560.

[0564] Thus the potential of an output 1560, corresponding to a detector 150 struck by a beam 120, will achieve the potential of power supply 1550(1) offset by the clamp potential V_clamp. It should be noted that the potential of power supply 1550(2) may be positive or negative with respect to power supply 1550(1) as a matter of design choice, for implementing suitable logic levels and choices of detectors 150 and clamping diodes 1540. The diode symbols used in FIG. 61 are not meant to limit a circuit implementation to the diode polarities indicated, but simply to show that a diode is used.

[0565] Power Combining Arrays

[0566] Ganging amplifiers is one way to increase the power output of amplifier embodiments while maintaining a wide signal bandwidth. Ganging may exploit a high input impedance of the deflector apparatus, such that many amplifiers may be driven from a common low-impedance source, for example, a 50 ohm transmission line.

[0567] The principle obstacle to ganging amplifiers is not input loading, but power-combining many outputs. In conventional technologies, such as solid state amplifiers, this type of combining may present a formidable problem. Simple electrical networks made of transmission lines or waveguides have significant ohmic losses that can drastically reduce the efficiency of the power summing, especially in large arrays. Efficient power combiners generally take two forms: waveguide combiners and free-space summing of electromagnetic waves. Waveguide power combiners suffer from ohmic losses, and are difficult to construct in a microfabricated form. The hierarchical structure of combiners, such as the Wilkinson type, also makes them suffer from wave reflections at the many summing nodes, resulting in high standing wave ratio and more lost efficiency.

[0568] As described below, free-space summing of electromagnetic waves is a preferred method of power-combining since there are no ohmic losses or standing waves. With free-space summing, amplifiers are coupled to radiating antenna elements, and the radiated fields naturally combine by coherent superposition. It is only desirable that the amplifiers be driven from a common signal input or sources that have the same frequency and similar phase. In many applications, these free-space fields may be used directly, as in a radar or communications transmitter. The effect of the phasing may, for example, create a directional RF beam. In other applications where RF radiation is not desired, the coherent sum can be collected in another, larger antenna, such as a horn or parabolic dish.

[0569] Thus, a radiating EBTX embodiment 4000 shown in FIG. 62 couples an antenna 4002 to a detector 4004, such as a clamping diode, to convert an incoming signal 4006 into a radiating field 4008. The incoming signal 4006 is pre-processed by an electron gun array as previously shown and described. In a preferred construction, the antenna 4002 is constructed with microfabrication and integrated with the detector 4004 to form a unitary assembly. In one variation, the detector 4004 and the antenna 4002 are separate components that are electrically coupled by intermediate wiring (not shown). In another variation the antenna 4002 is an integral part of the detector 4004. In a third variation, the detector 4004 is coupled to a waveguide (not shown), which is open-terminated to free-space as an aperture radiator. In a fourth variation the waveguide couples to a horn antenna which provides more directivity to the free-space radiation.

[0570] FIG. 63 shows one form of EBTX construction 4009 including the elements of FIG. 62. Incoming signal 4006 is applied to deflectors 4010 of an electron gun array 4012. A plurality of electron guns 4014, 4016 emit corresponding beamlets 4018, 4020, which are shaped using beam shaping electrodes 4022. Beamlets 4018, 4020 may be blanked by selective application of blanking signal 4024 to blanking electrodes 4026. A metal drift can 4028 is provided with lensing electrodes, such as electrodes 4030, 4032 to form a doublet lensing field 4034, 4036 that focuses an array of beamlets 4038 onto spot 4040, which mat be swept across detector 4004 to emit the radiating field 4008. Deletion of antenna 4002 would convert the EBTX construction 4009 into an EBRX device.

[0571] These radiating embodiments are termed here the EBTX (Electron Beam Transmit Amplifier) since they may amplify, as in a receiver mode, as well as transmit an electromagnetic field. Thus, free-space fields may be efficiently summed in large power generating arrays such as a phased array antenna.