Method for increasing of tunneling through a potential barrier

[0002] The present invention is concerned with methods for promoting the transfer of elementary particles across a potential energy barrier.

[0003] In Edelson's disclosure, filed Mar. 7, 1995, titled “Electrostatic Heat Pump Device and Method”, Ser. No. 08/401,038, now abandoned, incorporated herein by reference in its entirety, two porous electrodes were separated by a porous insulating material to form an electrostatic heat pump. In said device, evaporation and ionization of a working fluid in an electric field provided the heat pumping capacity. The use of electrons as the working fluid is disclosed in that application. In Edelson's subsequent disclosure, filed Jul. 5, 1995, titled “Method and Apparatus for Vacuum Diode Heat Pump”, Ser. No. 08/498,199, an improved device and method for the use of electrons as the working fluid in a heat pumping device is disclosed. In this invention, a vacuum diode is constructed using a low work function cathode.

[0004] In Edelson's further subsequent disclosure, filed Dec. 15, 1995, titled “Method and Apparatus for Improved Vacuum Diode Heat Pump”, Ser. No. 08/573,074, now U.S. Pat. No. 5,722,242, incorporated herein by reference in its entirety, the work function of the anode was specified as being lower than the work function of the cathode in order to optimize efficient operation.

[0005] In a yet further subsequent disclosure, filed Dec. 27, 1995, titled “Method and Apparatus for a Vacuum Diode Heat Pump With Thin Film Ablated Diamond Field Emission”, Ser. No. 08/580,282, now abandoned incorporated herein by reference in its entirety, Cox and Edelson disclose an improvement to the Vacuum Diode Heat Pump, wherein a particular material and means of construction was disclosed to further improve upon previous methods and devices.

[0006] The Vacuum Diode at the heart of Edelson's Vacuum Diode Heat Pump may also be used as a thermionic generator: the differences between the two devices being in the operation of the diode, the types and quantities of external energy applied to it, and the provisions made for drawing off, in the instance of the thermionic converter, an electrical current, and in the instance of the Vacuum Diode Heat Pump, energy in the form of heat.

[0007] In Cox's disclosure, filed Mar. 6, 1996, titled “Method and Apparatus for a Vacuum Thermionic Converter with Thin Film Carbonaceous Field Emission”, Ser. No. 08/610,599, incorporated herein by reference in its entirety, a Vacuum Diode is constructed in which the electrodes of the Vacuum Diode are coated with a thin film of diamond-like carbonaceous material. A Vacuum Thermionic Converter is optimized for the most efficient generation of electricity by utilizing a cathode and anode of very low work function. The relationship of the work functions of cathode and anode are shown to be optimized when the cathode work function is the minimum value required to maintain current density saturation at the desired temperature, while the anode's work function is as low as possible, and in any case lower than the cathode's work function. When this relationship is obtained, the efficiency of the original device is improved.

[0008] Many attempts have been made to find materials with low work function for use as cathodes for vacuum diodes and thermionic energy converters. Currently most research is in the field of cathodes for vacuum tubes. Research in thermionic converter technology is less intensive because of the difficulties of increasing thermionic emission of electrons from the flat surface, where field emission effect can not be applied. The practical importance of thermionic energy conversion is rapidly increasing due to increased needs for alternative energy sources. The most effective way of decreasing work function known today is the use of alkaline metal vapors, particularly cesium, and coating the emitter surface with oxide thin films. Use of Cs vapor is not without technical problems, and thin film coated cathodes generally show short lifetimes.

[0009] It is well known from Quantum Mechanics that elementary particles have wave properties as well as corpuscular properties. The density of probability of finding an elementary particle at a given location is |ψ|²where ψ is a complex wave function and has form of the de Broglie wave:

[0010] ψ=Aexp[(−i2π/h) (Et−pr)]  (1)

[0011] Here ψ is wave function; h is Planck's constant; E is energy of particle; p is impulse of particle; r is a vector connecting initial and final locations; t is time.

[0012] There are well known fundamental relationships between the parameters of this probability wave and the energy and impulse of the particle:

[0013] E is electron energy and p=(h/2π)k   (2)

[0014] Here k is the wave number of probability wave. The de Broglie wavelength is given by:

[0015] λ=2π/k   (3)

[0016] If time, t, is set to 0, the space distribution of the probability wave may be obtained. Substituting (2) into (1) gives:

[0017] ψ=A exp(ikr)   (4)

[0018] FIG. 1 shows an elementary particle wave moving from left to right perpendicular to a surface 7 dividing two domains. The surface is associated with a potential barrier, which means the potential energy of the particle changes it passes through it.

[0019] Incident wave 1 Aexp(ikx) moving towards the mainly reflect back as reflected wave 3 βAexp(−ikx), an small part leaks through the surface to give transmitted wave α(x)Aexp(ikx) (β≈1>>α). This is the well-known effect known as quantum mechanical tunneling. The elementary particle will pass the potential energy barrier with a low probability, depending on the potential energy barrier height.

[0020] Usagawa in U.S. Pat. No. 5,233,205 discloses a novel semiconductor surface in which interaction between carriers such as electrons and holes in a mesoscopic region and the potential field in the mesoscopic region leads to such effects as quantum interference and resonance, with the result that output intensity may be changed. Shimizu in U.S. Pat. No. 5,521,735 discloses a novel wave combining and/or branching device and Aharanov-Bohm type quantum interference devices which have no curved waveguide, but utilize double quantum well structures.

[0021] Mori in U.S. Pat. No. 5,247,223 discloses a quantum interference semiconductor device having a cathode, an anode and a gate mounted in vacuum. Phase differences among the plurality of electron waves emitted from the cathode are controlled by the gate to give a quantum interference device operating as an AB type transistor.

[0022] Other quantum interference devices are also disclosed by Ugajin in U.S. Pat. No. 5,332,952 and Tong in U.S. Pat. No. 5,371,388.

[0023] In their U.S. patent application Ser. No. 08/924,910 filed Aug. 9, 1991, incorporated herein by reference in its entirety, Edelson and Tavkhelidze describe vacuum diode devices in which the separation of the electrodes is effected using piezo-electric positioning elements. They also teach a method for fabricating electrodes in which imperfections on one are exactly mirrored in the other, which allows electrode to be positioned very closely together.

[0024] Broadly the present invention is a method for enhancing the passage of elementary particles through a potential energy barrier utilizing interference of de Broglie waves to increase the probability of emission. In a preferred embodiment, said elementary particles are selected from the group consisting of electrons, protons, neutrons, and leptons.

[0025] In another embodiment, the invention provides an elementary particle-emitting surface having a series of indents. The depth of the indents is chosen so that the probability wave of the elementary particle reflected from the bottom of the indent interferes destructively with the probability wave of the elementary particle reflected from the surface. This results in a reduction of reflecting probability and as a consequence probability of tunneling through the potential barrier is increased.

[0026] In further embodiments, the invention provides vacuum diode devices, including a vacuum diode heat pump, a thermionic converter and a photoelectric converter, in which either or both of the electrodes in these devices utilize said elementary particle-emitting surface.

[0027] In yet further embodiments, the invention provides devices in which the separation of the surfaces in such devices is controlled by piezo-electric positioning elements.

[0028] A further embodiment provides a method for making an elementary particle-emitting surface having a series of indents.

[0029] Objects of the present invention are, therefore, to provide new and improved methods and apparatus for particle emission, having one or more of the following capabilities, features, and/or characteristics:

[0030] An object of the present invention is to provide a method for promoting transfer of elementary particles across a potential barrier, comprising providing a surface on which the potential barrier appears having a geometrical shape for causing de Broglie interference between said elementary particles.

[0031] An advantage of the present invention is that destructive interference between the waves of emitted particles may be created, which allows for an increase in particle emission.

[0032] A further object of the present invention is to provide an elementary particle-emitting surface having a geometrical shape for causing de Broglie interference.

[0033] An advantage of the present invention is that thermionic emission is greatly enhanced and becomes an extremely practical technology.

[0034] An object of the present invention is to provide a surface having a series of indents, the depth of which is chosen so that the probability wave of the elementary particle reflected from the bottom of the indent interferes destructively with the probability wave of the elementary particle reflected from the surface.

[0035] An advantage of the present invention is that the effective work function of the material comprising the surface is reduced.

[0036] FIG. 1 shows in diagrammatic form, an incident probability wave, a reflected probability wave and a transmitted probability wave interacting with a substantially planar surface.

[0037] FIG. 2 shows in diagrammatic form, an incident probability wave, two reflected probability waves and a transmitted probability wave interacting with a surface having a series of indents.

[0038] FIG. 3 shows in a diagrammatic form, the behavior of an electron in a metal

[0039] FIG. 4 is a diagrammatic representation of one embodiment of a thermionic converter with electrode separation controlled by piezo-electric actuators.

[0040] FIG. 5 is a schematic showing a process for the manufacture of pairs of electrodes.

[0041] 11. Incident probability wave

[0042] 13. Reflected probability wave

[0043] 15. Transmitted probability wave

[0044] 17. Indented Surface

[0045] 21. Reflected probability wave

[0046] Referring now to FIG. 2, two domains are separated by a surface 17 having an indented shape, with height a.

[0047] An incident probability wave 11 is reflected from surface 17 to give reflected probability wave 13, and from the bottom of the indent to give reflected probability wave 21. The reflected probability wave will thus be:

[0048] Apβexp(−ikx)+Aβexp[−ik(x+2a)]=Aβexp(−ikx)[1+exp(−ik2a)]  (5)

[0049] When k2a=π, exp(−iπ)=−1 and equation (5) will equal zero.

[0050] Physically this means that for k2a=(2π/λ)2a=π and correspondingly a=(λ/4), the reflected probability wave equals zero. Further this means that the particle will not reflect back from the border. Leakage of the probability wave through the barrier will occur with increased probability and will promote tunneling and transfer of elementary particles across a potential barrier. This promotion will open many new possibilities for different practical applications.

[0051] Indents on the surface should have dimensions comparable to de Broglie wavelength of electron. In particular indent height should be

[0052] a=nλ+λ/4   (6)

[0053] Here n=0,1,2, etc

[0054] And the indent width should be of order of 2λ.

[0055] If these requirements are satisfied then elementary particles will accumulate on the surface.

[0056] For semiconductor material, the velocities of electrons in the electron cloud is given by the Maxwell-Boltsman distribution:

[0057] F(v)dv=n(m/2πK_BT) exp(−mv²/2 K_BT)dv  (7)

[0058] where F(v) is the probability of an electron having a velocity between v and v+dv.

[0059] The average velocity of the electrons is

[0060] V_av=(3 K_BT/m)^1/2  (8)

[0061] and the de Broglie wavelength corresponding to this velocity, calculated using formulas (2), (3) and the classical approximation p=mv is:

[0062] λ=h/(3m K_BT)^1/2=62 Å for T=300K.   (9)

[0063] This gives a value for a of 6214=155 Å. Indents of this depth may be constructed on a surface by a number of means known to the art of micro-machining. Alternatively, the indented shape may be introduced by depositing a series of islands on the surface.

[0064] For metals, free electrons are strongly coupled to each other and form a degenerate electron cloud. Pauli's exclusion principle teaches that two or more electrons may not occupy the same quantum mechanical state: their distribution is thus described by Fermi-Dirac rather than Maxwell-Boltsman. In metals, free electrons occupy all the energy levels from zero to the Fermi level (ε_f).

[0065] Referring now to FIG. 3, electron 1 has energy below the fermi level, and the probability of occupation of these energy states is almost constant in the range of 0-ε_fand has a value of unity. Only in the interval of a few K_BT around ε_fdoes this probability drop from 1 to 0. In other words, there are no free states below ε_f. This quantum phenomenon leads to the formal division of free electrons into two groups: Group 1, which comprises electrons having energies below the Fermi level, and Group 2 comprising electrons with energies in the interval of few K_BT around ε_f.

[0066] For Group 1 electrons, all states having energies a little lower or higher are already occupied, which means that it is quantum mechanically forbidden for them to take part in current transport. For the same reason electrons from Group 1 cannot interact with the lattice directly because it requires energy transfer between electron and lattice, which is quantum mechanically forbidden.

[0067] Electrons from Group 2 have some empty energy states around them, and they can both transport current and exchange energy with the lattice. Thus only electrons around the Fermi level are taken into account in most cases when properties of metals are analyzed.

[0068] For electrons of group 1, two observations may be made. The first is that it is only these electrons which have wavelengths comparable to dimensions achievable by current fabrication techniques: 50-100 A corresponds to about 0.01ε_f, (E˜k²˜(1/λ)²). Group 2 electrons of single valence metals on the other hand, where ε_f=2-3 eV, have a de Broglie wavelength around 5-10 A which is difficult to fabricate using current techniques.

[0069] The second is that for quantum mechanical interference between de Broglie waves to take place, the main free path of the electron should be large. Electrons from group 1 satisfy this requirement because they effectively have an infinite main free path because of their very weak interaction with the lattice.

[0070] Referring again to FIG. 3 electron 1, which is a group 1 electron, has k₀=π/2a and energy ε₀, and is moving to the indented surface 17. As discussed above, this particular electron will not reflect back from the surface due to interference of de Broglie waves, and will leave the metal. Consider further that the metal is connected to a source of electrons, which provides electron 2, having energy close to ε_f(group 2). As required by the thermodynamic equilibrium electron 2 will lose energy to occupy state ε₀, losing energy ε_f−ε₀, for example by emission of a photon with energy ε_p(ε_f−ε₀). If this is absorbed by electron 3, electron 3 will be excited to a state having energy ε_f+ε_p=2ε_f−ε₀.

[0071] Thus as a consequence of the loss of electron 1, electron 3 from the Fermi level is excited to a state having energy 2ε_f−ε₀, and could be emitted from the surface by thermionic emission. The effective work function of electron 3 is reduced from the value of φ to φ−ε_f+ε₀=φ−(ε_f−ε₀). In another words, the work function of electron 3 is reduced by ε_f−ε₀.

[0072] Thus indents on the surface of the metal not only allow electron 1 to be emitted into the vacuum with high probability by interference of the de Broglie wave, but also results in the enhanced probability of another electron (electron 3) by ordinary thermionic emission.

[0073] This approach will decrease the effective potential barrier between metal and vacuum (the work function).

[0074] This approach has many applications, including cathodes for vacuum tubes, thermionic converters, vacuum diode heat pumps, photoelectric converters, cold cathode sources, and many others in which electron emission from the surface is used.

[0075] In addition, an electron moving from vacuum into an anode electrode having an indented surface will also experience de Broglie interference, which will promote the movement of said electron into said electrode, thereby increasing the performance of the anode.

[0076] In a further embodiment, the separation of electrodes in a vacuum diode-based device may be controlled through the use of positioning elements, as shown in FIG. 4. The following description describes a number of preferred embodiments of the invention and should not be taken as limiting the invention.

[0077] Referring now to FIG. 4, which shows in a diagrammatic form a heat source 61, a heat sink 59, electrical connectors 65, and an electrical load 67 for a thermionic generator embodiment of the device shown. An electric field is applied to the piezo-electric actuators 63 via electrical connectors which causes it to expand or contract longitudinally, thereby altering the distance 55 between electrodes 51 and 53. Electrodes 51 and 53 are connected to a capacitance controller 69 which controls the magnitude of the field applied by a power supply. Heat from heat source 61 is conducted through a housing 57 and piezo-electric actuators 63 to an emitter 51. The surface of emitter 51 has an indented surface as described above. Electrons emitted from emitter 51 move across an evacuated space 55 to a collector 53, where they release their kinetic energy as thermal energy which is conducted away from collector 53 through housing 57 to heat sink 59. The electrons return to emitter 51 by means of external circuit 65 thereby powering electrical load 67. The capacitance between emitter 51 and collector 53 is measured and capacitance controller 69 adjusts the field applied to piezo-electric actuators 63 to hold the capacitance, and consequently the distance between the electrodes, at a predetermined fixed value. This means that as the thermionic converter becomes hot and its components expand, the distance between the electrodes can be maintained at a fixed distance.

[0078] For currently available materials, a device having electrodes of the order of 1×1 cm, surface irregularities are likely to be such that electrode spacing can be no closer than 0.1 to 1.0 μm. An approach to overcome this limitation which leads to enhanced performance in vacuum diode based devices is illustrated in FIG. 5, which describes in schematic form a method for producing pairs of electrodes having indented surfaces which mirror each other. The method involves a first step 100 in which an indented substrate 102 is provided. This forms one of the pair of electrodes. In a step 110 a thin layer of a second material 112, is deposited onto the surface of the substrate 102. This layer is sufficiently thin so that the shape of the substrate 102 is repeated with high accuracy. In a preferred embodiment, a thin layer of a third material 122 is deposited on layer 112 in a step 120, and in a step 130 this is grown electrochemically to form a layer 132. This forms the second electrode. In one preferred embodiment, second material 112 has a melting temperature approximately 0.8 that of first material 102 and third material 122. In a step 140 the composite formed in steps 100 to 130 is heated up to a temperature greater than the melting temperature of layer 112 but which is lower than the melting temperature of layers 102 and 132. As layer 112 melts, layers 102 and 132 are drawn apart, and layer 112 is allowed to evaporate completely. In another preferred embodiment, layer 112 may be removed by introducing a solvent which dissolves it, or by introducing a reactive solution which causes the material to dissolve. This leaves two electrodes 102 and 132 whose surfaces mirror each other. This means that they may be positioned in very close proximity, as is required, for example, for the thermo-tunnel converter. In a variation of the method shown in FIG. 5, piezo-electric elements may be attached to one or both of the electrodes 102 and 132 and used to draw the two apart as the intervening layer 112 melts. This ensures that the two electrodes are then in the correct orientation to be moved back into close juxtaposition to each other by the piezo-electric elements.

[0079] The method for enhancing passage of elementary particles through a potential barrier has many applications in addition to those described above.

[0080] The method may be applied to thermionic converters, vacuum diode heat pumps and photoelectric converters, where a reduction in work function gives real benefits in terms of efficiency or operating characteristics.

[0081] The elementary particle emitting surface has many further applications. The surface is useful on emitter electrodes and other cathodes because it promotes the emission of electrons. It is also useful on collector electrodes and other anodes because it promotes the passage of electrons into the electrode. The surface also has utility in the field of cold cathodes generally, and electrodes incorporating such a surface can be used. Cold cathode structures are useful electron sources for applications such as flat panel displays, vacuum microelectronic devices, amplifiers, heat pumps, and electron microscopes.