Threshold voltage convergence

[0001] 1. Field of Invention

[0002] The invention is related to flash electronically erasable programmable read only memory (flash EEPROM), and more particularly to convergence of threshold voltages of flash EEPROM transistors.

[0003] 2. Related Art

[0004] Flash EEPROM memory cells (typically field-effect transistors) are used as nonvolatile memory that can be programmed in the field. Some flash EEPROM integrated circuits are designed to receive and output data using single terminals and are known as serial flash EEPROM. Other flash EEPROM integrated circuits are designed to receive and output data in parallel using multiple terminals and are known as parallel flash EEPROM.

[0005] In some instances all memory cells in an array of flash EEPROM memory cells are simultaneously erased in a single, bulk erase procedure. In other instances, only a sector of the memory cells in the array is erased. In still other instances, the data storage addresses for the memory cells in the array are partitioned into logical memory pages, and one or more unique pages are erased. Each page typically includes logical words (e.g., 8-bit bytes).

[0006] Flash EEPROM erase operations generally include two basic operations. The first (erase) procedure lowers the threshold voltage of all memory cells so that the cells each have an unprogrammed state. This erase procedure typically results in a distribution of threshold voltages among the cells being erased with some cells having their threshold voltages lowered below a specified minimum threshold voltage. These cells are considered over-erased. Thus a subsequent second (threshold voltage convergence) procedure raises unacceptably low threshold voltages. The threshold voltage convergence procedure further reduces the threshold voltage distribution for all memory cells being erased.

[0007] Software application designers, especially when working with serial flash EEPROM integrated circuits, require fast page erase operations to allow for subsequent reprogramming of the erased page. A disadvantage of present erase and convergence procedures, however, is that these procedures require too much time. In one instance, for example, 0.1 second (sec) erase and convergence pulses are used. What is required, therefore, is a method of speeding up flash EEPROM memory cell erase operations, especially the convergence procedure, and a flash EEPROM integrated circuit capable of carrying out this fast convergence procedure.

[0008] Flash EEPROMs typically include a small number of memory cells for which charge is more rapidly stored, removed, or lost than for the remaining cells. These fast cells may lose charge after being programmed such that their threshold voltage falls below the lower threshold voltage limit that signifies a cell is programmed. Other programmed memory cells may have a marginally low threshold voltage for various reasons. It is therefore also desirable to have a way to converge the threshold voltage distribution of programmed cells by raising marginally programmed cells without significantly affecting programmed cells that are well within the programmed threshold voltage range.

[0009] A convergence signal includes a series of voltage pulses used to perform a convergence procedure in one or more flash EEPROM memory cells (transistors). In one instance subsequent voltage pulses in the convergence signal each have a higher voltage than the preceding pulse. The convergence signal having increasingly positive voltage pulses is applied to the control gate of a flash EEPROM transistor while the source, drain, and bulk regions of the transistor receive a negative voltage. The voltage pulses received by the control gate cause electrons to be drawn from the transistor's bulk channel region into the floating gate using Fowler-Nordheim tunneling. The pulse durations and voltages are selected to quickly raise the threshold voltage of transistors initially having low threshold voltages and to more slowly raise the threshold voltage of transistors initially having a higher threshold voltage. In another instance, subsequent voltage pulses in the convergence signal each have a longer duration than the preceding pulse.

[0010] An integrated circuit includes an array of memory cells and a control unit which controls the application of the convergence signal to one or more memory cells. The integrated circuit may be either serial flash EEPROM or parallel flash EEPROM in which bulk, sector, or page mode erasing is used.

[0011] FIG. 1 is a cross-sectional view of a memory cell.

[0012] FIG. 2. is a diagrammatic view of a memory array and peripheral circuits in an integrated circuit.

[0013] FIGS. 3A-3C are diagrammatic views of embodiments of a process.

[0014] FIGS. 4A-4D are signal timing diagrams.

[0015] FIGS. 5A-5E are signal timing diagrams.

[0016] FIG. 6 is a graph plotting memory cell threshold voltage versus time.

[0017] FIG. 7 is a second graph plotting memory cell threshold voltage versus time.

[0018] FIG. 8 is a third graph plotting memory cell threshold voltage versus time.

[0019] FIGS. 9A-9E are signal timing diagrams.

[0020] FIGS. 10A-10E are signal timing diagrams.

[0021] FIGS. 11A-11E are signal timing diagrams.

[0022] FIGS. 12A and 12B are graphs plotting number of memory cells versus threshold voltage.

[0023] The accompanying drawings are illustrative and not to scale. For example, various interval durations may exist between pulses shown and described herein. Skilled individuals will understand that pulse shapes shown in the drawings are illustrative of various pulse shapes that may be used. Skilled individuals will also understand that some well-known features have been omitted from the drawings so as to more clearly show the embodiments. The same reference number used in several drawings refers to the same or to a substantially similar element.

[0024] FIG. 1 is a cross-sectional view of an illustrative flash electronically erasable programmable read only memory (flash EEPROM) field effect transistor 100 (a memory cell) formed using conventional methods. Memory cell 100 includes P-type monocrystalline silicon substrate 102, deep N-well 104 formed in substrate 102, and P-well 106 (bulk region) formed in N-well 104. N-type source region 108 and N-type drain region 110 are formed in bulk region 106. Skilled individuals understand that in many cases the source and drain regions are interchangeable and each may therefore be referred to as a source/drain region. Tunnel oxide layer 112 (e.g., silicon dioxide about 90-100 Angstrom () thick) is formed over bulk region 106 between source region 108 and drain region 110. Floating gate 114 (e.g., approximately 0.15 micrometer (m) thick lightly N-doped polycrystalline silicon having a resistivity of about 6000-8000 Ohm per square) is formed over oxide layer 112. Gate insulation layer 116 (e.g., a silicon oxide, silicon nitride, silicon oxide (ONO) sandwich layer about 145-165 thick) is formed over floating gate 114. Control gate 118 (e.g., heavily N-doped polycrystalline silicon) is formed over insulation layer 116, and conductive layer 120 (e.g., tungsten silicide (WSi₂)) is formed directly on control gate 118. Bulk channel 122 is defined in bulk region 106 between source region 108 and drain region 110 underlying gates 114,118. In one embodiment cell 100 occupies an area of about 3F by 1.9F, where F is the minimum feature size (e.g., 0.18 m).

[0025] Memory cell 100 is typically included in an array of rows and columns of similar memory cells. In such arrays, source region 108 is electrically coupled via source terminal 124 to source line 126 and receives a source signal of voltage V_s. Control gate 118 is electrically coupled via control gate terminal 128 to word line 130 and receives a word line signal of voltage V_cg. Drain region 110 is electrically coupled via drain terminal 132 to bit line 134 and receives a bit line signal of voltage V_d. Bulk region 106 receives a bulk signal of voltage V_b via bulk terminal 136. Deep N-well 104 is coupled to terminal 137 and receives an N-well signal of voltage V_nw. Substrate 102 is grounded. In other embodiments, however, substrate 102 may receive other voltages.

[0026] FIG. 2 is a diagrammatic view illustrating an array 200 of integrated circuit memory cells that includes memory cells 100, formed on a single integrated circuit chip. FIG. 2 also illustrates peripheral circuits on the chip that drive the memory cells. Each set of memory cells coupled to a unique word line 130 is a row. Each set of memory cells coupled to a unique bit line 134 is a column. Skilled individuals will understand that word line driver 202 receives row address information 204 and in response sets the voltages on word lines 130. Likewise, column decoder 206 receives column address information 208 and in response sets the voltages on bit lines 134. Source driver 210 sets the voltages on source lines 126. N-well driver 212 sets the voltage in N-wells 104 (FIG. 1). Bulk driver 214 sets the voltage in bulk regions 106 (FIG. 1). Program/erase control unit 216 is coupled to and controls the operation of word line driver 202, column decoder 206, source driver 210, N-well driver 212, and bulk driver 214 during program and erase operations.

[0027] The circuit shown in FIG. 2 is illustrative of many memory circuit topologies. One such topology is serial read-only memory (ROM), in which data is serially received and written to the memory cells. Another such topology is parallel ROM, in which data is received in parallel and subsequently written to the memory cells. Other circuits related to writing and reading (e.g., sense amplifiers) are well known and are omitted for clarity. The circuit shown in FIG. 2 is illustrative of both serial flash EEPROM, in which data is serially received and output using single terminals, and parallel flash EEPROM, in which data is received and output in parallel using multiple terminals. FIG. 2 is also illustrative of many memory array 200 architectures that are used in accordance with the invention. For example, in one embodiment array 200 is a virtual ground array. Other embodiments include NAND and NOR memory array architectures.

[0028] In some embodiments, a particular physical set of memory cells is considered a logical set. For example, in the embodiment illustrated in FIG. 2, the set of transistors in row 218 is defined as a logical page 220 of memory. A page is further divided into words or bytes (e.g., eight bits). In an illustrative 64 Mbit (2²⁶) memory array there are about 16K (2¹⁴) rows and about 4K (2¹²) columns, thus allowing for 16,384 pages and 512 8-byte words per page. By setting voltages as described below, memory cells in page 220 (row 218) are erased while cells in other logical pages (physical rows) retain their programmed information. In some cases the set of transistors defining a page is less than all transistors in a single row. In some cases, all memory cells in the array are erased in a bulk erase operation.

[0029] Referring again to FIG. 1, the transistor's threshold voltage (V_T) represents the programming state of cell 100. In a programmed state the threshold voltage prevents current flow from source region 108 to drain region 110 when a read voltage applied to control gate 118. This programmed state typically represents a logical 0, low, or off. In an unprogrammed state, the threshold voltage allows current flow between source region 108 and drain region 110 when a read voltage is applied to control gate 118. The unprogrammed state typically represents a logical 1, or high, or on. Skilled individuals understand that the amount of charge (electrons, holes) stored in floating gate 114 controls the threshold voltage of memory cell 100. Such individuals understand that charge is added to or removed from the floating gate by introducing various voltages to the source, drain, and bulk regions, and to the control gate. Such individuals further understand that charge is moved by hot carrier injection or Fowler-Nordheim tunneling, depending on the points at which voltages are applied and upon the voltage levels. Since charge remains stored in the floating gate for a considerable time (e.g., years) memory cell 100 is considered non-volatile.

[0030] Due to slight physical variations in each transistor (e.g., variations in the tunnel oxide layers), there is a distribution of rates at which charge moves into or out of the floating gate. As compared with most memory cell transistors in a particular memory array, transistors in which charge moves relatively quickly into and out of the floating gate are considered fast, and transistors in which charge moves relatively slowly into and out of the floating gate are considered slow. During erase operations, fast transistors are may become over-erased. In an over-erase condition, a transistor's V_T is reduced such that current may leak from the source region to the drain region, or such that a subsequent programming voltage is insufficient to raise the V_T to a programmed state. Conversely, slow transistors may not have enough charge removed to reach an erased state.

[0031] FIGS. 3A, 3B, and 3C are diagrammatic views of erase process embodiments in accordance with the invention. The embodiments are used for erasing either a memory page or for bulk erase. FIGS. 3A and 3B show alternate beginnings which then proceed to FIG. 3C.

[0032] Referring to FIG. 3A, in 302 the programming status of one or more cells to be erased is verified. In one instance a read operation is performed by setting V_cg to 4.6 V and sensing current through one or more memory cells. Each read takes about 0.2 sec, and for 512 words the page read takes about 0.1 msec. If current (e.g., more than 1 A) is sensed, indicating an unprogrammed cell, the process moves to 304a. If no current is sensed, indicating a programmed cell, the process moves to 306.

[0033] In 304a a pre-erase programming (pre-program) is performed to program one or more unprogrammed memory cells that are to be erased. In one embodiment, the preprogram operation is performed one word at a time, although other cell combinations may be used during pre-programming. As illustrated by FIGS. 4A-4D, in one embodiment the pre-programming is performed by causing channel hot electrons to be injected into the floating gate of the unprogrammed cell. V_cg receives a 8.5 V pulse and V_d receives a 5 V pulse while V_s and V_b remain at ground. The V_cg and V_d pulses each last about 2 microseconds (sec), and for 512 words the pre-program operation takes about 1.1 msec. Thus the V_T for all cells to be erased is raised to approximately the same value. Programming to ensure that each cell to be erased has approximately the same V_T helps to reduce over-erasing during subsequent erase operations.

[0034] In 306 it is determined if any cells to be erased remain that require programming status verification. If cells remain, the process moves to 302. If no cells remain, the process moves to 308 (FIG. 3C).

[0035] Alternatively, the programming status verification described with reference to FIG. 3A is omitted and a pre-program operation 304b is performed on all cells to be erased, as illustrated by FIG. 3B. One embodiment of 304b uses the voltages shown in FIGS. 4A-4D as described above. A 2 sec pulse is sufficient to pre-program all cells. Since V_T change tends to slow as V_T rises, an additional programming pulse applied to programmed cells will not have significant impact on the programmed cells' V_T. Even so, the V_T distribution of all cells after preprogramming is likely to be slightly higher using the process in FIG. 3B than if using the process in FIG. 3A. The process in FIG. 3B is faster than the process in FIG. 3A. After 304b, the process moves to 308 (FIG. 3C).

[0036] Referring to FIG. 3C, in 308 an erase is performed to reduce the V_T for each cell below a specified maximum. As illustrated by FIGS. 5A-5D, in one embodiment the erase is done by applying a 6 V pulse to V_b, V_s, and V_d as V_cg receives a series (e.g., four) of 12.5 V pulses 500, the pulses each lasting about 1.5 milliseconds (msec). The number of pulses, and the voltage and duration of each pulse, is selected so that most cells other than abnormally fast or slow cells will be erased by the initial set of pulses 500. In the interval 502 following the last pulse in the series, an erase verify (described below) is performed. If additional erasing is required, one or more additional erase pulse and erase verify combinations are used until erasing is complete. Various other numbers of pulses and pulse durations may be used, and the potential difference between the control gate and source/drain/bulk regions may be varied. For example, FIG. 5E illustrates erasing using a single long pulse 506 (e.g., about 6 msec) instead of a series of short pulses. V_s, V_d, and V_b (and V_nw) settings are timed to match the V_cg erase pulse. The erase verify is performed in interval 504 following the long pulse. If additional erasing is required, one or more short pulse 508 (e.g., about 1.5 msec) and erase verify combinations are used until all cells are erased. Using a series of shorter erase pulses 500, as illustrated by FIG. 5A, produces a tighter V_T distribution than when a single, longer pulse 506 is used (V_T change during erase is similar to V_T change during convergence, as described below with reference to FIGS. 6, 7, and 8). Other erase methods may be used.

[0037] Referring to FIG. 3C, in 310 an erase verify is performed. In one instance the erase verify is performed to ensure that the threshold voltage for all cells to be erased (e.g., a page) has been lowered below 3.1 V (i.e., V_cg is set to 3.1 V). This erase verify reads a page (e.g., 512 8-bit words). Each word read takes about 0.2 sec, and the total erase verify time is about 0.1 msec. If one or more cells fail the erase verify (e.g., slow cells), the process returns to 308 and another erase is performed. If all cells pass the erase verify, the process moves to 312.

[0038] Since the erase performed in 308 may over-erase some cells (e.g., fast cells), in 312 an over-erase verify is performed. In one instance this over-erase verify is a read operation that determines if any cell to be erased has a V_T less than about 0.5 V. Over-erased cells may be considered to be in the depletion mode. Thus with V_cg set to zero volts, an over-erased cell still conducts current during a read operation. This leaky cell causes various failures such as sub-bitline failures. (A sub-bitline is a portion of a bitline to which several cells are connected. Extra current from the leaky over-erased cell causes the programming status of the whole sub-bitline to be in error.) Hence a 0.5 V level is chosen for the over-erase verify to eliminate cells that leak current at or below 0.5 V. Similar to the erase verify, the over-erase verify for 512 8-bit words takes a total of about 0.1 msec. If all cells pass the over-erase verify, then the process ends since the V_T for all cells is in the desired range set by the erase and over-erase verifications. If one or more cells fail the over-erase verify, the process moves to 314.

[0039] In 314 a Fowler-Nordheim V_T convergence is performed in accordance with the invention so as to tighten the V_T distribution of erased memory cells to within a specified range. This convergence operation raises the V_T of the fast cells more quickly than the V_T of normal and slow cells. Nevertheless, this convergence operation may raise the V_T of some cells above the maximum allowable erase V_T distribution limit, and so the process moves to 310 and another erase verify is performed. The process then continues among 308, 310, 312, and 314 as necessary until all cells are within the specified minimum and maximum V_T convergence limits.

[0040] In one instance the desired V_T for all erased cells is about 1-2 volts after convergence. In another instance, the desired V_T for all erased cells is about 1.5-2 volts after convergence. FIG. 6 is a graph showing how V_T (vertical axis) varies with time (horizontal axis) during a V_T convergence operation. In FIG. 6, V_cg is about 12 V and V_s, V_d, and V_b are about 4 V (i.e., about 16 volt potential across the floating gate). As shown in FIG. 6, if these voltages are applied for about 1 msec, the V_T of a cell initially having a 2 V V_T (curve defined by Xs) is raised to about 0 V, the V_T of a cell initially having 0 V V_T (curve defined by solid triangles) is raised to about 0.5 V, and the V_T of a cell having a 2 V V_T (curve defined by solid diamonds) remains substantially the same.

[0041] FIG. 7 is a graph similar to FIG. 6, but for V_cg about 12 V and V_s, V_d, and V_b about 5 V. The voltage conditions shown in FIG. 7 raise the cell V_Ts relatively more quickly than for those shown in FIG. 6. It can be seen in FIG. 7 that the V_T of a cell initially having a V_T of about 2 V (curve defined by solid diamonds) begins to increase if the voltages are applied for more than about 1 msec.

[0042] FIG. 8 is a graph similar to FIG. 6 but for V_cg about 12 V and V_s, V_d, and V_b about 3 V. The voltage conditions shown in FIG. 8 raise the cell V_Ts relatively more slowly than for those shown in FIG. 6. It can be seen in FIG. 8 that the V_T of a cell initially having a V_T of about 2 V (curve defined by solid diamonds) does not begin to increase until the voltages are applied for about 100 msec.

[0043] FIGS. 6, 7, and 8 illustrate that for some convergence pulse durations (e.g., 1 msec), various electric potentials across the floating gate will have little effect on the V_T of cells having a relatively high V_T (e.g., 2 V) but will control the amount of V_T change for cells having a relatively low V_T (e.g., 2 V). Furthermore, fast cells will have curve slopes that are steeper than those shown in FIGS. 6, 7, and 8 (i.e., V_T rises more quickly). In FIG. 6, for example, curve 602 represents V_T change for an illustrative fast cell having an initial V_T of about 2 V. Slow cells will have slopes that are less steep than those shown in FIGS. 6, 7, and 8 (i.e., V_T rises more slowly). In accordance with the invention, convergence pulse durations and voltages are selected so that memory cells having V_T within the desired V_T convergence distribution are relatively unaffected, but memory cells having V_T below the desired V_T distribution are quickly raised to within the desired V_T range. Lower voltage pulses are applied at first to move the fast bit V_T close to the desired V_T range. Then, increasingly larger voltage pulses are applied to move a larger number of cells into the desired V_T range.

[0044] FIGS. 9A-9D illustrate an embodiment of convergence 314 (FIG. 3C). V_s, V_d, and V_b are set to a negative voltage (e.g., 4 V) and V_cg receives a series of positive voltage pulses in a convergence signal. The voltage of each subsequent V_cg pulse is higher than the voltage of the preceding pulse. As shown in FIG. 9A, for example, V_cg first receives a 9 V pulse, followed by 10V, 11 V, and 12 V pulses. In one embodiment each V_cg pulse duration is approximately 300 sec. In some embodiments erase verify 310 (FIG. 3C) is performed during the interval following each V_cg pulse. In other embodiments V_cg receives two or more pulses before erase verify 310 is performed. FIG. 9E illustrates another convergence 312 embodiment. As shown in FIG. 9E, a series 902 of constant voltage V_cg pulses is used, followed by a series 904 of increasing voltage V_cg pulses. Each series 902,904 pulse duration is about 200-300 sec, although other pulse durations may be used. V_s, V_d, and V_b are as shown in FIGS. 9B-9D. In one embodiment an erase verify 308 is performed after the first series 902, and after every pulse in the second series 904. In other embodiments, a series of 8 pulses as illustrated by series 902 and 904 is performed prior to the erase verify.

[0045] The duration between convergence pulses in all embodiments may be very short (e.g., less than 1 sec) such that the duration is sufficient to cause charges to move as by short pulses rather than a longer pulse.

[0046] FIGS. 10A-10D illustrate another embodiment of convergence 314. V_s, V_d, and V_b are set to a negative voltage (e.g., 4 V) and V_cg receives a series of pulses in a convergence signal. The duration of each subsequent V_cg pulse is longer than the duration of the preceding pulse. As shown in FIG. 10A, for example, first V_cg pulse 1002 lasts about 300 sec and second V_cg pulse 1004 lasts about 600 sec. Subsequent pulse durations are progressively longer. These durations are illustrative and other pulse durations may be used. In one embodiment an initial series of same duration pulses is used (e.g., 902 in FIG. 9E) prior to using pulses of increasing duration. In one embodiment, erase verify 310 and over-erase verify 312 are performed after each V_cg pulse. In other embodiments, more than one V_cg pulse is received before erase verify 308 and over-erase verify 312 are performed. FIG. 10E illustrates another convergence 314 embodiment. Instead of increasing the duration of constant voltage V_cg pulses in the convergence signal, as illustrated in FIG. 10A, sets of short duration (e.g., 200-300 sec) positive voltage pulses are used, and each subsequent set includes more pulses than the preceding set. FIG. 10E shows, for example, that V_cg pulse set 1006 includes one pulse, pulse set 1008 includes two pulses, and so on. V_s, V_d, and V_b are as shown in FIGS. 10B-10D. In one embodiment, erase verify 310 and over-erase verify 312 are performed after each pulse set. In other embodiments, two or more pulse sets are performed prior to verify operations.

[0047] FIGS. 11A-11D illustrate yet another embodiment of convergence 314. V_s, V_d, and V_b are set to a negative voltage (e.g., 4 V) and V_cg receives a series of pulses in a convergence signal. Both the voltage and duration of each subsequent V_cg pulse is increased from the voltage and duration of the preceding pulse. As shown in FIG. 1A, for example, first V_cg pulse 1102 is about 9 V and lasts about 300 sec, second V_cg pulse 1104 is about 10 V and lasts about 600 sec, and so on. These pulse voltages and durations are illustrative and other voltages and durations may be used. In one embodiment an initial series of same voltage and same duration pulses is used (e.g., 902 in FIG. 9E) prior to using V_cg pulses of increasing voltage and duration. In one embodiment erase verify 310 and over-erase verify 312 are performed after each V_cg pulse. In other embodiments, more than one V_cg pulse is received before erase verify 310 and over-erase verify 312 are performed. FIG. 11E illustrates another convergence 314 embodiment. Instead of increasing the duration of the increasing voltage V_cg pulses in the convergence signal, as illustrated in FIG. 11A, sets of short duration (e.g., 200-300 sec) pulses are used in which each subsequent set includes more pulses at a higher voltage than the preceding set. FIG. 11E shows, for example, that V_cg pulse set 1106 includes one 9 V pulse, pulse set 1108 includes two 10 V pulses, and so on. V_s, V_d, and V_b are as shown in FIGS. 11B-11D. In one embodiment, erase verify 310 and over-erase verify 312 are performed after each pulse set. In other embodiments, two or more pulse sets are performed prior to the verify operations.

[0048] The 4 V settings for V_s, V_d, and V_b as described in relation to FIGS. 9A-9E, 10A-10E, and 11A-11E are illustrative, and other voltages that may be used. In other embodiments, for example, voltages in the range 4 V to 6 V are used. In one such embodiment voltages (e.g., V_b) are selectable within this voltage range.

[0049] In accordance with the invention, in one embodiment a complete page erase and convergence is performed in less than 10 msec. In a situation using a 512 word page length, the program verify takes about 0.1 msec (512*0.2 sec read), the pre-program takes about 1 msec (512*2 sec pulse), the erase verify takes about 0.1 msec (512*0.2 sec read), the erase takes about 6 msec (4 pulses*1.5 msec), the over-erase verify takes about 0.1 msec (512*0.2 sec read), and the convergence takes about 2.4 msec (8 pulses*300 sec), thus totaling about 9.7 msec.

[0050] In another aspect of the invention, a series of threshold convergence pulses is used to converge the V_T distribution of programmed cells. Using the convergence pulse and voltage embodiments described above, marginally programmed cells having a V_T at the tail (lower extreme) of the programmed V_T distribution are raised. FIG. 12A is a graph showing an illustrative programmed cell V_T distribution. Unprogrammed cells have a desired V_T in lower V_T range 1202 (e.g., 0.5-2.0 V). Programmed cells have a desired V_T in upper V_T range 1204. Curve 1206 represents the V_T distribution of programmed cells. A small number of programmed cells have a V_T that is just at the lower margin of upper V_T range 1204, as shown in highlight 1208. Programmed cells having marginal V_T 1208 may be, for example, fast bits that tend to lose programming charge or cells otherwise having a V_T disturbed from the desired programmed V_T.

[0051] In accordance with the invention, Fowler-Nordheim convergence pulses such as those described above with reference to 314 (FIG. 3C) are applied to programmed cells to converge the V_T of cells having marginal V_T 1208 towards the desired upper V_T range 1204. Since the curves for fast cells are relatively steep compared to the curves for typical cells as illustrated in FIGS. 6, 7, and 8, the V_T of fast cells is raised to within range 1204 without significantly affecting the V_T of other programmed cells. The convergence pulses may be applied in various ways. In one embodiment, the convergence pulses are applied to all programmed cells. In another embodiment, the convergence pulses are applied to select numbers of programmed cells. In yet another embodiment, the programmed cells having marginal V_T are identified and the convergence pulses are applied to the identified cells. The resulting programmed cell V_T distribution is shown in FIG. 12B. FIG. 12B shows at 1212 that the programmed cells having V_T at the lower margin of range 1204 now have V_T within range 1204. Erase control unit 212 (FIG. 2) is illustrative of the control unit used to effect the programmed cell V_T convergence.

[0052] Skilled individuals will understand that although embodiment have been described using V_cg pulses and constant V_s, V_d, V_b, and V_nw that other methods of shaping the waveform of the pulsed electric potential across the floating gate may be used to perform threshold voltage convergence. For example, V_s, V_d, V_b and/or V_nw may be made increasingly negative while the V_cg pulses are kept at the same voltage. As another example, V_cg is constant and V_s, V_d, V_b and/or V_nw is pulsed as described above for V_cg. Skilled individuals will further understand that various modifications and adaptations may be made to the embodiments disclosed herein. For example, P-type memory cells may be used, in which case voltage polarities are reversed, and various memory array architectures may be used. Thus the invention is limited only by the following claims.