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through the gut membrane of an organism (e.g., the intestinal epithelium of a mammal). Exposure to both dissolved and solid-bound contaminants can lead to chemical interaction with the membrane of an organism and subsequent uptake or absorption (these terms are used synonymously). "E" in Figure 1-1 refers to paths taken by the chemical following uptake across a membrane. For example, after passage across a biological membrane the chemical can exert a toxic effect within a particular tissue (among many possibilities).
It should be noted that A, B, and C in Figure 1-1 are sometimes considered to be fate and transport processes (which they are) rather than bioavailability processes. On the other hand, process D is more traditionally associated with bioavailability in contemporary risk assessment. The committee's definition of "bioavailability processes" incorporates all the steps that take a chemical from being bound or isolated in soil or sediment to being taken up into an organism (A through D). Figure 1-1 makes it clear that soils and sediments can affect exposure in various ways, both external and internal to the organism. For example, solid phases influence the extent of contaminant transfer from one medium to another, thereby determining soluble chemical concentrations. There is also differential uptake of contaminants into animals and plants depending on whether they are solubilized or solid-bound. Although of great importance in determining the overall effect of a contaminant on an organism, E processes—the toxic action or metabolic effect of a chemical—are not defined as bioavailability processes per se because soil and sediment are no longer a factor. However, because E processes are often measured endpoints, they are described at length in Chapters 3 and 4.

subset: commoncrawl


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Structures, methods of manufacturing and methods of use of electrically programmable read only memories (EPROM) and flash electrically erasable and programmable read only memories (EEPROM) include split channel and other cell configurations. An arrangement of elements and cooperative processes of manufacture provide self-alignment of the elements. An intelligent programming technique allows each memory cell to store more than the usual one bit of information. An intelligent erase algorithm prolongs the useful life of the memory cells. Use of these various features provides a memory having a very high storage density and a long life, making it particularly useful as a solid state memory in place of magnetic disk storage devices in computer systems.
1. For an array of electrically alterable memory cells divided into blocks of cells that are re-settable together to a starting state and having means for addressing individual cells within said blocks to program and read their states, said memory cells individually including a field effect transistor having a threshold voltage level that is variable in accordance with an amount of net charge stored therein, a method of operating the array, comprising the steps of:
establishing a plurality of effective threshold voltage levels in excess of two that correspond to a plurality of detectable states of the individual cells in excess of two,
programming the effective threshold voltage level of at least one addressed cell within one of said blocks from a starting level to one of the plurality of effective threshold voltage levels by altering the amount of charge stored in said at least one addressed cell until the effective threshold voltage of said at least one addressed cell is substantially equal to one of said plurality of effective threshold voltage levels, wherein the state of said at least one addressed cell is set to one of said plurality of states by a method comprising:
applying a given voltage to said addressed cell for a predetermined time sufficient to move the effective threshold voltage level of the addressed cell from the starting level toward said one of the plurality of threshold voltage levels,
thereafter reading an electrical parameter of the addressed cell to determine whether the effective threshold voltage of the addressed cell has reached said of the plurality of threshold voltage levels, and
repeating the voltage applying and reading steps until it is detected by reading step that the effective threshold voltage of the addressed cell has been set to said one of the plurality of threshold voltage levels,
reading the states of the memory cells of individual blocks with the assistance of an error correction scheme that can tolerate a number X of bad cells, and
applying erase conditions to the memory cells of individual blocks until a number of cells N remaining unerased is equal to or less than X.
2. The method according to
3. The method according to
This is a continuation of application Ser. No. 08/154,162, filed Nov. 17, 1993 now U.S. Pat. No. 6,570,790, which is a division of application Ser. No. 07/777,673, filed Oct. 15, 1991 and now issued as U.S. Pat. No. 5,268,319, which in turn is a division of application Ser. No. 07/381,139, filed Jul. 17, 1989 and now issued as U.S. Pat. No. 5,198,380, and which in turn is a division of original application Ser. No. 07/204,175, filed Jun. 8, 1988, now issued as U.S. Pat. No. 5,095,344. The foregoing patents are also incorporated herein by this reference.
This invention relates generally to semiconductor electrically programmable read only memories (Eprom) and electrically erasable programmable read only memories (EEprom), and specifically to semiconductor structures of such memories, processes of making them, and techniques for using them.
An electrically programmable read only memory (Eprom) utilizes a floating (unconnected) conductive gate, in a field effect transistor structure, positioned over but insulated from a channel region in a semiconductor substrate, between source and drain regions. A control gate is then provided over the floating gate, but also insulated therefrom. The threshold voltage characteristic of the transistor is controlled by the amount of charge that is retained on the floating gate. That is, the minimum amount of voltage (threshold) that must be applied to the control gate before the transistor is turned "on" to permit conduction between its source and drain regions is controlled by the level of charge on the floating gate. A transistor is programmed to one of two states by accelerating electrons from the substrate channel region, through a thin gate dielectric and onto the floating gate.
The memory cell transistor's state is read by placing an operating voltage across its source and drain and on its control gate, and then detecting the level of current flowing between the source and drain as to whether the device is programmed to be "on" or "off" at the control gate voltage selected. A specific, single cell in a two-dimensional array of Eprom cells is addressed for reading by application of a source-drain voltage to source and drain lines in a column containing the cell being addressed, and application of a control gate voltage to the control gates in a row containing the cell being addressed.
This type of Eprom transistor is usually implemented in one of two basic configurations. One is where the floating gate extends substantially entirely over the transistor's channel region between its source and drain. Another type, preferred in many applications, is where the floating gate extends from the drain region only part of the way across the channel. The control gate then extends completely across the channel, over the floating gate and then across the remaining portion of the channel not occupied by the floating gate. The control gate is separated from that remaining channel portion by a thin gate oxide. This second type is termed a "split-channel" Eprom transistor. This results in a transistor structure that operates as two transistors in series, one having a varying threshold in response to the charge level on the floating gate, and another that is unaffected by the floating gate charge but rather which operates in response to the voltage on the control gate as in any normal field effect transistor.
Early Eprom devices were erasable by exposure to ultraviolet light. More recently, the transistor cells have been made to be electrically erasable, and thus termed electrically erasable and programmable read only memory (EEprom). One way in which the cell is erased electrically is by transfer of charge from the floating gate to the transistor drain through a very thin tunnel dielectric. This is accomplished by application of appropriate voltages to the transistor's source, drain and control gate. Other EEprom memory cells are provided with a separate, third gate for accomplishing the erasing. An erase gate passes through each memory cell transistor closely adjacent to a surface of the floating gate but insulated therefrom by a thin tunnel dielectric. Charge is then removed from the floating gate of a cell to the erase gate, when appropriate voltages are applied to all the transistor elements. An array of EEprom cells are generally referred to as a Flash EEprom array because an entire array of cells, or significant group of cells, is erased simultaneously (i.e., in a flash).
EEprom's have been found to have a limited effective life. The number of cycles of programming and erasing that such a device can endure before becoming degraded is finite. After a number of such cycles in excess of 10,000, depending upon its specific structure, its programmability can be reduced. Often, by the time the device has been put through such a cycle for over 100,000 times, it can no longer be programmed or erased properly. This is believed to be the result of electrons being trapped in the dielectric each time charge is transferred to or away from the floating gate by programming or erasing, respectively.
It is the primary object of the present invention to provide Eprom and EEprom cell and array structures and processes for making them that result in cells of reduced size so their density on a semiconductor chip can be increased. It is also an object of the invention that the structures be highly manufacturable, reliable, scalable, repeatable and producible with a very high yield.
It is yet another object of the present invention to provide EEprom semiconductor chips that are useful for solid state memory to replace magnetic disk storage devices.
Another object of the present invention is to provide a technique for increasing the amount of information that can be stored in a given size Eprom or EEprom array.
Further, it is an object of the present invention to provide a technique for increasing the number of program/read cycles that an EEprom can endure.
These and additional objects are accomplished by the various aspects of the present invention, either alone or in combination, the primary aspects being briefly summarized as below:
1. The problems associated with prior art split channel Eprom and split channel Flash EEprom devices are overcome by providing a split channel memory cell constructed in one of the following ways:
(A) In one embodiment, one edge of the floating gate is self aligned to and overlaps the edge of the drain diffusion and the second edge of the floating gate is self aligned to but is spaced apart from the edge of the source diffusion. A sidewall spacer formed along the second edge of the floating gate facing the source side is used to define the degree of spacing between the two edges. Self alignment of both source and drain to the edges of the floating gate results in a split channel Eprom device having accurate control of the three most critical device parameters: Channel segment lengths L1 and L2 controllable by floating gate and control gate, respectively, and the extent of overlap between the floating gate and the drain diffusion. All three parameters are insensitive to mask misalignment and can be made reproducibly very small in scaled-down devices.
(B) In a second embodiment of the split channel Eprom a heavily doped portion of the channel adjacent to the drain diffusion is formed by a novel, well-controlled technique. The length Lp and doping concentration of this channel portion become the dominant parameters for programming and reading, thereby permitting the formation of a split channel structure which is relatively insensitive to misalignments between the floating gate and the source/drain regions.
2. A separate erase gate is provided to transform a Eprom device into a Flash EEprom device. The area of overlap between the floating gate and the erase gate is insensitive to mask misalignment and can therefore be made reproducibly very small.
3. In some embodiments of this invention, the erase gate is also used as a field plate to provide very compact electric isolation between adjacent cells in a memory array.
4. A new erase mechanism is provided which employs tailoring of the edges of a very thin floating gate so as to enhance their effectiveness as electron injectors.
5. A novel intelligent programming and sensing technique is provided which permits the practical implementation of multiple state storage wherein each Eprom or flash EEprom cell stores more than one bit per cell.
6. A novel intelligent erase algorithm is provided which results in a significant reduction in the electrical stress experienced by the erase tunnel dielectric and results in much higher endurance to program/erase cycling.
The combination of various of these features results in new split channel Eprom or split channel Flash EEprom devices which are highly manufacturable, highly scalable, and offering greater storage density as well as greater reliability than any prior art Eprom or Flash EEprom devices. Memories that utilize the various aspects of this invention are especially useful in computer systems to replace existing magnetic storage media (hard disks and floppy disks), primarily because of the very high density of information that may be stored in them.
Additional objects, features and advantages of the present invention will be understood from the following description of its preferred embodiments, which description should be taken in conjunction with the accompanying drawings.
There are two distinctly different approaches in the prior art of Flash EEproms. A triple polysilicon device was described by J. Kupec et al. in 1980 IEDM Technical Digest, p. 602 in an article entitled "Triple Level Polysilicon EEprom with Single Transistor per Bit". An improvement to the Kupec device was proposed by F. Masuoka and H. Iizuka in U.S. Pat. No. 4,531,203, issued Jul. 23, 1985. Variations on the same cell are described by C. K. Kuo and S. C. Tsaur in U.S. Pat. No. 4,561,004 issued Dec. 24, 1985, and by F. Masuoka et al. in an article titled "A 256K Flash EEprom Using Triple Polysilicon Technology", Digest of Technical Papers, IEEE International Solid-State Circuits Conference, Febraury 1985, p. 168.
The second approach is a double polysilicon cell described by G. Samachisa et al., in an article titled "A 128K Flash EEprom Using Double Polysilicon Technology", IEEE Journal of Solid State Circuits, October 1987, Vol. SC-22, No. 5, p. 676. Variations on this second cell are also described by H. Kume et al. in an article titled "A Flash-Erase EEprom Cell with an Asymmetric Source and Drain Structure", Technical Digest of the IEEE International Electron Devices Meeting, December 1987, p. 560, and by V. N. Kynett et al. in an article titled "An In-System Reprogrammable 256K CMOS Flash Memory", Digest of Technical Papers, IEEE International Solid-State Circuits Conference, February 1988, p. 132. A cross-section of the Samachisa cell is shown in FIG. 1. Transistor 100 is an NMOS transistor with source 101, drain 102, substrate 103, floating gate 104 and control gate 109. The transistor has a split channel consisting of a section 112 (L1) whose conductivity is controlled by floating gate 104, in series with a section 120 (L2) whose conductivity is controlled by control gate 109. Programming takes place as in other Eprom cells by injection of hot electrons 107 from the channel at the pinchoff region 119 near the drain junction. Injected electrons are trapped on floating gate 104 and raise the conduction threshold. voltage of channel region 112 and therefore of transistor 100. To erase transistor 100 the oxide in region 112 separating between the floating gate 104 and drain diffusion 102 and channel 112 is thinned to between 15 and 20 nanometers, to allow electronic tunneling of trapped electrons 108 from the floating gate to the drain. In the Samachisa cell the appropriate voltages applied to achieve programming are VCG=12V, VD=9V, VBB=0V, VS=0V, and to achieve erase are VCG=0V, VD=19V, VBB=0V, VS=floating. Samachisa points out that the electrical erase is not self-limiting. It is possible to overerase the cell, leaving the floating gate positively charged, thus turning the channel portion L1 into a depletion mode transistor. The series enhancement transistor L2 is needed therefore to prevent transistor leakage in the overerase condition.
The Samachisa cell suffers from certain disadvantages. These are:
The Kynett and Kume cells (
The Kynett cell can be contrasted with the Samachisa cell:
Kupec's cell employs essentially the Kynett cell without a thin tunnel dielectric over the source, channel, or drain, and with a third polysilicon plate covering the entire transistor and acting as an erase plate. A cross sectional view of the Kupec device is shown in
Masuoka's approach to Flash EEprom overcomes most of the disadvantages of the Samachisa, Kynett and Kupec cells.
The transistor channel width (W), as well as the edges of the source and drain diffusions are defined by the edges 305 of a thick field oxide formed by isoplanar oxidation. Oxide 332 of thickness in the 25 to 40 nanometers range is used as isolation between the floating gate and the substrate. Masuoka adds an erase gate 330 disposed underneath the floating gate along one of its edges. This erase gate is used to electrically erase floating gate 304 in an area of tunnel dielectric 331 where the floating gate overlaps the erase gate. Tunnel dielectric 331 is of thickness between 30 and 60 nanometers.
Masuoka specifies the following voltages during erase: VS=0V, VD=0V, VCG=0V, VERASE=20V to 30V.
Comparing the Masuoka cell with the Samachisa and Kynett cells:
From the foregoing analysis it is clear that while the Masuoka prior art cell successfully addresses most of the problems encountered by Samachisa and Kynett, it itself has disadvantages not encountered by Samachisa or Kynett.
Masuoka and Samachisa both use a split channel Eprom transistor for programming. In the split channel eprom transistor, the portion L2 of the channel length controlled by control gate 109, 309 has a fixed enhancement threshold voltage determined by the p+ channel doping concentration 360. The portion L1 of the channel length controlled by floating gate 104 (Samachisa) and 304 (Masuoka) has a variable threshold voltage determined by the net charge stored on the floating gate.
Other prior art split channel Eprom transistors are described by E. Harari in U.S. Pat. No. 4,328,565, May 4, 1982 and by B. Eitan in U.S. Pat. No. 4,639,893, Jan. 27, 1987. The Harari split channel Eprom transistor 300 d is shown in cross section in
The Eitan split channel Eprom transistor 400 is shown in cross sections in
The addition of a fixed threshold enhancement transistor in series with the floating gate transistor decouples the floating gate from the source diffusion. This allows the channel length L1 to be made very small without encountering punchthrough between source and drain. Furthermore, transistor drain-turnon due to the parasitic capacitive coupling between the drain diffusion and the floating gate is eliminated because the enhancement channel portion L2 remains off.
Eitan shows that the shorter the length L1 the greater the programming efficiency and the greater the read current of the split channel Eprom transistor. For Flash EEprom devices the series enhancement channel L2 acquires additional importance because it allows the floating gate portion L1 to be overerased into depletion thereshold voltage without turning on the composite split channel transistor.
The disadvantages incurred by the addition of the series enhancement channel L2 are an increase in cell area, a decrease in transistor transconductance, an increase in control gate capacitance, and an increase in variability of device characteristics for programming and reading brought about by the fact that L1 or L2 or both are not precisely controlled in the manufacturing process of the prior art split channel devices. Samachisa, Masuoka and Eitan each adopt a different approach to reduce the variability of L1 and L2:
Samachisa's transistor 100 (
Masuoka's transistor 300 (
Eitan's transistor 400 (
It should be pointed out that even with the most advanced optical lithography systems available today in a production environment it is difficult to achieve an alignment accuracy of better than �0.25 microns between any two mask layers. Therefore the variability in L2 or L1 inherent to any structure which is alignment sensitive can be as much as approximately 0.5 microns from one extreme to the other.
Another prior art split channel Eprom device which attempts to achieve the objective of accurately establishing L1 and L2 is disclosed by Y. Mizutani and K. Makita in the 1985 IEDM Technical Digest, p. 63, shown in cross section in
Yet another prior art device which has a split channel with a well controlled L1 and L2 is disclosed by A. T. Wu et al. in the 1986 IEDM Technical Digest, p. 584 in an article entitled "A Novel High-Speed, 5-Volt Programming Eprom Structure with Source-Side Injection". A cross section of the Wu prior art transistor is shown in
Another prior art Eprom transistor which does not have a split channel structure but which seeks to achieve two distinct channel regions to optimize the Eprom programming performance is disclosed by S. Tanaka et al. in 1984 ISSCC Digest of Technical Papers, p. 148 in an article entitled "A Programmable 256K CMOS Eprom with On Chip Test Circuits". A cross section of this device is shown in
I.a. Split Channel Eprom Transistor with Self Aligned Drain Diffusion and Self Aligned Spaced Apart Source Diffusion
P-type substrate 563 is typically 5 to 50 Ohms centimeter, p+ channel doping 560 a is typically in the range of 1�1016 cm−3 to 2�1017 cm−3, dielectric film 564 a is typically 20 to 40 nanometers thick, dielectric film 567 a is typically 20 to 50 nanometers thick, floating gate 504 a is usually a heavily N+ doped film of polysilicon of thickness which can be as low as 25 nanometers (this thickness will be discussed in Section VII) or as high as 400 nanometers. Control gate 509 is either a heavily N+ doped film of polysilicon or a low resistivity inter-connect material such as a silicide or a refractory metal. Of importance, edge 523 a of N+ drain diffusion 502 a formed by ion implantation of Arsenic or Phosphorus is self aligned to edge 522 a of floating gate 504 a, while edge 521 a of N+ source diffusion 501 a formed by the same ion implantation step is self aligned to, but is spaced apart from, edge 550 a of the same floating gate 504 a, using a sidewall spacer (not shown in
The key steps for the formation of channel portions L1 and L2 are illustrated in
The thickness of the conformal spacer layer determines the width of the sidewall spacer, and therefore also the length of channel portion L2. Typically for an L2 of 400 nanometers a spacer layer of approximately 600 nanometers thickness is used.
In the present invention, the spacer can be significantly wider, it is used along one edge only, and it is used not to define a lightly doped source or drain but rather to define the series enhancement transistor channel portion L2.
The next step is a masking step. Photoresist 591 a, 591 b (
Next, spacers 592 a, 592 b and the protective film 566 a are removed (
The remaining part of the process is standard:
The surface of the structure is covered with a thick passivation layer 568, usually phosphorous doped glass or a Borophosphosilicate glass (BPSG). This passivation is made to flow in a high temperature anneal step. Contact vias are etched (not shown in
Comparing split channel transistor 500 a of
A new method is disclosed for manufacturing the split channel Eprom transistor 1400 which results in much better control of the parameter Lp and of the surface channel doping concentration 1413 than is provided by the DSA (Diffusion Self Align) approach of the Tanaka prior art transistor 400 e (
The main steps in this new method for the fabrication of a memory array of transistors 1400 are as follows:
1. In the structure of
2. A photoresist mask P.R.1 (1470) is used to define source and drain regions in long parallel strips extending in width between edges 1471, 1472 of openings in the photoresist. Exposed oxide layer 1473 is now wet etched in a carefully controlled and timed etch step which includes substantial undercutting of photoresist 1470. The extent of undercutting, which is measured by the distance Lx between oxide edges 1476 and 1478, will eventually determine the magnitude of parameter Lp. Typically, Lx is chosen between 300 nanometers and 700 nanometers. The three parameters critical for a reproducible Lx are the concentration and temperature of the etch solution (hydrofluoric acid) and the density (i.e., lack of porosity) of the oxide 1473 being etched. These can be well controlled sufficiently so that a timed undercutting etch step results in well controlled etched strips of width Lx and running parallel to edges 1471, 1472 of the long openings in the photoresist. In fact, for values of Lx below approximately 500 nanometers, it is easier to achieve a reproducible Lx through controlled sideway etching than by controlling the line width of long, narrow line in a photoresist layer. An example of the use of sideway etching self aligned to an edge in a similar fashion (but to achieve the different purpose of forming a very narrow guard ring) can be found in the prior art article by S. Kim titled "A Very Small Schottky Barrier Diode with Self-Aligned Guard Ring for VLSI Application", appearing in the 1979 IEDM Technical Digest, p. 49.
3. At the completion of the sideway etch step a second, anisotropic etch is performed, using the same photoresist mask P.R.1 to etch away long strips of the exposed silicon nitride film 1474. Edges 1471, 1472 of P.R.1 (1470) are used to form edges 1480, 1481 respectively in the etched strips of nitride layers.
4. Arsenic ion implantation with an ion dose of approximately 5�1015 cm−2 is performed with an energy sufficient to penetrate oxide film 1475 and dope the surface in long strips of N+ doped regions (1402, 1401). Photoresist mask P.R.1 can be used as the mask for this step, but nitride layer 1474 can serve equally well as the implant mask. P.R.1 is stripped at the completion of this step.
5. An implant damage anneal and surface oxidation step follows, resulting in 200 to 300 nanometers of silicon dioxide 1462 grown over the source and drain diffusion strips. The temperature for this oxidation should be below 1000� C. to minimize the lateral diffusion of the N+ dopants in regions 1402, 1401. If desired it is possible through an extra masking step to remove nitride layer 1474 also from the field regions between adjacent channels, so as to grow oxide film 1462 not only over the source and drain regions but also over the field isolation regions.
6. In
7. Top oxide 1473, nitride 1474 and thin oxide 1475 are now removed by etching. This etching also reduces the thickness of the oxide layer 1462 protecting the source and drain diffusions. It is desirable to leave this film thickness at not less than approximately 100 nanometers at the completion of this etch step.
8. The remaining steps can be understood in relation to the structure of
9. A second dielectric 1466, 1411 is grown or deposited on top of the substrate and floating gate strips, respectively. This can be a layer of silicon dioxide or a combination of thin films of silicon dioxide and silicon nitride, of combined thickness in the range between 20 and 50 nanometers.
10. A second layer of polysilicon is deposited, doped N+ (or silicided for lower resistivity), masked and etched to form control gates 1409 in long strips running perpendicular to the strips of floating gates and source/drain strips. Each control gate strip is capacitively coupled to the floating gate strips it crosses over through dielectric film 1411 in the areas where the strips overlap each other. Control gates 1409 also control the channel conduction in channel portions L2 not covered by the floating gate strips. Each strip of control gates is now covered by a dielectric isolation film (can be thermally grown oxide).
11. Using the strips of control gates as a mask, exposed areas of dielectric 1466, 1411 and of the strips of first polysilicon floating gates are etched away. The resulting structure has long strips, or rows, of control gates, each row overlying several floating gates 1404 where the outer edges of each floating gate are essentially self aligned to the edges defining the width of the control gate strip. These edges are now oxidized or covered with a deposited dielectric to completely insulate each floating gate. Field areas between adjacent rows of cells or between adjacent strips of source and drain regions are now automatically self aligned to the active device areas and do not require space consuming isoplanar oxidation isolation regions. (Of course, it is also possible to fabricate transistor 1400 with source, drain and channel regions defined by the edges of a thick isoplanar oxidation isolation layer, or to rely for field isolation on oxide 1462 grown also in the field regions, see the option described in step 5 above.)
The Eprom cell of this embodiment has several advantages over the prior art Eprom cells:
Transistor 600 a of
Transistor 600 a is erased by tunneling of electrons from floating gate 504 a to erase gates 530, 535, across tunnel dielectrics 531 a, 561 a on the sidewalls and top surface of the floating gate where it is overlapped by the erase gate.
Tunnel dielectric film 531 a, 561 a is normally a layer of Silicon Dioxide grown through thermal oxidation of the heavily N+ doped and textured polycrystalline silicon comprising the floating gate. It is well known in the industry (see for example an article by H. A. R. Wegener titled "Endurance Model for textured-poly floating gate memories", Technical Digest of the IEEE International Electron Device Meeting, December 1984, p. 480) that such a film, when grown under the appropriate oxidation conditions over properly textured doped polysilicon allows an increase by several orders of magnitude of the conduction by electron tunneling even when the film is several times thicker than tunnel dielectric films grown on single crystal silicon (such as the tunnel dielectric films used in the prior art Samachisa and Kynett devices). For example, a tunnel dielectric oxide grown to a thickness of 40 nanometers on N+ doped and textured polysilicon can conduct by electronic tunneling approximately the same current density as a tunnel dielectric oxide of 10 nanometers thickness grown on N+ doped single crystal silicon under identical voltage bias conditions. It is believed that this highly efficient tunneling mechanism is a result of sharp asperities at the grain boundaries of the polysilicon which is specially textured to enhance the areal density of such asperities. A commonly practices technique is to first oxidize the surface of the polysilicon at a high temperature to accentuate the texturing, then stripping that oxide and regrowing a tunnel oxide at a lower temperature. The oxide film capping such an asperity experiences a local amplification by a factor of four to five of the applied electric field resulting in an efficient localized tunnel injector. The advantage provided by the thicker films of tunnel dielectric is that they are much easier to grow in uniform and defect-free layers. Furthermore the electric field stress during tunneling in the thick (40 nanometer) tunnel dielectric is only 25 percent of the stress in the thin (10 nanometer) tunnel dielectric, assuming the same voltage bias conditions. This reduced stress translates into higher reliability and greater endurance to write/erase cycling. For these reasons, all Flash EEprom embodiments of this invention rely on poly-poly erase through a relatively thick tunnel dielectric.
In the embodiment of
The manufacturing process can be somewhat simplified by implementing erase gates 530, 535 in the same conductive layer as that used for control gate 509. However the spacing Z between the edges of the control gate and the erase gate (and hence the cell size) would then have to be significantly greater than is the case when the control gate and erase gates are implemented in two different conductive layers insulated from each other by dielectric film 567 a. In fact, in the triple layer structure 600 a of
A point of significance is the fact that the tunnel dielectric area contributing to erase in each cell consisting of the combined areas of 531 a and 561 a, is insensitive to the mask misalignment between edges 532 a, 562 a of floating gate 504 a and erase gates 530, 535. (Note that each erase gate, such as 535, is shared between two adjacent cells, such as 600 a and 600 c in this case). Any such misalignment will result in a reduction of the area of the tunnel dielectric at one edge of the floating gate, but also in an increase of equal magnitude in the area available for tunneling at the other edge of the floating gate. This feature permits the construction of a cell with very small area of tunnel dielectric. By contrast the prior art triple layer Flash EEprom cells of Masuoka and Kuo referenced above are sensitive to mask misalignment and therefore require a structure wherein the nominal area provided for tunnel erase may be much larger than the optimum such area, in order to accommodate for the worst case misalignment condition.
Another distinguishing feature of this embodiment relative to the Masuoka cell of
Typical bias voltage conditions necessary to erase memory cells 600 a, 600 b, 600 c and 600 d are:
VERASE (on all erase gates 530, 535, 536)=15V to 25V applied for between 100 milliseconds and 10 seconds (the pulse duration is strongly dependent on the magnitude of VERASE) VCG=0V, VBB=0V. VD and VS can be held at 0V or at a higher voltage between 5V and 10V, so as to reduce the net voltage experienced during erase across dielectric film 565 a in areas such as 563 (
III. Self Aligned Split Channel Flash EEprom Cell with Field Plate Isolation
A 2�2 array of Flash EEprom cells in accordance with another embodiment of this invention is shown in topological view in
Split channel Flash EEprom transistor 700 a employs three conductive layers (floating gate 704 erase gates 730, 735 and control gate 709) formed in the same sequence as described in section II in conjunction with the Flash EEprom transistor 600 a of
The elimination of the thick isoplanar oxide inside the array of memory cells (this isoplanar oxide may still be retained for isolation between peripheral logic transistors) has several advantages:
1. The surface stress at the silicon-silicon dioxide boundary due to a prolonged thermal isoplanar oxidation cycle is eliminated inside the array, resulting in less leaky source and drain junctions and in higher quality gate oxides.
2. For a given cell width, the elimination of the isoplanar oxide allows the effective channel width W under floating gate 704 to extend all the way between the two edges 732 a, 762 a of the floating gate. By comparison, effective channel width W of transistor 600 a (
3. From capacitive coupling considerations (to be discussed in section VI below) the efficiency of tunnel erase is higher in cells where coupling of the floating gate to the silicon substrate 763 is greatest. In transistor 700 a the entire bottom surface area of the floating gate is tightly coupled to the substrate 763 through the thin gate dielectric 764. By contrast, in transistor 600 a (
4. The width of control gate 709 between its edges 744 and 774 defines channel width W2 of the series enhancement channel portion L2 (
In a memory array source diffusion 701 and drain diffusion 702 can be formed in long strips. If transistor 500 a is used as the Eprom transistor, then source diffusion edge 721 is self aligned to the previously discussed sidewall spacer (not shown) while drain diffusion edge 723 is self aligned to edge 722 of floating gate 704 a. In areas between adjacent floating gates 704 a, 704 c the source and drain diffusion edges (721 x, 723 x in
IV. Self Aligned Split Channel Flash EEprom Cell with Erase Confined to the Vertical Edges of the Floating Gate.
Another embodiment of the self aligned split channel Flash EEprom of this invention can result in a cell which has smaller area than cells 600 aand 700 a of the embodiments described in Sections II and III respectively. In this third embodiment the area for tunnel erase between the floating gate and the erase gate is confined essentially to the surfaces of the vertical sidewalls along the two edges of each floating gate. To best understand how cell 800 a of this embodiment differs from cell 700 a a 2�2 array of cells 800 a, 800 b, 800 c and 800 d are shown in
Cell 800 a has a floating gate 804 a formed in a first layer of heavily N+ doped polysilicon. This gate controls the transistor conduction in channel portion L1 (
The erase gates are insulated from control gate 809 by dielectric insulator 897 which is grown or deposited prior to deposition of erase gates 830, 835, 836. Tunnel erase dielectrics 831 a, 861 a are confined to the surface of the vertical edges 832 a, 862 a of the floating gate 804 a. Erase gate 830 also provides a field plate isolation over oxide 862 in the field between adjacent devices.
The thickness of all conducting and insulating layers in structure 800 are approximately the same as those used in structure 700 a. However, because the erase gate is implemented here after, rather than before the control gate, the fabrication process sequence is somewhat different. Specifically (see
1. Floating gates 804 a, 804 c are formed in long continuous and narrow strips on top of gate oxide 864. The width of each such strip is L1 plus the extent of overlap of the floating gate over the drain diffusion.
2. Dielectric 867 is formed and the second conductive layer (N+ doped polysilicon or a silicide) is deposited.
3. Control gates 809 are defined in long narrow strips in a direction perpendicular to the direction of the strips of floating gates. The strips are etched along edges 844, 874, and insulated with relatively thick dielectric 897.
4. Edges 844, 874 (or the edges of insulator spacer 899 formed at both edges of control gate strip 809) are then used to etch dielectric 867 and then, in a self aligned manner to also etch vertical edges 832 a and 862 a of the underlying floating gate strips, resulting in isolated floating gates which have exposed edges of polysilicon only along these vertical walls.
5. Tunnel dielectric films 831 a, 861 a are formed by thermal oxidation of these exposed surfaces.
6. A third conductive layer is deposited, from which are formed erase gates 830 in long strips running in between and parallel to adjacent strips of control gates. These erase gates also serve as field isolation plates to electrically isolate between adjacent regions in the memory array.
Flash EEprom transistor 800 a can be implemented in conjunction with any of the split channel Eprom transistors of this invention (transistors 500 a and 1400) or with any of the prior art split gate Eprom transistors of Eitan, Samachisa, Masuoka or Harari. For example, an array of Flash EEprom transistors 800 a can be fabricated by adding a few process steps to the fabrication process for the split channel Eprom transistor 1400 (
Steps 1 through 10 are identical to steps 1 through 10 described in Section I.b. in conjunction with the manufacturing process for split channel Eprom transistor 1400.
Steps 11, 12, and 13 are the process steps 4, 5, and 6 respectivly described in this section IV in conjunction with split channel Flash EEprom transistor 800 a.
Cell 800 a results in a very small area of tunnel erase, which is also relatively easy to control (it is not defined by a mask dimension, but rather by the thickness of the deposited layer constituting the floating gates). For this reason, this cell is the most highly scalable embodiment of this invention.
V. Self Aligned Split Channel Flash EEprom Cell with a Buried Erase Gate.
A 2�2 array of Flash EEprom cells 900 a, 900 b, 900 c and 900 d in accordance with a fourth embodiment of this invention is shown in topological view in
Transistor 900 a is a split channel Flash EEprom transistor having channel portions L1 and L2 formed by self alignment as in Eprom transistor 500 a or in a non self aligned manner as in Eprom transistor 1400. Erase gate 930 is a narrow conductive strip sandwiched between floating gate 904 a on the bottom and control gate 909 on top. Erase gate 930 is located away from edges 932 a, 962 a of the floating gate. These edges therefore play no role in the tunnel erase, which takes place through tunnel dielectric 931 confined to the area where erase gate 930 overlaps floating gate 904 a. Erase gate 930 also overlaps a width We of the series enhancement channel portion L2. During read or programming, erase gate 930 is held at 0V, and therefore the channel portion of width We does not contribute to the read or program current. The only contribution to conduction in channel portion L2 comes from widths Wp and Wq where the channel is controlled directly by control gate 909. Channel portion L1 however sees conduction contributions from all three widths, Wp, Wq and We. Edges 932 a, 962 a of floating gate 904 a can be etched to be self aligned to edges 944, 974 respectively of control gate 909. This then permits the formation of channel stop field isolation 998, by implanting a p type dopant in the field regions not protected by the control gate or floating gate (
One advantage of cell 900 a is that erase gate strips 930, 936 can be made very narrow by taking advantage of controlled undercutting by for example isotropic etchings of the conductive layer forming these strips. This results in a small area of tunnel erase, which is insensitive to mask misalignment. Furthermore the channel width Wp and Wq is also insensitive to mask misalignment. This embodiment of Flash EEprom can also be implemented in conjunction with prior art split channel Eproms cells such as the Eitan, Harari, Samachisa or Masuoka cells.
VI. Device Optimization
Specifically these are:
CG=Capacitance between Floating gate 1104 and control gate 1109.
CD=Capacitance between Floating gate 1104 and drain diffusion 1102.
CB=Capacitance between Floating gate 1104 and substrate 1163.
CE=Capacitance between Floating gate 1104 and erase gate 1130.
CT=CG+CD+CB+CE is the total capacitance. Q is the net charge stored on the floating gate. In a virgin device, Q=0. In a programmed device Q is negative (excess electrons) and in an erased device Q is positive (excess holes).
The voltage VFG on Floating gate 1104 is proportional to voltages VCG, VERASE, VD, VBB and to the charge Q according to the following equation:
In all prior art Eprom and Flash EEprom devices as well as in embodiment 600 a of this invention, the dominant factor in CT is CG, the coupling to the control gate. However, in embodiments 700 a, 800 a and 900 a CB is also a major contributor by virtue of the fact that the entire bottom surface of the floating gate is strongly coupled to the substrate.
a. Electrical Erase
During erase, the typical voltage conditions are VCG=0V, VD=0V, VS=0V, VBB=0V and VERASE=20V. Therefore, substituting in equation (1),
The split channel Flash EEprom device can be viewed as a composite transistor consisting of two transistors T1 and T2 in series—
Prior art split channel Flash EEprom devices erase with a single pulse of sufficient voltage VERASE and sufficient duration to ensure that VT1 is erased to a voltage below VT2 (curve b) in
This invention proposes for the first time a scheme to take advantage of the full memory window. This is done by using the wider memory window to store more than two binary states and therefore more than a single bit per cell. For example, it is possible to store 4, rather than 2 states per cell, with these states having the following threshold voltage:
Multistate memory cells have previously been proposed in conjunction with ROM (Read Only Memory) devices and DRAM (Dynamic Random Access Memory). In ROM, each storage transistor can have one of several fixed conduction states by having different channel ion implant doses to establish more than two permanent threshold voltage states. Alternatively, more than two conduction states per ROM cell can be achieved by establishing with two photolithographic masks one of several values of transistor channel width or transistor channel length. For example, each transistor in a ROM array may be fabricated with one of two channel widths and with one of two channel lengths, resulting in four distinct combinations of channel width and length, and therefore in four distinct Conductive states. Prior art multistate DRAM cells have also been proposed where each cell in the array is physically identical to all other cells. However, the charge stored at the capacitor of each cell may be quantized, resulting in several distinct read signal levels. An example of such prior art multistate DRAm storage is described in IEEE Journal of Solid-State Circuits, February 1988, p. 27 in an article by M. Horiguchi et al. entitled "An Experimental Large-Capacity Semiconductor File Memory Using 16-Levels/Cell Storage". A second example of prior art multistate DRAM is provided in IEEE Custom Integrated Circuits Conference, May 1988, p. 4.4.1 in an article entitled "An Experimental 2-Bit/Cell Storage DRAM for Macrocell or Memory-on-Logic Applications" by T. Furuyama et al.
To take full advantage of multistate storage in Eproms it is necessary that the programming algorithm allow programming of the device into any one of several conduction states. First it is required that the device be erased to a voltage VT1 more negative than the "3" state (−3.0V in this example). Then the device is programmed in a short programming pulse, typically one to ten microseconds in duration. Programming conditions are selected such that no single pulse can shift the device threshold by more than one half of the threshold voltage difference between two successive states. The device is then sensed by comparing its conduction current IDS with that of a reference current source IREF, i (i=0,1,2,3) corresponding to the desired conduction state (four distinct reference levels must be provided corresponding to the four states). Programming pulses are continued until the sensed current (solid lines in
Large memory systems typically incorporate error detection and correction schemes which can tolerate a small number of hard failures i.e. bad Flash EEprom cells. For this reason the programming/sensing cycling algorithm can be automatically halted after a certain maximum number of programming cycles has been applied even if the cell being programmed has not reached the desired threshold voltage state, indicating a faulty memory cell.
There are several ways to implement the multi-state storage concept in conjunction with an array of Flash EEprom transistors. An example of one such circuit is shown in
During programming, the four data inputs Ii (I0, I1, I2 and I3) are presented to a comparator circuit which also has presented to it the four sense amp outputs for the accessed cell. If Di match Ii, then the cell is in the correct state and no programming is required. If however all four Di do not match all four Ii, then the comparator output activates a programming control circuit. This circuit in turn controls the bit line (VPBL) and word line (VPWL) programming pulse generators. A single short programming pulse is applied to both the selected word line and the selected bit line. This is followed by a second read cycle to determine if a match between Di and Ii has been established. This sequence is repeated through multiple programming/reading pulses and is stopped only when a match is established (or earlier if no match has been established but after a preset maximum number of pulses has been reached).
The result of such multistate programming algorithim is that each cell is programmed into any one of the four conduction states in direct correlation with the reference conduction states IREF, i. In fact, the same sense amplifiers used during programming/reading pulsing are also used during sensing (i.e., during normal reading). This allows excellent tracking between the reference levels (dashed lines in
In actual fact, although four reference levels and four sense amplifiers are used to program the cell into one of four distinct conduction states, only three sense amplifiers and three reference levels are required to sense the correct one of four stored states. For example, in
Note that the same principle employed in the circuit of
c. Improved Charge Retention
In the example above, states "3" and "2" are the result of net positive charge (holes) on the floating gate while states "1" and "0" are the result of net negative charge (electrons) on the floating gate. To properly sense the correct conduction state during the lifetime of the device (which may be specified as 10 years at 125� C.) it is necessary for this charge not to leak off the floating gate by more than the equivalent of approximately 200 millivolts shift in VT1. This condition is readily met for stored electrons in this as well as all prior art Eprom and Flash EEprom devices. There is no data in the literature on charge retention for stored holes, because, as has been pointed out above, none of the prior art devices concern themselves with the value VT1 when it is more negative than VT2, i.e., when holes are stored on th floating gate. From device physics considerations alone it is expected that retention of holes trapped on the floating gate should be significantly superior to the retention of trapped electrons. This is because trapped holes can only be neutralized by the injection of electrons onto the floating gate. So long as the conditions for such injection do not exist it is almost impossible for the holes to overcome the potential barrier of approximately 5.0 electronvolts at the silicon-silicon dioxide interface (compared to a 3.1 electron volts potential barrier for trapped electrons).
Therefore it is possible to improve the retention of this device by assigning more of the conduction states to states which involve trapped holes. For example, in the example above state "1" had VT1=+2.0V, which involved trapped electrons since VT1 for the virgin device was made to be VT1=+1.5V. If however VT1 of the virgin device is raised to a higher threshold voltage, say to VT1=+3.0V (e.g. by increasing the p-type doping concentration in the channel region 560 a in
d. Intelligent Erase for Improved Endurance
The endurance of Flash EEprom devices is their ability to withstand a given number of program/erase cycles. The physical phenomenon limiting the endurance of prior art Flash EEprom devices is trapping of electrons in the active dielectric films of the device (see the Wegener article referenced above). During programming the dielectric used during hot electron channel injection traps part of the injected electrons. During erasing the tunnel erase dielectric likewise traps some of the tunneled electrons. For example, in prior art transistor 200 (
A second problem with prior art devices is that during the erase pulse the tunnel dielectric may be exposed to an excessively high peak stress. This occurs in a device which has previously been programmed to state "0" (VT1=+4.5V or higher). This device has a large negative Q (see equation (2)). When VERASE is applied the tunnel dielectric is momentarily exposed to a peak electric field with components from VERASE as well as from Q/CT (equations (2) and (3)). This peak field is eventually reduced when Q is reduced to zero as a consequence of the tunnel erase. Nevertheless, permanent and cumulative damage is inflicted through this erase procedure, which brings about premature device failure.
To overcome the two problems of overstress and window closure a new erase algorithm is disclosed, which can also be applied equally well to any prior art Flash EEprom device. Without such new erase algorithm it would be difficult to have a multistate device since, from curve (b) in
The sequence for a complete erase cycle of the new algorithm is as follows (see FIG. 12):
1. Read S. This value can be stored in a register file. (This step can be omitted if S is not expected to approach the endurance limit during the operating lifetime of the device).
1a. Apply a first erase pule with VERASE=V1+n ΔV, n=0, pulse duration=t. This pulse (and the next few successive pulses) is insufficient to fully erase all memory cells, but it serves to reduce the charge Q on programmed cells at a relatively low erase field stress, i.e., it is equivalent to a "conditioning" pulse.
1b. Read a sparse pattern of cells in the array. A diagonal read pattern for example will read m+n cells (rather than m�n cells for a complete read) and will have at least one cell from each row and one cell from each column in the array. The number N of cells not fully erased to state "3" is counted and compared with X.
1c. If N is greater than x (array not adequately erased) a second erase pulse is applied of magnitude greater by ΔV than the magnitude of the first pulse, with the same pulse duration, t. Read diagonal cells, count N.
This cycling of erase pulse/read/increment erase pulse is continued until either N≦X or the number n of erase pulses exceed nmax. The first one of these two conditions to occur leads to a final erase pulse.
2a. The final erase pulse is applied to assure that the array is solidly and fully erased. The magnitude of VERASE can be the same as in the previous pulse or higher by another increment ΔV. The duration can be between 1 t and 5 t.
2b. 100% of the array is read. The number N of cells not fully erased is counted. If N is less than or equal to X, then the erase pulsing is completed at this point.
2c. If N is greater than X, then address locations of the N unerased bits are generated, possibly for substitution with redundant good bits at the system level. If N is significantly larger than X (for example, if N represents perhaps 5% of the total number of cells), then a flag may be raised, to indicate to the user that the array may have reached its endurance end of life.
2d. Erase pulsing is ended.
3a. S is incremented by one and the new S is stored for future reference. This step is optional. The new S can be stored either by writing it into the newly erased block or off chip in a separate register file.
3b. The erase cycle is ended. The complete cycle is expected to be completed with between 10 to 20 erase pulses and to last a total of approximately one second.
The new algorithm has the following advantages:
(a) No cell in the array experiences the peak electric field stress. By the time VERASE is incremented to a relatively high voltage any charge Q on the floating gates has already been removed in previous lower voltage erase pulses.
(b) The total erase time is significantly shorter than the fixed VERASE pulse of the prior art. Virgin devices see the minimum pulse duration necessary to erase. Devices which have undergone more than 1�104 cycles require only several more ΔV voltage increments to overcome dielectric trapped charge, which only adds several hundred milliseconds to their total erase time.
(c) The window closure on the erase side (curve (b) in
In a Flash EEprom memory chip it is possible to implement efficiently the new erase algorithm by providing on chip (or alternatively on a separate controller chip) a voltage multiplier to provide the necessary voltage V1 and voltage increments ΔV to nΔV, timing circuitry to time the erase and sense pulse duration, counting circuitry to count N and compare it with the stored value for X, registers to store address locations of bad bits, and control and sequencing circuitry, including the instruction set to execute the erase sequence outlined above.
VII. Edge Tailored Flash EEprom with New Erase Mechanism
Flash EEprom embodiments 600 a, 700 a, 800 a, and 900 a of this invention use tunnel erase across a relatively thick dielectric oxide grown on the textured surface of the polysilicon floating gate. Wegener (see article referenced above) has postulated that asperities—small, bump-like, curved surfaces of diameter of approximately 30 nanometers, enhance the electric field at the injector surface (in this case, the floating gate) by a factor of 4 to 5, thereby allowing efficient tunnel conduction to occur even across a relatively thick tunnel dielectric film (30 to 70 nanometers). Accordingly, there have been in the prior art efforts, through process steps such as high temperature oxidation of the polysilicon surface, to shape the surface of the polysilicon so as to accentuate these asperities. Although such steps are reproducible, they are empirical in nature, somewhat costly to implement, and not well understood.
A new approach is disclosed in this invention which results in a highly reproducible, enhanced electric field tunnel erase which is more efficient than the asperities method yet simpler to implement in several EEprom and Flash EEprom devices. In this approach, the floating gate layer is deposited in a very thin layer, typically in the range between 25 and 200 nanometers. This is much thinner than floating gates of all prior art Eprom, EEprom or Flash EEprom devices, which typically use a layer of polysilicon of thickness at least 200 nanometers, and usually more like 350 to 450 nanometers. The prior art polysilicon thickness is chosen to be higher than 200 nanometers primarily because of the lower sheet resistivity and better quality polyoxides provided by the thicker polysilicon. In certain prior art devices such as the Eitan split channel Eprom the floating gate also serves as an implant mask (
The reason for going to such a thin layer of polysilicon is that the edges of the floating gate in such a thin layer can be tailored through oxidation to form extremely sharp-tipped edges. The radius of curvature of these tipped edges can be made extremely small and is dictated by the thickness of the thin polysilicon film as well as the thickness of the tunnel dielectric grown. Therefore, tunnel erase from these sharp tips no longer depends on surface asperities but instead is dominated by the tip itself.
As an illustration of this modification, consider Flash EEprom transistor 800 a (
By contrast, the cross section view of modified transistor 800M is shown in
During oxidation of the thin vertical edges of floating gate 804M to form tunnel dielectric layers 861M, 831M, both top and bottom surfaces of the thin floating gate at its exposed edges are oxidized. This results in extremely sharp tips 8701, 870 r being formed. These tips serve as very efficient electron injectors (shown by arrows across tunnel dielectrics 861M, 831M). Injected electrons are collected as in transistor 800 a by erase gates 835, 830, which overlap these sharp-tipped edges.
Apart from the very efficient and highly reproducible injector characteristics inherent to the thin floating gate of transistor 800M there is an additional benefit in that the capacitance between the floating gate at its tip and the erase gate is much smaller than the corresponding capacitance in all other embodiments, including transistor 800 a. Therefore, from equations (1), (2) and (3) in section VI.a., since
Two other points are worth noting. First, the very thin floating gate should not be overly heavily doped, to avoid penetration of the N+ dopant through polysilicon 804M and gate dielectric 864. Since floating gate 804M is never used as a current conductor, a sheet resistivity of between 100 and 10,000 Ohms per square in quite acceptable.
Secondly, it is necessary to ensure that the sharp tips of the floating gate are adequately spaced apart or isolated from control gate 809M as well as substrate 860 or the source or drain diffusions (not shown in
Although a thin floating gate layer provides a relatively straight forward approach to achieving after oxidation sharp-tipped edges, other approaches are possible to achieve sharp-tipped edges even in a relatively thick floating gate layer. For example, in
In the device of
VIII. Flash EEprom Memory Array Implementations
The Flash EEprom cells of this invention can be implemented in dense memory arrays in several different array architectures. The first architecture, shown in
A second Flash EEprom memory array architecture which lends itself to better packing density than the array of
The array can be erased in a block, or in entire rows by decoding the erase voltage to the corresponding erase lines.
While the embodiments of this invention that have been described are the preferred implementations, those skilled in the art will understand that variations thereof may also be possible. In particular, the split channel Flash EEprom devices 600 a, 700 a, 800 a and 900 a can equally well be formed in conjunction with a split channel Eprom composite transistor 500 a having channel portions L1 and L2 formed in accordance with the one-sided spacer sequence outlined in
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Jonathan Osbourne
Jonathan Osbourne
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Jonathan is a published author and recently completed a book on physics and applied mathematics.
Capacitors store charge and energy. Parallel plate capacitors generally composed of two oppositely charged plates separated by a distance. The equation that we use to determine capacitance is capacitance = stored charge / potential difference. The capacitance of a parallel plate capacitor is proportional to the area of the plates and inversely proportional to the distance between the plates. The unit for capacitance is the Farad.
Alright now let's talk about a very, very important circuit element called a capacitor alright now we know batteries what are they meant to do? Well they got to impose a constant potential difference and drive current through a circuit. What's a resistors job? A resistors job is to use energy that's what a resistor does anything that uses energy can be thought of as a resistor. What's a wire's job? A wire's job is to get current from one side of the battery to another to go, to allow current to flow between circuit elements. So what's a capacitors job? A capacitor is meant to store charge and energy so just like a resistor uses power a capacitor stores energy. Alright, so the way that capacitors look they are 2 plates, they're not always actually like this but you can think of them like this. 2 plates separated by a distance and what we're going to do is we're going to put some charge on this plate.
Alright now the big question is how good of a capacitor is it? In other words what's its capacity? Well here's the idea the more charge that I store here, the more of a potential difference there'll be across the plates. Because if I were to take another charge let's say it was a positive charge it would rather be on the negative plate than on the positive plate because positive charges don't like other positive charges. So the more charge I store the bigger the potential difference will be. And what we're going to do is we're going to define the capacitance as the amount of charge that I'm able to store divided by the potential difference. So that means if I'm able to store a lot of charge without having a huge potential difference then I'll get a very, very nice large capacitance. If on the other hand even storing a little bit of charge requires a huge potential difference then I'll have a really small capacitance. So that's the definition of capacitance, we write it in terms of symbols c equals charge which is q divided by the potential difference and sometimes people will write delta v there but let's just leave it with a v for right now.
Alright, so what should the unit be, well just like everything in SI everything is in SI now we're going to call it a Farad but 1 Farad is equal to 1 Coulomb stored per volt of potential difference across. So that's the idea capacitance charge divided by potential difference. The more charge you got the bigger the potential difference imposed across the capacitor. Alright now let's think about this I want to think about this parallel plate capacitor and what its capacitance should be. Well here's the idea the reason that we have limits to the capacitance is because this charge is force to congregate next to itself and it doesn't like it. Positive charges like negative charges, they don't like other positive charges, but I can kind of make that okay if the area of this plate is really big. The bigger the area the more room that, that charge has to spread out and the less it cares that it's sitting next each other.
You can think of the potential difference kind of as how much the charge cares alright, so our capacitance ought to be proportional to the area of the plates of this parallel plate capacitor. Alright another Geometric property of this parallel plate capacitor is how far apart are the plates? So we've got area and then we've got distance apart. Now let's think about this the further the plates are apart the larger distance we're separating this charge over and the charge doesn't want to be separated. So if we put the 2 plates real close together, then they say you know what yeah we don't like being separated but it's almost as if we're not separated. So we can store more with a smaller potential difference, so that means that when the distance between the plates get smaller the capacitance gets bigger I can store more because they don't care as much they're not really separated by that much. So that means that the capacitance should be proportional to 1 over the distance between the plates. So we can write the capacitance of a parallel plate capacitor as a constant times the area divided by the distance between the plates.
This constant has a numerical value 8.854 times 10 to the minus 12 Farads per meter. Now how did I work that out? Well jeez if I take that constant multiply it by meters squared the area and then I divide by meters the distance then I got to get Farads so it's Farads per meter. Alright this is called the permittivity of free space and it plays a major role in more advanced discussions about capacitors and electric fields. Alright now from our definition of capacitance the potential difference across any capacitor is equal to the amount of charge that it's holding divided by the capacitance. Now the neat thing about the capacitance is that it's just a Geometrical property. It's like resistance, it doesn't change depending on what situation the capacitor is put in, charge will, potential difference will but the capacitance will remain the same.
Alright, so the potential difference is charge divided capacitance. Now we said that the purpose of the capacitor was to store energy as well as charge so how much energy is stored? Well I'm not going to derive this for you it takes a little bit of work to derive it but what we end up with is q squared over 2c so it's the square of the charge divide by twice the capacitance. Now we can use this delta v equals q over c to rewrite this into 2 different or 3 different ways overall one half c delta v squared and one half charge times potential difference. So these 3 formulas are all saying the same thing but depending on what information you have, you might use this one as opposed to that one. Alright if you know the capacitance and you know the charge alright let's do q squared over 2c. Alright so let's do an example, I've got a 3 Farad capacitor and it's got a potential difference of 4 volts maintained across it. And I want to know how much energy does it store, alright so what have they told me? Well I've got the capacitance and I've got the potential difference.
Alright capacitance, potential difference so I want to use this formula one half capacitance potential difference right, squared. Okay so 16 divided by 2 is 8 and 8 times 3 is 24 joules. Alright so that's just the way it goes energy is stored in a capacitor, potential difference across the capacitor and the meaning of capacitance. Just think about it as a Geometrical quantity that will be big when the charge can spread out and will be small when the chargers are all confined to one space and it's not allowed to be next to its friends the opposite charge. Alright that's capacitors.
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I am a retired nurse, who loves doing Genealogy and have lived in Minnesota most of my life. I have just moved to La Mesa , NM and have found that I need help researching my families in MN due to the distance, I would like to be able to help others who need assistance help with their family information here in Dona Ana County, New Mexico
However I will not go across the Mexico border to any of the cemeteries.
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Nela and Roberta
RE: Gossett
John and Anna are now linked - along with her second husband.
Added by
Nela and Roberta
on Jul 06, 2014 10:22 AM
Tracy Anne
RE: Fournier in Woodlawn Saskatoon
His gave in unmarked. I put that in the caption under the photo (click on the photo to see it.)
Added by
Tracy Anne
on Jun 29, 2014 9:19 AM
RE: Deer Creek
I thank you for the transfers...I am working to add my info and do the linking now. Jill
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on Feb 05, 2014 8:29 PM
Espen Carlsen
RE: Bosaaen
Hello again Jean! Hope you are well!
If you are refering to the Bosaaen graves, I have got all the photos and info i need. I came in contact with a local Karin Halverson who has done a fantastic job for me this summer with photos and checking archives.
The latest and only request I have here on "Findagrave" and not got any reply on yet, is of Edward Bratlien born 26Feb 1890, died 14Jun 1965 and his wife Anna/Annie born 26Feb 1890, died unknown. They are bueried at Bethel Lutheran Cemetery,Mountrail,North-Dakota. If anyone could take a photo of this grave it would be nice!
Greetings from Espen Carlsen in Oslo, Norway.
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Espen Carlsen
on Aug 27, 2013 11:27 PM
RE: Lerud
Yeah I went out to get Henry Christopherson KIA in WWII and the cemetery is so small a snapped every veteran photo.
I might just stop out and take photos of every grave sometime.
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on Jun 23, 2013 9:24 AM
Emma Schoenecker
You will see that I also added a Memorial Page for Emma's husband, William.
I hope you enjoy the pictures.
If there is any more I can do for you please do not hesitate to let me know.
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on May 24, 2013 8:58 AM
Andy Baker
RE: Flores
No relation to Mr. Flores. I'm searching for a Texas death certificate (in an as-yet-unindexed collection) in El Paso Co., Texas, in Feb. 1982, and have been inputting and/or submitting edit requests for each certificate as I go through them.
Thanks for your help with Robert's memorial, and for everything you do at Find-A-Grave!
Added by
Andy Baker
on Feb 17, 2013 4:44 PM
Ruth Scott
RE: Nancy Gilbert
There are no other Tuffs that I know of there but other than his civil war service record, I haven't researched this branch of the family (I misspelled the name in my previous message). I found many family photos on ancestry.com which I really loved seeing. If there are others I'd love to connect with them and one day I'll make the drive from Duluth to Deer Creek.
Added by
Ruth Scott
on Jan 05, 2013 8:04 PM
Ruth Scott
RE: Nancy Gilbert
I received the transfer...thank you. Her mother and father were homesteading in deer creek back in the late 1800's. They were James and Adelia Tufts. I believe they are also buried in this cemetery. When Nancy died in Scanlon, her husband, IRA Sylveness took her to Deer Creek to be buried.....he stayed in Scanlon and remarried a few years later. I can't thank you enough....I've always wanted to make the trekk to Deer Creek but have never found the time. This is doubly nice because my mother's maiden name was also Nancy Gilbert.
Added by
Ruth Scott
on Jan 05, 2013 7:45 PM
Ruth Scott
RE: Nancy Gilbert
Thank you, I would love to manage great grandma's grave....you are very generous. Yes, I was raised in Duluth m until we moved to Oregon in 1969 when I was 16. Still have "Gilbert" relatives in Duluth and I was back for a reunion last August. There's just something about Duluth that always draws me back. Nice corresponding with you. Happy graving.
Added by
Ruth Scott
on Jan 05, 2013 7:19 PM
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Originally written on Fox Sports | Last updated 12/19/12
Jacksonville Jaguars running back Maurice Jones-Drew is making progress toward getting back on the field and getting his college degree. Jones-Drew started running for the first time in nearly two months Wednesday, but remains a long shot to play Sunday when the Jaguars (2-12) host New England (10-4). Jones-Drew has missed the last eight games because of a sprained left foot. Coach Mike Mularkey called his star running back ''questionable,'' an upgrade from his ''highly questionable'' status of recent weeks. ''I just don't want to go out there and put anybody else in jeopardy if I can't be full speed,'' Jones-Drew said. ''If I can't go out there and fully protect our quarterback, help our offensive line and block, I'm not going to go out there and put somebody else's life in jeopardy.'' With two games remaining, the Jaguars have little left to play for in what will go down as the worst season in franchise history. And Jones-Drew has nothing to prove. He led the NFL in rushing l...
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Originally written on The Majors Detroit | Last updated 8/18/12
DETROIT - SEPTEMBER 02: Matthew Stafford of the Detroit Lions talks with offensive coordinator Scott Linehan during the preseason game against the Buffalo Bills at Ford Field on September 2, 2010 in Detroit, Michigan. The Lions defeated the Bills 28-23. (Photo by Leon Halip/Getty Images)
The Lions first team looked much better this week in a 27-12 preseason win over the Ravens Friday night from Baltimore. Matthew Stafford looked very much like the dominant QB he was last season going 12 for 17 for 184 yards and two touchdowns. This included an impressive 18 yard connection with Calvin Johnson for the score. Less than five minutes later Stafford continued to look sharp through the air this time hooking up with Titus Young for a 24 yard touchdown. However Detroit got themselves into penalty trouble early looking very much like the undisciplined team they were last season. As a whole the Lions combined for 11 penalties for 98 yards, a number they'll definitely have to remedy before the start of the regular season. Unlike last season though Detroit's defense was able to somewhat recover from their sloppy play holding the Ravens to a field goal or forcing them to punt the ball away. Lions backups Shaun Hill was 7 of 13 for 61 yards while Kellen Moore who's looking to ear...
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With 220 watts of power, the Cuisinart ®5-Speed Hand Mixer handles everything from whipped cream to a double batch of cookie dough! And there's no need for a power boost button because it has a feedback system that automatically feeds extra power when needed. Extra-long beaters have no center posts, making cleanup a snap. The exclusive swivel cord allows left- or right-handed use. Includes a plastic spatula. Beaters and spatula are dishwasher safe. 8" l x 3 1/2" w x 5 1/2" h.
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Diageo PLC.
News about Diageo PLC., including commentary and archival articles published in The New York Times.
Big Companies Pay Later, Squeezing Their Suppliers
To help their cash flows, food and packaged goods companies are delaying payments to suppliers, a practice that at one time signaled trouble.
April 7, 2015, Tuesday
Jay Z Acquires Luxury Champagne Brand Armand de Brignac
A gold bottle of the Champagne, nicknamed "Ace of Spades," appeared in a music video in 2006. A spokeswoman for Sovereign Brands said Jay Z "made us an offer we simply couldn't refuse."
November 5, 2014, Wednesday
Diageo Is Said to Be in Talks on Exchange of Brands With Jose Cuervo
Under the proposed terms, Diageo would acquire control of the Don Julio tequila brand and Cuervo would gain Bushmills brand of Irish whiskey.
November 1, 2014, Saturday
United Spirits to Sell Whyte & Mackay Whiskey
India's largest distiller will sell its Whyte & MacKay whiskey business to Emperador of the Philippines in a deal that values the business at 430 million pounds, or about $726.5 million.
May 9, 2014, Friday
Diageo Makes New Bid for Controlling Stake in United Spirits of India
Diageo, the world's largest distiller, offered to pay about $1.9 billion for an additional 26 percent stake in United Spirits of India, after an unsuccessful bid to take a controlling stake last year.
April 15, 2014, Tuesday
Emerging, but No Longer a Mother Lode of Profits
Multinational corporations that crowed for years about their presence in booming emerging markets are now blaming turmoil in those regions for dents in their bottom lines.
March 5, 2014, Wednesday
Diageo Reports Slower Growth
The world's biggest distiller joined other consumer brands in saying that slower growth in developing economies last year hurt its business.
January 31, 2014, Friday
After Beam Deal, Few Big Liquor Mergers Left
Most of the big global liquor brands have been absorbed by Diageo, Pernod, Suntory or Brown-Forman, leaving little room for further consolidation.
January 13, 2014, Monday
A Bold Move by Suntory
The strategic imperative for the Japanese corporation is clear, as it is for just about any consumer goods company in the incredibly shrinking Japan, notes Rob Cox of Reuters Breakingviews.
January 13, 2014, Monday
Day Devoted to Hoisting Guinness Starts to Leave a Bitter Taste
Critics say Arthur's Day, which began in 2009 to mark the 250th anniversary of Guinness, is nothing but an excuse for binge drinking.
September 26, 2013, Thursday
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Northeast Iowa Community College Business and Community Solutions offers affordable courses designed to provide quality training for individuals wanting to upgrade job skills, explore new careers, start a new hobby or develop new personal or professional skills. In addition, programs are also provided for those needing basic instruction in math, reading, writing and much more.
These programs are offered locally, year-round, at the NICC campuses and centers. Prospective students can search, register and pay for their courses online
Courses and programs offered through NICC Business and Community Solutions include:
Those interested in earning a degree at NICC should review the College's credit programs.


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The Association of Directors of Adult Social Services (ADASS) represents directors of adult social services in local authorities in England and Northern Ireland. As well as having statutory responsibilities for the commissioning and provision of social care, ADASS members often also share a number of responsibilities for the commissioning and provision of housing, leisure, library, culture, arts and community services within their councils.
ADASS members are jointly responsible, through the activities of their departments, for the well-being, protection and care of their local communities, and for the promotion of that wellbeing and protection through the use of direct services as well as the co-ordination of, and liaison with, the NHS, voluntary agencies, private companies and other public authorities.
Lead sponsor
PricewaterhouseCoopers' government & Public Sector practice has been helping Government and public sector organisations locally, regionally, nationally and internationally for many years. We work with organisations across sectors as diverse as health, education, transport, home affairs, criminal justice, local government, housing, social welfare, defence and international development.
Our people combine deep specialist expertise with a genuine understanding of the public sector. The Public Sector Research Centre is PricewaterhouseCoopers' online community for insight and research into the most pressing issues and challenges facing government and public sector organisations, today and in the future. To register for this free resource please visit www.psrc-pwc.com
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The Social Care Institute for Excellence (SCIE) supports the transformation of social care by identifying and transferring knowledge about good practice. We provide practical guides, learning materials and information based on sound knowledge about what works in planning and delivering social care. We also ensure that the experiences and expertise of people who use services, their carers and workers are reflected in all aspects of our work.
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7 posts tagged with Veteran and military.
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"As the hymn says, you can lay your burden down."
The Things They Leave Behind. "When the Vietnam Veterans Memorial opened 30 years ago, something unexpected happened: People started leaving things at the wall. One veteran has spent decades cataloging the letters, mementos, and other artifacts of loss — all 400,000 of them." (Via.) [more inside]
"Look At Me Now"
American paratrooper Arthur Boorman suffered debilitating injuries during the first Gulf War. Doctors told him he'd never walk unassisted again. 15 years later.... [more inside]
Go to War. Do Art. (II)
The permanent collection of the (US) National Veterans Art Museum in Chicago contains more than 2,500 pieces of art by 250 artists, all of which can be seen at NVAM Collection Online. The site includes biographical material on the artists who created the work. Featured Artwork. A small selection. (Via. Images at links in this post may be nsfw, and/or disturbing to some viewers.)
"As long as you're breathing, life is worth living."
Six years ago, US Army Captain Ivan Castro was severely wounded in a mortar attack in Iraq that left him permanently and completely blinded. Today, he's one of only three blind active duty Army officers, and the very first to serve in the US Army Special Forces. Thirteen months and 36 surgeries after the attack, Castro ran the 2007 Marine Corps Marathon in 4:14 and the Army Ten Miler in 1:25. And he's still going: In the last 15 months, he's completed 14 marathons. Why? "Because I still can. Because people need to see what's possible." [more inside]
That smile will come, sooner or later. But I promise you, it will come.
For Memorial Day weekend, at TAPS (Tragedy Assistance Program for Survivors), Vice President Joe Biden talks about grief, and loss, and how "there will come a day, I promise you, and you parents, as well, when the thought of your son or daughter or your husband or wife brings a smile to your lips before it brings a tear to your eye."
"A cobra among garter snakes"
He was... "...the meanest, toughest, most ambitious S.O.B. I ever knew but he'll be a hell of a secretary of state." -- Richard NixonAlexander Meigs Haig, Jr.,, former NATO Supreme Allied Commander, Europe, who served US Presidents Nixon (as a military adviser, deputy assistant for national-security affairs, and chief of staff), Ford (chief of staff), and Reagan (secretary of state), has died at the age of 85. Haig commanded a batallion during the Vietnam War (where he was seriously wounded), managed the White House during the Watergate scandal that brought down President Nixon, and was himself a former Presidential candidate. [more inside]
Honor Guard
A military honor guardsman has been fired for saying God bless you, while he presented a folded American flag to the family of a deceased veteran, during the burial service. By way of obscurestore.
Page: 1


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Latest News
Late For Work Permission Slip
Frustrated with all the road construction in La Crosse? Is your boss angry because the congestion is making you late for work? Then print off this handy permission slip and hand it your boss, compliments of WIZM!
LaCrosse Talk
Information about and from LaCrosse Talk
Mark Meier's (Marc Meiner's) "Lifepod"
WI's Do Not Call List or call (866) 966-2255
MN's Do Not Call List or call (800) 921-4110
Federal Do Not Call List or call (888) 382-1222
Billings Named To Special Training Program
La Crosse state lawmaker, Jill Billings, has been chosen as an up-and-coming
leader by her peers to participate in a training program designed to
further develop leadership skills, and
analyze a variety of public policy issues, including the economy, economic development and corrections. Billings says not a lot of people are selected for the training.
Since 1995 more than 575 lawmakers have graduated from the Bowhay Institute, including Senator Jennifer Shilling, who attended in 2001.
Weak Job Growth Leads to Call for Special Legislative Session
Wisconsin certainly did have job growth last year. It was just pretty anemic. That's the evaluation of the feds this week in revised job totals. Real numbers on job growth show the state adding 20 thousand jobs last year. One of the worst rates in the nation. High time for governor Walker to call a special jobs session for the legislature, says Onalaska state rep, Steve Doyle.
Initial estimates had pegged Wisconsin with thirty thousand jobs losses until the feds revised those estimates sharply upward.
Lax Sheriff Satisfied With Koula Guilty Verdict
Throughout the Eric Koula murder trial in La Crosse, the defense argued that unknown professional killers might have shot Eric's parents two years ago.
Defense witnesses talked about suspicious people watching the neighborhood where Dennis and Merna Koula lived. Now that Eric Koula has been convicted of murdering his parents, La Crosse County Sheriff Steve Helgeson believes that the neighborhood may be a little more at ease. The sheriff realizes that those neighbors were quite worried in the weeks following the double murder.
Eric Koula was arrested eight weeks after the shootings, and was convicted in court this week. Helgeson describes the investigation leading to the arrest as 'remarkably quick.'
Lax Still Aiming To Put Pay Stations In Ramps This Year
You could start paying for some parking spaces in La Crosse's downtown ramps before the end of the year.
The city's Parking Utility Board is still studying gate systems, that would require drivers to pay 50 cents an hour to park in reserved sections of the ramps. Bob Haines with the city Public Works department is looking at how other cities the size of La Crosse charge for parking in ramps:
Haines says his department is now working on connecting all the ramps to City Hall through fiber optic cable...to provide security video, and to remotely operate those traffic gates.


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|ISSN 1088-6850(online) ISSN 0002-9947(print)
Another way to say harmonic
Abstract | References | Similar Articles | Additional Information
Abstract: It is known that solutions of , that is, the -harmonic functions, are exactly those functions having a comparison property with respect to the family of translates of the radial solutions . We establish a more difficult linear result: a function in is harmonic if it has the comparison property with respect to sums of translates of the radial harmonic functions for and for . An attempt to generalize these results for () and () to the general -Laplacian leads to the fascinating discovery that certain sums of translates of radial -superharmonic functions are again -superharmonic. Mystery remains: the class of -superharmonic functions so constructed for does not suffice to characterize -subharmonic functions.
Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35J70, 35J05, 35B50
Retrieve articles in all journals with MSC (2000): 35J70, 35J05, 35B50
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Garage RULZ
View Single Post
Ricardo Kuhn
a.k.a. Mr Rico Suave
Joined: Sep 2001
Location: Salt lake city, Utah
Oddometer: 12,501
Originally Posted by
I was discussing debate, not the science behind engineering and design, furthermore, I would have never guessed you had a degree after looking at your spelling errors. Now get out and turn a wrench and put an immediate end to that gas leak
While I debate about your 9 year degree
Do you Know what Dixlexia is...!?!?
, I'm being hunt by this since i was born, but I manage to delelope collateral ways to increase other sense, like a blind will be better at hearing, so lets not even go there.
Can you draw like this...!?!?
can you think about thing like this..!?!?
when you do,, when we can talk, if not I forgive you since is not your fault you can only write , like is not my fault I can only draw.
besides go and read
Nikola Tesla
René Descartes
Biografy and you will learn how they were varelly able to communicate with the comun man but with out them this world will be much less evolve.
Or take for example the many developers of the
Steam engine
over the centuries most of them THINKERs , but not exactlly shopworkers
i can produce at least 20 other names of Brilliant man of sciences and thinkers, that were totally unable to life a normal life, many times because they were a
Little to head
of their time.
Wanted: worn, ugly, cheap motorcycle cover for a big GS 1200
Ricardo Kuhn
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Capitals down Phillies
Brooks Laich scored a pair of goals and added an assist Sunday, as the Washington Capitals defeated the Philadelphia Phillies 5-3.
The Capitals were a -170 favorite in the game and the eight goals scored fell UNDER the posted over/under total (6).
Alexander Semin and Alexander Ovechkin each had a goal and an assist for Washington and Jose Theodore made 30 saves in the win.
Jeff Carter, James van Riemsdyk and Danny Briere scored for the Flyers.