Solid-State Electronic Devices: Integrated Circuits [part 4]

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5. Ultra large-scale Integration (ULSI)

In the early development of integrated circuits it was felt that the inevitable defects that occur in processing would prevent the fabrication of devices containing more than a few dozen logic gates. One approach to integration on a larger scale tried in the late 1960s involved fabricating many identical logic gates on a wafer, testing them, and interconnecting the good ones (a process called discretionary wiring). While this approach was being developed, how ever, radical improvements were made in device processing which increased the yield of good chips on a wafer dramatically. By the early 1970s it was possible to build circuits with many hundreds of components per chip, with reasonable yield. These improvements made discretionary wiring obsolete almost as soon as it was developed. By reducing the number of processing defects, improving the packing density of components, and increasing the wafer size, it is now possible to place millions of device elements on a single chip of silicon and to obtain many perfect chips per wafer.

A major factor in the development of integrated circuits has been the continual reduction in size of the individual elements (transistors, capacitors) within each circuit. Through improved design and better lithography, there has been a dramatic shrinking of the minimum feature size (e.g., a transistor gate) used in these devices. The results of shrinking the elements in a 256-Mb-DRAM are shown in FIG. 20. By reducing the minimum feature size in successive steps from 0.13 to 0.11 um, the die area was reduced from about 135 mm2 in the first-generation design to less than 42 mm2 in the fifth-generation device.

Obviously, more of the smaller chips can be made by batch fabrication on the wafer, and the effort in shrinking the design is rewarded in a more profitable device.

Successive designs using reduced feature sizes have made dramatically increased circuit complexity possible. DRAM design has set the pace over the past two decades, in which successive 1 -Mb, 4-Mb, and 16-Mb memories led to similar powers of two increase to the Gb range. FIG. 21 illustrates the size comparison of a 128-Mb memory with an equivalent amount of memory in the form of two 64-Mb and eight 16-Mb chips. These are examples of ULSI.

Although the achievement of many powers of two in memory is impressive and important, other ULSI chips are important for the integration of many different system functions. A microprocessor includes functions for a computer central processing unit (CPU), along with memory, control, timing, and interface circuits required to perform very complex computing functions. The complexity of such devices is shown in FIG. 22, which illustrates a microprocessor chip.

Before leaving this section it might be useful to provide some calibration regarding the dimensions we have been discussing. FIG. 23 com pares the size of 64-Mb DRAM circuit interconnect elements with a human hair, on the same scale. We can see that the densely packed 0.18 mm lines on this ULSI memory chip are dwarfed by the scanning electron micrograph of a human hair which has the diameter of about 50 microns. Current generation DRAMs have feature sizes of ~25 nm (0.025 mm).

Although the focus of this guide is devices and not circuits, it is important to look at some typical applications of MOS capacitors and FETs in semiconductor logic and memory ULSI, which constitute about 90, of all ICs. This should give the reader a better feel for why we have studied the physics of MOS devices in Section 6. This is clearly not a comprehensive discussion, because the design and analysis of circuits is a large subject covered in other books and courses. We will first look at some digital logic applications, followed by some typical memory devices.

FIG. 22 An example of ULSI, the Intel 22nm quad core processor with 1.4 billion transistors. (Photograph courtesy of Intel.)

FIG. 23 Size comparison of ULSI circuit elements with human hair: (a) densely packed 0.18-mm interconnect lines in the array of a 64-Mb DRAM chip; (b) scanning electron micrograph of a human hair. Both micrographs are shown to the same scale. (© 2004 Micron Technology, Inc. All rights reserved. )

FIG. 24 Resistor load inverter voltage transfer characteristics (VTC): (a) NMOSFET with load resistor RL and load parasitic capacitance C; (b) determination of VTC by superimposing the load line (linear I-V ohmic characteristics of the resistor) on NMOSFET output characteristics; (c) VTC showing output voltage as a function of input voltage. The five key points on the VTC are logic high (VOH), logic low (VOL), unity gain points (VIL and VIH), and logic threshold where input equals output (Vm).

5.1 Logic devices

A very simple and basic circuit element is the inverter, which serves to flip the logic state. When its input voltage is high (corresponding to logic "1"), its output voltage is low (logic "0"), and vice versa. Let us start the analysis with a resistor-loaded n-channel MOSFET inverter to illustrate the principles in the simplest possible manner (FIG. 24a). Then, we will extend the treatment to the slightly more complicated CMOS inverters which are much more useful and more common today.

A key concept for inverters is the voltage transfer characteristic (VTC), which is a plot of the output voltage as a function of the input bias (FIG. 24c). The VTC gives us information, for example, about how much noise the digital circuit can handle, and the speed of switching of the logic gates. There are five key operating points (marked I through V) on the VTC. They include VOH, corresponding to the logic high or "1", VOL, corresponding to the logic low or "0", and Vm, corresponding to the intersection of a line with unity slope (where Vout = Vin) with the VTC. Vm, known as the logic threshold (not to be confused with the VT of the MOSFETs), is important when two inverters are cross-coupled in a flip-flop circuit because the output of one is fed to the input of the other, and vice versa. Two other key points are the unity gain points, VIL and VIH. The significance of these points is that if the input voltage is between them, the change of the input is amplified and we get a larger change of the output voltage. Outside of this operating range, the change of the input voltage is attenuated. Clearly, any noise voltage which puts the input voltage between VIL and VIH would be amplified, and lead to a potential problem with the circuit operation.

Let us see how to go about determining the VTC. From the circuit in FIG. 24a, we see that in the output loop from the power supply to ground, the current through the resistor load is the same as the drain cur rent of the MOSFET. The power supply voltage is equal to the voltage drop across the resistor plus the drain-to-source voltage. To determine the VTC, we superimpose the load line of the load element (in this case a straight line for an ohmic resistor) on the output characteristics of the MOSFET (FIG. 24b). This is similar to our load line discussion. The load line goes through VDD on the voltage axis because when the current in the output loop is zero, there is no voltage drop across the resistor and all the voltage appears across the MOSFET. On the current axis, the load line goes through VDD/RL because when the voltage across the MOSFET is zero, the voltage across the resistor must be VDD. As we change the input bias, Vin, we change the gate bias on the MOSFET, and thus in FIG. 24b, we go from one constant VG curve to the next. At each input bias (and a corresponding constant VG curve) the intersection of the load line with that curve tells us what the drain bias VD is, which is the same as the output voltage. This is because at the point of intersection, we satisfy the condition that for the d-c case where the capacitor does not play any role, the current through the resistor is the same as the MOSFET current. (Later on, we shall see that in the a-c case when the logic gates are switched, we need to worry about the displacement current through the capacitor when it is charged or discharged.) It can be clearly seen from FIG. 24c that as the input voltage (or VG) changes from low to high, the output voltage decreases from a high of VDD to a low of VOL. We can solve for any point on this VTC curve analytically simply by recognizing whether the MOSFET is in the linear region or in saturation, using the corresponding drain current expression [Eq. ( 6-49) or ( 6-53)] and setting it equal to the resistor current. As an illustration, suppose we want to determine the logic "0" level, VOL. This occurs when the input VG is high and the output VD is low, putting the transistor in the linear region. Using Eq. ( 6-49), we can write

(eqn. 3a)

Since in the d-c case the current through the MOSFET is the same as that through the resistor,

(eqn. 3b)

We can solve for VOL if we know RL and the MOSFET parameters. Alternatively, we can design the value of RL to achieve a certain VOL. What might dictate the choice of RL? We shall see later in this section that for many applications we use two of these inverters in a cross-coupled manner to form a bistable flip-flop. The output of one inverter is fed back to the input of the other, and vice versa. Clearly, the VOL must be designed to be significantly less than the VT of the MOSFET. Otherwise, neither MOSFET will be fully turned off, and the flip-flop will not function properly. Similarly, all the other points on the VTC can be determined analytically by using the appropriate MOSFET drain current expression, and setting it equal to the current through the resistor.

We can make some general observations from this analysis. We want the transition region of the VTC (between VIL and VIH) to be as steep (i.e., high gain) as possible, and the transition should be around VDD/2. High gain guarantees a high-speed transition from one logic state to the other. It is necessary to increase the load resistance to increase this gain in the transition region.

The transition around VDD/2 guarantees high noise immunity or mar gin for both logic "1" and logic "0" levels. To appreciate the importance of noise immunity, we must recognize that in combinatorial or sequential digital circuits, the output of one inverter or logic gate is often fed into the input of the next stage. Noise immunity is a measure of how much noise voltage the circuit can tolerate at the input, and still have the digital outputs be at the correct logic level in the subsequent stages. For example in FIG. 24c, if the input is nominally at zero, the output should be high (logic "1"). If this is fed into another inverter stage, its output should be low, and so on. If a noise spike causes the input of the first stage to go above Vm, the output volt age decreases sufficiently to potentially create errors in the digital levels in subsequent stages. Having a symmetric transition of the VTC around VDD/2 ensures that the noise margin is high for both logic levels.

One problem with the resistor load inverter is that the VOL is low, but not zero. This, coupled with the fact that the load element is a passive resistor that cannot be turned off, causes high standby power dissipation in this circuit. These problems are addressed by the CMOS structure described next.

We can determine the VTC for the CMOS case exactly as for the resistor load, although the math is somewhat more messy (FIG. 25). As mentioned previously, for an input voltage Vin, the VG of the NMOSFET is Vin, but that of the PMOSFET is Vin -VDD. Similarly, if the output voltage is Vout, the VD of the NMOSFET is Vout, but that of the PMOS is Vout -VDD. The load element now is not a simple resistor with a linear current-voltage relationship, but instead is the PMOSFET device whose "load line" is a set of ID -VD output characteristics (FIG. 25b). The Vout can be determined as a function of the Vin by recognizing whether the NMOSFET and the PMOSFET are in the linear or saturation region of their characteristics, and using the appropriate current expressions. At each point, we would set the NMOSFET ID equal to the PMOSFET ID.

FIG. 25 CMOS inverter voltage transfer characteristics: (a) NMOSFET with PMOSFET load and load parasitic capacitance, C; (b) determination of VTC by superimposing load line (output characteristics of PMOSFET shown as dotted line) on NMOSFET output characteristics; (c) VTC showing output voltage as a function of input voltage. The five key points on the VTC are logic high (VOH), logic low (VOL), unity gain points (VIL and VIH), and logic threshold where input equals output (Vm); (d) switching current from VDD to ground when the input voltage is in a range where both the NMOSFET and the PMOSFET are on.

As in the case of the resistive load, there are five key points on the VTC (FIG. 25c). They are logic "1" equal to VDD, logic "0" equal to 0, logic threshold Vm where Vin = Vout, and the two unity gain points, VIH and VIL. In region I in FIG. 25c, the NMOSFET is OFF, and Vout = VDD. Similarly, in region V, the PMOSFET is OFF, and Vout = 0. We can illustrate the calculation in region II, where the NMOSFET is in saturation and the PMOSFET is in the linear region. In this case, we must use Eq. ( 6-53) for the saturation drain current of the NMOSFET. We are considering the long channel case.

(eqn. 4a)

On the other hand, we must use Eq. ( 6-49) for the PMOSFET in the linear region.

(eqn. 4b)

Here VTN and VTP are the n-and p-channel threshold voltages. In the d-c case, since the output load capacitor does not play a role, the drain current through the PMOSFET device must be equal in magnitude to that through the NMOSFET. (However, for the a-c case, we need to consider the displace ment current through the capacitor.)

IDN = IDP (eqn. 5a)

Using Eq. ( 6-53) for the NMOSFET in saturation, and Eq. ( 6-49) for the PMOSFET in the linear region.

(eqn. 5b)

From Eq. (eqn. 5b), we can get an analytical relation between the input and output voltages valid in region II. We can get similar relationships in the other regions of the VTC.

Region IV is very similar to region II in FIG. 25c, except that now the NMOS is in the linear regime, while the PMOSFET is in saturation. In region III, both the NMOSFET and the PMOSFET are in saturation. Since the output impedance of a MOSFET is very high, this is tantamount to a semi-infinite load resistor, thereby resulting in a very steep transition region. That is why a CMOS inverter switches faster than the resistor load case. The CMOS inverter is also preferable because in either logic state (regions I or V), either the NMOSFET or the PMOSFET is OFF, and the standby power dissipation is very low. In fact, the current in either logic state corresponds to the (very low) source/drain diode leakage.

We want the transition region (region III) to be at VDD/2 from the point of view of symmetry and noise immunity. Once again, by setting the NMOSFET ID equal to that of the PMOSFET, it can be shown that the transition occurs at

(eqn. 6a) where

(eqn. 6b)

We can design Vin to be at VDD/2 by choosing VTN = -VTP and x = 1. Since the effective electron mobility in the channel of a Si MOSFET is roughly twice that of the hole mobility, we must design CMOS circuits to have a (Z/L)P = 2(Z/L)N to achieve the condition x = 1.

We can combine such CMOS inverters to form other logic gates for combinatorial circuits such as NOR gates and NAND gates (FIG. 26). The truth tables for these gates are shown in FIG. 27 . By applying combinations of logic "high" or logic "low" to inputs A and B, we get the output states cor responding to the truth tables. The synthesis of logic circuits corresponding to these truth tables can be done using Boolean algebra and De Morgan's laws. The upshot of these laws is that any logic circuit can be made using inverters in conjunction with either NAND gates or NOR gates. Which would be preferable from a device physics point of view? We see from FIG. 26, that in the NOR gate the PMOSFET devices T3 and T4 are in series, while for the NAND it is the NMOSFETs (T1 and T2). Since the electron channel mobilities are twice hole mobilities, we would obviously prefer NMOSFETs. Therefore, the preferred choice is NAND, along with inverters.

FIG. 26 Logic gates and CMOS implementation of (a) NOR gate (b) NAND gate.

We can also estimate the power dissipation in the inverter circuit. We already know that the standby power dissipation is very small, being governed by the OFF state leakage current of either the NMOSFET or the PMOSFET, depending on the logic state. This leakage current depends on the source and drain diode leakage currents, or if the VT is low, on the sub-threshold leakage of the MOSFET that is turned OFF.

While the inverter is switching, there is also a transient current from the power supply to ground when both the transistors are ON (see FIG. 25d). This is known as the switching current or the commutator current. The magnitude of this current will clearly depend on the values of VTN and VTP. The higher the magnitudes of the thresholds, the less is the input voltage swing for which both the PMOSFET and the NMOSFET will be ON while the input voltage is being changed. The commutator current is then less during switching, which is desirable from a reduced power dissipation point of view. However, this reduction of power dissipation by increasing threshold voltages is obtained at the expense of reduced drive current and, therefore, overall speed of the circuit.

FIG. 27 (a) AND/NAND logic symbols and truth table; (b) OR/NOR logic symbols and truth table; (c) XOR logic symbol and truth table.

The speed penalty due to reduction of drive current is because in a digital circuit, while switching between logic states, the MOSFET drive currents must charge and discharge the parasitic capacitors that are inevitably associated with the output node (FIG. 25a). There is also some power dissipation involved in charging and discharging load capacitors attached to the output of the inverter. This load capacitance depends mostly on the input gate oxide capacitance of the MOSFETs of the next inverter stage (or logic gate) that this inverter (or logic gate) may be driving, along with some small parasitic capacitances. The input load capacitance of a single inverter is given by gate oxide capacitance per unit area Ci times the device areas.

(eqn. 7)

The total load capacitance is then multiplied by a factor that depends on the fan-out of the circuit, which is the number of gates that are being driven in parallel by the inverter (or logic gate). It is necessary to add up the load capacitances for all the inverters or logic gates that are being driven by this inverter stage. The energy expended in charging up the equivalent load capacitor, C, is the integral of the product of the time-dependent voltage times the time-dependent displacement current through the capacitor during the charging cycle.

(eqn. 8a)

The energy stored in C is then obtained by considering the displacement current (ip(t) = C dv/dt) through the capacitor:

(eqn. 8b)

Similarly, during one discharging cycle we get

(eqn. 9)

If the inverter (or gate) is being charged and discharged at a frequency f, we get an active power dissipation

(eqn. 10)

In addition to power dissipation, we are also concerned with the speed of logic circuits. The speed of a gate, such as the one shown in FIG. 25, is determined by the propagation delay time tP. We define the time required for the output to go from the logic high VOH to VOH/2 as tPHL. The converse (to go from logic low VOL(= 0) to VOH/2) is defined as tPLH. We can write down approximate estimates for these times by recognizing that for the output to go from high to low (or logic "1" to "0"), the NMOSFET has to discharge the output node toward ground. During this period, the NMOSFET will be in saturation. Assuming a constant saturation current as an approximation, we obtain

(eqn. 11a)

This is the decrease of charge on the capacitor divided by the discharging current. Conversely,

(eqn. 11b)

Knowing these times helps us considerably in designing circuits that meet the speed requirements of a design. Of course, for accurate numerical estimates of these propagation time delays or of the power dissipation we need to use computers. A very popular program to do so is the Simulation Program with Integrated Circuit Emphasis (SPICE). This discussion illustrates that the device physics plays an important role in the design and analysis of such circuits.

5.2 Semiconductor Memories

In addition to logic devices such as microprocessors, integrated circuits depend on semiconductor memories. We can illustrate many key MOS device physics issues by looking at three of the most important types of semiconductor memory cells: the static random-access memory (SRAM), the dynamic random-access memory (DRAM), and the non-volatile flash memory cell. SRAMs and DRAMs are volatile in the sense that the information is lost if the power supply is removed. For flash memories, however, information is stored indefinitely. For SRAMs, the information is static, meaning that as long as the power supply is on, the information is retained. On the other hand, the information stored in the cells of a DRAM must periodically be refreshed because stored charge representing one of the logic states leaks away rapidly. The refresh time must be short compared with the time needed for stored charge to degrade.

FIG. 28 Organization of a random access memory (RAM): The memory array consists of memory cells arranged in an orthogonal array. There is one memory cell at the intersection of one row (wordline) and one column (bitline). To address a particular memory cell, the N row addresses are latched in from the N address pins, and decoded by the 2N row decoders. All the memory cells on the selected row are read by the 2N sense amplifiers. Of those, a cell (one bit) or group of cells (byte or word) is selected for transfer to the data output buffers depending on the column addresses that are decoded by the 2N column decoders. Generally, to save pin count on the package, the N column addresses are provided in a multiplexed fashion to the same N address pins as the row addresses, after the row addresses have already been latched in.

The overall organization of all these types of memories is rather similar, and is shown in FIG. 28. We will not describe the memory organization in great detail here, but will instead focus on the device physics. We need to know the type of cell that is used at the intersection of the rows or word lines, and the columns or bitlines. These memories are all random access in the sense that the cells can be addressed for write or read operations in any order, depending on the row and column addresses provided to the address pins, unlike memories such as hard disks or floppy disks on a computer which can only be addressed sequentially. Generally, the same set of pins is used for both the row and the column addresses, in order to save pin count. This forces us to use what is known as address multiplexing. First, the row addresses are provided at the address pin, and decoded using row decoders. For N row addresses, we can have 2N rows or wordlines. The row decoders then cause the selected wordline to go high, so that all the 2N cells (corresponding to N column addresses) on this wordline are accessed for either read or write, through sense amplifiers at the end of the 2N columns or bitlines. After the appropriate row has been decoded, the appropriate column addresses are provided to the same address pins, and the column decoders are used to select the bit or group of bits (known as byte or word) out of all the 2N bits on the selected wordline. We can either write into or read from the selected bit (or group of bits) using the sense amplifiers, which are basically flip-flops or differential amplifiers.

FIG. 29 An array of 4 CMOS SRAM cells. The bitline and bitline ( bitline-bar) are logical complements of each other.

SRAMs. A group of four 6-transistor CMOS SRAM cells is shown in FIG. 29. Each cell is found in this case at the intersection of a row or wordline, and a column or bitline (along with its logical complement known as bitline-bar). The cell is a flip-flop, consisting of two cross-coupled CMOS inverters. Clearly, it is bistable: if the output of one inverter is high (corresponding to the NMOSFET being OFF, and the PMOSFET ON), that high voltage is fed to the input of the other cross-coupled inverter, and the output of the other inverter will be low. This is one logic state (say "1") of the SRAM. Conversely, the other stable state of the flip-flop can be considered to be the other logic state (say "0"). Many of the device issues are identical to those described earlier in connection with the VTC of inverters. We aim for a symmetric transition from VOH to VOL at VDD/2 with a high gain in the transition region, to improve noise immunity and speed of convergence of the SRAM cell. The speed of convergence determines how fast the SRAM flip-flop latches into one stable logic state or the other. The cells are accessed through two access transistors whose gates are controlled by the wordline. That is why this is called a 6-transistor cell. Other SRAM cells use load resistors in the inverters, rather than PMOSFETs, leading to a 4-transistor, 2-resistor cell. As discussed, the CMOS cell has superior performance, but at the expense of occupying more area.

Unless the row decoders cause a particular wordline to go high, the SRAM cells on that wordline are electrically isolated. By selecting a particular wordline, the access transistors on that row are turned ON and act as logic transmission gates between the output nodes of the SRAM cell and the bitline and its complement, the bitline-bar. During a read operation, the bitline and its complement are both precharged to the same voltage. Once the access transistors are turned ON, a small voltage differential develops between bitline and bitline-bar because the output nodes of the SRAM are at different voltages (0 and VDD). The voltage differential that is established is due to a charge redistribution that occurs between the parasitic capacitance associated with the output nodes of the SRAM and the bitline capacitance. This voltage difference is amplified by the sense amplifiers. As mentioned previously, the sense amplifiers are differential amplifiers, very similar in configuration to the SRAM flip-flop cell itself. The bitline and bitline-bar (complement of the bitline) are fed to the two inputs of the sense amplifier, and the voltage differential is amplified until the voltage separation is VDD.

FIG. 30 One transistor, one capacitor DRAM cell equivalent circuit: the storage MOS capacitor is connected to the bitline through the pass transistor (MOSFET switch) whose gate is controlled by the wordline.

DRAMs. The DRAM cell structure is shown in FIG. 30. The information is stored as charge on an MOS capacitor, which is connected to the bitline through a switch which is an MOS pass transistor, the gate of which is controlled by the wordline. There is one such cell at each intersection of the orthogonal array of wordlines and bitlines, exactly as for SRAMs. When the wordline voltage becomes higher than the VT of the pass transistor (MOSFET between the bitline and the storage capacitor), the channel is turned ON, and connects the bitline to the MOS storage capacitor. The gate of this capacitor (or capacitor plate) is permanently connected to the power supply voltage VDD, thereby creating a potential well under it which tends to be full of inversion electrons for a p-type substrate (FIG. 31a). We apply either 0 V to the bitline (generally corresponding to logic "0"), or VDD (corresponding to logic "1"), and the appropriate voltage appears as the substrate potential of the MOS capacitor. For a stored "0" in the cell, the potential well that is created under the MOS capacitor by the plate voltage is full of inversion charge (FIG. 31b,c). When the wordline voltage is turned low such that the MOS pass transistor is turned off, the inversion charge under the storage capacitor stays the same; this is the stable state of the capacitor. On the other hand, if a positive voltage (VDD) is applied to the bitline, it draws out the inversion electrons through the pass transistor (FIG. 31d,e). When the pass transistor is cut off, we end up with an empty potential well under the MOS capacitor plate. Over a period of time, the potential well tends to be filled up by minority carrier electrons that are constantly created by thermal generation-recombination in the substrate and are collected under the charged MOS capacitor plate. Hence, the logic "1" degrades towards the logic "0". That is why a DRAM is considered to be "dynamic" unlike an SRAM. It is necessary to periodically restore the logic levels or "refresh" the stored information.

FIG. 31 DRAM cell structure and cell operation: (a) cell structure corresponding to equivalent circuit of FIG. 30; (b)-(e) potentials under bitline, pass transistor channel and storage capacitor during write "0", store "0", write "1" and store "1" operations. It shows that the logic state "0" corresponds to a filled potential well (stable state), while the logic state "1" corresponds to an empty potential well (unstable state) that is filled up over time by minority carriers generated in the substrate and leakage through the pass transistor.

There are interesting device physics issues regarding the pass transistor. This is like the access transistor in the SRAM, or a logic transmission gate. We see that in this MOSFET, neither the source nor the drain is permanently grounded. In fact, which side acts as the source and which as the drain depends on the circuit operation. When we are writing a logic "1" into the cell, the bitline voltage is held high (=VDD). As this voltage is writ ten into the cell, it is as if the source of the pass transistor gets charged up to VDD. Another way of looking at this is that with respect to the source, the substrate bias of the pass transistor is -VDD. The body effect of the MOSFET causes its VT to increase. This is very important because for the pass transistor to operate as a transmission gate it is necessary that it be in the linear regime throughout, and not get into saturation (with a concomitant voltage drop across the pinch-off region). Hence, the gate or the wordline voltage must be held at VDD (which is the final voltage of the source/drains) plus the VT of the MOSFET, taking body effect into account. It is also important to make sure that the leakage of the pass transistor is low enough to satisfy refresh requirements of the DRAM. Not only must the source/drain diodes be low leakage, but the VT and the sub-threshold slope must be optimized such that sub-threshold leakage for the grounded wordline case is low enough.

FIG. 32

C-V characteristics of DRAM MOS capacitor in stored "0" and stored "1" states. The difference of area under the C-V curves shown by hatch-marked pattern reflects the charge differential between the two states.

The stored charge difference between the two logic states can be deter mined by looking at the capacitance-voltage ( C-V) characteristics of the MOS capacitor (FIG. 32). For a stored "1", essentially there is a substrate bias applied to the MOS capacitor, which raises its VT due to the body effect. Hence, the C-V characteristics shift to the right for a stored "1". Since the MOS capacitance is not a fixed capacitance, but is voltage dependent, we saw earlier that it must be defined in a differential form. Alternatively, we can write down the stored charge under the capacitor as

(eqn. 12)

FIG. 33 Equivalent circuit showing charge redistribution between cell capacitance (CC) and bitline capacitance (C ) on one side, versus dummy cell (C ) and bitline capacitance (C ) on other.

This is simply the area under the C-V curve. The charge differential that distinguishes the logic "1" and the logic "0" is the difference of areas under the capacitance-voltage curves in the two cases (FIG. 32).

When reading the cell, the pass transistor is turned on, and the MOS storage capacitor charge is dumped on the bitline capacitance CB, precharged to VB (typically = VDD). The swing of the bitline voltage will clearly depend on the voltage VC stored in the storage cell capacitance CC. As in the case of the SRAM, the change of the bitline voltage depends on the capacitance ratio between the bitline and the cell. To do differential sensing in the case of DRAMs, we do not use two bitlines per cell as for SRAMs. Instead, we compare the bitline voltage for the selected cell with a reference bitline voltage to which is connected a dummy cell whose MOS capacitance, CD, is roughly half that of the actual cell capacitance, CC. Typical values of CB, CC, and CD in a DRAM are 800 fF, 50 fF, and 20 fF, respectively. The voltage differential that is applied to the sense amplifier then becomes (FIG. 33)

(eqn. 13a)

If VD is set to zero, the expression simplifies to:

(eqn. 13b)

Putting the cell voltage VC equal to 0 V or 5 V, and typical, acceptable bitline-to-cell capacitance ratios CB/CC(= 15-20) in Eq. (eqn. 13b), we get different polarities of the differential voltage of the order of {100 mV for logic "1" and logic "0", respectively, which can be detected by sense amplifiers. From Eq. (eqn. 13b), it can be seen that for much higher bitline-to-cell capacitance ratios, the swing of the bitline voltage will be negligible, regardless of the cell voltage. The minimum required cell capacitance CC is about 50 fF, governed by so-called soft errors. DRAMs, like everything else on Earth, are constantly being bombarded by cosmic rays, and high-energy alpha particles can create electron-hole pairs in semiconductors. A typical collected charge due to one of these events is about 100 fC. This spurious charge can be neglected if the cell capacitance is 50 fF and 5 V is applied to the cell, for which the stored charge is roughly 250 fC. The DRAM cell then becomes immune to typical alpha particle hits.

FIG. 34 Various approaches (past, present, and future) of achieving higher DRAM cell capacitance and charge storage density without increasing cell size. As = Area on wafer taken by capacitor; Ac = Area of capacitor. For a planar capacitor Ac = As; however, for non-planar structures Ac 7 As. C = Ac P/d is the capacitance; and Q = CV is the total stored charge in a fixed, voltage-independent capacitor.

Maintaining a cell capacitance of 50 uF as the cell dimensions are reduced from one generation of DRAM to the next is a tremendous technological challenge. One way to look at this problem is shown in FIG. 34. The challenge is to store more charge per unit area on the planar surface (As) of the Si substrate. Approximating the MOS capacitance as a fixed, voltage-independent capacitor, we can write the stored charge Q as

Q = CV = (PAC / d)V (eqn. 14)

where g is the permittivity of the dielectric, d is its thickness, and AC is the capacitor area. As shown in FIG. 34, the historical way of achieving the desired capacitance has been to scale the dielectric thickness, d. But that runs into the problems discussed in Section 6.4.7. Another approach, which is being taken currently, is to use fabrication schemes to increase the area devoted to the MOS storage capacitor, Ac, even as we reduce the planar surface area on the wafer, As, used for making this storage capacitance. Obviously, this can be done by moving away from a purely planar structure, and exploiting the third dimension. We can go down into the Si by digging "trenches" in the substrate with RIE and forming a trench storage capacitor on the sidewalls of the trench (FIG. 35a). Alternatively, we can go up from the substrate by stacking multiple layers of capacitor electrodes to increase the "stacked" capacitor area (FIG. 35b). Other tricks that have been tried are to purposely create a rough polysilicon surface on the capacitor plates to increase the surface area. In the future, alternative materials may be used. For example, the ferroelectrics have much higher dielectric constant than SiO2 and offer larger capacitance without increasing area or reducing thickness. Promising materials include barium strontium titanate and zirconium oxide.

FIG. 35 Increasing cell capacitance by exploiting the vertical dimension: (a) trench capacitors involve etching a trench in the substrate so that the larger area on the sidewalls can be used to increase capacitance; (b) stacked capacitors go "up" rather than "down" as in trenches, and increase capacitor area by using multiple polysilicon capacitor plates or "fins," as well as by exploiting the topography of the cell surface.

FIG. 36 Flash memory cell structure: (a) cell structure shown along the channel length showing the control gate (wordline), floating gate below it, the source and the drain (bitline); (b) view of cell along the width of the MOSFET. The various coupling capacitors to the floating gate are shown.

Flash Memories. Another interesting MOS device is the flash memory, which is the most important type of nonvolatile memory. The memory cell structure is shown in FIG. 36. It is very simple and compact, and looks just like a MOSFET, except that it has two gate electrodes, one on top of the other. The top electrode is the one that we have direct electrical access to, and is known as the control gate. Below that we have a so-called "floating" gate that is capacitively coupled to the control gate and the underlying silicon.

The capacitive coupling of the floating gate to the various terminals is illustrated in FIG. 36 in terms of the various coupling capacitance components. The floating gate and the control gate are separated by a stacked oxide-nitride-oxide dielectric in typical flash devices. The capacitance between these two gates is called CONO because of the oxide-nitride-oxide makeup of the dielectric stack. The total capacitance CTOT is the sum of all the parallel components shown in FIG. 36.

CTOT = CONO + CTOX + CFLD + CSRC + CDRN (eqn. 15)

where CTOX is the floating gate-to-channel capacitance through the tunnel oxide, CFLD is the floating gate-to-substrate capacitance in the LOCOS field oxide region, and CSRC and CDRN are the gate-to-source/drain overlap capacitances.

Since it is isolated by the surrounding dielectrics, the charge on the floating gate QFG is not changed by (moderate) changes of the terminal biases.

QFG = 0 = CONO(VFG -VG) + CSRC(VFG -VS) + CDRN(VFG -VD) (eqn. 16)

We assume that the substrate bias is fixed, and hence ignore the contributions from CTOX and CFLD, which couple the floating gate to the substrate. The floating gate voltage can be indirectly determined by the various terminal voltages, in terms of the gate, drain, and source coupling ratios as defined in Eq. (eqn. 17).

VFG = VG ~ GCR + VS ~ SCR + VD ~ DCR (eqn. 17)








The basic cell operation involves putting charge on the floating gate or removing it, in order to program the MOSFET to have two different VT/ s, corresponding to two logic levels. We can think of the stored charge on the floating gate to be like the fixed oxide charge in the VT expression. If many electrons are stored in the floating gate, the VT of an NMOSFET is high; the cell is considered to have been "programmed" to exhibit the logic state "0". On the contrary, if electrons have been removed from the floating gate, the cell is considered to have been "erased" into a low VT state or logic "1".

How do we go about transferring charges into and out of the floating gate? To program the cell, we can use channel hot carrier effects that we discussed. We apply a high field to both the drain (bitline) and floating gate (wordline) such that the MOSFET is in saturation. It was discussed that the high longitudinal electric field in the pinch-off region accelerates electrons toward the drain and makes them energetic (hot). We maximize such hot carrier effects near the drain pinch-off region in a flash device by making the drain junction somewhat shallower than the source junction (FIG. 37a). This can be achieved by a separate higher energy source implant that is masked in the drain region. If the kinetic energy of electrons is high enough, a few can become hot enough to be scattered into the floating gate. They must surmount the 3. 1-eV energy barrier that exists between the conduction band of Si and that of SiO2, or hot electrons can tunnel through the oxide (FIG. 37b). Once they get into the floating gate, electrons become trapped in the 3. 1-eV potential well between the floating polysilicon gate and the oxides on either side. This barrier is extremely high for a trapped (low kinetic energy) electron. Therefore the trapped electrons essentially stay in the floating gate forever, unless the cell is intentionally erased. That is why a flash memory is nonvolatile.

FIG. 37 Hot carrier programming of the flash cell: (a) flash memory cell structure with typical biases required for writing into the cell. The channel of the MOSFET is pinched off in saturation; (b) band diagram along a vertical line in the middle of MOSFET channel showing hot electrons in the channel being injected across the gate oxide and getting trapped in the floating gate.

FIG. 38

Fowler-Nordheim tunneling erasure: (a) flash memory cell structure with typical biases required for erasing the cell; (b) band diagram as a function of depth in the gate/source overlap region of the MOSFET showing quantum mechanical tunneling of carriers from the floating gate into the oxide, and subsequent drift to the source.

To erase the cell, we use Fowler-Nordheim tunneling between the floating gate and the source in the overlap region (FIG. 38a). A high positive voltage (say ~12 V) is applied to the source with the control gate grounded. The polarity of the field is such that electrons tunnel from the floating gate into the source region, through the oxide barrier. The band diagram (along a vertical line in this overlap region) during the operation is shown in FIG. 38b. Interestingly, in a flash device we make use of two effects that are considered to be "problems" in regular MOS devices: hot carrier effects and Fowler-Nordheim tunneling.

FIG. 39 Drain (bitline) current versus control gate (wordline) voltage transfer characteristics of the MOSFET in a flash cell: if the cell is programmed to a high VT (logic "0"), and a read voltage is applied to the wordline that is below this VT , the MOSFET does not conduct, and there is negligible bitline current. On the other hand, if the cell had been erased to a low VT state (logic "1") the MOSFET is turned ON, and there is significant bitline current.

During the read operation, we apply a moderate voltage (~1 V) to the bitline (drain of the MOSFET), and a wordline (control gate) voltage VCG that causes the capacitively coupled floating gate voltage to be between that of the high VT and the low VT state of the programmed flash memory cell (FIG. 39). There will be negligible drain current flow in the bit line (drain) for the high VT case because the gate voltage is less than the threshold voltage. We will then interpret the selected cell as being in state "0". For the low VT case, since the applied gate voltage is higher than the threshold voltage of the cell, there will be drain current flow in the bitline (drain), and this can be interpreted as state "1". The read operation can be understood by looking at the transfer characteristics of the MOSFET in the programmed and erased states (FIG. 39).

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