8 CHAPTER-2 BASICS The Basics chapter emphasizes upon the various concepts that are involved in the functioning of MOS devices, effect of threshold voltage on characteristics, sub threshold conduction, MOSFET based circuits and the description of software that is used to carry out the research work reported in this thesis. 2.1 MOSFET Basic Study The MOSFET is a four terminal device with the terminal s source, drain, gate and substrate [1]. The MOSFET may be an N-channel MOSFET or P-channel MOSFET. The N-channel MOSFET consists of a lightly doped p type substrate into which two heavily doped n+ diffusion regions called source and drain are diffused. Similarly the p- channel MOSFET consists of N type substrate into which two p+ diffusion regions called source and drain are diffused. There are also two categories into which the MOSFET devices can be split 1) Enhancement MOSFET (EMOSFET) and 2) Depletion MOSFET (DMOSFET). A MOSFET which has no conducting region at zero gate bias is called EMOSFET and if a conducting channel exists already at zero gate bias it is called DMOSFET. The structure of both MOSFET s is explained below.
9 2.1.1 N - Channel Enhancement MOSFET Structure Figure 2.1(a): Structure of N-Channel Enhancement MOSFET N-channel Enhancement MOSFET (EMOSFET) structure is shown in Figure 2.1(a). It consists of p-type substrate, in which the source and drain regions are formed by diffusing n- type impurities.the surface of the substrate region between the drain and source is covered with a thin oxide layer and the (poly silicon) gate is deposited on top of this dielectric. The channel length is the distance between the drain and source diffusion regions and the channel width is the lateral extent of the channel (perpendicular to the length dimension). The oxide layer thickness is denoted by tox. For Vd=Vs=Vgs=0, the channel is not established and the device is in a non conducting condition. When a positive voltage is applied to gate with respect to source, an electric field is established between gate and substrate, and causes a charge inversion region in the substrate, under the gate insulation. A conduction channel is formed between source and drain. 2.1.2 N-channel Depletion MOSFET structure Figure 2.1(b) shows the structure of N-channel Depletion MOSFET (DMOSFET). This n-channel Depletion MOSFET S are formed on p-type substrate. By implanting suitable impurities in the region between source
10 and drain, the channel is established between the source and drain regions at Vgs=0. Figure 2.1(b): Structure of N-Channel Depletion MOSFET The structure of p-channel EMOSFET S and DMOSFET can be explained on similar grounds. 2.1.3 N channel EMOSFET operation The EMOSFET can be operated in three different modes. They are 1) Accumulation 2) Depletion and 3) Inversion modes. When a negative voltage is applied to the gate, the mobile holes are accumulated to the region below the gate. This is called the accumulation region and is shown in Figure 2.2(a).A depletion region is formed when a small positive voltage is applied to the gate and the holes in the substrate are repelled from the region directly beneath the gate. This region is shown in Figure 2.2(b).When a large positive voltage greater than threshold voltage (V T) is applied, more and more positively charged holes are repelled and a few number of free electrons in the substrate are accumulated in the region beneath the gate.this accumulation of free electrons, form a conductive
11 layer of electrons in the p type body and is called inversion layer.this mode of operation is called Inversion mode and is shown in Figure 2.2( c ) (a) (b) (c) Figure 2.2(a),(b) and (c):modes of operation of N-Channel EMOSFET 2.1.4 N channel DMOSFET operation Depletion mode MOSFET transistor conducts even when V gs=0.it is because that the channel is implanted between source and drain during manufacturing. When the gate voltage is made negative, positive charged particles are induced in the channel through the sio 2 of the gate capacitance. Since the drain current is due to majority carries( electrons for an n-type material ), the induced positive charges make the channel less conductive and as V gs is made more negative, drain current drops.a depletion MOSFET can also be operated in an enhancement mode by applying a positive gate voltage into the n-type channel. This is the way how the conductivity of channel increases. 2.1.5 Characteristics of N channel EMOSFET and N channel DMOSFET
12 In this section the characteristics and region of operation of MOSFET s are discussed [2]. 2.1.5.1 Transfer characteristics of EMOSFET Figure 2.3: Transfer characteristics of N channel EMOSFET The figure 2.3 shows the transfer characteristics of N-channel EMOSFET. It may be noted from the figure 2.3 that when the gate to source voltage (Vgs) is less than threshold voltage (Vtn), almost zero current flows between S and D i.e. (I ds=0). This region of operation of EMOSFET is called cutoff region or weak inversion region. Increasing the gate to source voltage above threshold voltage, bias the NMOSFET into the active region of operation by forming the electron charge layer Q e. The drain source voltage (V ds) provides the difference in potential needed to move the charge which results in the current Ids(n) flowing through the device. 2.1.5.2 Drain characteristics of EMOSFET Figure 2.4: Drain characteristics of EMOSFET
13 The drain characteristics (Id vs Vds) of N channel EMOSFET is shown in figure 2.4. At the very beginning, as Vds first increases, Ids increases linearly.this mode of operation is called linear or triode or non saturation mode. In this mode, the gate voltage is greater than threshold voltage (Vgs>Vtn) and Vds is small i.e ( Vds < Vgs-Vtn). The transistor is turned on and a channel has been created which allows current to flow between the drain and source. The current from drain to source in linear mode is modeled as I ds = µ n C ox( W/L)(( v gs-v tn)v ds- v ds 2/2)---------Equation 2.1 Where µn is the charge carrier mobility, W is gate width, L is the gate length and C ox is the gate oxide capacitance per unit area. From the drain characteristics, it can be observed that when V gs>v tn and Vds > Vgs-Vtn, Ids stops increasing and almost remains constant. This mode of operation of EMOSFET is called saturation mode.in this saturation mode, the current is controlled by only the gate to- source voltage and modeled as Ids = (µncox)/2(w/l)(vgs-vtn) 2 ---------------Equation 2.2 2.1.5.3 The transfer characteristics of DMOSFET Figure 2.5: Transfer characteristics of DMOSFET
14 The transfer characteristics of DMOSFET are shown in figure 2.5. When Vgs is zero and negative, the MOSFET operates in the depletion mode. On the other hand, if V gs is zero and positive, the MOSFET operates in the enhancement mode. The drain current Ids at any point along the transfer characteristics is given by the relation 2 1 Vgs I ds = I dss ------------------Equation 2.3 Vgs( off ) It may be noted that even if V gs=o the device has a drain current equal to Idss. Due to this fact, it is called normally- ON MOSFET. In depletion mode, when V gs=0, maximum current will flow between source to drain. Thus I ds=i dss. Similarly when V gs increased continuously, after a certain extent, the positive charges induced by gate completely depletes the channel. Thus no drain current flows. In enhancement mode of operation, increasing V gs >0, more free electrons are induced in the channel.thus it enhances the electrons, which results in increase in Ids. 2.1.5.4 Drain characteristics of DMOSFET The drain characteristics for the N channel DMOSFET is given in figure 2.6 Figure 2.6: Drain characteristics of DMOSFET
15 These curves are plotted for both negative and positive values of gate to source (Vgs) voltage. The curves shown above the Vgs =0, have a positive value where as those below it have a negative value of V gs. When Vgs is zero and negative, the MOSFET operates in depletion mode.on the other hand, if Vgs is zero and positive, the MOSFET operates in the enhancement mode. When V ds =0, there is no conduction take place between source to drain. If V gs <0 and V ds >0, then drain current increases linearly. As a result of Vgs <0 is applied to the gate induces positive charged holes in the channel and also it controls the channel width. Thus the conduction (between source to drain is maintained as constant) i.e Ids is constant. If Vgs >0, the gate induces more electrons in channel side. It is added with free electrons generated by source. Again the potential applied to gate determines the channel width and maintains constant current flow through it as shown in figure 2.6. Throughout the thesis, only EMOSFETS are considered. PMOSFETS can be explained on similar grounds and the Table 2.1 gives the structure, transfer characteristics, output characteristics of both NMOSFET and PMOSFET devices. It may be seen from the above discussion that the current voltage relationships depends on applied voltages and the characteristic parameters of FET. Important characteristic parameters are width of the channel, length of channel, thickness of oxide, in addition to the source and drain junction depths. There are other material parameters like mobility carries (µn and µp), the silicon material permittivity and the
16 conductivity of the channel.the next section deals with the effect of these parameters on the characteristics of MOSFETS. Type Cross Section Output Characteristics Transfer Characteristic s N- Channel DMOSFET N-Channel EMOSFET P- Channel DMOSFET P-Channel EMOSFET Table 2.1-Structure, Output and Transfer characteristics of MOSFET Devices
17 2.1.6 Effect of Threshold voltage on the characteristics As seen from the equations (2.1) and (2.2), there is a characteristics parameter of the device which indicates the extent of conduction, i.e threshold voltage which is possible for a given set of voltages. This threshold voltage in turn depends on the conductivity of substrate, oxide thickness and surface potential. 2.1.6.1 Threshold voltage (V T) of MOSFET The threshold voltage of MOSFET is discussed by C.Zhang,T.Xin [3,4] and is presented in this section. Figure 2.7 shows a long-channel enhancement mode n-mosfet where body, source and drain terminals are grounded. A voltage, Vgs is applied to the gate and initially it is zero. As the gate voltage is increased from a zero value to a positive magnitude, initially a depletion region is created followed by weak inversion region close to the Si SiO2 interface. As the gate voltage is further increased, a condition of strong inversion sets in where a p-type silicon is inverted to an n-type silicon. This condition occurs at a certain value of the gate to source voltage and is called the threshold voltage (VT). There are three Voltage components which contribute to the threshold voltage (V T) of a MOSFET. These voltage components are the gate to semiconductor work function difference ( φ GC), Q OX due to fixed oxide C OX charge present in the oxide and at the Si SiO2 interface, and a gate voltage QB 2 φ F to change the surface potential to the strong COX
18 inversion condition and to offset the induced depletion region charge, Q B. φ F is Fermi energy and C OX is the gate oxide capacitance per unit area. Figure 2.7: The cross-section of an NMOS transistor The threshold voltage, V T can be expressed as follows V T QOX Q B = φ + GC 2 φf -----------------------Equation (2.4) COX COX The first part φ GC Q C OX OX represents voltage required to establish flat- band (FB) condition.the second part QB 2 φ F represent voltage COX required to bend the bands in Si through a potential of 2φ F. The voltage required for establishing the FB condition is described by VFB = QOX φ GC -------------------------------Equation (2.5) C OX For n MOSFET, the charge in the depletion region per unit area, QB is given by
19 Q B = qn X = 2 qn ε φ φ for φs φf 0------Equation (2.6) A d A Si s F Where NA is the substrate doping density, Xd is thickness of the depletion region and ε Si is the permittivity of silicon. The electrostatic potential at the silicon surface with respect to Si bulk is described byφ s. At the condition of strong inversion, with no body bias (VSB = 0), the depletion region charge, Q BO is given by Q = 2 ε 2φ -------------------------- Equation (2.7) BO qn A si F In presence of body bias (V SB 0), the surface potential required to produce the inversion region is modified to 2 φ + V. The corresponding charge stored in the depletion region, Q B is given by F SB Q = 2qN ε 2φ + V ---------------- Equation (2.8) B A si F SB For the n-mosfet, Eq.(2.4) can be written as V V T T = φ Q Q Q Q BO OX B B φgc 2 F, or------------ Equation (2.9) COX COX COX TNO ( 2φ F + VSB φf ) = V + γ 2 -----------------Equation(2.10) Where VT is the threshold voltage of n-mosfet and VTNO is the zero bias threshold voltage with V SB = 0. The Parameters, γ is called the body 1 effect coefficient or body factor and is given by γ = 2qε si N A. C Normally, V SB 0, results in VT VTO. With the substrate bias, V SB 0, V T is less than V TO. Thus, an n- MOSFET can be designed to operate at a reduced voltage.equation (2.10) can be used for the p-mosfet with the use of proper sign. The threshold voltage of p-mosfet, VTP is given by OX
20 V TP TPO ( 2φ F + VSB φf ) = V γ 2 -----------------Equation(2.11) Where VTPO is the zero biased threshold voltage of n- MOSFET 1 γ = 2qε si N D and N D is the doping density in n substrate. C OX 2.1.7 Effect of length and width on the characteristics of MOSFETS It may be seen from the equation 2.1 and 2.2, that the current flowing through the device varies as a ratio of W/L. By increasing the W/L, one can increase the current that flows for a certain set of terminal voltages. 2.1.8 Effect of Technology on the characteristics of MOSFETS As the feature size of the device shrinks, the I-V relations given by the earlier equations get modified by what are called short channel effects and the corresponding I-V relationships for n-channel devices are given below by [5]. I D=0, V gs<v T (cutoff) I D W eff V (1 + θl eff ) ds = k Vgs VT V ds 1+ λ Vds Leff 2 θleff -------------Equation 2.12 [V gs>v T, V gs-v T>V ds (ohmic)] I D W ( V V ) (1 + δ L 1+ λ δ Leff ) V eff 2 eff = k gs T Vgs ds Leff ---------------- Equation 2.13 θ has units (length) -1 = 0.2 [Vgs>VT, Vgs-VT>Vds (ohmic)] µ 1 k=trans conductance parameter
21 Weff, Leff denote the effective channel width and length Weff =W-WR Leff = L-2LD-LR V gs=gate to source voltage, V ds=drain to source voltage, V T=Threshold voltage Where W, L are drawn width and length. WR and LR are constants representing width and length reduction due to processing. L D is the lateral diffusion of source or drain under the gate. Where λ = channel length modulation parameter 2.1.9 Sub threshold conduction So far the discussion is around I-V relationships in the normal operating region (Vgs>Vt). With the need for reducing the power, the use of FET in sub threshold region (V gs<v t) is becoming popular. In the present section, there is a brief discussion of sub threshold behavior of MOSFET. Basically the sub threshold conduction or sub threshold leakage or sub-threshold drain current is the current that flows between the source and drain of a MOSFET, when the transistor is in the sub threshold region or weak inversion region, that is for gate to source voltages below the threshold voltage (Vgs<VT) The sub threshold current varies exponentially with V gs and the current voltage relation is given by equation I ds( sub) V gs VT Vds = ηvt VT I oe 1 e --------------- Equation 2.14
22 Where W I o= µ oc ox VT 2 and η = sub threshold swing coefficient L C defined as η =1+ C dep OX where Cdep=Depletion capacitance C OX =oxide capacitance VT= Thermal voltage = K q T µ o= zero bias electron mobility in the channel W/L= width over length ratio of the device VT= Threshold voltage In sub threshold logic, the drive current (I on) is the sub threshold current modeled by equation (2.15) as Ion= Isub (Vgs=Vds=Vdd< VT) ------------------------ Equation (2.15) Also the transistor off state current (Ioff) is the drain current when gate-voltage is zero is given by equation (2.16) Ioff = Isub(Vgs=0,Vds=Vdd<VT)-----------------------Equation (2.16) It is observed that the drain current changes exponentially with Vgs where as in strong inversion, drain current responds quadratically with V gs. The transfer characteristics of MOSFET is sub threshold region is usually plotted as in terms of log Id vs gate voltage and typical curve looks like in the figure 2.8[6].
23 Figure 2.8: Transfer characteristics of MOSFET in sub threshold region There are two parameters that are normally defined in this region and they are 1) sub threshold slope and 2) sub threshold Swing 2.1.9.1 Sub threshold slope and sub threshold swing The dependence of gate voltage swing needed to change the drain current by an order of magnitude is defined as a sub threshold slope S and S is defined as S = d ( Log I ) dv 10 gs d 1 ------------------------------Equation (2.17) The sub threshold slope S is an important device parameter in the sub threshold region. The smaller the S value is the higher the drive I on current is, and thus the faster the device.the sub threshold swing is inversely proportional to slope.
24 In this section the basic MOSFET structure, behavior and its characteristics have been discussed.the following section deals with the CMOS Inverter, which is the fundamental logic gate. 2.2 CMOS inverter structure and operation Figure 2.9-CMOS Inverter structure So for, the basics of MOSFET devices have been considered. In the present section a detailed description of CMOS inverter circuit is considered, as the thesis mainly deals with the CMOS circuits. The figure 2.9 shows the circuit diagram of a static CMOS inverter. When the input voltage (V IN) is high and equal to V DD, the NMOS transistor is on and PMOS transistor is off. When the input voltage (VIN) is low, NMOS and PMOS transistors are off and on respectively and a path exists between V DD and V OUT yielding a high output voltage. 2.2.1 Voltage transfer characteristics of CMOS inverter The voltage transfer characteristics give the response of the inverter circuit, V out to specific input voltage V in. The resultant voltage transfer characteristics of static CMOS inverter is given in figure 2.10. From the voltage transfer characteristics, the input and output logic levels are obtained. In the figure 2.10, V OH refers to the high level output voltage of
25 the circuit, when input voltage applied is 0v. Similarly VOL represents the low level output voltage of the circuit when input voltage applied is 0.2v. The input logic levels V IH (high level input voltage) and V IL(low level input voltage) are the points at which the voltage transfer characteristics has slope of -1. 2.2.1.1 Noise Margins of CMOS Inverter Figure 2.10-VTC characteristics with logic levels For a gate to be insensitive to noise disturbance, it is essential that the logic 0 and logic 1 intervals to be as large as possible. A measure of sensitivity of a gate to noise is given by the noise margin low (NM L) and noise margin high (NMH). The low level noise margin is given by NML= VIL-VOL---- Equation 2.18 The high level noise margin is given by NM H=V OH-V 1H. ---Equation 2.19 2.2.1.2 Dynamic characteristics of CMOS inverter The dynamic characteristics of CMOS inverter include the power dissipation, propagation delay, rise and fall time delay and power delay product.
26 2.2.1.2.1 Delay time definitions of CMOS Inverter The input and output voltage waveforms of a typical inverter circuit are shown in figure 2.11.The delay parameters include T PHL(high to low propagation delay), TPLH (low to high propagation delay), T rise(rise time) and T fall(fall time). Figure 2.11 propagation delays and rise and fall times The propagation delay times TpHL and TpLH determines the input to output signal delay during the high to low and low to high transition of the output respectively. By definition, TpHL is the time delay between the 50% transition of the rising input voltage and the 50% transition of the falling output voltage. Similarly, TpLH is the time delay between the 50% transition of the falling input voltage and the 50% transition of the raising output voltage. The average Propagation delay T p of the inverter characterizes the average time required for the input signal to propagate through the inverter. ( T ) p HL + Tp LH Propagation delay T p = 2 ------------- Equation 2.20
27 The rise time Trise is defined as the time required for the output voltage to rise from the 10% level to 90% level. Similarly, the fall time Tfall is defined as the time required for the output voltage to drop from the 90% level to 10% level. Reducing gate delays in digital circuits allows the data processing at a faster rate and improves overall performance. 2.2.1.2.2 Power consumption of CMOS Inverter The second performance metric of the CMOS inverter is the power consumption.the average power consumption in conventional CMOS digital circuits is the sum of three main components. 1) The dynamic (switching) power consumption. 2) The short circuit power consumption 3) The leakage power consumption or static power consumption. 2.2.1.2.2.1 The Dynamic (Switching) power consumption of CMOS Inverter In conventional CMOS technologies, the dynamic (switching) power consumption is the major contributor to the total power dissipation. It is due to switching capacitance, diffusion capacitance, inter connect capacitances and the junction capacitance. The CMOS inverter circuit is shown in Figure 2.9. The output capacitor C constitutes the lumped parasitic capacitances.when input switches from high to low, the NMOS transistor is turned OFF and PMOS transistor is ON and capacitor C is charged.the total energy that is drawn from power supply during this charging process is equal to CV D D 2.Half of the energy is dissipated in PMOS transistor and other half is stored in capacitor C.When input switches from low to high, the NMOS transistor turns ON and the
28 capacitance C discharges through NMOS transistor. For any logic gate, if inputs to the gate are assumed to switch at a rate of f times per second, then the average switching power for that gate is given by Psw=α.C.V 2.fclk -------------------------------------------------Equation 2.21 Where α is the switching activity factor which indicate the probability of the output switching from 0 to 1,C is the switching capacitance,v is the voltage swing and f clk is the switching frequency. 2.2.1.2.2.2 The Short circuit power consumption of CMOS Inverter Short-circuit power arises when a conducting path exists between supply and ground. i.e when both PMOS and NMOS are simultaneously ON. Short circuit current flows when the rise time and fall time of the input signal is slow. The pull-up and pull-down devices should be sized properly to achieve slow rise/fall time. This component of power consumption can be significant in pre charge and evaluate circuits. Careful design is required to keep this component of power dissipation small enough to be ignored. 2.2.1.2.2.3 The Static power consumption of CMOS Inverter For a clear understanding of static power consumption, the CMOS inverter modes are considered and are shown in Figure 2.12.As shown in Figure 2.12, case 1, if the input is at logic 0, p-mos device is on and the n-mos device is off. The output voltage is logic 1. Similarly, when logic 1 input is applied, the n-mos device is on and the p-mos device is off. The output voltage is logic 0. From the figure 2.12 it is observed that one of the transistors is always off. When the gate input is in either of these logic states, dc current that flows from V DD to GND, is only the sub
29 threshold conduction or leakage current. Static power consumption is the product of the device leakage current and the supply voltage. Total static power consumption, P S, can be obtained as shown in below equation (2.22). PS = Σ (leakage current) *(supply voltage) ------------- Equation (2.22) Compared to the dynamic power consumption, static power consumption have been considered as negligible. But in modern CMOS processes, due to decrease in supply voltage and sub threshold voltage, the leakage current increases, causing increase in static power consumption. Hence in modern CMOS technologies, the static power dissipation component cannot be neglected. Figure 2.12 CMOS Inverter Mode for Static Power Consumption 2.2.1.2.3 Power delay product of CMOS Inverter Power delay product (PDP) is the product of the propagation delay (usually in nanoseconds )and the power dissipation( usually in milli watts).it has dimensions of energy and usually expressed in the unit
30 called pico joule.the smaller the power delay product is, the better the logic family is considered to be. 2.3 Combinational circuits In combinational circuits, at any instant of time, the output depends upon the inputs present at that instant of time.this indicates that there is no memory in these circuits. Combinational logic circuits are built from basic logic gates like Inverter,NAND and NOR gates.the common combinational circuits built from basic logic gates include Multiplexers, Decoders,De-multiplexers and full adder circuits and full subtracter circuits etc. 2.4 Sequential circuits In sequential circuits,the output at any instant of time depend upon the present inputs as well as past inputs and outputs.that means there are memory elements available in sequential circuits for storing past information.sequential circuits are classified into two main categories known as synchronous sequential logic circuit and asynchronous sequential logic circuit. In synchronous sequential logic circuits, the changes in state occurs by a clock signal applied to the circuit. In the case of asynchronous sequential logic circuits,the changes in state occurs after inputs change and the changes do not depend upon clock signal.flip-flop is the basic sequential logic circuit.flip-flop is used as the logic storage device in more complex sequential circuits.
31 2.5 Conclusions This chapter is devoted to basics of MOS devices,combinational and sequential circuits which is important to understand the contents of this thesis.in the next chapter the literature survey and the work carried out by various people to address the problem of power reduction, especially in sub threshold region of operation of CMOS circuits is dealt with.