A CAD-oriented non-quasistatic MOSFET model for transient analysis

Abstract

IN RECENT YEARS: several digital MOS integrated circuits operating at high speed have been presented. In order to model the behavior of the transistors appearing in these circuits, several approaches to the transient analysis of the MOST have been developed' " and are currently in use for circuit simulation. All of these approaches, however, while guaranteeing charge conservation, are valid only for qnasistatic operation and thus, in principle, cannot be used for circuits operating at very high operating speeds.Two four-terminal approaches for the transient analysis of the intrinsic MOSFET valid for non-quasistatic operation will be presented in this paper. The first approach has been developed by coupling the current-continuity equation with an expression for the carrier current density which accounts for both drift and diffusion and which holds in all the operating regimes of the device. In this way, the time dependence of the distribution of the free charge density along the channel Qn(Y, t) is obtained as the solution of a non linear parabolic differential equation. The time dependence of the currents at the device terminals is then achieved by using'the standard procedure outlined in an earlier report' .The second approach was developed by using the weighted residual method to solve the partial differential equation which describes the transient behavior of the channel charge. The trial function selected for this procedure (and required from such a method to approximate the Qn(y, t) distribution): ( a ) satisfies the boundary conditions at the source and at the drain extrema of the channel, ( b ) has a quadratic dependence on the coordinate y along the channel, and (c) contains only one time-dependent unknown function x(t). Besides, it can be shown that, hy imposing a zero value for the integral of the residual over the channel length, the function x(t) can be calculated as the solution of a simple ordinary differential equation of the form x'(t) = f(x, t). Moreover, an explicit current formulation which accounts for short-channel effects3 has been adopted for the channel charge. In this way, a very simplified analysis has been obtained; in fact, the time evolution of the currents at the four terminals can easily be calculated as a function of x(t).static behavior of the intrinsic MOST has been checked and verified by making several comparisons with the numerical non-quasistatic approach. Figures 1 and 2 show, as continuous lines, the terminal currents vs time when a 0.25ns/(2-10)V voltage ramp is applied to the gate of a MOST biased in the linear regime (VDS = 1V; VBS = OV; L = 5pm).As can be seen, the simple model favorably compares with the results 'Oh, S., Ward, D., Dutton, R., IEEE-JSSC, Vol. SC-15, 2 The ability of the simple model to predict the transient non-quasi-__ p. 636; 1980.

A Nonquasi-Static Empirical Model of Electron Devices

“…The equivalent voltages (16) provide the same conductive current into a virtually quasi-static device described by (4) and (5) or, equivalently, by (6). Then, by substituting (16) into (14), we obtain (17) which gives the total nonquasi-static current of the actual device in an equivalent voltage-controlled form through equations which are analogous to the quasi-static model (6). Model equations (17) are coherent with the circuit schematic shown in Fig.…”

“…Then, by substituting (16) into (14), we obtain (17) which gives the total nonquasi-static current of the actual device in an equivalent voltage-controlled form through equations which are analogous to the quasi-static model (6). Model equations (17) are coherent with the circuit schematic shown in Fig. 2.…”

“…According to (17), a nonlinear nonquasi-static model is obtained by considering an associated virtual quasi-static device described by the nonlinear algebraic functions and defined in (6), where and are controlled by equivalent, instead of actual, port voltages ( and , respectively). This formulation is convenient since, in order to guarantee that no charge perturbation is introduced in the off-state (where the device behavior is practically quasi-static), the and voltage deviations do not need to become vanishingly small when applied to the strictly intrinsic device (which acts as an open circuit in the off-state).…”