Abstract−This paper presents a new analytical propagation delay model for a nanoscale CMOS inverter. By using a nonsaturation current model, the analytical input-output transfer responses and propagation delay model are derived. The model is used for calculating inverter delays with different input transition times, load capacitances and supply voltages. Delays predicted by proposed model are in good agreement with that of transistor level simulation results from SPICE, and errors are less than 3%.
I.INTRODUCTION As one of the most important performance parameters in CMOS digital circuits, the propagation delay is of concern to designers and users. A circuit's speed/frequency and dynamic power dissipation are both affected significantly by propagation delay, and hence timing analysis has been investigated for several decades [1][2][3][4][5][6][7]. With the increasing complexity of modern very large scale integration (VLSI) systems, transistor level simulation consumes much more computation time because of the nonlinear transfer characteristics of CMOS gates [8][9][10]. Therefore, an analytical delay model that does not need numerical iterations is needed to extract delay efficiently, and much work has been published on the topic [3,[6][7][8][9][10][11][12][13][14][15][16][17][18][19].For extracting the propagation delay, development of a delay model for a CMOS inverter is considered as the first step [14], and a number of inverter delay models have been developed [6][7][8][9][10][11][12][13][14][15]. The first inverter delay expression was introduced by Burns [1]. Early models were based on Shockley's square law MOSFET model which does not include the carrier velocity saturation effect [1,2]. As the drain current (I ds ) deviates significantly from the Shockley model in the submicron region, Sakurai et al. [3] proposed a model using an α-power law current model which includes the carrier velocity saturation effect of short channel devices. Several analytical delay expressions based on the α-power law model were introduced thereafter [10, 13]. However, in modern small dimension MOSFETs, I ds does not show saturation [20][21][22]. Therefore, α-power law based delay models would underestimate inverter propagation delay by using higher I ds (at V ds =V dd ) as the saturation current in the nominal saturation region.On the other hand, some delay models did not take the current through the loading transistor into account [3, 13], including both the overshooting and short-circuit current [10,14,23]. Moreover, with continuous scaling down of transistor dimensions, the charging/discharging of input-output coupling capacitance (C M ) inevitably affects inverter characteristics and propagation delays, which should be considered in developing delay models [7,8,10,12,14,16,23].The reported propagation delay expressions for a submicron inverter are complex [8][9][10]14], which limits the exten-