Chapter 3

Chapter 3

The Physical AlphaPower Law MOSFET Model

3.1 Introduction

In 1999, the proposal of the physical alphapower law MOSFET model [8] eliminated the

drawbacks of the previously widely utilized alphapower law MOSFET model [9]. In this

regard, it included the helpful features of the low power transregional MOSFET model

[10]. The addition of the low power transregional model brings in the salient features of

operation in all the regions (subthreshold, triode and saturation). To mention that the low

power transregional model [10] was an advantageous choice for predicting performance

of future technology generations and in particular for analyzing on/off drain current

tradeoffs. Due to the complex drain current equations the involvement with the alphapower

law MOSFET model brought the physical alphapower law MOSFET model. This

model included these salient features: 1) extension into the subthreshold region of

operation, 2) the effects of vertical and lateral high field mobility degradation and

velocity saturation and 3) threshold rolloff. 

3.2 Model Derivation

The physical alphapower law MOSFET model was derived by coupling the simple

empirical alphapower law MOSFET model [9] and the more complex physics based low

power transregional MOSFET model [10]. The derivation of the model started by

equating the saturation drain current of the alphapower law MOSFET model [9],

equation (3.1) and the low power transregional model [10], equation (3.2)

Where ID0 (3.5) is a modified drive current that includes an effective mobility dependence

on VGS. Neglecting the small weak inversion contribution and performing a three term

binomial expansion of the bulk charge terms in DS AT I , the low power transregional

model’s saturation drain current [10] was simplified as

Where, (W/L) is the channel widthtolengthratio, Cox is the oxide capacitance per unit

area, meff is the effective mobility. meff depends on the gate bias voltage (VGS) as the

influence of gate bias is dominant in the expression of meff. Rather we can say for a more

accurate expression that meff depends on the transverse field, which, in turn, depends on

all terminal voltages [11]. A general expression of meff is given as follows:

A feature of the physical alphapower law MOSFET model describes that dependence of

carrier velocity on VGS is jointly described by ID0, (3.3)(3.6), as well as a (3.10). This

yields improved accuracy of the model for VGS near VT compared to the original alphapower

law model [8] that describes carrier velocity as a function of VGS solely through a.Therefore,

 the values of a calculated by the physical alphapower law model re slightly larger than the 

measured a values of the original alphapower law model [8] for short channel MOSFETs.

For further insight into the a parameter, analyses of the long channel MOSFET with

negligible carrier velocity saturation (ECL >> VDD VT) and the short channel MOSFET

with severe carrier velocity saturation (ECL << VDD VT) are performed in the model. In

the long channel case, the saturation voltage (3.4) may be simplified by performing a two

term binomial expansion such that