A new and improved physics-based model for MOS transistors

An improved MOS device model is derived based upon a first-order model for the dependency of MOS surface mobility on surface field and lateral drain field. A comparison with experimental data shows that a consistent set of physical parameters can be used to describe both long-channel nMOS devices and short-channel devices. The model can form the basis for improved compact MOS models for circuit analysis.

I. Introduction

Accurate analytical models of MOS device current are very important for circuit analysis and for projecting the performance of CMOS to future nanoscale device dimensions. Our understanding of MOS device physics has greatly improved over the past several decades. However, not all this improved understanding has been incorporated into MOS device models. The basic “quadratic” MOS current expression developed in the early 1960s [1]–[3] can be expressed below the current saturation region by

$$I_{d}=\mu_{n}C_{\rm ox}\left({W\over L}\right)(V_{g}-V_{T}-{0.5}V_{d})V_{d}.\eqno{\hbox{(1)}}$$ This basic model has been recognized as inadequate for many years and various modifications have been made to this basic starting equation. One of the most common is to modify the mobility so that it becomes a function of the form $$\mu_{n}={\mu_{o}\over\left[1+\theta_{1}(V_{g}-V_{T})+\theta_{2}(V_{g}-V_{T})^{2}\right]\left[1+{V_{d}\over E_{c}L}\right]}\eqno{\hbox{(2)}}$$ where the first term in square brackets in the denominator is intended to account for the known reduction in mobility due to the vertical gate oxide field and the second term in square brackets is intended to account for velocity saturation effects due to a large horizontal drain field. An extensive literature exists describing various modifications to the basic MOS current equation.