Device modeling

This paper reviews the progress in device modeling with emphasis on numerical modeling approaches. The reason for this is its ever-increasing importance for the design of small-scale devices suited for VLSI applications. First, the basic field equations with their respective boundary conditions are given. Followed by a description of empirical models for the physical device mechanisms, i.e., mobility, avalanche generation, band-gap narrowing. Subsequently, different numerical models, mainly developed in the past decade, are outlined briefly and discretization as well as solution methods are being discussed. Some remarks are given concerning the relations between finite-difference and finite-element methods. Simplified numerical models are also mentioned and their usefulness for certain type of applications is stressed. In order to clearly demonstrate the power of numerical device modeling, a number of representative examples is given. The last sections deal with analytical device modeling. Bipolar transistor models are only briefly reviewed since the evolution has led to some kind of standardization, but the development of MOS transistor models, where the same is not true, is described in more detail. Cross references to numerical results should clarify that with decreasing device dimensions the model parameters of analytical MOST models tend to loose their physical significance and change increasingly into fitting parameters.