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.

http://ieeexplore.ieee.org/iel5/5/31321/01456792.pdf

Device modeling

The forward-biased current-voltage and forward-to-reverse biased switching characteristics of p+-n-n+epitaxial diodes are investigated. The manner in which the n-n+junction affects the flow of injected minority carriers in the epitaxial region is characterized by a leakage parameter a. Experimentally, for diodes with epitaxial film widths much less than a diffusion length, a "box" profile accurately describes the injected minority carriers in the n region. The current is found to increase with increased epitaxial width at a fixed bias. A general switching expression for epitaxial diodes is presented and the validity of the expression is shown experimentally. The experimental values of a, determined independently from the current-voltage and switching characteristics, are in good agreement and show that the leakage of the high-low junction is dominated by the recombination of minority carriers in the n-n+space-charge region.

Forward current&#8212;Voltage and switching characteristics of p + -n-n + (epitaxial) diodes

For pt. I see ibid., vol. 49, pp. 1250-1257 (2002). Terminal current noise is investigated with Langevin-type drift-diffusion (DD) and hydrodynamic (HD) noise models for one-dimensional (1-D) N/sup +/ NN/sup +/ and P/sup +/ PP/sup +/ structures and a realistic two-dimensional (2-D) SiGe NPN HBT. The new noise models, which are suitable for technology computer aided design (TCAD), are validated by comparison with Monte Carlo (MC) device simulations for the 1-D structures including noise due to particle scattering and generation of secondary particles by impact ionization (II). It is shown that the accuracy of the usual approach based on the DD model in conjunction with the Einstein relation degrades under nonequilibrium conditions. 2-D MC noise simulations are found to be feasible only if the current correlation functions decay on a subpicosecond scale, what is not always the case.

Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices II. Results

A comprehensive investigation of the SPICE and unified compact noise models is performed by comparison with the more fundamental hierarchical hydrodynamic device model. It is shown that the rather simple SPICE and unified compact noise models yield good results for frequencies up to 10 GHz for state-of-the-art SiGe HBTs with a low base resistance. The base noise resistance, a key parameter of the compact noise models turns out to be independent of frequency and bias. It can be well estimated based on the sheet resistance of the intrinsic and extrinsic base or with the modified circle-fit method. The unified model, which in comparison to the SPICE model considers in addition the finite transit time of shot noise, is found to be somewhat more accurate than the SPICE model, especially at higher frequencies and collector currents. But this is achieved at the expense of a transit time parameter which cannot be determined without accurate and detailed noise measurements or physics-based numerical simulations.

https://ieeexplore.ieee.org/iel5/16/28898/01300831.pdf

Investigation of Compact Models for RF Noise in

Investigation of compact models for RF noise in SiGe HBTs by hydrodynamic device simulation

Measured dependence of lifetime upon local defect density and temperature in depletion layers of epitaxial silicon diodes

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Measured dependence of lifetime upon local defect density and temperature in depletion layers of epitaxial silicon diodes