Learn the basic properties and designs of modern VLSI devices, as well as the factors affecting performance, with this thoroughly updated second edition. The first edition has been widely adopted as a standard textbook in microelectronics in many major US universities and worldwide. The internationally-renowned authors highlight the intricate interdependencies and subtle tradeoffs between various practically important device parameters, and also provide an in-depth discussion of device scaling and scaling limits of CMOS and bipolar devices. Equations and parameters provided are checked continuously against the reality of silicon data, making the book equally useful in practical transistor design and in the classroom. Every chapter has been updated to include the latest developments, such as MOSFET scale length theory, high-field transport model, and SiGe-base bipolar devices.

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Fundamentals of Modern VLSI Devices

A self-consistent iterative scheme for the numerical calculation of dc potentials and currents in a one-dimensional transistor model is presented. Boundary conditions are applied only at points representing contacts. Input data are: doping profile, parameters governing excess carrier recombination, parameters describing the dependence of mobility on doping and on electric field, applied emitter and collector voltages, and a trial solution for the electrostatic potential. The major limitation of the present approach results from use of Boltzmann rather than Fermi statistics. Convergence of the iteration scheme is good for low and moderate injection levels.

A self-consistent iterative scheme for one-dimensional steady state transistor calculations

We present in this paper a compact model of bipolar transistors, suitable for network analysis computer programs. Through the use of a new charge control relation linking junction voltages, collector current, and base charge, the model includes high injection effects. The performance substantially exceeds that of existing models of comparable complexity. For low bias and with some additional idealization, the model reduces to the conventional Ebers-Moll model.

An integral charge control model of bipolar transistors

We start with a mathematical definition of a real interval as a closed, connected set of reals. Interval arithmetic operations (addition, subtraction, multiplication, and division) are likewise defined mathematically and we provide algorithms for computing these operations assuming exact real arithmetic. Next, we define interval arithmetic operations on intervals with IEEE 754 floating point endpoints to be sound and optimal approximations of the real interval operations and we show that the IEEE standard's specification of operations involving the signed infinities, signed zeros, and the exact/inexact flag are such as to make a correct and optimal implementation more efficient. From the resulting theorems, we derive data that are sufficiently detailed to convert directly to a program for efficiently implementing the interval operations. Finally, we extend these results to the case of general intervals, which are defined as connected sets of reals that are not necessarily closed.

http://fab.cba.mit.edu/classes/S62.12/docs/Hickey_interval.pdf

Interval arithmetic: From principles to implementation

Part 1 Introduction: nonlinear programming local methods global methods Numerica outline. Part 2 A tour of Numerica: getting started generic constraints constants ranges input parameters aggregation operators functions sets unconstrained optimization constrained optimization local constraint solving local unconstrained optimization soft constraints real constraints and uncertain data display accuracy. Part 3 The meaning of Numerica: interval analysis constraint solving unconstrained optimization interpretation of the results. Part 4 Modelling in Numerica: what can go wrong in Numerica improving Numerica statements. Part 5 The syntax of Numerica: overall structure expressions the constant section the input section the set section the variable section the function section the body section the display section the pragma section scoping rules. Part 6 The semantics of Numerica: interval arithmetic semantics of constraint solving semantics of unconstrained minimization semantics of constrained minimization non-canonical boxes. Part 7 An implementation of Numerica: overview of the algorithm domain-specific and monotonic interval extensions constraint solving unconstrained optimization constrained optimization advanced techniques an implementation of box consistency. Part 8 Experimental results: constraint solving unconstrained optimization constrained optimization appendices.

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Numerica: A Modeling Language for Global Optimization

In the consideration of the junction transistor as a switch there are three characteristics of primary interest, the open impedance, the closed impedance, and the switching-time. A generalized two-terminal-pair theory of junction transistors is presented which is applicable, on a dc basis, in all regions of operation. Using this theory, the open and closed impedances of the transistor switch are expressible in terms of easily measurable transistor parameters. For the ideal transistor these parameters are the saturation currents of the emitter and collector junctions and the normal and inverted alphas. The transition of the transistor switch from open to closed, or vice versa, is discussed, including the effects of minority carrier storage. This transition can be expressed in analytic form in terms of the alphas and the normal and inverted alpha cut-off frequencies.

J. J. Ebers

Papers

Large-Signal Behavior of Junction Transistors