Preface

Continuous efforts to develop semiconductor devices enable us to realize significant development of IT (Information Technology) of these days. Bipolar transistors and MOSFETs are two distinguished devices that construct very large scale integrated (VLSI) circuits, where the scaling of these devices realizes it’s high speed and high packing density with suppressing the increase of power consumption. Models for these devices have been intensively developed. It is important to know the assumptions and approximations of these models to understand their limitations, which makes us to use the models properly, and give a chance to improve them. Many text books have been published on this subject. However, the full derivations of the advanced models are rarely described. The derivation processes for the advanced models include many subjects: one should learn how we should define the outline of the related phenomenon, set the tackling strategy to solve the problem, make some assumptions and approximations without losing accuracy, and learn many techniques to reach the final simple and clear expressions. Therefore, one can learn much from the derivation process of advanced models to become an expert in the field. Here, the derivation processes of models from fundamental ones to the advanced ones are shown step by step. I treat the following subjects in this book. Semiconductor devices are based on solid state physics and statistical mechanics. I briefly review the outline of these subjects. The concept of bandgap, energy density, probability function, mobility, carrier flux, Poisson equation, and current continuity equation are emerged, which are the starting equations to derive various models. pn junction is then treated, which is a fundamental component for understanding characteristics of bipolar transistors and MOSFETs. The models for potential distribution and current-voltage characteristics are derived. Bipolar transistors are treated next, where minority carries are injected into the base region. The characteristics of the device are significantly influenced whether the injected carrier concentration is higher than the base doping concentration or not. Models in low injection region are treated first. Uniformly doped devices are treated, and the models are then extended to the models with the arbitrarily doped devices. High injection models are treated next, where the injected carrier concentration is not negligible with respect to the doping concentration. The injected carriers influence electric field in the base and collector/base depletion regions. Base doping modulation, Kirk effects, and emitter current crowding are significant phenomenon in high injection region. MOSFET is a major device in modern VLSI. Models for long channel ones are treated first. Influence of velocity saturation, gate length modulation is described. Uniform channel with respect to vertical direction of the channel is first assumed and then it is extended to the ones for arbitrarily doped one. This non-uniform channel doping device overcomes the tradeoff between threshold voltage adjustment and short channel immunity. The short channel effects of the devices are further treated. SOI devices and double-gate SOI, surrounded gate SOI devices are proposed and fabricated to overcome the limitation of the bulk MOSFETs. The characteristics of these devices are significantly different from those of the bulk MOSFETs since the depletion region is limited by SOI thickness. The related models for these devices including its short channel effects are described. Finally, parasitic effect of MOS devices is treated: Silicide/Si substrate contact resistance, and gate fringe capacitance. The influence of impurity penetration through thin gate oxide to the threshold voltage variation is also studied. I aim at the readers who are experts or non-experts in various fields associated with semiconductor devices, hope that various members can cover some knowledge to collaborate with one another. It is not easy for non-expert members to understand this book. However, I believe that one can do it with time and efforts and believe that it is worth for devotion.