A one-dimensional solution of the Boltzmann transport equation with application to the compact modeling of modern bipolar transistors

• Main Author: St.Denis, Anthony Robert
• Format: Others
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/10098

The role of device design in the development of semiconductor technologies is an important one. To effectively design devices, the device engineer needs to understand the physics of device operation. The models used to predict device behavior should therefore be cast in such a form that the physics is readily identifiable. This is true for both compact device models and the detailed models of transport from which they are derived. A considerable effort has been expended here to develop models exhibiting this feature. The fundamental starting point for the transport analysis in this work is a one-dimensional, time-independent form of the Boltzmann transport equation (BTE). There are three main contributions made herein regarding the use of the BTE for analyzing transport in semiconductor devices. First, a field-free solution, valid for arbitrary boundary conditions and quite general collision integrals, is developed and used to study transport in the base of bipolar transistors, including both homojunction and heterojunction devices. Secondly, a kinetic approach to transport is used to develop an analogous solution for field-dependent transport. The field-dependent solution is used to make a study of the nature of carrier mobility in a forward-biased semiconductor barrier. Thirdly, forms for the incoming collision integrals are developed which involve integration over a single angle only, which makes them particularly well suited for use in both the field-free and field-dependent solutions developed in this work. In the device design process, it is very useful to appeal to compact device models in order to do preliminary designs, and to aid in the understanding of results from more detailed transport analyses. Compact models are closed form expressions describing device behavior, usually based on approximations of detailed device equations. In this work, compact models are developed which approximate the solution of the BTE in modern, short-base, bipolar transistors. Two models for collector current are derived. The first of these is appropriate for homojunction, and graded-heterojunction, devices. The second is appropriate for abruptheterojunction devices. A third compact model is derived for the base transit time in abrupt heterojunction devices. Throughout this work, an attempt is made to understand transport phenomena in terms of the electron distribution function. This leads to a more fundamental understanding of device operation than can be gained by applying concepts inherent to drift-diffusion analyses, such as drift and diffusion current densities and quasi-Fermi levels. Such an understanding is necessary for the design and analysis of future, and state of the art present, devices whose intended very high frequency of operation demands that certain critical dimensions be reduced below the limits within which traditional drift-diffusion analysis applies. === Applied Science, Faculty of === Electrical and Computer Engineering, Department of === Graduate