Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation

We present a multi-mode drift-diffusion equation as reformulation of the Boltzmann equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M x 1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon

Computational and experimental study of transport in advanced silicon devices

In this thesis, we investigate electron transport in advanced silicon devices by focusing on two important classes of devices: the bipolar junction transistor (BJT) and the silicon MOSFET. In regards to the BJT, we will compare and assess solutions of a physically detailed microscopic model to the standard Drift-Diffusion model. In so doing, we will explain why the Drift-Diffusion model has been prevalent and speculate about its prospect in the future. In connection with the MOSFET, we present a new theory, which calculates the upper-limit performance for a given CMOS technology. Using this theory, we assess the performance of a present-day technology by using experimental data and make predictions about the performance of future CMOS technologies as specified in the Roadmap for Semiconductor Industry. Finally, we will speculate on whether or not CMOS technology will be viable in the future