654_ch5 - ECE 654 Prof. S. Mohammadi Solid State Devices II...

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ECE 654 Solid State Devices II Prof. S. Mohammadi - 89 - Chapter 5 Transport and Scattering Mechanisms in Silicon and Compound Semiconductors In this chapter we start with various scattering mechanisms that affect the electron and hole transports in semiconductors. We will the overview high field electron and hole transports in Si and Compound Semiconductors (CS). Electron Transport in Semiconductors: In order to understand how electron gas moves through the material, one needs to know various scattering rates as well as the distribution function of the electron gas. The distribution would tell us how the electrons are distributed in k-space and E-space. We know that at equilibrium the distribution of electrons f(E) follows the Fermi-Dirac function 1 ( ) exp( ) 1 F B f E E E k T = - + (5.1) where E F is the Fermi level, k B is the Boltzman constant and T is the absolute temperature. This distribution function is independent of any collision (scattering) that may be present. While the collisions continuously remove electrons from one k-state to another, the net distribution of electrons is always given by the Fermi-Dirac function as long as there are no external influences to disturb the equilibrium. To describe the distribution function in the presence of external forces, one needs to use Boltzman transport equation instead of Fermi-Dirac. According to Boltzman, there are three possible reasons for change in electron distribution in k-space or x-space: 1. Electron diffusion 2. Electron drift caused by external forces _ field ext E h = / dk dt 3. Electron scattering The resulting Boltzman transport equations can be solved using iterative approaches. Only in special cases, one can solve the function analytically to predict electron transport through the
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ECE 654 Solid State Devices II Prof. S. Mohammadi - 90 - semiconductor. One of these special cases is transport under low electric field, which is unrealistic for many real devices. In many cases, one has to rely on averaging process and use parameters such as mobility, diffusion coefficient etc. to express the transport. In our case, we consider two types of transport formalism: 1. Drift/diffusion approach which is based on Fermi-Dirac statistics. This approach is an oversimplification for many high speed transistors. 2. Energy-Balance approach, which is based on Boltzman equations. This approach is very useful for transport under high electric fields which is the case for many advanced transistors. Before we end this chapter, let us discuss various scattering mechanisms in semiconductors. We will not go through details of numerical calculations and leave that to software suits like MEDICI. Instead, we will stick to physical meaning of these scattering mechanisms. Ionized Impurity Scattering
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This note was uploaded on 02/19/2012 for the course ECE 654 taught by Professor Mohammadi during the Spring '08 term at Purdue.

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654_ch5 - ECE 654 Prof. S. Mohammadi Solid State Devices II...

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