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3Q3%20assignment%20solution_modif

# 3Q3%20assignment%20solution_modif - 6 February 2006 MTLS...

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6 February 2006, MTLS 3Q3 Materials for Electronic Applications Assignment 1, Due Feb 13 th at Class time (SOLUTION) In all answers use diagram and concise explanations. 1) Free electron theory and energy distribution electrons in solids. a) For solid Al, draw a schematic diagram of the energy distributions of valence electrons indicating the position of the Fermi energy E F at a temperature T = 0 K. b) Draw the same diagram at a finite temperature T>0K and T >> 0 K. c) What energy distribution would you need to use to calculate the probability of finding an electron with an energy E>E F at T > 0 K. d) Sketch a density of states diagram for a non free-electron metal such as Fe. (5 points) Answer: (a) and (b) T=0 (c) The probability of finding an electron with an energy E > E F at T>0 K is represented by the Fermi-Dirac distribution: F ( E ) = {(exp( E - E F ) /kT )+1} -1 which is the function of energy, E , for a given kT . The occupancy probability of electron at T = 0 K and T > 0 K are shown in figures below. E F Energy 2p electrons Bands full 3 s electrons Parabolic band. Sharp transition at T = 0K but for T>>0 we have electrons at E > E F . T > 0 K T >> 0 K

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(d) Sketch of density of states diagram for Fe: 2) Band theory and properties of solids. a) Using the Ziman model of band theory, explain the origin of the gap in solids. b) What distinguishes metals and insulators in a simple one-dimensional Ziman model. (Hint, discuss the trends as a function of number of valence electrons).
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