# ch10 - andDevices Topic10: inSemiconductors Fall2007...

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Topic 10 : Charge Carrier Concentrations                in Semiconductors                       Fall 2007 ECE 3500 - Semiconductor Materials  and Devices

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Learning Objectives In this topic you will learn: The distribution of electrons and holes over  energy levels in a semiconductor. The concepts of density of states and effective  density of states. How to calculate the concentration of electrons  and holes at thermal equilibrium in an intrinsic  semiconductor at different temperatures. How to calculate the concentration of electrons  and holes at thermal equilibrium in a doped  semiconductor at different temperatures.
Fermi-Dirac Statistics Since we are dealing with large numbers of e -  s and h +  s distributed over a large number of very closely spaced energy levels, the approach that we will use will be a  statistical approach . The appropriate statistics to use for e -  s and h +  s is  Fermi-Dirac statistics .

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Fermi-Dirac Statistics (cont’d) The  probability of occupancy , f(E), of an energy level E in Fermi-Dirac statistics is given by: where k = 1.38 x 10 -23  JK -1  ( Boltzmann’s constant )           T = the  absolute temperature   of the                            semiconductor in degrees Kelvin and    E F Fermi Energy f E E E kT F ( ) exp[( ) / ] = + - 1 1
Fermi-Dirac Distribution Function A plot of the probability of occupancy of an energy level E as a function of energy at different temperatures is shown below:

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## This note was uploaded on 03/11/2010 for the course ECE 4350 taught by Professor Singh during the Spring '07 term at Villanova.

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ch10 - andDevices Topic10: inSemiconductors Fall2007...

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