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EMS172-2009-Homework4_Solutions

# EMS172-2009-Homework4_Solutions - UNIVERSITY OF CALIFORNIA...

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EMS 172 Profs. Y. Takamura and A. Moulé, 2009 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 172: Electronic, Magnetic, and Optical Properties of Materials Homework 4 Due Date: Tuesday, Oct. 27 th , 2009 in class Note: You must show all the steps you used to obtain your answer in order to receive full credit. 1. Intrinsic Semiconductors [16 pts] [ Computer problem ] The equation for the intrinsic carrier concentration, N i , is given by: N i = ( N c N υ ) 1/2 exp[- E g /2 k B T ] [Eqn. 1] Within this equation, several terms depend on temperature according to the following relationships: Barber [ Solid State Electronics, 10, 1039 (1967)] showed that the temperature dependence of the effective mass of the electrons and holes for silicon over the temperature range 200 K< T < 700 K could be approximated by: ( ) ( ) 2 7 4 0 * 10 09 . 3 10 11 . 6 028 . 1 T T m m e × × + = [Eqn. 2] ( ) ( ) 2 7 4 0 * 10 46 . 4 10 83 . 7 61 . 0 T T m m h × × + = [Eqn. 3] In order to match experimental data, Barber had to include an additional term when computing the band gap energy, such that E g (T) = E gT – E ex , where D g gT T T E E θ ξ + = 2 0 . E ex is the exciton correction factor, E g0 is the bandgap at 0K , ξ is a coefficient, θ D is the Debye temperature, and T is in Kelvin . (see Table I). (a) With this information use your favorite plotting software (Matlab, Mathematica, etc…) to create a plot of log ( N i ) [cm -3 ] as a function of temperature [K] for silicon from 200 K < T < 700 K. Note :

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EMS172-2009-Homework4_Solutions - UNIVERSITY OF CALIFORNIA...

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