EMS172-2009-Homework5_Solutions

# EMS172-2009-Homework5_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 5 - Solutions Due Date: Tuesday, Nov. 10 th , 2009 in class Note: You must show all the steps you used to obtain your answer in order to receive full credit. 1. Extrinsic Semiconductors [34 pts] [Computer problem] Consider an n -type silicon sample that has been doped with 2x10 15 phosphorus atoms per cm 3 . The donor level for P in Si is 0.045 eV below the conduction band energy. (a) Use your Matlab / Mathematica program from HW 4 to create plots of log(N e ) (#/m 3 ) vs. temperature AND log( N e ) (#/m 3 ) vs. (1/T) *1000 [K -1 ] for the full temperature range from 25 K < T < 700 K. Hand sketches will not be given full credit. Hint for making sure you get the correct magnitude on your plots: if you use ALL SI units for all the constants (Joules, kg, meters, etc…), you will get an answer for N i /N e with units of [#/m 3 ]. An ‘easy’ number to remember is that for Si, N i = 10 10 #/cm 3 at 300 K. As discussed in lecture, the full temperature range is broken down into three regimes, intrinsic , extrinsic , and freeze-out , and each of these regimes is described by a separate equation. In the freeze-out regime, the equation is given by: = = + T k E E N N N N B D C D C D e 2 ) ( exp 2 1 2 1 Label these three regimes in both of your plots. When creating your plots, consider the following questions: (i) What equation governs N e in the intrinsic regime? (ii) What equation governs N e in the extrinsic regime? [6 pts for perfect plot] [-1 pt for missing labels] [-1 plot if shape of curve is correct but magnitude of data is incorrect] [-1 pt if one of the regions is missing] [-1 pt if the transition regions are incorrect]

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EMS 172 Profs. Y. Takamura and A. Moulé, 2009 (b) Using your plot in (a), estimate the lowest temperature above which all the donors are ionized. You can estimate the temperature above which all the donors are ionized according to when 3 21 2 1 10 2 2 ) ( exp 2 1 + × = = = = m N T k E E N N N N D B D C D C D e
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EMS172-2009-Homework5_Solutions - UNIVERSITY OF CALIFORNIA...

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