HW%20_1%20Solutions

# HW%20_1%20Solutions - EEE 436 Spring 2010HW#1 SolutionsB...

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EEE 436 Spring 2010—HW #1 Solutions—B. Skromme (100 pts. total) (12 pts.; 6 pts. ea.) (10 pts.)

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2 1.12(b) . The {110} family consists of the following 12 symmetry equivalent planes: () 110 , 110 , 110 , 101 , ( ) 101 , ( ) 101 , ( ) ( ) 011 , ( ) 011 , 011 . One could however consider this to be only 6 equivalent planes, since for example 110 and 110 are really just opposite “sides” of the same plane (note that all parallel planes have the same Miller indices). Either answer (6 or 12) is acceptable with this understanding. (10 pts.) (5 pts.) (12 pts., 6 pts. ea.)
3 Spreadsheet Exercise #1. (6 pts.) a) i) Probability of being occupied at the Fermi level is 0.5. ii) Probability of being occupied at 0.1 eV above E F is 0.0201 (very small) at 300 K. iii) Probability of being occupied at 0.1 eV below E F is 0.980 (fairly high) at 300 K. b) (2 pts.) Check: () -5 0.1 eV 8.617x10 eV K 300 K 1 0.0205 1 FD fE e == + . c) (6 pts.) 100 K: i) Probability of being occupied at the Fermi level is 0.5. ii) Probability of being occupied at 0.1 eV above E F is 8.61x10 –6 (very small) at 100 K. iii) Probability of being occupied at 0.1 eV below E F is about (1 – 8.61x10 –6 ) 1 (very high) at 100 K.

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HW%20_1%20Solutions - EEE 436 Spring 2010HW#1 SolutionsB...

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