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ECE 3080: Homework #2, Solutions September 14, 2007 Page 1 of 5 G EORGIA I NSTITUTE OF T ECHNOLOGY S CHOOL OF E LECTRICAL AND C OMPUTER E NGINEERING ECE 3080: Semiconductor Devices for Computer Engineering and Telecommunication Systems Fall Semester 2007, Homework #2 SOLUTIONS 1. Short Questions (2 points each): (a) What can you say about the Fermi level in a semiconductor device in thermodynamic equilibrium? Answer: In equilibrium, the Fermi level is constant throughout the device. (b) Given is the E(k) relationship for the conduction band in a semiconductor material. How can you calculate the effective mass of the electrons from this E(k) relation? Answer: The effective masses are calculated from the curvature of the E(k) relationship, i.e. the band structure: 1/ m * = 1/ ! 2 ! d 2 E ( k )/ dk 2 (c) Name a typical donor atom for doping silicon. Where are the additional electron states located? Are those states occupied with an electron at absolute zero (T = 0 K)? Justify your answer. Answer: Phosphorous (P) and arsenic (As) are the most common donor atoms for silicon; the additional electron states E D are located in the “forbidden” band gap close to E C ; at absolute zero, these electron states are ALL occupied; with increasing temperature, electrons in these gain sufficient energy to be excited into the conduction band. (d) Why is the intrinsic Fermi level in a silicon semiconductor not exactly in the middle of the band gap, i.e. at (E C +E V )/2? Answer: The Fermi level is not exactly in the center of the band gap, because the
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