ECE3080_Homework1_Solution - GEORGIA INSTITUTE OF...

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ECE 3080: Homework #1, Solutions May 28, 2009 Page 1 of 10 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 Summer Semester 2009, Homework #1 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 (conduction band in case of electrons): 1/ m * = 2 d 2 E ( k )/ dk 2 (c) Name a typical acceptor 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: Boron (B) is the most common acceptor atom for silicon; the additional electron states E A are located in the “forbidden” band gap close to E V ; at absolute zero, these electron states are NOT occupied; only with increasing temperature, electrons from the valence band are excited into states at E A , thus generating holes in the valence band, which contribute to the conduction. (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 effective masses for electrons and holes are different. (e) How does the electron mobility of a low-doped silicon sample change with increasing temperature (around room temperature)? Justify your answer. Answer: In a low-doped silicon sample, lattice scattering is the dominant carrier scattering mechanism; with increasing temperature, lattice scattering increases (because of increased lattice vibrations) and the electron mobility thus decreases.
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This note was uploaded on 07/30/2009 for the course ECE 3080 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.

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ECE3080_Homework1_Solution - GEORGIA INSTITUTE OF...

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