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Homework%203_Solution

# Homework%203_Solution - Problem I Calculate the magnitude...

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Problem I Calculate the magnitude of the velocity of an electron in GaAs with energy of 3/2 k B T above the conduction band edge (the thermal average energy) with T = 300K, assuming the validity of the effective mass approximation. Repeat for Si, treating the system as isotropic (not directionally dependent) using the conductivity, effective mass. (This actually works.) In each case, put your answers in units of m/s = nm/ns (relevant for current device scales and clock frequencies) and km/hour (relevant to everyday experience). Appendix III may be helpful. Note that the conductivity effective masses are provided in Example 3-6 of the text, or could be calculated for Si as done in the example. (Also, just FYI for now, note that the average velocity of charge carriers through conventional transistors now approaches this velocity.) Solution: The effective mass approximation means that the electrons can be treat as “free” particle inside the semiconductor, if the mass is the effective mass. In another word, the effect of crystal potentials are all contained in the E(k) relationship, therefore effective mass. For GaAs: *2 23 56 *3 1 31 22 3 3 1.38 10 300 / 4.5 10 / 1.6 10 / 0.067 9.1 10 BG a A s B GaAs kT m v v nmn s s kmh r m       For Silicon: , 23 55 1 , 3 3 1.38 10 300 / 2.3 10 / 8.2 10 / 0.26 9.1 10 B Si cond B Si cond m v v s s r m Problem II Consider conduction-band minimum energy valleys centered at the X points, and assume that for the valley centered at the X point along the (100) direction ( 2/ kx a ), specifically, the

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Homework%203_Solution - Problem I Calculate the magnitude...

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