Homework%2006

# Homework%2006 - EEE 352-Spring 2008 Homework 6 3.23...

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EEE 352—Spring 2008 Homework 6 3.23 Determine the total number of energy states in GaAs between E c and E c + k B T at 300 K. The number of states per unit volume is given by integrating the density of states over this energy range: 3 23 2 34 23 31 2 2 / 3 2 2 0 2 / 1 2 / 3 2 2 10 27 . 3 ) 10 055 . 1 ( 300 10 38 . 1 10 1 . 9 067 . 0 2 3 1 2 3 1 2 2 1 × = × × × = = = m T mk dE E m n B T B k E π π π h h 3.30 Determine the probability that an electron is occupied by an electron if the state is above the Fermi level by (a) k B T, (b) 5k B T, and (c) 10k B T. The probability is given by the Fermi-Dirac distribution as + = T k E E P B F exp 1 1 (a) 269 . 0 1 1 ) ( 1 = + = e T k P B . (b) 3 5 10 7 . 6 1 1 ) 5 ( × = + = e T k P B (c) 5 10 10 54 . 4 1 1 ) 10 ( × = + = e T k P B 3.31 Determine the probability that an electron is occupied by an electron if the state is below the Fermi level by (a) k B T, (b) 5k B T, and (c) 10k B T.

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