20111ee2_1_2011_EE2_HW2 Solution

20111ee2_1_2011_EE2_HW2 Solution - Physics for Electrical...

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Physics for Electrical Engineers Prof. B. Jalali EE 2 Homework #2 Due: Jan 27, 2011 You may or may not find the following information useful: h=6.626 × 10 -34 J-s Mass of the electron=9.1 × 10 -31 kg 1. a. Show that the Fermi function is symmetric about E F , i.e., f ( E F + Δ E )=1 - f ( E F - Δ E ) b. Show that when ( E - E F ) 2 kT , f ( E ) exp EE kT F Actually, calculate f ( E ) for ( E - E F ) equal to 2 kT , 3 kT and 4 kT by using the Fermi function. Compare the results with those obtained by using the exponential approximation. (a) To Prove f (E F + Δ E) = 1 – f (E F Δ E) ⎛ Δ + = Δ + + = Δ + kT E kT E E E E E f F F F exp 1 1 exp 1 1 ) ( Δ + Δ + = Δ + = Δ + = Δ kT E kT E kT E kT E E E E E f F F F exp 1 1 exp 1 exp 1 1 1 exp 1 1 1 ) ( 1 ) ( exp 1 1 exp 1 exp E E f kT E kT E kT E F Δ + = ⎛ Δ + = Δ + Δ = (b) + = kT E E E f F exp 1 1 ) (
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+ E E F exp 1 For E – E F 2kT, kT E E kT F exp ( since, 1 exp >>
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20111ee2_1_2011_EE2_HW2 Solution - Physics for Electrical...

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