ECE340_L12_S14_Distribution

# ECE340_L12_S14_Distribution

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Unformatted text preview: at energy “E” in Material 2 ༉ ¢༊ ༉ Density of States in Material 1: N1 ( E ) Density of States in Material 2: N 2 ( E ) Probability State Occupied in Material 1: f1 ( E ) Probability State Empty in Material 2: ⎡1 − f2 ( E ) ⎤ ⎣ ⎦ { Rate1→2 : R = a { N1 ( E ) f1 ( E )} N 2 ( E ) ⎡1 − f2 ( E ) ⎤ ⎣ ⎦ # electrons # empty states 9 } Case 2: Electrons Moving From 2 to 1 •  At a given energy “E” the mo[on of an electron from material 2 to material 1 requires a full state in material 2 and an empty state in material 1 •  The rate of mo[on is propor[onal to the product of the number of electrons at energy “E” in material 2 and the number of empty states at energy “E” in Material 1 ¢༊ ༉ ༉ Density of States in Material 1: N1 ( E ) Density of States in Material 2: N 2 ( E ) Probability State Empty in Material 1: ⎡1 − f1 ( E ) ⎤ ⎣ ⎦ Probability State Occupied in Material 2: f2 ( E ) { Rate 2→1 : R = a N1 ( E ) ⎡1 − f1 ( E ) ⎤ ⎣ ⎦ # empty states }{ N 2 ( E ) f2 ( E )} # electrons 10 Equilibrium Fermi Level •  There is no net charge transfer or energy transfer between regions in equilibrium, so the rates from Case 1 and Case 2 must balance –  We assume that the constant of propor[onality “a” for the rate of mo[on from 1 to 2 is the same as that from 2 to 1 (reciprocity) ༉ ༉ è༎ = ç༎ R1→2 = aN1 ( E ) f1 ( E ) × N 2 ( E )[1 − f2 ( E )] = aN...
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## This note was uploaded on 03/06/2014 for the course ECE 340 taught by Professor Leburton during the Spring '11 term at University of Illinois, Urbana Champaign.

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