ECE340_L12_S14_Distribution

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: at energy “E” in Material 2 Ÿ༉ ¢༊ Ÿ༉ 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 ¢༊ Ÿ༉ Ÿ༉ 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) Ÿ༉ Ÿ༉ è༎ = ç༎ R1→2 = aN1 ( E ) f1 ( E ) × N 2 ( E )[1 − f2 ( E )] = aN...
View Full Document

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.

Ask a homework question - tutors are online