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ECE440_Carney_L8

# ECE440_Carney_L8 - ECE440Lecture8 Fall2010...

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ECE440 Lecture 8 Fall 2010 Sec\$on E: MWF 1:00‐1:50PM Everi5 241 • Prof. P Sco5 Carney

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Topics Available carriers Density of states Effec?ve density Carrier densi?es
Available carriers dn 0 = f E ( ) N E ( ) dE n 0 = f E ( ) N E ( ) dE electrons: What is N? p 0 = 1 f E ( ) N E ( ) dE

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Free electron model Let’s pretend the conduc?on band electrons are really free par?cles with modified mass They’re s?ll described by QM, so we need a pathway to “freedom” Start by puPng the p’cle in a bow and take the large box limit
k x k y Momentum states in a finite volume k x = 2 π n x L x k y = 2 π n y L y k z = 2 π n z L z Volume (k‐space) per state: V k = 2 π L x 2 π L y 2 π L z = 8 π 3 V r L y L x L z quan?za?on volume (coordinate space) The box Quana?za?on from the box, NOT due to the laPce

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More states in momentum space dn k = V k 1 d 3 k = V r 8 π 3 d 3 k differen?al number of states differen?al volume in k‐space
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ECE440_Carney_L8 - ECE440Lecture8 Fall2010...

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