EEE 537 L11 Electronic 4

EEE 537 L11 Electronic 4 - l t d H l i Electrons and Holes...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: l t d H l i Electrons and Holes in emiconductors Semiconductors EEE537_Fall 2010 C.Z. Ning EECE ASU 1 Carrier Distributions: Fermi-Dirac Distribution F-D Distribution: (Fermi and Dirac 1926, Jordan 1925): Probability that a state of energy E is occupied by a Fermion 1 = f(E) 100 F B E T k = ) f( ε 1 + T k E E B F e 10 F B E T k = 2 1 = ) f(E F 2 F B E T k = E T k = F B As T increases, more ectrons move to higher EEE537_Fall 2010 C.Z. Ning EECE ASU F E E / = ε (wikipedia.com) electrons move to higher energy states : band filling 2 Carrier Concentrations at Equilibrium: Thermal Population = T T increase Equilibrium: T and E F e-density of states h-density of states ) ( ) ( E N E f e c e ) ( )] ( 1 [ E N E f h v e − * m * m h f EEE537_Fall 2010 C.Z. Ning EECE ASU 1/2 c 2 / 3 2 e 2 ) E (E ) 2m ( 2 1 − = h π e N 1/2 v 2 / 3 2 h 2 E) (E ) 2m ( 2 1 − = h π h N 3 Electron Concentration at Equilibrium he concentration of electrons in the conduction band )dE )f ∞ The concentration of electrons in the conduction band (E)dE (E)f N e E e c ∫ = n ) the electron density of states N e (E) is the electron density of states. ∞ − 1/2 * E ) E (E 2m 1 ⎞ ⎛ − E E C ∫ − + = E T k E E c 2 / 3 2 e 2 dE 1 e ) ( 2 c B F n h π ⎟ ⎟ ⎠ ⎜ ⎜ ⎝ = T k x B ∫ ∞ − = 2 / 3 2 * e ) m ( 4 E E B F dx x T k EEE537_Fall 2010 C.Z. Ning EECE ASU + + 1 2 x T k B e h π π 4 Electron Concentration at Equilibrium: Non-degenerate limit , 1 >> − T k E E B F C e if T k E E 3 > − ( ) 20 ., . 3 ≈ e g e , f E E C F x ∞ − ∞ * * B F C x T k B x T k E E B B B F C dx e x e T k e dx x T k n − + − = + = ∫ ∫ 2 / 3 2 e 2 / 3 2 e ) 2 m ( 4 1 ) 2 m ( 4 h h π π π π T k E E c B F C e N n − − = 2 / π 2 / 3 : 1 2 2 3 2 cm T k m N B e c ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = h π k E 2 / 3 , T m N e c ∝ EEE537_Fall 2010 C.Z. Ning EECE ASU Effective density of states of conduction band k E F 5 Hole Concentration at Equilibrium E)dE E)f E v = The concentration of holes in the valence band 1 1 1 1 = − = =-f f ; ( ) d ( ) f N p h h ∫ ∞ − 1 1 + + T B k E F E T B k F E E e h e e In complete analogy to the case for electrons: E E E / v / * h v F dE E E ) m ( p − − = ∫ ) (...
View Full Document

This note was uploaded on 01/02/2012 for the course ECE 537 taught by Professor Czning during the Fall '10 term at ASU.

Page1 / 20

EEE 537 L11 Electronic 4 - l t d H l i Electrons and Holes...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online