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EEE 537 L11 Electronic 4

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

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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 − − = ∫ ) (...
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EEE 537 L11 Electronic 4 - l t d H l i Electrons and Holes...

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