05+Doping - Review: Carrier Statistics ( ) ( ) dE E f E g n...

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Unformatted text preview: Review: Carrier Statistics ( ) ( ) dE E f E g n C E C ∫ ∞ = ( ) ( ) [ ] dE E f E g p V E V ∫ ∞ − − = 1 For Boltzmann approximation, ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = kT E E N p f V V exp ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = kT E E N n C f C exp 2 / 3 2 * 2 2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = h π kT m N n C 2 / 3 2 * 2 2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = h π kT m N p V Review: np Product • The product of n and p gives: ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = kT E m m kT np G p n exp 2 4 2 / 3 * * 3 2 h π ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = kT E N N np G V C exp n = p ≡ n i Intrinsic semiconductor : ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + = * * ln 4 3 2 n p V C i m m kT E E E E i =E f for intrinsic semiconductor • For intrinsic semiconductor, Fermi energy lies near the middle of the bandgap, shifts depending on effective mass and temperature EECS 320 Doping Doping Intrinsic material • n=p=n i • Carrier density is fixed for given material and T • We would like to selectively alter n, p Q: How do we alter n, p in a semiconductor? A: Provide substitutional impurity that provides an additional electron or hole. Donors • Donors – impurity atoms that provide additional electrons....
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05+Doping - Review: Carrier Statistics ( ) ( ) dE E f E g n...

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