PROBLEM SET 6

PROBLEM SET 6 - Semiconductor Dopant Knowledge Block N-Type...

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MSE 110 - UA N-Type P-Type Name Donor impurity Acceptor impurity Elements Group V Group III Electronic band feature of neutral dopant Filled electronic state spatially localized to donor atom having an energy 0.05 eV below bottom of conduction band Empty electronic state spatially localized to acceptor impurity having an energy 0.1 eV greater than the top of the valence band Action - when ionized Donates electrons to conduction band Accepts electrons from valence band Majority Carrier Electrons in conduction band (negative N-type) Holes in valence band (positive P-type) Semiconductor Dopant Knowledge Block
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MSE 110 - UA T dependence of Carrier Concentration SEMICONDUCTOR DEVICES = kT 2 E exp N n b D ex = kT 2 E exp N n g C i kT=0 n=0 kT<E b n=N D + kT E b kT<E g n=N D kT E g n=n i •The number of extrinsic carriers is: Where E b is the gap between the band edge and the defect state and N D is the concentration of dopant atom. •The number of intrinsic carriers is: where Eg is the band gap. T Only ionized dopants All dopants
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MSE 110 - UA SEMICONDUCTOR DEVICES •I n intrinsic semiconductors , charge carriers are thermally excited across the bandgap and are generated according to Fermi statistics. n extrinsic semiconductors most carriers are free at room temperature and the number of carriers is constant in the intrinsic region. = kT E N n g c 2 exp Temperature dependence of number of charge carriers In the upper T limit, electrons get thermally promoted across the bandgap and the semiconductor reverts to intrinsic behavior. In the freeze out region, T is too low to ionize the defects. ⎛ − = kT E N b D in 2 exp Room Temperature
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MSE 110 - UA Conductivity in semiconductors CONDUCTIVITY IN SOLIDS • The conductivity σ is proportional to the charge density n : μ σ e n = •Hence, n and σ follow the same temperature dependence: σ = σ kT 2 E exp g o •So, taking the natural log of both sides indicates that a plot of ln( σ ) vs 1/T should be a straight line of slope –E/2k. Be sure to use T in absolute temperature (K). T k E o 1 2 ) ln( ) ln( ⎛ − + = σσ = kT E b ob 2 exp In the freeze out region In the intrinsic region
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MSE 110 - UA Slope of the natural log curve is –E g /2k Elements of Materials Science and Engineering, Van Vlack, Addison-Wesley, 1989 Conductivity of intrinsic Ge CONDUCTIVITY IN SOLIDS
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MSE 110 - UA SEMICONDUCTOR DEVICES Schematic of T dependence of Conductivity of Extrinsic Semiconductor Extrinsic Freeze out range Intrinsic range Not exactly flat because of the T dependence of the mobility μ σ e n =
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This note was uploaded on 10/06/2009 for the course MSE 110 taught by Professor Lucas during the Spring '08 term at Arizona.

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PROBLEM SET 6 - Semiconductor Dopant Knowledge Block N-Type...

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