05_carrier+density+calculation

05_carrier+density+calculation - Carrier Density...

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EECS-320, L.J. Guo 1 Carrier Density Calculation How to determine carrier density and the associated Fermi energy level? What are the necessary conditions to determine the carrier densities? What are intrinsic and extrinsic semiconductors? How can semiconductors be compensated? Carrier density as a function of temperature
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EECS-320, L.J. Guo 2 Density Of States How many electron states are there at certain energy? Density Of States for conduction band and for valence band *3/ 2 1/ 2 23 2( ) () eC C mE E gE π = h *3/ 2 1/ 2 ) hV V E = h E ρ (E) E V E C Valence band Conduction band
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EECS-320, L.J. Guo 3 Fermi Function and Fermi Energy Electronic states are not uniformly populated, but obey the F-D distribution At T=0, all states below E f are filled and all states above are empty; For metals, Fermi energy/level represents the highest energy level that is occupied by electrons. For semiconductors, Fermi level is a function of carrier density, as we will see later. Approach Boltzmann distribution () + = kT E E E f f exp 1 1 k = 8.617x10 -5 eV/ o K
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EECS-320, L.J. Guo 4 Carrier Density Distribution ( ) ( ) ( ) C nE g E f E = () ( ) 1 V pE g E f E ⎡⎤ =− ⎣⎦
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EECS-320, L.J. Guo Degenerate versus Non-Degenerate Define where Boltzmann approximation is valid E C E V For E V + 3kT < E f < E C – 3kT, Boltzmann approximation is accurate Semiconductor is said to be “non-degenerate” 3kT 3kT E F here: non-degenerate, Boltzmann valid E F here: degenerate (large n) E F here: degenerate (large p)
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EECS-320, L.J. Guo Alternative expression for n, p (non-degenerate) = kT E E N n C f C exp = kT E E N p f V V exp For Boltzmann approximation, exp iC EE nN kT
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This note was uploaded on 07/22/2011 for the course EECS 320 taught by Professor Sun during the Fall '10 term at University of Florida.

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05_carrier+density+calculation - Carrier Density...

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