04_DOS, Fermi function _ equilibrium carrier concentration

# 04_DOS, Fermi function _ equilibrium carrier concentration...

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Density of states, Fermi-Dirac Distribution, Fermi energy What is the number of electrons and holes that can contribute to current flow? What is the number of available electron (hole) states in a semiconductor? How are charge carriers distributed in energy? What is Fermi function and Fermi energy/level? How is Fermi energy (level) related to carrier density What does “degenerate” and “non-degenerate” semiconductor mean? 1

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EECS-320, L.J. Guo Review: effective mass Effective mass approximation allows us to treat electrons in conduction band and holes in valence band as “free” classical charged particles, without having to resort to full QM treatment 2
EECS-320, L.J. Guo Objective of 320: find I-V relationship Current density is related to charge density Not referring to total electron density but conduction electron density Need to compute the electron density in conduction band and hole density in valence band Charge number density unit 1/cm 3 3

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EECS-320, L.J. Guo State and Carrier Distributions How do we calculate the electron and hole densities? n = # occupied states in the conduction band/unit volume p = # empty states in the valance band/unit volume Need to know 1) how many states are available; and 2) probability that each state is occupied. 4
EECS-320, L.J. Guo Football Stadium analogy 5

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EECS-320, L.J. Guo States In Conduction/Valence Band and DOS Recall Conduction and Valence Band E C E V E No states in the bandgap Define “hole” states in valence band Define electron states in conduction band Number of states Unit volume x Unit energy Density Of States (DOS) = Electronic states are not uniformly distributed in energy! g(E)dE : No. of states lying in the energy range between E and E+dE 6
EECS-320, L.J. Guo Energy states in a crystal material are distributed uniformly in k-space, but not in energy space Density of states may be determined if bandstructure is known Near bandedge (E C and E V ), approximate using effective mass m n * and m p * (You will see this in detail in classes like in 420) 7

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EECS-320, L.J. Guo
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04_DOS, Fermi function _ equilibrium carrier concentration...

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