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Lecture%2016 - EEE 352: Lecture 16 Intrinsic Semiconductors...

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1 EEE 352: Lecture 16 Intrinsic Semiconductors—Last time we pointed out that we still need to determine “ How many electrons and holes are present at temperature T? To do this, we need to determine: * Density of states Electrons Holes * Electron and hole carrier densities Intrinsic Semiconductors ± By INTRINSIC semiconductors, we mean: ¾ There are NO IMPURITIES ¾ That is, the semiconductor is ideally PURE ± Hence, we study the properties of the thermally excited electrons and holes. ± We recall that Si would be an insulator, but has a small band gap (only 1.1 eV) so that thermal excitation across the gap gives free carriers that make it a very poor insulator (but a good semiconductor). ± Previously we saw that SEMICONDUCTORS are materials with a SMALL energy gap between empty and filled energy bands ± Electrons can be EXCITED across this gap at higher temperatures thus INCREASING the conductivity Density of States AT FINITE TEMPERATURES CURRENT IS CARRIED BY HOLES IN THE VALENCE BAND AND ELECTRONS IN THE CONDUCTION BAND FULL VALENCE BAND EMPTY CONDUCTION BAND ABSOLUTE ZERO T = 0 K ENERGY GAP E g E F P(E) FINITE TEMPERATURE T > 0 K E F P(E) The THERMAL excitation of electrons across the GAP creates electrons in the conduction band and holes in the valence band. HOW MANY ARE THERE? Density of States n ( E),p(E) ENERGY GAP E THE UPPER BRANCH IS THE ELECTRON DENSITY OF STATES THE LOWER BRANCH IS THE HOLE DENSITY OF STATES THE ELECTRON AND HOLE DENSITY OF STATES VANISH AT CONDUCTION AND VALENCE BAND EDGES , RESPECTIVELY Previously we say that the density of states VANISHES for energies in the gap * In semiconductors we can then define TWO types of density of states: One for ELECTRONS excited ABOVE the energy gap And one more for HOLES left BELOW the energy gap
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2 Definition of Energy Levels This is a plot of the energy levels in the momentum space. We desire to discuss them in the REAL SPACE. E c -- the lowest conduction band state E v -- the highest valence band state The DENSITY OF STATES counts the NUMBER os states at any energy E. Band Structure ρ ( E ) E This is our real space plot: ± NEAR the gap we assume that the density of states takes the form we derived earlier Remembering too that INCREASING hole energy corresponds To moving DOWN the valence band ± We can then compute the EFFECTIVE number of electrons and holes available as a function of TEMPERATURE Density of States [] G v c v h c e E E E E E m E p Holes E E m E n Electrons = = = 2 / 1 2 / 3 2 * 2 2 / 1 2 / 3 2 * 2 2 2 1 ) ( : 2 2 1 ) ( : h h π THE ELECTRON AND HOLE DENSITY OF STATES ARE DEFINED IN THE FOLLOWING MANNER: n ( E),p(E) ENERGY GAP E E c E v To compute the EFFECTIVE number of electrons and holes at any temperature: * We need to know where the Fermi level lies
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Lecture%2016 - EEE 352: Lecture 16 Intrinsic Semiconductors...

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