chap12 - Chapter 12: Semiconductors Bardeen &...

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Unformatted text preview: Chapter 12: Semiconductors Bardeen & Shottky May 18, 2001 Contents 1 Band Structure 4 2 Charge Carrier Density in Intrinsic Semiconductors. 7 3 Doping of Semiconductors 12 4 Carrier Densities in Doped semiconductor 15 1 Semiconductors are of obvious technological importance - so much so, that a whole chapter will be dedicated to them. Semiconductors are distinguished from metals in that they have a gap at the Fermi surface, and are distinguished from insulators in that the gap is small < 1 eV . Most condensed metal insulator semiconductor Figure 1: There is no band gap at the Fermi energy in a metal, while there is a band gap in an insulator. Semiconductors on the other hand have a band gap, but it is much smaller than those found in insulators. matter physicists make the distinction on the basis of the con- ductivity and its temperature dependence. In the Drude model (parabolic band) = ne 2 m * , = e m * , = ne (1) Almost always 1 increases as T increases, ie the thermal exci- tations increase the scattering rate and decrease the lifetime of 2 the quasiparticle. For example, we have seen that 1 T at high temperatures due to electron-phonon interactions. In metals, n is about con- stant, so the temperature dependence of metals is dictated by . metals 1 T , as T (2) However, in semiconductors, the population of free carriers n is temperature dependent. The exponential always will dominate E g e n-E /2kT g Figure 2: This shows the temperature dependence for the excitation of electrons, thus allowing the number of free carriers to vary with changes in temperature. the power law dependence of . n 1 T e- E g /kT (3) as T (4) The same is true for insulators, of course, except here n is so 3 small that for all realistic purposes 0. 1 Band Structure Clearly the band structure of the semiconductors is crucial then for their device applications. Semiconductors fall into several categories, depending upon their composition, the simplest, type IV include silicon and germanium. The type refers to their valence. r P S r E conduction band valence band B AB E g E T g sp 4 electrons per band 3 Figure 3: Sketch of the sp 3 bands in Si vs. Si-Si separation. Recall that Si and Ge have a s 2 p 2 atomic shell, which forms highly directional sp 3 hybrid bonds in the solid state (with tetragonal symmetry). It is the covalent bonding, or rather the splitting between the bonding and antibonding bands, that 4 forms the gap. The band structure is also quite rich K L X 000 100 111 110 K X K L Si E g Figure 4: Sketch of quasiparticle bands in Si (right) along the high symmetry directions (left)....
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chap12 - Chapter 12: Semiconductors Bardeen &...

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