Unformatted text preview: 68 Physics Formulary by ir. J.C.A. Wevers absorption 6 absorption 6 ... ... . .. .. . . . . .. . . . Eg + hΩ ¯ h ¯ ωg -E -E Direct semiconductor Indirect semiconductor So indirect semiconductors, like Si and Ge, cannot emit any light and are therefore not usable to fabricate lasers. When light is absorbed holds: kh = −ke , Eh (kh ) = −Ee (ke ), vh = ve and mh = −m∗ if the e conduction band and the valence band have the same structure. Instead of the normal electron mass one has to use the effective mass within a lattice. It is deﬁned by: m∗ = dp/dt dK F = =h ¯ = h2 ¯ a dvg /dt dvg d2 E dk 2
−1 with E = hω and vg = dω /dk and p = hk . ¯ ¯ With the distribution function f e (E ) ≈ exp((µ − E )/kT ) for the electrons and f h (E ) = 1 − fe (E ) for the holes the density of states is given by: D(E ) = 1 2π 2 2 m∗ h ¯2
3/2 E − Ec with Ec the energy at the edge of the conductance band. From this follows for the concentrations of the holes p and the electrons n: n=
∞ De (E )fe (E )dE = 2
3 Ec m∗ kT 2π ¯ 2 h 3/2 exp µ − Ec kT kT Eg m∗ mh exp − e kT 2π ¯ 2 h For an intrinsic (no impurities) semiconductor holds: n i = pi , for a n − type holds: n > p and in a p − type holds: n < p. For the product np follows: np = 4 An exciton is a bound electron-hole pair, rotating on each other as in positronium. The excitation energy of an exciton is smaller than the bandgap because the energy of an exciton is lower than the energy of a free electron and a free hole. This causes a peak in the absorption just under E g . 12.8 Superconductivity
A superconductor is characterized by a zero resistivity if certain quantities are smaller than some critical values: T < Tc , I < Ic and H < Hc . The BCS-model predicts for the transition temperature T c : Tc = 1.14ΘD exp while experiments ﬁnd for H c approximately: Hc (T ) ≈ Hc (Tc ) 1 − T2 2 Tc . −1 U D(EF ) ...
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