Semiconductor Physics: An Introduction by Professor Karlheinz Seeger (auth.)

By Professor Karlheinz Seeger (auth.)

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A discussion of these levels can be confined to the first Brillouin zone. We saw in the last chapter that due to the crystal periodicity, the electron wave functions, which in one dimension are 'lj;(x) = u(x) exp(i k x), also have to be periodic (Bloch functions). 3) or k = n 2 1riN a; n = 0, ±1, ±2, ... 4) where a is the lattice constant. 1) is actually valid for a ringshaped chain which means that we neglect surface states (Sect. 1). Since for the first Brillouin zone k has values between -7r I a and +1r I a, we find that the integer n is limited to the range between -NI2 and +NI2.

2)]. For the case of nearly but not exactly equal densities of electrons and holes, one has to solve an equation of the 44 3. 8, 18). co. At somewhat lower temperatures, however, there is a considerable freeze-out of carriers and hence No » N A » n » p and the concentration of ionized donors is nearly equal to that of acceptors since most of the electrons have just gone from donors to acceptors. co in the exponential. Similar results are obtained for p-type conductivity. 14]. At the transition from n » N 0 (at high temperature) ton« No (at low temperature), there is a kink at 10 11 cm- 3 which is the concentration of compensating donor impurities.

7 and 8. The volume element in v space is then given by d3 v = 4 1r v 2 dv ex c 112 dc. 23) where f~ = 8fo/8(c/kBT). 8). 13) and 17n is the reduced Fermi energy. 752. To. 752To. 27) 52 4. ". 28) In the Boltzmann equation, the term (8ff8vz)eEz/m is replaced by X E). 30) Since this calculation does not assume an effective mass, it is valid not only for the simple model of a parabolic band structure but also for a nonparabolic band structure. There are always both electrons and holes present in a semiconductor.

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