By J. S. Blakemore
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Additional info for Semiconductor Statistics
1). This means that the electron energy E(k) can be plotted as a multi valued function of k within the first Brillouin zone, as indicated by the dashed curves of Fig. 1. Such a representation is known as that of E(k) \ V \ \\ \ \\ \ -37Γ α -27Γ α Vu -7Γ o / /, s. +s x / / /Q' / \ \ 0 / / / / / A Q A / 7Γ a 2j a 37Γ a FIG. 1. Multi-zone and reduced zone representation of the energy-wavevector relationship for a one-dimensional monatomic lattice. the reduced zone, and the value of k corresponding to a whole series of possible energies is known as the reduced wave-vector.
4, that if Vki? is small, the density of states and the effective mass are large. The effective mass in the heavy-hole band, m^ is some three times larger than the mass m\ for the light-hole band with which it is degenerate at k = 0 . These masses are not isotropie, for the sur faces of constant energy are warped from truly spherical shapes in k-space. The energy surface for the heavy-hole band protrudes in  directions, while for light holes the corresponding surface for the same energy is squashed in  directions and protrudes in  directions.
I t is interesting that the electron's behavior can be described without knowing the absolute value of k. As will be seen below, it is necessary only to know the value of k relative to that at a zone bound ary. This leads to a useful simplification of the zone scheme. 2, it was noted that zone boundaries occurred whenever kx was a multiple of π/α. I t is not in fact necessary to use values of kx larger than ± ττ\α in describing any state. For suppose the wave-vector of a position outside the first zone is described as (kx + 2nnla), where n is a (positive or negative) integer and kx is the wave-vector of a position inside the first zone.
Semiconductor Statistics by J. S. Blakemore