Page 260 - Materials Chemistry, Second Edition

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4.1. Properties and Types of Semiconductors

minimum of the conduction band (CB) is directly above the maximum of the
valence band (VB). Accordingly, we refer to such solids as direct bandgap materi-
als. In contrast, for Si and Ge, the CB minimum and VB maximum are offset,
resulting in an indirect bandgap.
h
ð2Þ l ¼
p
For Si, in order for an electron at the bottom of the CB to recombine with a hole from
the top of the VB, the momentum of the electron must shift from k cb to k vb
(Figure 4.9b). However, this is not allowed by the Law of Conservation of Momen-
tum. Instead, an indirect recombination mechanism must take place, wherein the
electron is captured by an interstitial defect with energy E r , which facilitates its
relaxation to the top of the VB. This process is accompanied by the emission of
phonons, or lattice vibrations rather than light emission. In contrast, efficient
electron-hole recombination may occur without any change in momentum for direct
bandgap materials, resulting in the emission of photons. We will describe some
important applications for direct bandgap semiconductors later in this chapter.
The band diagram for real solids is not as straight forward as what we have
illustrated thus far. Figure 4.10 presents the real band diagrams for indirect and
direct bandgap semiconductors Si and GaAs, respectively, showing a great deal of
complexity associated with valence and conduction bands. [2] As noted in Chapter 2,
the Brillouin zones (BZ; primitive unit cell of the reciprocal lattice) for 3-D crystal
lattices are complex polyhedra (Figure 2.76). Hence, the band energy varies in 3-D
k-space and the resultant lines are slices through the BZ polyhedron in specific

Figure 4.10. Electronic energy bands for Si and GaAs. The bands below the gray zone (bandgap) are
completely filled (valence band – VB), and those above are completely empty (conduction band – CB) at
0 K. Reproduced with permission from Hofmann, P. Solid State Physics: An Introduction, Wiley:
New York, 2008. Copyright 2008 Wiley-VCH Verlag GmbH & Co.