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Electronic Properties of Strain-Engineered Semiconductors
4.4 Energy Gap and Band Structure
4.4.1 Bulk Si Band Structure
The structure of crystalline silicon is a network face-centred cubic (FCC),
with a diamond-like structure, and is illustrated in Figure 4.2.
Each node in the network is composed of two atoms placed in positions
(0, 0, 0) and (1/4, 1/4, 1/4). The basic cell (cell Wigner–Seitz) reciprocal lattice,
commonly known as the Brillouin zone, is represented in Figure  4.3 and
depends on the wave vector K.
An electron in a solid is defined by its energy E and its wave function ψ
linked by the Schrödinger equation (4.13) as
HΨ = EΨ
(4.12)
where H is the Hamiltonian of the system. In a periodic crystal lattice, the
structure of the band is described in reciprocal space by the relations of dispersion E(K). There are several methods for calculating the effect of strain
on E(K):
1. Ab initio method: Based on the approximation of the local density
(LDA) and the density functional theory (DFT) within the framework of LDA.
2. Deformation potential theory: Developed by Bardeen and Shockley.
The perturbation caused by strain is attributed to an additional
Hamiltonian that is linearly proportional to the deformation potential operator and strain. First-order perturbation theory is used to
calculate the effect of strain on the band structure, and analytical
expressions for the strain-induced energy shifts of the conduction
and valence bands can be obtained.
FIGURE 4.2
Crystalline structure of silicon.