118
5 Mechanical Properties
Fig. 5.28 Linear thermal expansion coefficient of silicon (solid circles) and germanium (open circles). Adapted from
[394] based on experimental data from various sources. Dashed lines are guide to the eye
5.3 Elasticity
The elastic properties of the semiconductor are important if the semiconductor is subjected to external
forces (pressure, temperature) or to lattice mismatch during heteroepitaxy.
5.3.1 Thermal Expansion
The lattice constant depends on temperature. The (linear) thermal expansion coefficient is defined as
α(T 0 ) =
∂a 0 (T )
∂ T
T =T 0
(5.49)
and is temperature dependent. The temperature dependence of α for silicon and germanium is shown
in Fig. 5.28. α is approximately proportional to the heat capacity (C V ) except at low temperatures.
The negative values are due to negative Grüneisen parameters [394]. These anharmonicity effects are
discussed in detail in [366].
5.3.2 Stress–Strain Relation
In this section, we recall the classical theory of elasticity [395]. The solid is treated as a continuous
medium (piecewise homogeneous) and the displacement vector is thus a continuous function u(r) of
the spatial coordinates. When the spatial variation ∇u of u is small, the elastic energy can be written as
5 Mechanical Properties
Fig. 5.28 Linear thermal expansion coefficient of silicon (solid circles) and germanium (open circles). Adapted from
[394] based on experimental data from various sources. Dashed lines are guide to the eye
5.3 Elasticity
The elastic properties of the semiconductor are important if the semiconductor is subjected to external
forces (pressure, temperature) or to lattice mismatch during heteroepitaxy.
5.3.1 Thermal Expansion
The lattice constant depends on temperature. The (linear) thermal expansion coefficient is defined as
α(T 0 ) =
∂a 0 (T )
∂ T
T =T 0
(5.49)
and is temperature dependent. The temperature dependence of α for silicon and germanium is shown
in Fig. 5.28. α is approximately proportional to the heat capacity (C V ) except at low temperatures.
The negative values are due to negative Grüneisen parameters [394]. These anharmonicity effects are
discussed in detail in [366].
5.3.2 Stress–Strain Relation
In this section, we recall the classical theory of elasticity [395]. The solid is treated as a continuous
medium (piecewise homogeneous) and the displacement vector is thus a continuous function u(r) of
the spatial coordinates. When the spatial variation ∇u of u is small, the elastic energy can be written as