Chapter 5
Mechanical Properties
If you want to find the secrets of the universe, think in terms of energy, frequency and
vibration.
N. Tesla
Abstract Lattice vibrations and phonons are treated with one-dimensional models and examples
for real phonon dispersions for several semiconductors including phonons in alloys and disordered
materials are given. Then the theory of linear elasticity and its application to semiconductors with
regard to epitaxial strain, substrate bending and sheet-scrolling is given. Finally plastic relaxation
effects such as critical thickness and wafer breakage are discussed.
5.1 Introduction
The atoms making up the solid have an average position from which they can deviate since they are
elastically bonded. The typical atomic interaction potential looks like the one shown in Fig. 2.1. The
atoms thus perform a vibrational motion (including zero point fluctuations) and the solid is elastic.
The potential is essentially asymmetric, being steeper for small distances due to quantum-mechanical
overlap of orbitals. However, for small amplitudes around the minimum a harmonic oscillator can be
assumed (harmonic approximation). Beyond the elastic regime, plastic deformation occurs such as
generation of defects, e.g. dislocations. Eventually also the crystal can break.
5.2 Lattice Vibrations
In the following we will discuss the dispersion relations for lattice vibrations, i.e. the connection
between the frequency ν (or energy hν = ω) of the wave and its wavelength λ (or k-vector k = 2π/λ).
Acoustic and optical vibrations are introduced in one-dimensional models. A detailed treatment of the
physics of lattice vibrations is given in [366].
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_5
95
Mechanical Properties
If you want to find the secrets of the universe, think in terms of energy, frequency and
vibration.
N. Tesla
Abstract Lattice vibrations and phonons are treated with one-dimensional models and examples
for real phonon dispersions for several semiconductors including phonons in alloys and disordered
materials are given. Then the theory of linear elasticity and its application to semiconductors with
regard to epitaxial strain, substrate bending and sheet-scrolling is given. Finally plastic relaxation
effects such as critical thickness and wafer breakage are discussed.
5.1 Introduction
The atoms making up the solid have an average position from which they can deviate since they are
elastically bonded. The typical atomic interaction potential looks like the one shown in Fig. 2.1. The
atoms thus perform a vibrational motion (including zero point fluctuations) and the solid is elastic.
The potential is essentially asymmetric, being steeper for small distances due to quantum-mechanical
overlap of orbitals. However, for small amplitudes around the minimum a harmonic oscillator can be
assumed (harmonic approximation). Beyond the elastic regime, plastic deformation occurs such as
generation of defects, e.g. dislocations. Eventually also the crystal can break.
5.2 Lattice Vibrations
In the following we will discuss the dispersion relations for lattice vibrations, i.e. the connection
between the frequency ν (or energy hν = ω) of the wave and its wavelength λ (or k-vector k = 2π/λ).
Acoustic and optical vibrations are introduced in one-dimensional models. A detailed treatment of the
physics of lattice vibrations is given in [366].
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_5
95