3. Strain Effects on the Electronic Band Structure

Electrons in a semiconductor experience the periodic potential of the crystal lattice. This potential leads to the formation of energy bands. The electronic band structure of a semiconductor describes the energy states that an electron is allowed or forbidden to be in. Intrinsic to the band structure are several symmetry properties which are influenced by the application of stress.

The general concepts of stress and strain come from the theory of elasticity. Both are tensorial quantities and their inter-dependence is related through Hook's law. The definitions of stress and strain along with their connection to the Si crystal structure are introduced in Section 3.1.

The crystal structure of Si belongs to the cubic system of Bravais lattice and consists of two interspersed face centered cubic lattices. It comprises of 8 atoms per unit cell. The basic properties of the crystal structure are reflected in its band structure. A detailed description of the crystal and the band structure of Si, together with the methods for obtaining the band structure are discussed in Section 3.2.

Finally, the effect of strain on the band structure is presented in Section 3.3. The strain-induced shift in the energy levels of the conduction and valence bands is discussed within the framework of the deformation potential theory and the ${\bf {k\cdot p}}$ method. Different stress configurations including biaxial stress as well as uniaxial stress applied along high-symmetry and arbitrary directions are then analyzed. Lastly, the influence of shear stress on the band structure is outlined. It is shown that the presence of shear stress not only brings about a change in the curvature of the energy bands, but also produces an additional energy shift, which is non-linear in strain.