Strain Characterization of Semiconductor Structures and Superlattices

Abstract

The effects of strains on the Raman-active optical phonons of crystalline materials are reviewed, with emphasis on Si and zincblende (ZB) or wurtzite (W) cubic crystals, their strained epilayers (EL) and superlattices (SL). In the presence of strains the symmetry of the crystal is altered and the phonon degeneracies may be lifted with an upward or downward shift of their frequencies. To a first approximation the shifts are linear in the strain components; the corresponding rates lead to the so-called phonon deformation potentials (PDP). The latter allow the calculation of built-in strains from any observed frequency shifts. The dynamical secular equation (DSE) associated with the phonon provides the necessary phenomenological basis for converting frequency shifts to strains and vice versa. The same problem, i.e., the DSE of triply-degenerate q≈0 optical phonons of cubic crystals, is treated here in an arbitrary system of axis x’₁x’₂x’₃ relative to the system x₁x₂x₃ of the crystallographic axes <100>. This generalization is dictated by the need of handling phonon shifts and splittings in EL and SL which are grown along an arbitrary direction x’₃. For this purpose, it is necessary to have precise knowledge of the strain field, namely, the fuL.L. array of its non-zero tensor components. This is a problem of elasticity theory and will be addressed independently. Strained polycrystalline films will also be treated. For this purpose, the PDP of a polycrystal are expressed in terms of the PDP of the corresponding single crystal, by use of averaging procedures. Examples will be given of recent determinations of reliable PDP values in materials of current interest, and also selective cases from the literature, where strain characterization through Raman Scattering (RS) is successfully demonstrated. In what follows, Greek (Latin) tensor indices stand for single cartesian (suppressed) indices running from 1(1) to 3(6), according to the usual code of crystal physics¹ .