Optical Properties of Crystalline and Amorphous Semiconductors

(a) Diamond-, Zinc-Blende-, and Wurtzite-Type Crystals—The modern age of solid-state electronics is based upon materials which are neither metals nor insulators. Such materials are called semiconductors, and their electronic properties are intermediate between those of metals and insulators. Almost all the semiconductors of practical interest have the diamond, zinc-blende, or wurtzite (hexagonal) structure. In Fig. 1.1 we schematically illustrate the unit cell of these crystal structures [1]. Table 1.1 summarizes the crystal structure, space group, and lattice constant of some semiconductors considered in this book.

The strong IR absorption band found in heteropolar semiconductors is essentially bonded by the TO and LO frequencies for long-wavelength vibrations. The difference between these frequencies can be related to the amount of polar character in the chemical bond in these compounds. Below the reststrahlen range in optical spectra, the real part of the dielectric constant asymptotically approaches the static (or low-frequency) dielectric constant ε_s. The optical constant connecting the reststrahlen-near-IR range is called the high-frequency (or optical) dielectric constant ε The high-frequency dielectric constant ε thus, measured for frequencies well above the long-wavelength LO phonon frequency but below the fundamental absorption edge.

The optical constants in the interband transition region of semiconductors depend fundamentally on the electronic energy-band structure of the semiconductors. The relation between the energy-band structure and ε₂(E) can be given by [1] where u is the combined DOS mass, the Dirac 5 function represents the spectral joint DOS between the valence- [E_vk)] and conduction-band [E_c(k)] states differing by the energy E=hω of the incident light, F_cv(K:) is the momentum-matrix element between the valence- and conduction-band states, and the integration is performed over the first BZ. There have been several analytic models that can be used to explain ε(E) spectra in the interband transition region of semiconductors. In the following, we briefly review such analytic models, namely HOA, SCP, and MDF, and show the analyzed results of ε(E) for GaAs using these models.

(a) Definition—The analysis of optical spectra is one of the most useful tools for understanding electronic structure of amorphous semiconductors. Pierce and Spicer [1] performed photoemission measurements on a-Si to study the electronic structure and optical properties of the material. They used a conventional retarding-field energy analyzer and a high-resolution screened-emitter analyzer to measure the energy distribution curves from this material. When the energy distribution curves from c-Si are examined, one finds variations in the position and strength of structure as a result of the conservation of wave vector k in the crystal. However, in amorphous materials no such variations had been found in the energy distribution curves. This is not unexpected because the absence of long-range order in amorphous materials renders the Bloch theorem inapplicable and leaves the crystalline momentum M undefined. They suggested optical transitions in amor- phous semiconductors to be described, to a first approximation, by the nondirect transition model in which conservation of the energy but not wave vector is significant [1].

(a) Direct-Gap Edge—In obtaining Eq. (3.5), we assumed that the matrix element P_cv(k) is constant in its value so that we can obtain the well-known line shape of ε₂ at the 3D M_o CP [Eq. (3.14)]. In cases where transitions are forbidden in the electric-dipole approximation, one can make use of the k dependence of the matrix element and expand around the CP at k_c and keep only the linear term. We can, then, obtain for “forbidden” direct transitions at the 3D M_o CP [1]

This book discusses optical properties and constants of the group-IV elemental, III-V, II-VI, and IV-VI binary semiconductors, and their alloys. We list in Table 6.1 some physical properties of Si, GaAs, ZnSe, and PbTe at 300 K. These semiconductors are typical of the group-IV elemental, III-V, II-VI, and IV-VI binary semiconductors, respectively.