Institute of Metals Division - Solid Solutions of CdTe and InTe in PbTe and SnTe. I: Crystal Chemistry

Extensive solid solubilities of CdTe (zincblende-type struckre) and InTe (B37 type) in each of the rock salt-type compounds, PbTe and SnTe, have been observed. Partial phase diagrams have been determined by thermal analysis and X-ray metallography. The limiting mol fraction. X,, of the solute in the rock salt-type a phase and the corresponding eutectic temperatures, T,, are: (PbTe)l-x(CdTe)x: X,- 0.2, T, =866°C; (PbTe),-,(lnTe),: X, - 0.35, T, = 646"C; (SnTe),-,(CdTe),:X,- 0.11, T, = 784 "C; (SnTe),-,(lnTe),: X,-0.53, T, = 630°C. The lattice parameters of the a phase decrease linearly with X, even in (PbTe),-,(CdTe),, where a, (CdTe) = 6.481A > %(PbTe) = 6.459A. This is taken as proof that the cadmium atom enters an octahedral interstice of the tellurium atom sublattice; i.e., the formation of the a phase entails the direct replacement of lead by cadmium. The a, us X curve extrapolates to 6.16A at X = 1, in agreement with the value predicted for an ionic crystal of CdTe; it is also consistent with the reported lattice parameter It is well-established that the compositions of intrinsic semiconducting and semimetallic compounds conform to normal valence rules.1"5 The apparent exceptions can be explained by taking account of anion-anion covalences, as in CdSb, or of multiple cation valences, as in In Te.'This empirical generalization is the basis of the chemical approach to semiconductors2 by which the properties of an intrinsic semiconductor are rationalized in terms of the ionic-covalent bonds necessary to saturate the valence-electron complement of the anion sublattice. A fundamental shortcoming of this approach is its disregard of long-range crystal interactions. It cannot, accordingly, deal with the phenomenon of charge conduction except through the use of ad hoc postulates. As an example, a crystal of CdTe would, in the valence-bond picture: be described in terms of electron pairs, each with the same discrete energy, localized between every cadmium and tellurium atom. This is, of course, contrary to the Pauli of the high-pressure rock-salt form of CdTe, corrected for decompression from 36 kbar. The free energy of formation of the a phase of pure CdTe at room temperature is calculated from the phase diagram to be +10 kcal per g-atom, in accmd with the value calculated from the transformation pressure. The standard enthalpy is +13 kcal per g-atom, and the standard entropy is +9 eu. The latter value implies the formation of extra classical particles, such as vacancies, interstitials, or nondegenerate charge carriers, but these alternatives are not consistent with the semiconducting properties and the densities of the a phase. The extrapolated values of the lattice parameters of (PbTe),-,(lnTe), and Spectively, for the rock salt-type modification of InTe. The corresponding interatomic separation is intermediate between monovalent and trivalent indium. The qualitative implications of the results are considered from the viewpoints of both valence-band theory and energy-band theory. principle, and is corrected by methods of molecular-orbital theory in which bonds are replaced by bands of molecular orbitals whose energies, E, depend upon a crystal-momentum vector, k.7 Each band is derived from a linear combination of atomic orbitals with two electrons required to saturate each molecular orbital in the band. In a crystal of N atoms containing z atoms in its primitive unit cell, there are 2 N/z states per band which lie in a region of k space bound by the Brillouin zone. In an intrinsic semiconductor, the bands can be grouped into valence bands which are normally filled and conduction bands which are normally empty. If the highest valence band and the lowest conduction band overlap anywhere within the Brillouin zone, the material is rendered semimetallic. The quantity defines the effective mass, m*, of an electron in a conduction band (or of a hole, i.e., an electron deficiency, in the valence band) and leads directly to the concept of charge mobility through the relation \x = et/m*, where e is the electron charge and t is the lattice relaxation time.