Robert F. Brebrick

Measurement and analysis of the phase diagram and thermodynamic properties in the Hg–Cd–Te system

The liquidus surface of Hg1−xCdxTe(s) solid solutions, the liquidus lines in the Hg–Te and Cd–Te binaries, the pseudobinary liquidus and solidus, and the extensive partial pressure data are fit simultaneously. The liquid model assumed is one of which the interactions of the Hg, Cd, Te, HgTe, and CdTe species are represented in the excess Gibbs energy of mixing as a sum of quadratic and cubic terms in the species mole fractions with linarly temperature dependent coefficients. The overall fit is quantitatively satisfactory.

CdTe I: Solidus curve and composition-temperature-tellurium partial pressure data for Te-rich CdTe(s) from optical density measurements

Abstract Known weights of Cd and Te in a silica optical cell of known volume were reacted and the partial pressure of Te2 determined by measuring the optical density of the vapor in the visible. The composition of the condensed phase or phases was calculated from the original weights and the amount of material in the vapor phase. The partial pressure measurements showed that the condensed phase was within the CdTe(s) homogeneity range at high temperatures and so Te-rich solidus points could be established as well as xTe-T-PTe2 data. The values of 105( X Te − 1 2 ) are in the 1–10 range between 960 and 1320 K and are in fair agreement with the findings of Greenberg et al.

Partial Pressures over the Pseudobinary Solid Solution Hg[sub 1−x]Cd[sub x]Te(s) for x = 0.70 and 0.95 and over Four Te-rich Ternary Melts

The partial pressures of Hg, Cd, and Te/sub 2/ have been determined between 420/sup 0/ and 840/sup 0/C from optical absorption measurements for four Te-rich compositions and for the Te-saturated solid solution (Hg /SUB 1-x/ Cd /SUB x/ ) Te(s) with x = 0.70 and 0.95. In addition to further thermodynamically characterizing the melt, the former measurements yield ternary liquidus points. They also yield tie lines when combined with the present and previous measurements on Te-saturated solid solutions. These results, from an essentially steady-state technique, agree well with those of Harman. The measurementss on the solid solutions yield values for the mixing quantities which are more accurate than our previous values. These are described well in terms of a quasi-regular solution of HgTe and CdTe components with an enthalpy of mixing of 1074 cal/g-atom and an excess entropy of mixing of 0.893 cal/K-g-atom at 50 mole percent CdTe.

Analysis of the solidus lines for PbTe and SnTe

Experimental valúes of p-n, PTe2, and T along the solidus lines of PbTe and SnTe, and for compositions within the homogeneity range of SnTe are fit using the simple model of a nondegenerate semiconductor compound containing fully-ionized native defects. As a result values for the intrinsic material parameters of these compounds at high temperature are obtained as well as some indication of the uncertainty in these.

Quantitative fits to the liquidus line and high temperature thermodynamic data for InSb, GaSb, InAs, and GaAs

Quantitatively satisfactory fits are obtained for the liquidus lines of the congruently-melting, “line-compounds”, InSb, GaSb, InAs, and GaAs using a recently derived basic liquidus equation. In addition the fits are consistent with 1) the relations imposed by a zero Gibbs free energy change on congruent melting and 2), except for GaAs, the experimental, compound-V element, eutectic temperature. The successful liquid phase model is a simple one in which the enthalpy and excess entropy of mixing are cubic functions of the atomic fraction. With all parameters fixed by these fits, other high temperature properties are calculated and agree satisfactorily with experiment. All fits are shown in tabular form. They appear so good that it seems likely the model will prove adequate for all the III–V systems. A small temperature dependence, consistent with the presently incomplete data, can be incorporated into the enthalpy and excess entropy without adversely affecting the fits obtained. On the other hand, extensive calculation and comparison with experiment conclusively shows that the two-parameter, quasiregular, or simple solution model does not give a satisfactory overall fit.

Interatomic potentials for Cd, Zn, and Hg from absorption spectra

The absorption coefficient has been measured over a 65 nm range in the red wing of the 213.8 nm line for Zn vapor at 1000 °C. It has also been measured in the blue wing and over a 60 nm range in the red wing of the 228.7 nm line for Cd vapor at five temperatures between 642 and 955 °C and over a 75 nm range in the red wing of the 253.7 nm line for Hg vapor at five temperatures between 460 and 860 °C. These data are analyzed in terms of the statistical theory of broadening. Oscillator strengths of 1.42±0.01 and 1.61±0.06 are obtained for, respectively, the Cd line and the Zn line. Pair potentials for both the ground and lowest excited state are also obtained in all three cases. For Cd this is done assuming no functional form and then assuming Lennard‐Jones potentials. Both methods agree and give a ground state minimum of −47.5 meV at 0.482 nm separation and an excited state minimum of −1.06 eV at 0.410 nm. A functional form is required for the less extensive Zn data and the Lennard‐Jones form leads to a ra...

Defect chemistry and intrinsic carrier concentration for Hg1−x Cdx Te(s) for x = 0.20, 0.40, and 1.0

The theoretical equations governing the crystal-vapor equilibrium for Hg1−x Cdx Te(s) are summarized for a model with doubly-ionized native defects and applied to the data for x = 0.20, 0.40, and 1. The basic equations (Eq. (1) or (19)) are shown to contain those used elsewhere as special cases. Allowing the intrinsic carrier concentration, n1, to vary, but under constraints, to obtain an optimum fit and assuming a non-degenerate semiconductor, the hole con-centration-mercury pressure isotherms can be fitted satis-factorily and better than before with standard deviations between 22 and 24% for x = 0.20 and 0.40. A number of sets of model parameters give these fits, some of which give values as large as 10/cm at 500δC for the square root of the Schottky constant for ionized vacancies. In agreement with experiment, each of these parameter sets for x = 0.20 and 0.40 predicts a negligible dependence of the 77 and 192 K Hall mobilities upon equilibration temperature and predicts that metal saturation between 250 and 300δC with foreign donors in the 1015/cm3 range will result in elec-tron concentrations in the same range and dependent on saturation temperature to less than 26%. The enthalpy to create a “Hg-vacancy” and two holes is an invariant of the fits and is 2.00 ± 0.04 eV for x = 0.40 and 1.94 ± 0.02 eV for x = 0.20. Then ni is calculated independently assuming a parabolic valence band and a Kane conduction band. With an exact density of states for the latter obtained here, the momentum matrix element, P = 8.5 × 10−8 eV-cm, the spin-orbit splitting, Δ = 1 eV, and E (x, T) from Hansen et al., the experimental values below 300 K for 0 ≤x = 0.3 and at high temperature for x = 1 are fitted well with mh∗/m = 0.70. With these independently calculated values for ni the electron concentration-cadmium pressure isotherms for CdTe can be fitted to about 7% for either of two incon-sistent data sets assuming 2 × 1016 /cm3 foreign donors. However data for x = 0.40 can be fitted to only 42% and that for x = 0.20, which is degenerate, to only 28%.

Stoichiometry invariants for ternary and quatenary solid solutions with two nearly perfect sublattices

Abstract We consider a quatenary semiconductor compound, ( A 1− u B u ) 1− y ( C 1− v D v ) y , in which the A and B atoms occupy sites in one sublattice. the C and D atoms occupy sites in a second sublattice, and for which y is always near 1 2 . A statistical thermodynamic analysis for a specific defect model gives three independent “stoichiometry invariants” for the chemical potentials, e.g. μ B + μ D , μ A − μ B , and μ C − μ D , which are independent of approximation for small ratios of defect to site concentration. This result is independent of the specific defects chosen, but is obtained under the assumptions that the distribution of the A and B atoms among themselves and that of C and D atoms among themselves are random. A more general analysis that removes these assumptions still yields the same stoichiometry invariants. These invariants provide simple, model-independent relations among the chemical potentials that are extremely useful and to some extent already employed. They also provide the basis for a check on internal self-consistency when all the chemical potentials are measured. The analogous results for a ternary compound are readily extracted as a special case.

Thermodynamic modeling of the Hg-Cd-Te and Hg-Zn-Te systems

Abstract The basic thermodynamic equations governing the equilibrium between (A 1- u B u ) 2- y Te y (s) with y near unity and its liquid and vapor phases are summarized. These are used along with an associated solution model for the liquid with species, Hg, Cd, Te, HgTe, and CdTe, to obtain quantitatively good fits to the diverse experimental data. The less extensive data for the Hg-Zn-Te system are also fit and based upon the parameters established, some properties are calculated for which there are no experimental data at present.

CdTe. II: Defect chemistry

A statistical thermodynamic derivation of the equilibrium equations for two defect models for CdTe(s) at high temperatures is given. In the first the predominant defects are assumed to be doubly ionizable Cd vacancy acceptors and singly ionizable Te antisite donors in Te rich material and doubly ionizable Te vacancy donors in Cd rich material. A variant in which the Te antisite defect is neutral is readily extracted from the equations by setting the donor level far enough below the conduction band edge. In the second model the Te antisite defect is replaced by a neutral Te interstitial defect. The models are then applied to the high temperature data. It is concluded that the singly ionizable Te antisite model gives the best overall fit and various high temperature properties are calculated with two sets of the adjustable parameters.