Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

Statistical Exchange-Correlation in the Self-Consistent Field

The calculation of electron-transport properties of direct-gap semiconductors has been generalized to include arbitrary electron degeneracy as well as scattering by ionized impurities and heavy holes. Conduction-band nonparabolicity and electron wave-function admixture are retained throughout the calculation of drift mobility and thermoelectric power. Extensive comparison of the results with experiment confirms the present description over wide ranges of temperature and ionized-impurity concentration. Effects of multivalley conduction due to electron transfer into ${L}_{1c}$ satellite valleys appear in InSb above 700 \ifmmode^\circ\else\textdegree\fi{}K (just below the melting point at \ensuremath{\sim} 780 \ifmmode^\circ\else\textdegree\fi{}K) and in InP above 800 \ifmmode^\circ\else\textdegree\fi{}K. The lowest satellite valleys of InAs are sufficiently remote from the conduction-band edge at ${L}_{1c}$ that the results are expected to be accurate up to the melting point at \ensuremath{\sim} 1200 \ifmmode^\circ\else\textdegree\fi{}K.

Electron Transport in InSb, InAs, and InP

The conduction‐band structure of In1−xGaxP has been studied by cathodoluminescence (CL) and photoluminescence (PL). An accurate determination of the direct energy gap (± 10 meV) as a function of alloy composition (Δx = ± 0.025) is achieved by the simultaneous electron probe microanalysis of alloy composition and spectral measurements of the CL excited by the microprobe electron beam. Similar measurements in InP, GaAs, and GaAs1−xPx, as well as absorption edge measurements and the temperature dependence of the PL spectrum, indicate that essentially free‐carrier recombination is observed in the PL and CL measurements of lightly n‐type In1−xGaxP at 300 °K. These results indicate that the ``cross over'' between the direct and indirect conduction‐band minima occurs at the composition x = 0.74 and energy gap = 2.26 eV.

Electronic Structure and Luminescence Processes in In1−xGaxP Alloys

The In‐Ga‐As‐P quaternary phase diagram required for the growth of lattice‐matched In1−xGaxAs1−yPy layers on InP substrates has been determined experimentally at 650 °C. The liquidus isotherms were obtained by the seed‐dissolution technique. The solidus iostherms were determined by electron‐microprobe analysis performed on surfaces of quaternary epitaxial layers grown on Sn‐doped InP (111) B substrates from quaternary saturated melts. Lattice constants of layers were measured by an x‐ray‐diffraction technique. The liquid‐phase‐epitaxy growth conditions of lattice‐matched In1−xGaxAs1−yPy (0⩽x⩽0.47, 0⩽y⩽1.0) layers on InP were found from the results of the phase diagram and lattice constant measurements. Lattice‐matched layers with various band gaps (from 1.34 to 0.74 eV at room temperature) were grown by using these conditions. Band gaps of the layers were determined by photoluminescence measurements at 300 and 77 K. The band gap at each temperature was found to be linearly dependent on alloy‐composition p...

Composition dependence of the band gaps of In1−xGaxAs1−yPy quaternary solids lattice matched on InP substrates

Single crystal epitaxial layers of Gaxln1−xP alloys have been grown by the steady-state liquid phase epitaxial growth technique on (111)B GaAs substrates. The crystal growth process has been studied in detail and the resultant epitaxial layers have been characterized with respect to their structural, electrical and optical properties. Epitaxial layers of good structural quality could be grown only in the composition range x = 0.48 to 0.53, where the lattice parameter is close to that of the GaAs substrate. The band gap of these crystals was in the range 1.86 – 1.92 eV as determined by optical absorption and photoluminescence measurements.

Liquid phase epitaxial growth of Ga x In 1-x P

Using the technique of energy-distribution analysis of photoemitted electrons, we have accurately located the position of several band-structure features of InP, including the next higher conduction-band minimum above the ${\ensuremath{\Gamma}}_{1}$ minimum at 1.95 eV above the valence-band maximum, independent of temperature. This minimum is tentatively associated with the ${L}_{1}$ symmetry point. High-temperature Hall-effect measurements confirm that there are no minima between the lowest two observed by photoemission. A band structure for InP has been computed using these new data in an empirically adjusted first-principles orthogonalized-plane-wave (OPW) calculation. The velocity-field characteristic has been calculated for a range of lattice temperatures. A negative differential mobility is predicted, with a room-temperature threshold field of 11 500 V/cm and a peak drift velocity of 3\ifmmode\times\else\texttimes\fi{}${10}^{7}$ cm/sec.

L. W. James

Papers

Band Structure and High-Field Transport Properties of InP