We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...

Semiconducting and other major properties of gallium arsenide

A thorough discussion of the various features of the photoluminescence spectra of undoped, p‐doped and n‐doped AlxGa1−xAs (0≤x≤1) alloys is given. This review covers spectral features in the energy region ranging from the energy band gap down to ≂0.8 eV, doping densities from isolated impurities to strongly interacting impurities (heavy‐doping effects) and lattice temperatures from 2 to 300 K. The relevance of photoluminescence as a simple but very powerful characterization technique is stressed also in comparison with other experimental methods. The most recent determinations of the Al concentration dependence of some physical properties of the alloy (energy gaps, carrier effective masses, dielectric constants, phonon energies, donor and acceptor binding energies, etc.) are given. The main physical mechanisms of the radiative recombination process in semiconductors are summarized with particular emphasis on the experimental data available for AlxGa1−xAs. The effects of the nature of the band gap (direct ...

Photoluminescence of AlxGa1−xAs alloys

Structural, FTIR and photoluminescence studies of Cu doped ZnO nanopowders by co-precipitation method

Modulation spectroscopy is a powerful method for the study and characterization of a large number of semiconductor configurations, including bulk/thin film, microstructures (heterojunctions, quantum wells, superlattices, quantum dots), surfaces/interfaces and actual device structures in addition to semiconductor growth/processing. Furthermore, the influence of external perturbations such as temperature, electric fields, hydrostatic pressure, uniaxial stress, etc. can be investigated. This optical technique utilizes a very general principle of experimental physics, in which a periodically applied perturbation (either to the sample or probe) leads to sharp, derivative-like spectral features in the optical response of the system. Because of the richness of the derivative-like spectra, the information in the lineshape fits, room temperature performance and relative simplicity of operation this method is becoming increasingly more important as a tool to study these materials and structures. This article will review developments in the field during the last decade.

Modulation spectroscopy of semiconductors: bulk/thin film, microstructures, surfaces/interfaces and devices

The piezomodulated and the photomodulated reflectivity spectra of Mn-based diluted magnetic semiconductors (${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te,${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ Te,${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se,${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se) reveal sharp signatures associated with the excitonic transitions near the band gap. The dependence of the excitonic energy on the manganese concentration (x), on temperature (T), and, in the wurtzite structure, on the polarization with respect to the optic axis, are determined from the modulation experiments. The excitonic energy in the ``hypothetical'' tetrahedrally coordinated MnTe and MnSe, viewed as the end members of the alloy systems, are deduced from the x dependence of the excitonic transition. A signature associated with ${\mathrm{Mn}}^{2+}$ is observed in piezomodulated ``pseudoreflection,'' when the energy gap is sufficiently large; its energy is insensitive to x. The absence of the Zeeman effect for the ${\mathrm{Mn}}^{2+}$ signature, in contrast to the large Zeeman effect of the excitonic feature, demonstrates that the former is an optical transition associated with the 3${d}^{5}$ shell of ${\mathrm{Mn}}^{2+}$.

Energy gap, excitonic, and "internal" Mn2+ optical transition in Mn-based II-VI diluted magnetic semiconductors.

A new compact algorithm has been developed for the calculation of the band structure of III-V or II-VI compound semiconductor superlattices. Within the envelope-function approximation, the procedure yields a transfer matrix of dimension 2n\ifmmode\times\else\texttimes\fi{}2n for an n-band k\ensuremath{\cdot}p model. The boundary conditions for the wave functions at the interfaces between layers are built into the calculation in a natural manner. The method readily adapts itself to the case where an external magnetic field is present along the superlattice axis. The effects of strain, due to lattice mismatch or an applied external stress, can also be taken into account. This extended transfer-matrix method enjoys the advantages of the usual one-band transfer-matrix method which is employed in solving the Kronig-Penney model. The standard eight-band k\ensuremath{\cdot}p description of the band structures of the individual layers is used in obtaining results for specific superlattices. Our results are in excellent agreement with earlier calculations which have used the k\ensuremath{\cdot}p and the tight-binding approximations.

Transfer-matrix algorithm for the calculation of the band structure of semiconductor superlattices.

We have measured the stress-modulated magnetoreflectance in germanium at \ensuremath{\sim} 30\ifmmode^\circ\else\textdegree\fi{}K over the energy range 0.9-1.3 eV with magnetic fields up to 85 kG applied along a [110] direction. The measurements were made in the Faraday configuration with right and left circularly polarized light. The structure in piezoreflectance observed at zero magnetic field is correlated with transitions from the $J=\frac{3}{2}$ valence-band edge (${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}^{\frac{3}{2}}={\ensuremath{\Gamma}}_{8}^{+}$) and the spin-orbit split-off valence-band edge (${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}^{\frac{1}{2}}={\ensuremath{\Gamma}}_{7}^{+}$) to the conduction-band edge (${\ensuremath{\Gamma}}_{{2}^{\ensuremath{'}}}={\ensuremath{\Gamma}}_{7}^{\ensuremath{-}}$) at the center of the Brillouin zone. The structure in the magnetopiezoreflectance spectra is analyzed in terms of interband transitions between Landau levels for the valence and conduction bands. Considering the split-off valence-to-conduction-band transitions, we obtain the reduced mass for these transitions, ${m}_{r}\ensuremath{\equiv}\frac{{m}_{c}{m}_{\mathrm{so}}}{({m}_{\mathrm{so}}\ensuremath{-}{m}_{c})}=(27.2\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}m$, the sum of the $g$ factors ${{g}_{c}}^{+}{g}_{\mathrm{so}}=\ensuremath{-}13\ifmmode\pm\else\textpm\fi{}3$, and the spin-orbit splitting $\ensuremath{\Delta}=0.296\ifmmode\pm\else\textpm\fi{}0.002$ eV. The light- and heavy-mass valence-to-conduction-band transitions have been analyzed using the coupled-band scheme of Pidgeon and Brown in which the valence bands are treated together with the conduction band. With the valence-band parameters of Luttinger ${\ensuremath{\gamma}}_{1}^{L}=13.38$, ${\ensuremath{\gamma}}_{2}^{L}=4.30$, ${\ensuremath{\gamma}}_{3}^{L}=5.68$, and ${\ensuremath{\kappa}}^{L}=3.41$ as determined by Hensel and Suzuki from combined resonances in uniaxially stressed $p$-type germanium, the best fit to the experimental data for the light- and heavy-mass transitions is obtained with the following parameters: the interaction energy between the conduction and valence bands ${E}_{p}=26.8\ifmmode\pm\else\textpm\fi{}0.4$ eV, the parameter $F=(\ensuremath{-}1.1\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{m}$) which represents the conduction-band interaction with the other bands. These parameters give ${m}_{c}=(0.0380\ifmmode\pm\else\textpm\fi{}0.0005)m$, and ${g}_{c}=\ensuremath{-}3.0\ifmmode\pm\else\textpm\fi{}0.2$, which are in excellent agreement with those obtained from the conventional magnetoabsorption measurements. With these values of ${m}_{c}$ and ${g}_{c}$, we deduce from our results for the split-off transitions ${m}_{\mathrm{so}}=\ensuremath{-}(0.095\ifmmode\pm\else\textpm\fi{}0.007)m$ and ${g}_{\mathrm{so}}=\ensuremath{-}10\ifmmode\pm\else\textpm\fi{}3$.

R. L. Aggarwal

Papers

Energy gap, excitonic, and "internal" Mn2+ optical transition in Mn-based II-VI diluted magnetic semiconductors.

Transfer-matrix algorithm for the calculation of the band structure of semiconductor superlattices.

Stress-Modulated Magnetoreflectance for the Direct Transitions Γ 25 ′ 3 2 → Γ 2 ′ and Γ 25 ′ 1 2 → Γ 2 ′ in Germanium

EuO. II. Dependence of the Insulator-Metal Transition on Magnetic Order

Split-Off Valence-Band Parameters for GaAs from Stress-Modulated Magnetoreflectivity