Full Band Structure Calculation Research Articles

Modeling semiconductor amplifiers and lasers: from microscopic physics to device simulation

We combine the results of full many-body band-structure calculations of the semiconductor optical response and a full space–time-resolved laser propagation model. Two quantum-well structures are chosen, one showing a sharp increase of the linewidth enhancement factor with density; the other, a clamping of this factor with increasing density. The average far-field broadening of two weakly turbulent broad-area high-power semiconductor lasers is shown to be quite different for the two structures.

Inelastic Lifetimes of Hot Electrons in Real Metals

We report a first-principles description of inelastic lifetimes of excited electrons in real Cu and Al, which we compute, within the GW approximation of many-body theory, from the knowledge of the self-energy of the excited quasiparticle. Our full band-structure calculations indicate that actual lifetimes are the result of a delicate balance between localization, density of states, screening, and Fermi-surface topology. A major contribution from $d$-electrons participating in the screening of electron-electron interactions yields lifetimes of excited electrons in copper that are larger than those of electrons in a free-electron gas with the electron density equal to that of valence ($4s^1$) electrons. In aluminum, a simple metal with no $d$-bands, splitting of the band structure over the Fermi level results in electron lifetimes that are smaller than those of electrons in a free-electron gas.

Shubnikov-de haas oscillations in a new stable organic metal κ-(BETS) 2C(CN) 3

Shubnikov-de Haas oscillations in a new radical cation salt κ-(BETS) 2C(CN) 3 have been studied in magnetic fields 7–14 T applied perpendicular to the highly conducting plane. The Fourier spectrum of the oscillations exhibits four prominent peaks, revealing a multiple-connected magnetic breakdown network of the electron orbits typical of the κ-type organic conductors. The obtained data are discussed in the framework of the full tight-binding band structure calculations. The cyclotron masses are considerably smaller than those found in κ-(BEDT-TTF) 2X superconductors suggesting a lower role of many body interactions in the present compound.

Two New Binary Calcium−Aluminum Compounds: Ca13Al14, with a Novel Two-Dimensional Aluminum Network, and Ca8Al3, an Fe3Al-Type Analogue1

Ca13Al14 and Ca8Al3 are obtained by fusion of the appropriate mixture of the elements in Ta containers at 1100 °C followed by annealing at 600 °C or slow cooling, respectively. The structures of both compounds were determined by single-crystal X-ray means. Ca13Al14 crystallizes with monoclinic symmetry (space group C2/m (no. 12), Z = 2, a = 15.551(4) A, b = 9.873(2) A, c = 9.726(2) A, β = 108.09(2)°), and Ca8Al3 has the triclinic Ca8In3-type structure (P1 (no. 2), Z = 2, a = 9.484(3) A, b = 9.592(3) A, c = 9.671(3) A, α = 99.02(3)°, β = 101.13(3)°, γ = 119.55(3)°). Ca13Al14 contains a two-dimensional Al network structure composed of planar hexagonal six-membered rings, planar rhombus (four-membered) rings, and trigonal three-membered rings. An electron count on the basis of the simple Zintl−Klemm formalism for three- and four-bonded Al in Ca13Al14 suggests the phase is closed shell. However, full band-structure calculations within the extended Huckel formalism indicate that it is metallic, with considera...

Full band structure calculation of minority carrier lifetimes in HgCdTe and thallium-based alloys

We have calculated the full band structures-based minority carrier lifetimes in small-gap semiconductor alloys. The contribution from first-order Coulomb interactions and second-order electron-electron interactions coupled through optical phonons are included. Our results agree reasonably well with experiments in Hg0.78Cd0.22Te. Similar calculations were carried out for lifetimes in In0.67Tl0.33P, In0.85Tl0.15As, and In0.92Tl0.08Sb. The minority carrier lifetimes in In0.67Tl0.33P and In0.92Tl0.08Sb are shorter than that in Hg0.78Cd0.22Te at all temperatures. However, the low-temperature minority carrier lifetime in In0.85Tl0.15 As is an order of magnitude longer than that in Hg0.78Cd0.22Te. Our calculations further suggest the possibility of increasing the lifetimes of minority carriers either by decreasing the density of states inside a critical energy and momentum region or by increasing the total hole population outside that critical region. Experimental observations that substantiate this suggestion are discussed.

Second-harmonic generation in p-type asymmetric GaAs-AlxGa1-xAs-AlAs superlattices due to excitations between valence minibands.

We present full pseudopotential band-structure calculations of the frequency dependence of the second-order susceptibility due to transitions between valence minibands in p-type asymmetric stepped-well superlattices. These theoretical predictions are supported by experimental observations of second-harmonic generation. From an analysis of the theoretical results the microscopic processes that contribute to the response are identified and the features of the response are related to the superlattice band structure over a range of temperatures. We demonstrate that simple particle-in-a-box models are unable to correctly describe the positions of the peaks, or the mechanisms involved, in the second-order susceptibility. Experimental results confirming the detection of second-harmonic generation in these structures are presented and compared with the theoretical predictions. An enhancement over the response in bulk of approximately 8 times is observed. The angular dependence observed is consistent with the directional properties of the second-order susceptibility predicted by the theoretical calculations.

Full band structure calculation of the linear electro-optic susceptibility

We have derived a complete microscopic quantum mechanical expression for the frequency-dependent (clamped lattice) linear electro-optic (EO) susceptibility, χ⇊(2) (−ω;ω,0), of crystalline solids in the independent particle approximation. The expression is free of the unphysical divergent terms at zero frequency which often plague such calculations. Using these expressions and utilizing a linear combination of Gaussian orbitals technique in conjunction with the Xα method we have carried out a full band structure calculation of the frequency-dependent linear EO susceptibility of GaAs. Our calculated results are in good agreement with the available experimental measurements.

Polarization analysis of hot-carrier light emission in silicon

In this paper a theoretical-evaluation is given of the absolute intensity and polarization of light emission from silicon devices due to conduction-conduction (c-c) and valence-valence (v-v) direct transitions. The matrix elements of the momentum operator between Bloch states have been obtained from a full band-structure calculation performed with the pseudopotential method. Results have been obtained by using both analytical model distribution functions and realistic hot-carrier distributions obtained from Monte Carlo (MC) simulations based on the same band model. They show a polarization degree of a few per cent, which should be observable for these transitions.

Acoustic band structure of periodic elastic composites.

We present the first full band-structure calculations for periodic, elastic composites. For transverse polarization of the vibrations we obtain a ``phononic'' band gap which extends throughout the Brillouin zone. A complete acoustic gap or a low density of states should have important consequences for the suppression of zero-point motion and for the localization of phonons, and may lead to improvements in transducers and in the creation of a vibrationless environment.

Enhancement of zone-folding effects in the second order response of the [(Si)5/(Ge)5]/(Si0.4Ge0.6)(001) superlattice

We have carried out a full band structure calculation of the second harmonic generation (SHG) coefficient and the linear response function of a [(Si)5/(Ge)5] superlattice (SLS) on a Si0.4Ge0.6 alloy substrate. Our calculation gives the first indication of the magnitude, frequency dependence, and anisotropy of the second order response in this SLS. The ratio of the features due to zone-folded transitions to those due to bulk-like transitions is an order of magnitude larger than the same ratio in the linear response. Yet these zone-folded effects are still very small. Nonetheless, the overall size of the SHG coefficient for this SLS is slightly larger than that of the corresponding SLS on a Si(001) substrate.

Electronic structure of unconventional antimony chalcogenides: Theoretical calculations and121Sb Mössbauer spectroscopy

The electronic structure of five antimony compounds is investigated and the Sb Mossbauer isomer shift is calculated. Its value obtained from the full band structure calculation gives a quantitative account for the chemical notion of delocalization of the 5s(Sb) lone pair. A simple molecular description is also derived which relates the lone pair to the Sb local environment.

Second-harmonic generation in odd-period, strained, (Si)n(Ge)n/Si superlattices and at Si/Ge interfaces.

We report the first full band-structure calculation of frequency-dependent second-harmonic generation in odd-period (Si${)}_{\mathit{n}}$(Ge${)}_{\mathit{n}}$ superlattices. We use these results in conjunction with a simple model to estimate second-harmonic generation at Si/Ge interfaces.

Band-structure calculation of dispersion and anisotropy in chi

We perform a full band-structure calculation of the dispersion, anisotropy, and magnitude of the nonlinear response \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$ for optical third-harmonic generation in Si, Ge, and GaAs, using both an empirical tight-binding (ETB) and a semi--ab initio band-structure technique. The calculation is performed with use of standard perturbation theory within the random-phase approximation and neglect of local-field corrections, with the minimal-coupling interaction Hamiltonian. The sign of \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$(0) is positive, independent of the tight-binding approximation, and in agreement with experimental results from the literature. We find that intraband contributions to \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$ are small, in contrast with earlier results obtained by using the dipole interaction Hamiltonian. While both expressions for \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$ yield a positive \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$(0), the minimal-coupling expression is dominated by the interband response, whereas the dipole expression is dominated by the intraband response. The resulting anisotropy in \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$ obtained from the ETB bands for all materials agrees with the experiment better than other calculations to date at frequencies far below the optical band gap. For silicon, the anisotropy calculated from the ETB band structure also agrees well with recent measurements on the dispersion of the anisotropy at frequencies comparable to the optical band gap. The values of \ensuremath{\Vert}\ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$(0)\ensuremath{\Vert} obtained from the ETB bands overestimate the experimental values by factors of 2 (for Si and GaAs) to 5 (for Ge), while the results obtained from the semi--ab initio bands underestimate the experimental values by a factor of approximately 2 (for Si) and 7 (for Ge and GaAs). While the (ETB) results for Si and GaAs are approximately within experimental error, the difference between the results from the two band-structure calculations reflects the high sensitivity of \ensuremath{\chi}\ensuremath{\rightarrow} $^{(3)}$ to the details of the energy bands and wave functions.

Dispersion in the anisotropy of optical third-harmonic generation in silicon

We present what are to our knowledge the first theoretical and experimental results for dispersion in the anisotropy (sigma) of chi?((3)) associated with optical third-harmonic generation in Si. The theory is based on a full empirical tight binding band-structure calculation, and the results agree well with our measurements for 0.72 microm < lambda < 1.9 microm. The calculated low-frequency limit of sigma agrees with measurements from the literature better than earlier calculations do. In addition, the dispersion in the relative phase of chi1212((3))/chi1111((3)) also shows good agreement with experiment.

Ballistic transport in II–VI semiconductor compounds and alloys

Realistic band structures are used in calculating the group velocity and scattering rates for electrons with injection energies up to 1 eV in ZnTe, CdTe, and the low-effective-mass alloy Hg0.7Cd0.3Te. Scattering from longitudinal optical phonos, ionized impurities, and alloy disorder have been included in our full band-structure calculation, which automatically includes both intra- and intervalley scattering. Of the II–VI materials considered, at 77 K HgCdTe is superior for low injection energies (up to 0.25 eV) while CdTe is superior at higher injection energies (1 eV) at room temperature. The attainable mean free paths ( ≥ 1000 Å) and group velocities ( ≥108 cm/s) for both systems are comparable to values found in III–V systems.

Electronic properties of antimony chalcogenides.

The electronic structure of five antimony chalcogenides, Sb${\mathrm{I}}_{3}$, ${\mathrm{Sb}}_{2}$${\mathrm{Te}}_{3}$, SbTeI, TlSb${\mathrm{S}}_{2}$, and ${\mathrm{Tl}}_{3}$Sb${\mathrm{S}}_{3}$, is investigated. Information from x-ray diffraction, M\"ossbauer spectroscopy, electrical measurements, and photoemission spectroscopy is combined with band-structure calculations to get a coherent picture of these materials. The chemical notion of the asymmetry and delocalization of the $5{s}^{2}$ antimony lone pair is given a quantitative interpretation both from the full band-structure calculation and from a simple molecular description.

Indirect gap resonant tunneling in GaAs/AlAs

A full band structure calculation of resonant tunnelling through AlAs barriers using a nearest neighbour tight binding method has been compared with experiment. We report good agreement of our calculation with measurements both qualitatively and quantitatively. The peak resonant current densities agree to within 20%, without the parameter adjustments used in other studies. The major contribution to the tunnelling current is found to result from X-like states in the AlAs barriers. This is the first rigorous theoretical confirmation of the conclusions arrived at from a number of other experimental studies.

Optical properties of pure and ultraheavily doped germanium: Theory and experiment.

We have measured by spectroellipsometry the dielectric function \ensuremath{\epsilon} of pure and ultraheavily doped germanium from the near-infrared (\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\simeq}1.6 eV) to the near-ultraviolet (\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\simeq}5.6 eV) regions. The dependence of the ${E}_{1}$, ${E}_{1}$+${\ensuremath{\Delta}}_{1}$, ${E}_{0}^{\mathcal{'}}$, and ${E}_{2}$ critical energies on impurity concentration was obtained. A red shift of the different critical-point energies, together with an increase of the lifetime broadening, has been observed. Amplitudes and phase angles for the corresponding critical points were also obtained. The results are compared with full band-structure calculations of the effect of the impurities on the band structure of germanium.

Analytic methods for the calculation of the electronic structure of solids.

Andersen's atomic-sphere approximation has been utilized with approximations based upon linear-combination of atomic orbitals (LCAO) theory to obtain approximate energy-band parameters for solids. Simple analytic expressions for the bandwidth and position of the band center have been derived that require only free-atom wave functions evaluated at the Wigner-Seitz atomic-sphere radius. For convenience, the method has been named the atomic surface method (ASM). The following simple analytic expressions for the band parameters have been derived from the ASM: (i) The bandwidth is equal to the product of ${\ensuremath{\Elzxh}}^{2}$/m, the gradient of the electron density at the atomic-sphere radius, and the surface area of the sphere; (ii) the average band energy is shifted from the atomic-term-value energy by an amount given by the product of the bandwidth, electron density at the atomic-sphere radius, and atomic-sphere volume. The theory has been applied without adjustable parameters to the transition metals and f-shell metals with use of tabulated Hartree-Fock wave functions and is in reasonable agreement with full band-structure calculations. The same analysis is applied to atomic core states under compression and is also in reasonable agreement with complete band-structure calculations. The 2s and 2p states of Na and Al have been calculated to the point where they merge with the conduction band as free-electron states. These bandwidths and shifts are also written in terms of the atomic term values by using the asymptotic form of the radial wave function. Finally, the LCAO energy bands of Ni are calculated with use of the ASM parameters. The average d-band energy relative to the conduction-band minimum and the hybridization of the conduction band with the d band are calculated with use of the asymptotic form of the radial wave function, giving approximate energy bands entirely in terms of free-atom parameters.

Radiative recombination in heavily dopedp-type germanium

Low-temperature photoluminescence studies on heavily doped $p$-type germanium are reported. In addition to the indirect-band-gap (0.75 eV) luminescence, direct recombination of nonthermalized minority carriers located at the conduction-band minimum at point $\ensuremath{\Gamma}$ is observed. The direct recombination occurs across the gaps ${E}_{0}$ and ${E}_{0}+{\ensuremath{\Delta}}_{0}$ (0.89 and 1.19 eV, respectively) and resonates strongly for exciting photon energies close to the energy gap ${E}_{0}$. The emission across the gap ${E}_{0}$ can be described as a mixture of band-to-band transitions with and without momentum conservation. From the luminescence spectra the shift of the indirect band gap as well as the direct band gap ${E}_{0}$ is determined as a function of carrier concentration and compared to full pseudopotential band-structure calculations.