Session B24: Electronic Structure: Theory and Spectra

Valence band effective Hamiltonians in nitride semiconductors

Valence band effective Hamiltonians are useful to determine the electronic states of shallow impurities, quantum wells, quantum wires and quantum dots within the effective mass approximation. Although significant experimental and theoretical work has been performed, basic parameters such as the Rashba Sheka Pikus (RSP) Hamiltonian parameters are still uncertain. In this work, the electronic band structures of AlN, GaN and InN, all in the wurtzite crystal structure, as well as the RSP Hamiltonian parameters~are determined by using the QSGW approximation in a FP-LMTO implementation. The corrections offered by this approach beyond the LDA are important to obtain the splittings and effective masses accurately. The present GW implementation, which allows for a real space representation of the self-energy, enables us to interpolate exactly to a fine k-mesh and hence to obtain accurate effective masses. We find the crystal field splitting in GaN (12 meV) in much closer agreement with experiment than previous work and obtain a negative SO coupling for InN. Moreover, we have generalized the method of invariants to crystals with orthorombic symmetry, such as ZnSiN$_{2}$ ZnGeN$_{2}$, ZnSnN$_{2}$ and CdGeN$_{2}$ and determined the corresponding Hamiltonian parameters.   

Hybrid Density Functional Study of (Hg,Cd)Te Systems

The HgCdTe alloy is used in high-performance infrared detection applications with a band gap range extending across the infrared spectrum. HgTe in particular has sparked interest for its topological insulating behavior in quantum well devices due to its band inverted nature. We test the quality of the newer hybrid screened functional, HSE, on the two contrasting materials: HgTe (semimetal) and CdTe (semiconductor) to see how well it performs under a range of computational setups [1]. A direct comparison of HSE with the standard DFT functional PBE to experiment for the HgCdTe alloy reveals HSE is able to reproduce the experimental crossover composition of 17\% Cd concentration when the alloy goes from a semimetal to semiconductor, whereas PBE overestimates this composition at 67\% Cd concentration. HSE also predicts a higher valence band offset of 0.53 eV in the HgTe/CdTe heterostructure than previous first-principle and early experimental results, but in good agreement with the more recent experimental results. Supported by DOE-Basic Energy Science DOE-BES-DMS (DEFG02-99ER45795). Computing resources are provided by NERSC and OSC. \\[4pt] [1] Jeremy W. Nicklas and John W. Wilkins, Phys. Rev. B 84, 121308(R) (2011)   

Ab-initio description of satellites in graphite

The GW method from Many-Body Perturbation Theory has been very successful in describing photoemission spectra in a variety of systems. In particular, GW is known to give good quasiparticle properties like band-gaps, but it has shown some limitations in the description of complex correlation effects like satellites. Satellite peaks in photoemission come from higher-order excitations and are still poorly studied in the valence bands. In perturbative GW the spectral function can describe additional features beside the quasiparticle peaks, but these satellites are known to be too weak and too low in energy, as it appears from calculations on the Homogeneous Electron Gas and some real materials. We have recently shown that including additional diagrams in the Green's function (similarly to what has been done with the cumulant expansion) we obtain an excellent description of satellites series in the test case of bulk silicon, where GW is unable to cope. We now focus on a more complex system, i.e. graphite, with this same approach. Using our newly measured XPS valence data, we investigate the effects of anisotropies on satellites and give a prediction on the spectral changes following the transition towards a single graphene layer.   

Isotope dependence of band gap in semiconductors

Recently, carrier confinement was observed in diamond superlattice consisting of pure $^{12}$C and $^{13}$C layers. This interesting phenomenon comes from large isotope dependence of fundamental gap width in diamond. To understand this carrier confinement and design related nanodevices, we investigate the effect of electron-phonon couplings on quasiparticle energies in semiconductors composed of carbon and other light elements using first-principles methods based on the density functional theory. The calculated isotope dependence as well as temperature dependence of band gap in diamond is found to agree well with the experiment. We also discuss the isotope dependence in binary compounds such as boron nitride and silicon carbide.   

Clarification of the relations between stacking structures of ${\it sp}^3$ network materials and their band gaps

Silicon carbide (SiC) has been discovered in various polymorphs. Each polymorph is characterized by its stacking of atomic planes. The band gap varies substantially in each polymorph from 2.40 eV to 3.33 eV in spite that the local atomic structures are identical to each other [1]. The mechanism of this intriguing property have been poorly understood. To clarify the fundamental reasons for this band-gap variation, we have performed the electronic-structure calculations in the density functional theory. We have found that the Kohn-Sham orbital at the conduction-band bottom distributes broadly around the interstitial channel, thus floating in the matter. The way of the floating depends on the stacking of the atomic planes and determines the band gap in each polymorph. We also find that the floating state appears in other ${\it sp}^3$-bonded materials, and the band-gap variation is common to the covalent materials. References [1] Properties of Silicon Carbide edited by G. L. Harris (INSPEC, London, 1995).   

Nonequilibrium ``melting'' of a charge density wave insulator via an ultrafast infrared laser pulse

In equilibrium, electrons interacting with lattice vibrations have a transition either to a charge density wave phase (a static modulation of the electronic charge) or to a superconductor (electron pairs move without resistance). If the coupling is weak, the system orders in the Bardeen-Cooper-Schrieffer scenario, where the ordering occurs at some transition temperature Tc and a gap simultaneously forms in the density of states. In strong-coupling, preformed pairs bind at a high temperature (forming a gap in the density of states) and the ordering only occurs at a lower temperature. We employ an exact solution of a model for pump-probe time-resolved photoemission spectroscopy to show how, in nonequilibrium, a third scenario arises: the gap disappears in the presence of a nonzero order parameter, and then reforms well after the pulse has passed. This nonequilibrium ``phase transition'' scenario qualitatively describes all of the available experiments on the ultrafast melting of a charge density wave.   

Engineering Electronic Band Structure for New Elpasolite Scintillators

The utilization of scintillator materials is one of the primary methods for radiation detection. Elpasolites are a large family of quaternary halides that have recently attracted considerable interest for their potential applications as $\gamma $-ray and neutron scintillators. A large number (on the order of 10$^{3})$ of different chemical compositions exist in the elpasolite family of compounds. This wide range of compositions offers numerous opportunities for fine-tuning the material chemistry to target specific scintillation properties, but they also pose significant challenges in identifying the most promising ones. Many elpasolite scintillator materials currently under development suffer from low light output and long scintillation decay time. The low light output is partially due to a large band gap while the long scintillation decay time is a result of the slow carrier transport to Ce impurities, where carriers recombine to emit photons. We suggest that these problems may be mitigated by optimizing the band gap and carrier mobility by selecting constituent elements of proper electronegativity. For example, cations with lower electronegativity may lower the conduction band and increase the conduction band dispersion simultaneously, resulting in higher light output and faster scintillation. We demonstrate by first-principles calculations that the strategy of manipulating electronegativity can lead to a number of new elpasolite compounds that are potentially brighter and faster scintillators.   

Origin of the variation of exciton binding energy in semiconductors

Electron-hole interaction plays a crucial role in optical properties, and the exciton binding energy ($E_{b})$ in technologically important semiconductors varies from merely a few meV to around 100 meV, which is not well understood. In this work, we investigate the origin of the variation of $E_{b}$ in semiconductors, employing first-principle calculations based on the density functional theory (DFT) and the many-body perturbation theory with Green's function (GW/BSE). Our results clearly show that $E_{b}$ decreases as the spread of electron distribution, which measures the magnitude of electron delocalization, increases. This is due to the increased electronic screening when electrons tend to be more delocalized. Furthermore, the spread distribution of the top valence electrons is of central importance in determining excitonic screening, which leads to weakly bound electrons and holes in semiconductors. Thus, the variation of exciton binding energy in semiconductors can be understood from the computed magnitude of electron delocalization of top valence bands of these materials using DFT.   

Modeling Shallow Core-Level Transitions in the Reflectance Spectra of Gallium-Containing Semiconductors

The electronic structure of covalent materials is typically approached by band theory. However, shallow core level transitions may be better modeled by an atomic-scale approach. We investigate shallow d-core level reflectance spectra in terms of a local atomic-multiplet theory, a novel application of a theory typically used for higher-energy transitions on more ionic type material systems. We examine specifically structure in reflectance spectra of GaP, GaAs, GaSb, GaSe, and GaAs$_{1-x}$P$_{x}$ due to transitions that originate from Ga3d core levels and occur in the 20 to 25 eV range. We model these spectra as a Ga$^{+3}$ closed-shell ion whose transitions are influenced by perturbations on 3d hole-4p electron final states. These are specifically spin-orbit effects on the hole and electron, and a crystal-field effect on the hole, attributed to surrounding bond charges and positive ligand anions. Empirical radial-strength parameters were obtained by least-squares fitting. General trends with respect to anion electronegativity are consistent with expectations. In addition to the spin-orbit interaction, crystal-field effects play a significant role in breaking the degeneracy of the d levels, and consequently are necessary to understand shallow 3d core level spectra.   

Ab-initio study of dilute nitride substitutional and split-interstitial impurities in gallium antimonide (N-GaSb)

We present an ab-initio density functinal theory study of dilute-nitride GaSb. Adding dilute quantities of nitrogen causes rapid reduction in bandgap of GaSb ($\sim$300 meV for 2\% N). Due to this rapid reduction in bandgap, dilute-nitrides provide a pathway for extending the emission of GaSb based type-I diode lasers into the mid-infrared wavelength region (3-5 micron). In this study we look at the effect of substitutional N impurity on the electronic properties of our system and compare it with the band-anticrossing model, a phenomenological model, which has been used to explain giant band bowing observed in dilute-nitride alloys. We also study the effect of Sb-N split interstitials which are known to be non-radiative recombination centers. Furthermore we also discuss the stability of the Sb-N split interstitial relative to substitutional nitrogen to determine if the split interstitials can be annihilated using post-growth annealing to improve the radiative lifetime of the material which essential for laser operation.   

Electronic properties of InP in terms of an ab-initio LDA

We present results from ab-initio local density approximation (LDA) calculations of electronic and related properties of zinc blende indium phosphide (InP). Our computations employed the Ceperley and Alder LDA potential and the linear combination of atomic orbital (LCAO) formalism. The implementation of the LCAO formalism followed the Bagayoko, Zhao, and Williams (BZW) method. Consequently, we solved self consistently both the Kohn sham equation and the one giving the ground state charge density in terms of the wave functions of the occupied states. Self-consistency, for the latter equation, requires a search for the optimal basis set. This search entails increases of the size of the basis set and the related modifications of angular symmetry and of available radial functions. Our calculated, direct band gap of 1.398 eV (1.40 eV), at the ? point, is in excellent agreement with experimental values. The calculated density of states (DOS) also agree with experimental finding. The calculated electron and hole effective masses differ by 10\% from some corresponding experimental ones. We discuss the equilibrium lattice constant and optical properties.   

Self Consistent Calculations of Electronic Properties of Systems with an Energy or a Band Gap

We re-examine the process of performing self consistent calculations of electronic and related properties of finite systems (with an energy gap) and of crystals with a band gap. This work applies to calculations utilizing density functional and X? potentials and to other approaches that entail solving a system of inherently coupled equations. In particular, the local density approximation (LDA) is defined by a system of equations that reduces to two equations upon the selection of Vxc. We show how the Bagayoko, Zhao, and Williams (BZW) method solves the relevant system of equations and leads to results in excellent agreement with experimental ones. We discuss such results for w-ZnO, rutile TiO2, w-CdS, zb-CdS, zb-InP, Ge, Ca B6, and other materials. Work funded by the National Science Foundation, through LASiGMA [NSF AwardEPS-1003897 and No. NSF (2010-15)-RII-SUBR], LONI [Award No. 2-10915], and Ebonyi State, Federal Republic of Nigeria.   

Infrared Refractive Index of Silicon: Parity and Sum-Rule Tests

We have resolved conflicting reports for the IR refractive index of silicon using general considerations of linear response theory. We find that use of unphysical series expansions in the analysis of channel spectra has been a significant source of systematic error. Recognition that the index is an even function of photon energy is crucial for analysis of these measurements and clarifies data presentation. In the region of high IR transparency of elemental semiconductors, the index may be expanded in a rapidly convergent Taylor series. Coefficients of terms in the (2n)$^{th}$ power of energy are proportional to the (2n+1)$^{th}$ inverse moment of the electronic absorption spectrum. In the favorable case of intrinsic Si, the electronic absorption is sufficiently well known that independent values of the intercept, slope and curvature of plots of index \textit{vs}. the square of photon energy may be calculated. Index data sets with parameters significantly different from these suffer from systematic errors or refer to impure samples. Using these parity and sum-rule tests we have prepared a composite index data set for intrinsic silicon that represents a best fit to reliable measurements from microwaves to the visible. Applications to germanium and diamond will be discussed.   

Electronic Structure of NiFe$_2$O$_4$ using screened Hybrid Functionals

As an insulating ferrimagnet with a high Curie temperature, NiFe$_2$O$_4$ (NFO) may be a promising candidate for future spin-based applications. Recent demonstration of spin-Seeback effect in magnetic insulators indicates that important new phenomena may be discovered in such materials. Unfortunately, density functional theory cannot give a full account of its properties; most notably, LDA calculations find it to be metallic. LDA+U yields an insulator but underestimates the band gap. The recently-implemented screened hybrid functionals method (HSE06) represents only a moderate increase in computational effort compared to traditional DFT. This method allows one to modify the PBE-approximated exchange potential with a portion of the Hartree-Fock exchange. We present LDA, LDA+U, and HSE06 calculations of the density of states and band structure of NFO. We show that hybrid methods greatly improve agreement with the experimental band gap over LDA +U. We find that NFO is an indirect band gap system with the spin-down channel having the lower, indirect gap, whereas the majority channel possess a direct gap with over a 0.5eV difference with the minority gap. Comparison of our theoretical results with recent optical measurements on NFO thin films is also presented.