Session B22: Theory and Simulation of Excited-State Phenomena in Semiconductors and Nanostructures I

Hole localization, water dissociation mechanisms, and band alignment at aqueous-titania interfaces

Photocatalytic water splitting is a promising method for generating clean energy, but materials that can efficiently act as photocatalysts are scarce. This is in part due to the fact that exposure to water can strongly alter semiconductor surfaces and therefore photocatalyst performance. Many materials are not stable in aqueous environments; in other cases, local changes in structure may occur, affecting energy-level alignment. Even in the simplest case, dynamic fluctuations modify the organization of interface water. Accounting for such effects requires knowledge of the dominant local structural motifs and also accurate semiconductor band-edge positions, making quantitative prediction of energy-level alignments computationally challenging. Here we employ a combined theoretical approach to study the structure, energy alignment, and hole localization at aqueous-titania interfaces. We calculate the explicit aqueous-semiconductor interface using ab initio molecular dynamics, which provides the fluctuating atomic structure, the extent of water dissociation, and the resulting electrostatic potential. For both anatase and rutile TiO$_{\mathrm{2}}$ we observe spontaneous water dissociation and re-association events that occur via distinct mechanisms. We also find a higher-density water layer occurring on anatase. In both cases, we find that the second monolayer of water plays a crucial role in controlling the extent of water dissociation. Using hybrid functional calculations, we then investigate the propensity for dissociated waters to stabilize photo-excited carriers, and compare the results of rutile and anatase aqueous interfaces. Finally, we use the \textit{GW} approach from many-body perturbation theory to obtain the position of semiconductor band edges relative to the occupied 1b$_{\mathrm{1}}$ level and thus the redox levels of water, and examine how local structural modifications affect these offsets.   

Role of excited states in Shockley-Read-Hall recombination in wide band-gap semiconductors

Defect-assisted recombination is an important limitation on efficiency of optoelectronic devices. However, since nonradiative capture rates decrease exponentially with energy of the transition, the mechanisms by which such recombination can take place in wide-band-gap materials are unclear. We investigate the role of electronic excited states in the recombination process, focusing on group-III nitrides, for which accumulating experimental evidence indicates that defect-assisted recombination is an important limiting factor in efficiency. Based on first-principles electronic structure calculations, we show that excited states of gallium vacancy complexes make these defects very efficient recombination centers. Our work provides new insights into the physics of nonradiative recombination. The mechanism discussed in this work is suggested to be very critical and ubiquitous in wide-band-gap semiconductors. This work was supported by DOE and the European Union.   

Auger recombination in InN from first principles

Group-III Nitride materials are used in numerous electronic and optoelectronic devices including solid-state lighting, energy conversion, sensor technologies, and high-power electronics. Indium nitride in particular is interesting for fast electronics and optoelectronics in the infrared. Auger recombination is a non-radiative carrier recombination process that would limit the efficiency of these devices. The small band gap (0.7 eV) and the high intrinsic free-electron concentrations in InN possibly make Auger recombination particularly important in this material. We used first-principles computational methods to determine the Auger recombination rates in InN. Our results suggest that direct Auger recombination is dominant in this material and that phonon-assisted Auger processes are not as important as in wider-gap nitrides such as GaN.   

Electronic coherence and the kinetics of energy transfer in light-harvesting systems

Recent 2D-spectroscopy experiments have observed transient electronic coherence in natural and artificial light harvesting systems, which raises questions about the role of electronic coherence in facilitating excitation energy transfer (EET) processes. In this talk, we introduce the recently developed partial linearized path-integral (PLPI) method, which can accurately simulate exciton transfer dynamics across multiple reaction regimes, as well as reliably describe the electronic coherence among excitonic states. Further, we develop a strategy that enables the analysis of the relative impact of static and dynamic electronic coherence. With PLPI simulations, we find that energy transfer dynamics are almost entirely dominated by static coherence effects; dynamic coherence is found to cause only minor effects. These conclusions are consistent with the historical view that emphasizes the importance of energy-level alignment for efficient incoherent energy transfer,while suggesting a less important role for more exotic electronic coherence effects that have been recently emphasized.   

The Optical Spectrum of LaAlO$_3$: Quasiparticle Energies and the Effect of Lattice Screening

Lanthanum aluminate (LaAlO$_3$) is a commonly used high-$\kappa$ dielectric material but its exact optical properties are not well understood. By solving the Bethe-Salpeter Equation for the optical polarization function, which describes the interaction between electrons and holes, a precise prediction of the dielectric function can be obtained. However, for LaAlO$_3$, there are two major problems limiting the computational study: The first problem is that due to the complicated conduction band structure, the quasiparticle effect needs to be taken into account, which makes the calculations costly. We resolved this problem by interpolating accurate eigenenergies computed using a hybrid exchange-correlation functional to a dense k-point grid. Another problem is that for such high-$\kappa$ materials, the lattice contribution to the dielectric screening may be important. We investigated this by computing the optical spectrum using electronic constant, static dielectric constant and the average of both and found that taking lattice contribution into account significantly reduces excitonic effects. All results are compared to available experiments.   

Electronic and optical properties of Ga$_{\mathrm{2}}$O$_{\mathrm{3}}$ from first principles

Wide band-gap semiconductors such as Ga$_{\mathrm{2}}$O$_{\mathrm{3}}$ are used in numerous applications including high voltage/temperature electronics, deep-UV emission, and transparent contacts. We have investigated the electronic and optical properties of Ga$_{\mathrm{2}}$O$_{\mathrm{3}}$ with first-principles calculations based on density functional theory. The electronic and optical properties are calculated with many-body perturbation theory using the GW and Bethe-Salpeter equation methods. The semicore states of Ga are treated as valence electrons to accurately determine the band gap and band structure. We will present results for the structural, electronic, and optical properties of the various Ga$_{\mathrm{2}}$O$_{\mathrm{3\thinspace }}$polymorphs, including $\beta $-Ga$_{\mathrm{2}}$O$_{\mathrm{3}}$. This research was supported by the National Science Foundation through Grant No. DMR- 1534221. Computational resources were provided by the DOE NERSC facility.   

Substrate Screening Induced Renormalization of Excited-States in 2D Materials

Two-dimensional (2D) materials offer an emerging platform for exploring novel electronic phenomena in reduced~dimensionality systems.~ However, because of~their atomic scale thickness, their excitation energy levels in 2D materials are strongly renormalized due to the screening by the surrounding environment. This effect is expected to have strong impact when the materials are integrated into functional devices.~ For example, the presently available GW calculations significantly overestimate the band gaps in graphene nanoribbons (GNRs) by as much as one eV compared to experiment. Here, we outline an integrated computational approach combining DFT, the GW approximation, and a classical image charge model to include substrate screening effects in a computationally tractable manner. We investigate the band gaps and defect charge transition levels (CTLs) in a prototypical 2D material, hexagonal boron nitride (hBN) and a prototypical 1D nanostructure, GNR. The band gaps and defect CTLs are strongly renormalized by several tenths of an eV in the substrate-supported versus the free-standing configurations. In the case of GNRs, the predicted band gaps are in an excellent agreement with~recent STS experiments.   

Electronic structure, transport properties, and excited states in CoTiSb, CoZrSb, and CoHfSb half-Heusler compounds

CoTiSb is a member of a large family of half-Heusler compounds with 18 valence electrons. CoTiSb is semiconductor material with a band gap a little over 1 eV, and it has been considered promising for thermoelectric applications. It can be grown on conventional III-V semiconductors, and could potentially be integrated in III-V devices. Here we present results of first-principles calculations of electronic structure, transport properties, and excited states in CoTiSb, as well as CoZrSb and CoHfSb. Electronic structures are studied using density functional theory within the local density approximation, hybrid functional and quasiparticle GW methods. Both room-temperature Seebeck coefficient and carrier mobility are calculated from first-principles. We also determine the band alignments to III-V semiconductors, and all the results are presented and discussed in the light of available experimental data.   

Ab Initio Calculations of Excited Carrier Dynamics in Gallium Nitride

Bulk wurtzite GaN is the primary material for blue light-emission technology. The radiative processes in GaN are regulated by the dynamics of excited (or so-called “hot”) carriers, through microscopic processes not yet completely understood. We present ab initio calculations of electron-phonon (e-ph) scattering rates for hot carriers in GaN. Our work combines density functional theory to compute the electronic states, and density functional perturbation theory to obtain the phonon dispersions and e-ph coupling matrix elements. These quantities are interpolated on fine Brillouin zone grids with maximally localized Wannier functions, to converge the e-ph scattering rates within 5 eV of the band edges. We resolve the contribution of the different phonon modes to the total scattering rate, and study the impact on the relaxation times of the long-range Fr\"{o}hlich interaction due to the longitudinal-optical phonon modes.   

Time Evolution of Charge Carriers & Phonons after Photo-Excitation by an Ultra-Short Light Pulse in Bulk Germanium

We have calculated the time-evolution of carriers and generated phonons in Ge after ultrafast photo-excitation above the direct band-gap. The relevant electron-phonon and anharmonic phonon scattering rates are obtained from first-principles electronic structure calculations. Measurements of the x-ray diffuse scattering after excitation near the L point in the Brillouin zone find a relatively slow (~5 ps, compared to the typical electron-phonon energy relaxation of the Gamma-L phonon) increase of the phonon population. We find this is due to emission caused by the scattering of electrons between the Delta and L valleys, after the initial depopulation of the Gamma valley. The relative slowness of this process is due to a combination of causes: (i) the finite time for the initial depopulation of the conduction Gamma valley; (ii) the associated electron-phonon coupling is relatively weaker (compared to Gamma-L, Gamma-Delta and Delta-Delta couplings) ; (iii) the TA associated phonon has a long lifetime and (iv) the depopulation of the Delta valley suppresses the phonon emission.   

Constrained Density Functional Theory by Imaginary Time-Step Method

Constrained Density Functional Theory (CDFT) has been a popular choice within the last decade for sidestepping the self interaction problem within long-range charge transfer calculations.\footnote{Q. Wu and T. Voorhis, \textbf{J. Chem. Theory Comput.} 2, 765-774 (2006).} Typically an inner constraint loop is added within the self-consistent field iterations of DFT in order to enforce this charge transfer state by means of a Lagrange multiplier method.\footnote{Q. Wu and T. Voorhis, \textbf{Phy. Rev. A} 72, 024502 (2005).} In this work, an alternate implementation of CDFT is introduced, that of the imaginary time-step method, which lends itself more readily to real space calculations in the ability to solve numerically for 3D local external potentials which enforce arbitrary given densities. This method has been shown to reproduce the proper $1/R$ dependence of charge transfer systems in real space calculations as well as the ability to generate useful constraint potentials. As an example application, this method is shown to be capable of describing defects within periodic systems using finite calculations by constraining the 3D density to that of the periodically calculated perfect system at the boundaries.   

Density functional study on a light-harvesting carotenoid-porphyrin-C$_{\mathrm{60}}$ molecular triad in explicit solvent

We investigate the effect of solvent on the electronic structure of a biomimetic molecular triad that shows photoinduced charge transfer in laboratory. The supramolecular triad contains three different units - C60, porphyrin, and beta-carotenoid. We have performed classical molecular dynamics simulation of the triad surrounded by 15000 water molecules using NAMD for 20 nanoseconds. Subsequently, we performed an all-electron density functional calculations (DFT) using large basis sets on the 50 snap-shots taken from the molecular dynamics simulation. The solvent effects in the DFT calculations are treated using both the explicit water molecules as well as using the point charge representation of water. The excitation energies and absorption spectra show that the polar solvent induces significant changes in the electronic structure of the triad.   

Ab-Initio Computations of Electronic and Related Properties of cubic Lithium Selenide (Li$_{2}$Se)

We present theoretical predictions, from ab-initio, self-consistent calculations, of electronic and related properties of cubic lithium selenide (Li$_{2}$Se). We employed a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). We performed the computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Our results include electronic energies, total and partial densities of states, effective masses, and the bulk modulus. The theoretical equilibrium lattice constant is 5.882 {\AA}. We found cubic Li$_{2}$Se to have a direct band gap of 4.363 eV (prediction), at $\Gamma $. This gap is 4.065 eV for a room temperature lattice constant of 6.017 {\AA}. The calculated bulk modulus is 31.377 GPa. Acknowledgments: This work was funded in part by the National Science Foundation (NSF) and the Louisiana Board of Regents, through LASiGMA [Award Nos. EPS- 1003897, NSF (2010-15)-RII-SUBR] and NSF HRD-1002541, the US Department of Energy -- National, Nuclear Security Administration (NNSA) (Award No. DE- NA0002630), LaSPACE, and LONI-SUBR.