Session B9: Theory of Semiconductors

Large Valley Splitting in Slightly Misaligned Uniaxially Strained Silicon Films

We have numerically computed the subband structure in a thin silicon film by using the Hensel-Hasegawa-Nakayama model for the conduction band. It is demonstrated that unprimed subbands in a (001) films are not equivalent at small thicknesses. Application of tensile stress in [110] direction removes the subband degeneracy. For small stress the subband splitting is linear in shear strain. It is inversely proportional to the third power of the film thickness, in agreement with previous results. For a film slightly misaligned from the (001) direction the ground subband develops the two minima symmetrically situated around the point $k_x=k_y=0$. In the magnetic field these two minima produce the two ladders of the Landau levels. Due to Zener tunneling between the two minima the difference between the cyclotron frequencies decays exponentially with the inverse magnetic field. This effect was previously interpreted as an exponential decrease in valley splitting due to disorientation. We show that for stress values employed by the semiconductor industry the large value for the valley splitting is recovered.   

Large relativistic spin splittings in the band structures of III-V and II-VI semiconductors

The Quasiparticle Self-consistent GW approximation, including spin-orbit coupling has been used to derive the spin splittings over the full Brillouin zone (BZ) for several III-V and II-VI semiconductors. Also, the magnitude and direction of the associated spin polarization of the states were determined. The spin splitting effect is a consequence of the non-centrosymmetric structure of these semiconductors. They are small in the vicinity of the center of the BZ (order of meV), but reach for the lowest conduction band in some parts of the BZ very large values, order of 1 eV. The locations of the largest splittings and their physical origin depend on the compound.   

Electronic and optical properties of body-centered tetragonal Si and Ge

We present a first-principles calculation of the quasiparticle and optical excitation spectra of recently predicted silicon and germanium polytypes in the bct structure. The quasiparticle spectra, calculated within the GW approximation, predicts that both silicon and germanium in the bct structure are small band gap materials with direct gaps of 1.1 eV and 0.79 eV, respectively. The optical spectra is evaluated by solving the Bethe-Salpeter equation taking into account electron-hole interactions. We then make comparison to the cubic phases of Si and Ge which suggest the possible utility of the bct phases in photovoltaic applications.   

Rashba effects in bulk wurtzite materials

The spin-splitting energies in strained bulk wurtzite AlN are studied using the linear combination of atomic orbital method. It is found that strain and crystal field induce not only a Rashba linear-$k (\alpha _{wz} )$ but also two Rashba cubic$-k$ terms ($\gamma _R$ and $\lambda _R )$ in the two-band $k\cdot p,$ Hamiltonian $H_{SO} (\vec {k})=(\alpha _{wz} -\gamma _R k_{//}^2 +\lambda _R k_z^2 )(\sigma _x k_y -\sigma _y k_x)+H_{SO}^0 $ where $H_{SO}^0 =(-\gamma _0 k_{//}^2 +\lambda _0 k_z^2 )(\sigma _x k_y -\sigma _y k_x )$ generates a cone-shaped minimum-spin-splitting (MSS) surface and ${\lambda _0} \mathord{\left/ {\vphantom {{\lambda _0} {\gamma _0}}} \right. \kern-\nulldelimiterspace} {\gamma _0}\approx 4$. As tensilely biaxial strain increases, the shape of the MSS surface changes from a hexagonal hyperboloid of two sheets in unstrained AlN to a hexagonal cone, and eventually becomes a hyperboloid of one sheet.   

Quasiparticle band structures of PbS, PbSe and PbTe including pressure effects

The electronic quasiparticle energies of PbS, PbSe and PbTe are calculated with the quasiparticle self-consistent GW approximation (QSGW, van Schilfgaarde, Kotani and Faleev) including spin-orbit coupling. The semiconducting gap is formed between states of L$_{6}$ symmetry (L$_{6}^{+}$ and L$_{6}^{-})$, which is the reason why these materials are semiconductors even in the local-density approximation (LDA) due to band repulsion. Closer inspection reveals that in PbS and PbSe the order of the L$_{6}$ states is reversed in the LDA compared to the QSGW bands. This leads to the wrong sign of the band gap deformation potentials for PbS and PbSe in the LDA. With QSGW both sign and magnitude of the deformation potentials are in agreement with experiments. Also, results obtained for effective masses and band gaps as functions of pressure will be discussed.   

Fullerene Molecules and Other Clusters of III-V Compounds

The goal of the our work is to derive geometries of fullerene-like cages and other clusters of atoms from groups III and V of the periodic table. Our previous research focused on Carbon Fullerenes and on Ga$_{n}$As$_{n}$ clusters (n = 1 thru 12). Our research group has made an original discovery about Ga$_{n}$As$_{n}$ clusters. In our work on nanotechnology to date, we used the hybrid ab initio methods of quantum chemistry to derive the different geometries for the clusters of interest. We also calculated binding energies, bond-lengths, ionization potentials, electron affinities and HOMO-LUMO gaps, and IR spectra for these geometries. Of particular significance was the magic number for GaAs cluster stability that we found at n = 8. This is important because materials containing controlled III-V nanostructures provide the capability of preparing new classes of materials with enhanced optical, magnetic, chemical sensor and photo-catalytic properties. The second phase of the investigation will examine the effects of confinement on the optical properties the clusters. It will be interesting to observe novel linear as well as nonlinear optical processes in them. The third phase of the investigation will focus on the improved design of solar cells based on the optical properties of the clusters.   

Effective band structure of random III-V alloys

Random substitutional alloys have no long range order (LRO) or translational symmetry so rigorously speaking they have no $E(\vec k)$ band structure or manifestations thereof. Yet, many experiments on alloys are interpreted using the language of band theory, e.g. inferring Van Hove singularities, band dispersion and effective masses. Many standard alloy theories (VCA- or CPA-based) have the LRO {\em imposed} on the alloy Hamiltonian, assuming only on-site disorder, so they can not be used to judge the extent of LRO that really exists. We adopt the opposite way, by using large (thousand atom) randomly generated supercells in which chemically identical alloy atoms are allowed to have different local environments (a polymorphous representation). This then drives site-dependent atomic relaxation as well as potential fluctuations. The eigenstates from such supercells are then mapped onto the Brillouin zone (BZ) of the primitive cell, producing effective band dispersion. Results for (In,Ga)X show band-like behaviour only near the centre and faces of the BZ but rapidly lose such characteristics away from $\Gamma$ or for higher bands. We further analyse the effects of stoichiometry variation, internal relaxation, and short-range order on the alloy band structure.   

First-principles study of Fermi-level pinning at Al/SiON/SiC(0001) interfaces

Schottky barrier generally emerges at metal-semiconductor interfaces and its height could ideally be estimated from the difference between the work function of the metal and the electron affinity of the semiconductor, which is called Schottky limit. However, for many semiconductors such as silicon, this condition is not satisfied due to the presence of interface states, which is referred as Fermi-level pinning. Recently, spectroscopic measurements and first-principles calculations showed that silicon oxynitride (SiON) formed on a 6H-SiC (0001) surface has a band gap as large as crystalline SiO$_2$. [T. Shirasawa, Y. Ando, S. Tsuneyuki, and H. Tochihara, et.al., PRB 79, 241301(R) (2009).] Since the Schottky barrier height depends on the kind of the metal at metal-SiO$_2$ interfaces, we expect that SiON on SiC also does not exhibit Fermi-level pinning. In this study, we have investigated electrostatic properties of Al/SiON/SiC and Al/Si interfaces based on density functional theory. Effects of the applied electric field have also been studied using the effective screening medium (ESM) method [M. Otani and O. Sugino, PRB 73 115407 (2006).] We have found that distribution of the internal electric field induced by the applied field is qualitatively different between them. Further, Al/SiON/SiC has less interface states than Al/Si, which is indicative that Al/SiON/SiC is in the Schottky limit.   

Electronic properties of copper aluminate examined by three theoretical approaches

Electronic properties of 3R.CuAlO$_{2}$ are derived vs. pressure from ab initio band structure calculations within the local-density approximation (LDA), LDA+U scheme as well as the quasiparticle self-consistent GW approximation (QSGW, van Schilfgaarde, Kotani, and Falaev). The LDA underestimates the gap and places the Cu-3d states at too high energies. An effective U value, 8.2 eV, can be selected so that LDA+U lowers the 3d states to match XPS data and such that the lowest gap agrees rather well with optical absorption experiments. The electrical field gradient (EFG) on Cu is in error when calculated within the LDA. The agreement with experiment can be improved by LDA+U, but a larger U, 13.5 eV, is needed for full adjustment. QSGW yields correct Cu-EFG and, when electron-hole correlations are included, also correct band gaps. The QSGW and LDA band gap deformation potential values differ significantly.   

First-principle calculation of elastic and piezoelectric tensors and zone center phonons in LiGaO$_{2}$

The elastic, piezoelectric tensor and vibrational modes of LiGaO$_{2}$ have been studied by means of first-principles density functional calculations using the pseudopotential linear-response approach in the local density approximation. The lattice constants of the orthorhombic structure are obtained in agreement with experiment to better than 2\%. The calculated dielectric constants in the a, b, and c directions are obtained to be about 6.37, 6.98, and 7.44, comparing to 6.5, 7.0 and 8.3 from experimental data. Elastic constant were calculated from the second derivatives of total energy versus strain while piezoelectric constants were calculated from the second mixed derivatives of total energy versus electric field and strain. Our results for both elastic constants and piezoelectric constants agree well with experimental results. Using the calculated oscillator strengths and high-frequency dielectric tensor, the infrared reflectivity for the $a_{1}$,$b_{1}$ and $b_{2}$ modes are obtained in excellent agreement withexperimental data both in terms of peak positions and relative peak heights.   

Effect of Geometry and Electronic Structure on Current Switching in Organic Molecules

Unlike in the bulk inorganic semiconductor, electron transport in organic molecules exhibit strong dependence on the details of molecular geometry, nature of chemical bonds, and the electronic structure. The dependence of electron transport in organics also offers new mechanisms for current switching, not possible in bulk-inorganic semiconductors. In order to further understand and potentially utilize the molecular mechanisms of current switching in organic molecules, we have investigated the effect of molecular geometry, especially the change in the dihedral angle, on electron transport and current-voltage characteristics of tolane molecule with the use of \textit{ab initio} Hartree-Fock (HF), density functional theory, and tight-binding methods within non-equilibrium Green's function approximation. The calculated results obtained from three quantum mechanical approaches vary substantially from each other. The \textit{ab initio} HF calculations yield a maximum value for the current in the planar geometry of the molecule and minimum when the two phenyl rings are aligned perpendicular to each other.   

Three, Two and One-dimensional MoS2: A First Principle Investigation

This study presents our study on atomic, electronic, magnetic and phonon properties of three, two and one dimensional honeycomb structures of molybdenum disulfide (MoS$_2$) using first-principles pseudopotential plane wave method. The dimensionality effects on various properties are examined. The calculations of phonon frequencies indicate the stability of two dimensional, single layer MoS$_2$, which consists of a positively charged molybdenum atomic plane between two negatively charged sulfur atomic planes. Three and two dimensional MoS$_2$ are semiconductors. Their band gaps are calculated within density functional theory and corrected by GW$_0$ self energy method. Specific foreign adatoms can be chemisorbed at the sulfur plane of the single layer of MoS$_2$ with significant binding energy and attribute magnetic properties. While bare MoS$_2$ armchair nanoribbons are nonmagnetic semiconductors, zigzag MoS$_2$ nanoribbons are ferromagnetic metals. Vacancy defects in bare armchair and bare zigzag nanoribbons affect also the magnetic state and electronic structure of nanoribbons. Variation of the total energy and atomic structure with stretching of nanoribbons exhibit sequential elastic and yielding stages. In the harmonic elastic deformation range force constant and in-plane stiffness are calculated. Plastic deformation with irreversible structural transformation can lead to dramatic changes in honeycomb structure.   

Two- and one-dimensional honeycomb structures of silicon and germanium

First-principles calculations of structure optimization, phonon modes and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low -buckled, honeycomb structures. Similar to graphene, these puckered structures are ambipolar and their charge carriers can behave like a massless Dirac fermions due to their $\pi$- and $\pi^{*}$-bands which are crossed linearly at the Fermi level. In addition to these fundamental properties, bare and hydrogen passivated nanoribbons of Si and Ge show remarkable electronic and magnetic properties, which are size and orientation dependent. These properties offer interesting alternatives for the engineering of diverse nanodevices.   

New insights into the electronic properties of ordered semiconductor alloys: non-parabolic and non-analytic dependence on the order parameter

It is both fundamentally and practically important to understand the dependence of a physical property on order parameter $\eta $ for an ordered semiconductor alloy like Ga$_{x}$In$_{1-x}$P that is often found to be in a partially ordered phase. A conventional statistical theory based on a cluster expansion approach predicts that for any physical property P(x,$\eta )$ the leading term of the dependence is $\eta ^{2}$ with higher order corrections $\eta ^{4}$and etc., thus, always an analytic function of $\eta ^{2}$. From the practical application point of view, it is highly desirable to see that the $\eta ^{2}_{ }$term, corresponding to the pair correlation, alone can give adequate accuracy. However, we have found that for the electronic structure not only $\eta ^{2}_{ }$term is often inadequate but also non-analytic dependence on $\eta ^{2}_{ }$may sometimes arise, depending on the strength of the coupling among virtual crystal states caused by the alloying and ordering.[1] The predictions have been confirmed experimentally.[2] The results provide \textit{a priori} principle about the applicability of the conventional cluster expansion method to the description of the electronic structure of the semiconductor alloy, and a general understanding of the order parameter dependence of an electronic property in a semiconductor alloy. [1]Zhang et al, PRB80,045206(09). [2] Steiner et al, JAP106,063525(09). DOE/BES