Lara K. Teles

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA), together with the half-occupation (transition state) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half-ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half-occupation is equivalent to introducing the hole self-energy (electrostatic and exchange-correlation) into the Schroedinger equation. The argument then becomes simple: the eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the SIC equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self-energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Phase separation suppression in InGaN epitaxial layers due to biaxial strain

In this letter, we show that external biaxial strain suppress spinodal phase separation in thin InGaN epitaxial layers pseudomorphically grown on thick unstrained cubic ~c! GaN~001! buffer layers. The InGaN films are terminated by a top GaN layer forming GaN/InGaN/GaN double heterostructures. By monitoring the alloy composition and thickness for a fixed growth temperature, we control the presence of biaxial strain induced by the rigid GaN buffer in the InGaN layers. We start by first showing from ab initio calculations of the alloy free energy taking strain into account that the biaxial strain is expected to induce a suppression of the miscibility gap leading to a single homogeneous phase for the InGaN alloys. We use high resolution x-ray diffraction ~HRXRD! reciprocal space maps to select the strained layers. We have shown recently that micro-Raman is an accurate tool to observe separate phases in InGaN epitaxial layers. 4,8 Micro-Raman spectroscopy measurements are also used in this work to demonstrate conclusively the suppression of the spinodal phase separation process in strained quantum wells. The c-GaN/In x Ga 12x N/GaN double heterostructures were grown on GaAs~001! substrates by molecular-beam epitaxy using a rf plasma nitrogen source. The GaN buffer layers were grown at T5720 °C with thicknesses of about 400 nm. The c-InGaN films were deposited at lower growth temperatures of 600 °C. The films were deposited at growth rates of 40 nm/h. The GaN cap layers, of about 30 nm thick, were grown at low temperatures of about 600 °C in order to reduce In desorption and interdiffusion. The growth front was continuously monitored by reflection high-energy electron diffraction and the diffraction patterns exhibited a cubic symmetry along all major azimuths.

STRUCTURAL PROPERTIES AND RAMAN MODES OF ZINC BLENDE INN EPITAXIAL LAYERS

We report on x-ray diffraction and micro-Raman scattering studies on zinc blende InN epitaxial films. The samples were grown by molecular beam epitaxy on GaAs(001) substrates using a InAs layer as a buffer. The transverse-optical (TO) and longitudinal-optical phonon frequencies at Γ of c-InN are determined and compared to the corresponding values for c-GaN. Ab initio self-consistent calculations are carried out for the c-InN and c-GaN lattice parameters and TO phonon frequencies. A good agreement between theory and experiment is found.

Lattice parameter and energy band gap of cubic AlxGayIn1−x−yN quaternary alloys

First-principles total energy calculations, combined with a generalized quasichemical approach to disorder and compositional effects, are used to obtain the lattice parameter and the energy band gap of cubic AlxGayIn1−x−yN quaternary alloys. It is found that the lattice parameter a(x,y) fulfills a Vegard’s-like law; that is, it shows a linear dependence on the alloy contents x and y. The range of compositions for which the alloy is lattice-matched to GaN is obtained. The energy band gap Eg(x,y) of the quaternary alloy deviates from a planar behavior displaying a two-dimensional gap bowing in the x–y plane. Analytical expressions that fit the calculated a(x,y) and Eg(x,y) surfaces are derived in order to provide ready access to the lattice parameter and energy band gap of the alloy for the entire range of compositions. The results are compared with data for the wurtzite phase alloys.

Slater half-occupation technique revisited: the LDA-1/2 and GGA-1/2 approaches for atomic ionization energies and band gaps in semiconductors

The very old and successful density-functional technique of half-occupation is revisited [J. C. Slater, Adv. Quant. Chem. 6, 1 (1972)]. We use it together with the modern exchange-correlation approximations to calculate atomic ionization energies and band gaps in semiconductors [L. G. Ferreira et al., Phys. Rev. B 78, 125116 (2008)]. Here we enlarge the results of the previous paper, add to its understandability, and show when the technique might fail. Even in this latter circumstance, the calculated band gaps are far better than those of simple LDA or GGA. As before, the difference between the Kohn-Sham ground state one-particle eigenvalues and the half-occupation eigenvalues is simply interpreted as the self-energy (not self-interaction) of the particle excitation. In both cases, that of atomic ionization energies and semiconductor band gaps, the technique is proven to be very worthy, because not only the results can be very precise but the calculations are fast and very simple.

Full-relativistic calculations of the SrTiO3 carrier effective masses and complex dielectric function

We perform fully relativistic band-structure calculations for cubic SrTiO3, which are used to obtain carrier effective masses and the frequency behavior of its complex dielectric function e(ω). The obtained values and anisotropy of the carrier effective masses are shown to be highly influenced by the relativistic contributions. In order to evaluate the static dielectric constant, the low-frequency behavior of e(ω) is obtained by taking into account also the optical phonon contributions to the imaginary part of e(ω), adopting a simplified classical oscillator dispersion model. It is found that the phonon contribution leads to about 240 times (at T=85 K) the value of the bare electronic contribution to the dielectric constant. The calculated temperature dependence of the dielectric constant is shown to be consistent with that observed in bulk SrTiO3 static permittivity measurements.

Spinodal decomposition in BxGa1−xN and BxAl1−xN alloys

We present first-principles calculations of the structural and thermodynamic properties of cubic BxGa1−xN and BxAl1−xN alloys. The calculations are based on the generalized quasichemical approach to disorder and composition effects and a pseudopotential-plane-wave approximation. The bulk moduli and lattice constants are found to vary linearly with the alloy composition. Due to the large lattice mismatch between BN and binaries GaN and AlN, the phase diagrams display large miscibility gaps in the temperature range usually adopted to grow the corresponding alloys. This explains the difficulties reported in growing these alloys with boron content higher than 0.1.

Magnetic properties of MnN: Influence of strain and crystal structure

For manganese mononitride (MnN), the total energy versus lattice constant is obtained using the spin density functional theory. Instead of the tetragonally distorted NaCl structure, we study the zinc blende and wurtzite structures in which AlN, GaN, and InN crystallize. The ground state with nonmagnetic, antiferromagnetic (AFM), or ferromagnetic (FM) arrangement of spins depends on the polymorph of MnN and on the lattice constant. At equilibrium lattice constants, in zinc blende it is AFM in [100] direction, and in wurtzite it is FM. The zinc blende polytype of MnN under hydrostatic pressure at the InN lattice constant presents FM ground state. For the wurtzite polytype at the GaN and AlN lattice constants, the AFM is the ground state, but goes back to a FM ground state for the InN lattice constants. For both structures, the system presents a half-metallic state at InN lattice constants (with a total magnetic moment of 4μB per Mn atom) instead of the metallic state obtained for smaller lattice constants. ...

Phase diagram, chemical bonds, and gap bowing of cubic InxAl1−xN alloys: Ab initio calculations

Thermodynamic, structural, and electronic properties of cubic InxAl1−xN alloys are studied by combining first-principles total energy calculations and the generalized quasichemical approach. Results for bond-lengths, second-nearest-neighbors distances, and bond angles in the alloy are presented. The calculated phase diagram of the alloy shows a broad and asymmetric miscibility gap. The gap fluctuations in the alloy allow for the definition of a minimum gap and an average gap with different bowing parameters, that can provide an explanation for the discrepancies found in the experimental values for the bowing parameter. It is also found that lattice matched In0.2Al0.8N with GaN is suitable to form a barrier material for electronic and optoelectronic nitride based devices.

Phase separation and gap bowing in zinc-blende InGaN, InAlN, BGaN, and BAlN alloy layers

Abstract We present first-principles calculations of the thermodynamic and electronic properties of the zinc-blende ternary In x Ga 1− x N, In x Al 1− x N, B x Ga 1− x N, and B x Al 1− x N alloys. They are based on a generalized quasi-chemical approximation and a pseudopotential-plane-wave method. T – x phase diagrams for the alloys are obtained. We show that due to the large difference in interatomic distances between the binary compounds a significant phase miscibility gap for the alloys is found. In particular for the In x Ga 1− x N alloy, we show also experimental results obtained from X-ray and resonant Raman scattering measurements, which indicate the presence of an In-rich phase with x ≈0.8. For the boron-containing alloy layers we found a very high value for the critical temperature for miscibility, ∼9000 K , providing an explanation for the difficulties encountered to grow these materials with higher boron content. The influence of a biaxial strain on phase diagrams, energy gaps and gap bowing of these alloys is also discussed.