Marcelo Marques

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.

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.

Anomalous Lattice Parameter of Magnetic Semiconductor Alloys

The addition of transition metals to III-V semiconductors radically changes their electronic, magnetic, and structural properties. We show by ab initio calculations that in contrast to the conventional semiconductor alloys, the lattice parameter in magnetic semiconductor alloys, including those with diluted concentration, strongly deviates from Vegard’s law. We find a direct correlation between the magnetic moment and the anion-transition metal bond lengths and derive a simple and general formula that determines the lattice parameter of a particular magnetic semiconductor by considering both the composition and magnetic moment. This dependence can explain some experimentally observed anomalies and stimulate other kind of investigations.

Comparing LDA-1/2, HSE03, HSE06 and G 0 W 0 approaches for band gap calculations of alloys

It has long been known that the local density approximation and the generalized gradient approximation do not furnish reliable band gaps, and one needs to go beyond these approximations to reliably describe these properties. Among alternatives are the use of hybrid functionals (HSE03 and HSE06 being popular), the GW approximation or the recently proposed LDA-1/2 method. In this work, we compare rigorously the performance of these four methods in describing the band gaps of alloys, employing the generalized quasi-chemical approach to treat the disorder of the alloy and to obtain judiciously the band gap for the entire compositional range. Zincblende InGaAs and InGaN were chosen as prototypes due to their importance in optoelectronic applications. The comparison between these four approaches was guided both by the agreement between the predicted band gap and the experimental one, and by the demanded computational effort (time and memory). We observed that the HSE06 method provided the most accurate results (in comparison with experiments), whereas, surprisingly, the LDA-1/2 method gave the best compromise between accuracy and computational resources. Due to its low computational cost and good accuracy, we decided to double the supercell used to describe the alloys, and employing LDA-1/2 we observed that the bowing parameter changed remarkably, only agreeing with the measured one for the larger supercell, where LDA-1/2 plays an important role.

Influence of the composition fluctuations and decomposition on the tunable direct gap and oscillator strength of Ge1-xSnx alloys

In this work, we include disorder effects in order to analyze electronic and optical properties of Ge1−xSnx alloys, by means of a cluster expansion method combined with density functional theory. We derive the T-x phase diagram, which allows us to discuss phase separation versus composition fluctuations, especially in the Ge-rich range between binodal and spinodal curves for different growth temperatures. The gaps and their mean-square deviations resulting for random alloys and decomposed systems within an approximate quasiparticle theory are compared with available spectroscopic data. We relate deviations to the methods used and the local distribution of atoms. No significant indication for decomposition is observed. We show that the direct transitions possess optical oscillator strengths of the order of that of the E0 gap of pure germanium. The dependence of the indirect-direct crossover on preparation conditions is also discussed.

The LDA-1/2 technique: Recent developments

This paper is a review of the LDA(GGA)-1/2 method for band calculation. We review the many applications of the method: band gaps, semiconductor interfaces, semiconductor alloys. The number of applications where the method fails is minimal. Leading to results with a precision comparable to Hedin’s GW method, LDA-1/2 has the advantage of being orders of magnitude faster. The paper begins by a short theoretical review in which we try not repeat what is already published. Then we present some results that are scattered in the literature. We find that LDA(GGA)-1/2 is the recommended method for excited state energy calculations.

Theoretical study of the indium incorporation into III-V compounds revisited: The role of indium segregation and desorption

Indium based III-V compounds are very important technological materials. However, the indium incorporation depends on several phenomena, among them, the influence of indium segregation has been the most studied. In this paper, we show that to predict accurately the energy levels of In based III-V quantum structures, besides the indium segregation, the indium desorption must also be considered. In order to verify this assumption, we consider InGaAs/GaAs quantum wells as a benchmark case, and simulate 48 different quantum wells comparing with photoluminescence results.

Biaxial strain-induced suppression of spinodal decomposition in GaMnAs and GaCrAs

The thermodynamic properties of the magnetic semiconductors GaMnAs and GaCrAs are studied under biaxial strain. The calculations are based on the projector augmented wave method combined with the generalized quasichemical approach to treat the disorder and composition effects. Considering the influence of biaxial strain, we find a tendency to the suppression of binodal decomposition mainly for GaMnAs under compressive strain. For a substrate with a lattice constant 5% smaller than the one of GaAs, for GaMnAs, the solubility limit increases up to 40%. Thus, the strain can be a useful tool for tailoring magnetic semiconductors to the formation or not of embedded nanoclusters.

Deposition of topological silicene, germanene and stanene on graphene-covered SiC substrates

Growth of X-enes, such as silicene, germanene and stanene, requires passivated substrates to ensure the survival of their exotic properties. Using first-principles methods, we study as-grown graphene on polar SiC surfaces as suitable substrates. Trilayer combinations with coincidence lattices with large hexagonal unit cells allow for strain-free group-IV monolayers. In contrast to the Si-terminated SiC surface, van der Waals-bonded honeycomb X-ene/graphene bilayers on top of the C-terminated SiC substrate are stable. Folded band structures show Dirac cones of the overlayers with small gaps of about 0.1 eV in between. The topological invariants of the peeled-off X-ene/graphene bilayers indicate the presence of topological character and the existence of a quantum spin Hall phase.

General procedure for the calculation of accurate defect excitation energies from DFT-1/2 band structures: The case of the NV− center in diamond

A major challenge in creating a quantum computer is to find a quantum system that can be used to implement the qubits. For this purpose, deep centers are prominent candidates, and ab initio calculations are one of the most important tools to theoretically study their properties. However, these calculations are highly involved, due to the large supercell needed, and the computational cost can be even larger when one goes beyond the Kohn-Sham scheme to correct the band gap problem and achieve good accuracy. In this work, we present a method that overcomes these problems and provides the optical transition energies as a difference of Kohn-Sham eigenvalues; even more, provides a complete and accurate band structure of the defects in a semiconductor. Despite the original motivations, the presented methodology is a general procedure, which can be used to systematically study the optical transitions between localized levels within the band gap of any system. The method is an extension of the low-cost and parameter-free DFT-1/2 approximate quasiparticle correction, and allows it to be applied in the study of complex defects. As a benchmark, we apply the method to the