Pawel Scharoch

First-principles calculations of bismuth induced changes in the band structure of dilute Ga–V–Bi and In–V–Bi alloys: chemical trends versus experimental data

Bi-induced changes in the band structure of Ga–V–Bi and In–V–Bi alloys are calculated within the density functional theory (DFT) for alloys with Bi ≤3.7% and the observed chemical trends are discussed in the context of the virtual crystal approximation (VCA) and the valence band anticrossing (VBAC) model. It is clearly shown that the incorporation of Bi atoms into III–V host modifies both the conduction band (CB) and the valence band (VB). The obtained shifts of bands in GaP1−xBix, GaAs1−xBix, GaSb1−xBix, InP1−xBix, InAs1−xBix, and InSb1−xBix are respectively, 15, −29, −16, −27, −15, and −10 meV/%Bi for CB, 82, 62, 16, 79, 45, and 16 meV/%Bi for VB, and −17, −3, −2, −8, −6, and 14 meV/%Bi for spin–orbit split off band. The Bi-induced reduction of the band gap is very consistent with the available experimental data. The chemical trends observed in our calculations as well as in experimental data are very clear: in a sequence of alloys from III–P–Bi to III–Sb–Bi the Bi-induced changes in the band structure weaken. For dilute GaSb1−xBix and InSb1−xBix alloys the band structure modification, in the first approximation, can be described within the VCA, while for Ga–V–Bi and In–V–Bi alloys with V = As or P another phenomenological approach is needed to predict the Bi-induced changes in their band structure. We have found that a combination of the VCA with the VBAC model, which is widely applied for highly mismatched alloys, is suitable for this purpose. The chemical trends for III–V–Bi alloys observed in our DFT calculations are also exhibited by the coupling parameter which describes the magnitude of interaction between Bi-induced levels and VB states in the VBAC model. This coupling parameter monotonously decreases along the sequence of alloys from III–P–Bi to III–Sb–Bi.

Quantum-size effect in thin Al(110) slabs

The work function and surface energy have been calculated for relaxed thin Al(110) slabs using local density-functional theory, first-principles pseudopotentials and a plane-wave basis set. A significant quantum-size effect (QSE) exhibited by both these quantities as well as surface relaxation can be interpreted on the basis of existing jellium calculations. Our calculations show that the QSE persists for slabs up to 15 to 16 atomic layers thick. So even for thick slabs, oriented with the open (110) surface plane, the calculated surface quantities are given with some uncertainty due to the QSE.

Experimental and theoretical studies of band gap alignment in GaAs1−xBix/GaAs quantum wells

Band gap alignment in GaAs1−xBix/GaAs quantum wells (QWs) was studied experimentally by photoreflectance (PR) and theoretically, ab initio, within the density functional theory in which the supercell based calculations are combined with the alchemical mixing approximation applied to a single atom in a supercell. In PR spectra, the optical transitions related to the excited states in the QW (i.e., the transition between the second heavy-hole and the second electron subband) were clearly observed in addition to the ground state QW transition and the GaAs barrier transition. This observation is clear experimental evidence that this is a type I QW with a deep quantum confinement in the conduction and valence bands. From the comparison of PR data with calculations of optical transitions in GaAs1−xBix/GaAs QW performed for various band gap alignments, the best agreement between experimental data and theoretical calculations has been found for the valence band offset of 52 ± 5%. A very similar valence band offse...

Theoretical and experimental studies of electronic band structure for GaSb1−xBix in the dilute Bi regime

Photoreflectance (PR) spectroscopy was applied to study the band gap in GaSb1−xBix alloys with Bi < 5%. Obtained results have been interpreted in the context of ab initio electronic band structure calculations in which the supercell (SC) based calculations are joined with the alchemical mixing (AM) approximation applied to a single atom in the cell. This approach, which we call SC-AM, allows on the one hand to study alloys with a very small Bi content, and on the other hand to avoid limitations characteristic of a pure AM approximation. It has been shown that the pure AM does not reproduce the GaSb1−xBix band gap determined from PR while the agreement between experimental data and the ab initio calculations of the band gap obtained within the SC-AM approach is excellent. These calculations show that the incorporation of Bi atoms into the GaSb host modifies both the conduction and the valence band. The shift rates found in this work are respectively −26.0 meV per % Bi for the conduction band and 9.6 meV per % Bi for the valence band that consequently leads to a reduction in the band gap by 35.6 meV per % Bi. The shifts found for the conduction and valence band give a ~27% (73%) valence (conduction) band offset between GaSb1−xBix and GaSb. The rate of the Bi-related shift for the split-off band is −7.0 meV per % Bi and the respective increase in the spin–orbit split-off is 16.6 meV per % Bi.

Pressure coefficients for direct optical transitions in MoS2, MoSe2, WS2, and WSe2 crystals and semiconductor to metal transitions.

The electronic band structure of MoS2, MoSe2, WS2, and WSe2, crystals has been studied at various hydrostatic pressures experimentally by photoreflectance (PR) spectroscopy and theoretically within the density functional theory (DFT). In the PR spectra direct optical transitions (A and B) have been clearly observed and pressure coefficients have been determined for these transitions to be: αA = 2.0 ± 0.1 and αB = 3.6 ± 0.1 meV/kbar for MoS2, αA = 2.3 ± 0.1 and αB = 4.0 ± 0.1 meV/kbar for MoSe2, αA = 2.6 ± 0.1 and αB = 4.1 ± 0.1 meV/kbar for WS2, αA = 3.4 ± 0.1 and αB = 5.0 ± 0.5 meV/kbar for WSe2. It has been found that these coefficients are in an excellent agreement with theoretical predictions. In addition, a comparative study of different computational DFT approaches has been performed and analyzed. For indirect gap the pressure coefficient have been determined theoretically to be −7.9, −5.51, −6.11, and −3.79, meV/kbar for MoS2, MoSe2, WS2, and WSe2, respectively. The negative values of this coefficients imply a narrowing of the fundamental band gap with the increase in hydrostatic pressure and a semiconductor to metal transition for MoS2, MoSe2, WS2, and WSe2, crystals at around 140, 180, 190, and 240 kbar, respectively.

Direct optical transitions at K- and H-point of Brillouin zone in bulk MoS2, MoSe2, WS2, and WSe2

Modulated reflectance (contactless electroreflectance (CER), photoreflectance (PR), and piezoreflectance (PzR)) has been applied to study direct optical transitions in bulk MoS2, MoSe2, WS2, and WSe2. In order to interpret optical transitions observed in CER, PR, and PzR spectra, the electronic band structure for the four crystals has been calculated from the first principles within the density functional theory for various points of Brillouin zone including K and H points. It is clearly shown that the electronic band structure at H point of Brillouin zone is very symmetric and similar to the electronic band structure at K point, and therefore, direct optical transitions at H point should be expected in modulated reflectance spectra besides the direct optical transitions at the K point of Brillouin zone. This prediction is confirmed by experimental studies of the electronic band structure of MoS2, MoSe2, WS2, and WSe2 crystals by CER, PR, and PzR spectroscopy, i.e., techniques which are very sensitive to critical points of Brillouin zone. For the four crystals besides the A transition at K point, an AH transition at H point has been observed in CER, PR, and PzR spectra a few tens of meV above the A transition. The spectral difference between A and AH transition has been found to be in a very good agreement with theoretical predictions. The second transition at the H point of Brillouin zone (BH transition) overlaps spectrally with the B transition at K point because of small energy differences in the valence (conduction) band positions at H and K points. Therefore, an extra resonance which could be related to the BH transition is not resolved in modulated reflectance spectra at room temperature for the four crystals.

Electronic band structure of compressively strained Ge1−xSnx with x < 0.11 studied by contactless electroreflectance

Contactless electroreflectance is applied to study direct optical transitions from the heavy hole, light hole, and spin-orbit split-off band to the conduction band in compressively strained Ge1−xSnx layers of various Sn concentrations at room temperature. It is shown that the energies of these transitions are in very good agreement with theoretical predictions, which take into account non-linear variation of bandgap and spin-orbit splitting plus the strain-related shifts obtained from the Bir-Pikus theory. The bowing parameter for the direct bandgap has been determined to be 1.8 ± 0.2 eV and agree with this one obtained within ab initio calculations, which is 1.97 eV (for indirect bandgap the bowing parameter is 0.26 eV).

Ab initio study of InxGa1−xN – Performance of the alchemical mixing approximation

Abstract The alchemical mixing approximation which is the ab initio pseudopotential specific implementation of the virtual crystal approximation (VCA), offered in the ABINIT package, has been employed to study the wurtzite (WZ) and zinc blende (ZB) In x Ga 1− x N alloy from first principles. The investigations were focused on structural properties (the equilibrium geometries), elastic properties (elastic constants and their pressure derivatives), and on the band-gap. Owing to the ABINIT functionality of calculating the Hellmann–Feynmann stresses, the elastic constants have been evaluated directly from the strain–stress relation. Values of all the quantities calculated for parent InN and GaN have been compared with the literature data and then evaluated as functions of composition x on a dense, 0.05 step, grid. Some results have been obtained which, to authors’ knowledge, have not yet been reported in the literature, like composition dependent elastic constants in ZB structures or composition dependent pressure derivatives of elastic constants. The band-gap has been calculated within the MBJLDA approximation. Additionally, the band-gaps for pure InN and GaN have been calculated with the Wien2k code, for comparison purposes. The evaluated quantities have been compared with the available literature reporting supercell-based ab initio calculations and on that basis conclusions concerning the performance of the alchemical mixing approach have been drawn. An overall agreement of the results with the literature data is satisfactory. A small deviation from linearity of the lattice parameters and some elastic constants has been found to be due to the lack of the local relaxation of the structure in the VCA. The big bowing of the band-gap, characteristic of the clustered structure, is also mainly due to the lack of the local relaxation in the VCA. The method, when applied with caution, may serve as supplementary tool to other approaches in ab initio studies of alloy systems.

First principles prediction of structural and electronic properties of TlxIn1−xN alloy

Abstract Structural and electronic properties of zinc blende TlxIn1−xN alloy have been evaluated from first principles. The band structures have been obtained within density functional theory (DFT) with the modified Becke–Johnson (MBJLDA) approach for the exchange–correlation potential, and atoms represented by the fully relativistic pseudopotentials. The calculated band-gap dependence on Tl content in this hypothetical alloy exhibits a linear behavior up to the 25% of thallium content where its value approaches zero. In turn, the split-off energy at the Γ point of the Brillouin zone, related to the spin-orbit coupling, is predicted to be comparable in value to the band-gap for relatively low thallium content of about 5%. These findings point to TlxIn1−xN alloy as a promising material for optoelectronic applications. Furthermore, the band structure of TlN reveals some specific properties exhibited by topological insulators.

Anomalous band-gap bowing of AlN1−xPx alloy

Abstract Electronic structure of zinc blende AlN1−xPx alloy has been calculated from first principles. Structural optimization has been performed within the framework of LDA and the band-gaps calculated with the modified Becke–Jonson (MBJLDA) method. Two approaches have been examined: the virtual crystal approximation (VCA) and the supercell-based calculations (SC). The composition dependence of the lattice parameter obtained from the SC obeys Vegard’s law whereas the volume optimization in the VCA leads to an anomalous bowing of the lattice constant. A strong correlation between the band-gaps and the structural parameter in the VCA method has been observed. On the other hand, in the SC method the supercell size and atoms arrangement (clustered vs. uniform) appear to have a great influence on the computed band-gaps. In particular, an anomalously big band-gap bowing has been found in the case of a clustered configuration with relaxed geometry. Based on the performed tests and obtained results some general features of MBJLDA are discussed and its performance for similar systems predicted.