Abstract: In this article we study excitons and trions in fractional dimensional spaces using the model suggested by C. Palmer [ J. Phys. A: Math. Gen. 37 6987 (2004)] through variational quantum Monte Carlo. We present a direct approach for estimating the exciton binding energy and discuss the von Neumann rejection- and Metropolis sampling methods. A simple variational estimate of trions is presented which shows good agreement with previous calculations done within the fractional dimensional model presented by D. R. Herrick and F. H. Stillinger [ Phys. Rev. A 11 42 (1975) and J. Math. Phys. 18 1224 (1977)]. We explain the spatial physics of the positive and negative trions by investigating angular and inter-atomic distances. We then examine the wave function and explain the differences between the positive and negative trions with heavy holes. As applications of the fractional dimensional model we study three systems: First we apply the model to estimate the energy of the hydrogen molecular ion H2+. Then we estimate trion binding energies in GaAs-based quantum wells and we demonstrate a good agreement with other theoretical work as well as experimentally observed binding energies. Finally, we apply the results to carbon nanotubes. We find good agreement with recently observed binding energies of the positively charged trion.

Abstract: By considering a cylindrically symmetric generalization of a plane wave, the first-order Born approximation of screened Coulomb scattering unfolds two new dimensions in the scattering problem: transverse momentum and orbital angular momentum of the incoming beam. In this paper, the elastic Coulomb scattering amplitude is calculated analytically for incoming Bessel beams. This reveals novel features occurring for wide-angle scattering and quantitative insights for small-angle vortex scattering. The result successfully generalizes the well-known Rutherford formula, incorporating transverse and orbital angular momentum into the formalism.

Abstract: We have performed a first-principles study of the p- and n-type conductivity in CuIn1−xGaxSe2 due to native point defects, based on the HSE06 hybrid functional. Band alignment shows that the band gap becomes larger with x due to the increasing conduction band minimum, rendering it hard to establish n-type conductivity in CuGaSe2. From the defect formation energies, we find that In/GaCu is a shallow donor, while VCu, VIn/Ga and CuIn/Ga act as shallow acceptors. Using the total charge neutrality of ionized defects and intrinsic charge carriers to determine the Fermi level, we show that under In-rich growth conditions InCu causes strongly n-type conductivity in CuInSe2. Under increasingly In-poor growth conditions, the conductivity type in CuInSe2 alters to p-type and compensation of the acceptors by InCu reduces, as also observed in photoluminescence experiments. In CuGaSe2, the native acceptors pin the Fermi level far away from the conduction band minimum, thus inhibiting n-type conductivity. On the other hand, CuGaSe2 shows strong p-type conductivity under a wide range of Ga-poor growth conditions. Maximal p-type conductivity in CuIn1−xGaxSe2 is reached under In/Ga-poor growth conditions, in agreement with charge concentration measurements on samples with In/Ga-poor stoichiometry, and is primarily due to the dominant acceptor CuIn/Ga.

Abstract: Modeling the oxidation process of silicon nanowires through reactive force field based molecular dynamics simulations suggests that the formation of Si epoxide defects occurs both at the Si/SiOx interface and at the nanowire surface, whereas for flat surfaces, this defect is experimentally observed to occur only at the interface as a result of stress. In this paper, we argue that the increasing curvature stabilizes the defect at the nanowire surface, as suggested by our density functional theory calculations. The latter can have important consequences for the opto-electronic properties of thin silicon nanowires, since the epoxide induces an electronic state within the band gap. Removing the epoxide defect by hydrogenation is expected to be possible but becomes increasingly difficult with a reduction of the diameter of the nanowires.

Abstract: Chalcopyrite semiconductors are of considerable interest for application as absorber layers in thin-film photovoltaic cells. When growing films of these compounds, however, they are often found to contain CuAu-like domains, a metastable phase of chalcopyrite. It has been reported that for CuInS2, the presence of the CuAu-like phase improves the short circuit current of the chalcopyrite-based photovoltaic cell. We investigate the thermodynamic stability of both phases for a selected list of I-III-VI2 materials using a first-principles density functional theory approach. For the CuIn-VI2 compounds, the difference in formation energy between the chalcopyrite and CuAu-like phase is found to be close to 2 meV per atom, indicating a high likelihood of the presence of CuAu-like domains. Next, we calculate the spectroscopic limited maximum efficiency (SLME) of the CuAu-like phase and compare the results with those of the corresponding chalcopyrite phase. We identify several candidates with a high efficiency, such as CuAu-like CuInS2, for which we obtain an SLME of 29% at a thickness of 500 nm. We observe that the SLME can have values above the Shockley-Queisser (SQ) limit, and show that this can occur because the SQ limit assumes the absorptivity to be a step function, thus overestimating the radiative recombination in the detailed balance approach. This means that it is possible to find higher theoretical efficiencies within this framework simply by calculating the J-V characteristic with an absorption spectrum. Finally, we expand our SLME analysis to indirect band gap absorbers by studying silicon, and find that the SLME quickly overestimates the reverse saturation current of indirect band gap materials, drastically lowering their calculated efficiency.

Abstract: van der Waals (vdW) forces play an important role in the adsorption of molecules on the surface of solids. However, the choice of the most suitable vdW functional for different systems is an essential problem which must be addressed for different systems. The lack of a systematic study on the performance of the vdW functionals in the bulk and adsorption properties of metal-oxides motivated us to examine different vdW approaches and compute the bulk and molecular adsorption properties of alpha-Cr2O3, alpha-Fe2O3, and alpha-Al2O3. For the bulk properties, we compared our results for the heat of formation, cohesive energy, lattice parameters and bond distances between the different vdW functionals and available experimental data. Next we studied the adsorption of benzene and CH3 molecules on top of different oxide surfaces. We employed different approximations to exchange and correlation within DFT, namely, the Perdew-Burke-Ernzerhof (PBE) GGA, (PBE)+U, and vdW density functionals [ DFT(vdW-DF/DF2/optPBE/optB86b/optB88)+U] as well as DFT-D2/D3(+U) methods of Grimme for the bulk calculations and optB86b-vdW(+U) and DFT-D2(+U) for the adsorption energy calculations. Our results highlight the importance of vdW interactions not only in the adsorption of molecules, but importantly also for the bulk properties. Although the vdW contribution in the adsorption of CH3 (as a chemisorption interaction) is less important compared to the adsorption of benzene (as a physisorption interaction), this contribution is not negligible. Also adsorption of benzene on ferryl/chromyl terminated surfaces shows an important chemisorption contribution in which the vdW interactions become less significant.

Abstract: Recently, Sr-doped LaCrO3 has been experimentally introduced as a new p-type transparent conducting oxide. It is demonstrated that substituting Sr for La results in inducing p-type conductivity in LaCrO3. Performing first principles calculations we study the electronic structure and formation energy of various point defects in LaCrO3. Our results for the formation energies show that in addition to Sr, two more divalent defects, Ca and Ba, substituting for La in LaCrO3, behave as shallow acceptors in line with previous experimental reports. We further demonstrate that under oxygen-poor growth conditions, these shallow acceptors will be compensated by intrinsic donor-like defects (an oxygen vacancy and Cr on an oxygen site), but in the oxygen-rich growth regime the shallow acceptors have the lowest formation energies between all considered defects and will lead to p-type conductivity.