arXiv subjects

Stefan Schulz

Publications and source records attributed to Stefan Schulz.

30 records · Page 2Linked to original sources

arXiv2019

Fully analytic valence force field model for the elastic and inner elastic properties of diamond and zincblende crystals

Using a valence force field model based on that introduced by Martin, we present three related methods through which we analytically determine valence force field parameters. The methods introduced allow easy derivation of valence force field parameters in terms of the Kleinman parameter $ζ$ and bulk properties of zincblende and diamond crystals. We start with a model suited for covalent and weakly ionic materials, where the valence force field parameters are derived in terms of $ζ$ and the bulk elastic constants $C_{11}$, $C_{12}$, and $C_{44}$. We show that this model breaks down as the material becomes more ionic and specifically when the elastic anisotropy factor $A = 2C_{44}/(C_{11}-C_{12}) > 2$. The analytic model can be stabilised for ionic materials by including Martin's electrostatic terms with effective cation and anion charges in the valence force field model. Inclusion of effective charges determined via the optical phonon mode splitting provides a stable model for all but two of the materials considered (zincblende GaN and AlN). A stable model is obtained for all materials considered by also utilising the inner elastic constant $E_{11}$ to determine the magnitude of the effective charges used in the Coulomb interaction. Test calculations show that the models describe well structural relaxation in superlattices and alloys, and reproduce key phonon band structure features.

cond-mat.mtrl-sci↗

arXiv2019

Comparison of first principles and semi-empirical models of the structural and electronic properties of Ge$_{1-x}$Sn$_{x}$ alloys

We present and compare three distinct atomistic models -- based on first principles and semi-empirical approaches -- of the structural and electronic properties of Ge$_{1-x}$Sn$_{x}$ alloys. Density functional theory calculations incorporating Heyd-Scuseria-Ernzerhof (HSE) and modified Becke-Johnson (mBJ) exchange-correlation functionals are used to perform structural relaxation and electronic structure calculations for a series of Ge$_{1-x}$Sn$_{x}$ alloy supercells. Based on HSE calculations, a semi-empirical valence force field (VFF) potential and $sp^{3}s^{\ast}$ tight-binding (TB) Hamiltonian are parametrised. Comparing the HSE, mBJ and TB models, and using the HSE results as a benchmark, we demonstrate that: (i) mBJ calculations provide an accurate first principles description of the electronic structure at reduced computational cost, (ii) the VFF potential is sufficiently accurate to circumvent the requirement to perform first principles structural relaxation, and (iii) TB calculations provide a good quantitative description of the alloy electronic structure in the vicinity of the band edges. Our results also emphasise the importance of Sn-induced band mixing in determining the nature of the conduction band structure of Ge$_{1-x}$Sn$_{x}$ alloys. The theoretical models and benchmark calculations we present inform and enable predictive, computationally efficient and scalable atomistic calculations for disordered alloys and nanostructures. This provides a suitable platform to underpin further theoretical investigations of the properties of this emerging semiconductor alloy.

cond-mat.mtrl-sci↗

arXiv2018

Hybrid functional study of non-linear elasticity and internal strain in zincblende III-V materials

We investigate the elastic properties of selected zincblende III-V semiconductors. Using hybrid functional density functional theory we calculate the second and third order elastic constants, and first and second-order internal strain tensor components for Ga, In and Al containing III-V compounds. For many of these parameters, there are no available experimental measurements, and this work is the first to predict their values. The stricter convergence criteria for the calculation of higher order elastic constants are demonstrated, and arguments are made based on this for extracting these constants via the calculated stresses, rather than the energies, in the context of plane-wave-based calculations. The calculated elastic properties are used to determine the strain regime at which higher order elasticity becomes important by comparing the stresses predicted by a lower and a higher order elasticity theory. Finally, the results are compared with available experimental literature data and previous theory.

physics.comp-ph↗

arXiv2018

Interface roughness, carrier localization and wave function overlap in $c$-plane InGaN/GaN quantum wells: Interplay of well width, alloy microstructure, structural inhomogeneities and Coulomb effects

In this work we present a detailed analysis of the interplay of Coulomb effects and different mechanisms that can lead to carrier localization effects in c-plane InGaN/GaN quantum wells. As mechanisms for carrier localization we consider here effects introduced by random alloy fluctuations as well as structural inhomogeneities such as well width fluctuations. Special attention is paid to the impact of the well width on the results. All calculations have been carried out in the framework of atomistic tight-binding theory. Our theoretical investigations show that independent of the here studied well widths, carrier localization effects due to built-in fields, well width fluctuations and random alloy fluctuations dominate over Coulomb effects in terms of charge density redistributions. However, the situation is less clear cut when the well width fluctuations are absent. For large well width (approx. > 2.5 nm) charge density redistributions are possible but the electronic and optical properties are basically dominated by the spatial out-of plane carrier separation originating from the electrostatic built-in field. The situation changes for lower well width (< 2.5 nm) where the Coulomb effect can lead to significant charge density redistributions and thus might compensate a large fraction of the spatial in-plane wave function separation observed in a single-particle picture. Given that this in-plane separation has been regarded as one of the main drivers behind the green gap problem, our calculations indicate that radiative recombination rates might significantly benefit from a reduced quantum well barrier interface roughness.

cond-mat.mes-hall↗

arXiv2017

Impact of second-order piezoelectricity on electronic and optical properties of $c$-plane In$_{x}$Ga$_{1-x}$N quantum dots: Consequences for long wavelength emitters

In this work we present a detailed analysis of the second-order piezoelectric effect in $c$-plane In$_{x}$Ga$_{1-x}$N/GaN quantum dots and its consequences for electronic and optical properties of these systems. Special attention is paid to the impact of increasing In content $x$ on the results. We find that in general the second-order piezoelectric effect leads to an increase of the electrostatic built-in field. Furthermore, our results show that for an In content $\geq$30\% this increase in the built-in field has a significant effect on the emission wavelength and the radiative lifetimes. For instance, at 40\% In, the radiative lifetime is more than doubled when taking second-order piezoelectricity into account. Overall our calculations reveal that when designing and describing the electronic and optical properties of $c$-plane In$_{x}$Ga$_{1-x}$N/GaN quantum dot based light emitters with high In contents, second-order piezoelectric effects cannot be neglected.

cond-mat.mes-hall↗

arXiv2016

Experimental and theoretical analyses of strongly polarized photon emission from non-polar InGaN quantum dots

We present a comprehensive investigation of the polarization properties of non-polar a-plane InGaN quantum dots (QDs) and their origin with statistically significant experimental data and rigorous k.p modelling. The unbiased selection and study of 180 individual QDs allow us to compute an average polarization degree of 0.90, with a standard deviation of only 0.08. When coupled with theoretical insights, we show that a-plane InGaN QDs are highly insensitive to size differences, shape anisotropies, and indium content fluctuations. Furthermore, 91% of the studied QDs exhibit a polarization axis along the crystal [1-100] axis, with the other 9% polarized orthogonal to this direction. When coupled with their ability to emit single-photons, a-plane QDs are good candidates for the generation of linearly polarized single-photons, a feature attractive for quantum cryptography protocols.

cond-mat.mes-hall↗

arXiv2016

Random alloy fluctuations and structural inhomogeneities in $c$-plane In$_{x}$Ga$_{1-x}$N quantum wells: theory of ground and excited electron and hole states

We present a detailed theoretical analysis of the electronic structure of $c$-plane InGaN/GaN quantum wells with indium contents varying between 10\% and 25\%. The electronic structure of the quantum wells is treated by means of an atomistic tight-binding model, accounting for variations in strain and built-in field due to random alloy fluctuations. Our analysis reveals strong localisation effects in the hole states. These effects are found not only in the ground states, but also the excited states. We conclude that localisation effects persist to of order 100~meV into the valence band, for as little as 10\% indium in the quantum well, giving rise to a significant density of localised states. We find, from an examination of the modulus overlap of the wave functions, that the hole states can be divided into three regimes of localisation. Our results also show that localisation effects due to random alloy fluctuations are far less pronounced for electron states. However, the combination of electrostatic built-in field, alloy fluctuations and structural inhomogeneities, such as well-width fluctuations, can nevertheless lead to significant localisation effects in the electron states, especially at higher indium contents. Overall, our results are indicative of individually localised electron and hole states, consistent with the experimentally proposed explanation of time-dependent photoluminescence results in $c$-plane InGaN/GaN QWs.

cond-mat.mtrl-sci↗

arXiv2015

Origin of non-linear piezoelectricity in III-V semiconductors: Internal strain and bond ionicity from hybrid-functional density functional theory

We derive first- and second-order piezoelectric coefficients for the zinc-blende III-V semiconductors, {Al,Ga,In}-{N,P,As,Sb}. The results are obtained within the Heyd-Scuseria-Ernzerhof hybrid-functional approach in the framework of density functional theory and the Berry-phase theory of electric polarization. To achieve a meaningful interpretation of the results, we build an intuitive phenomenological model based on the description of internal strain and the dynamics of the electronic charge centers. We discuss in detail first- and second-order internal strain effects, together with strain-induced changes in ionicity. This analysis reveals that the relatively large importance in the III-Vs of non-linear piezoelectric effects compared to the linear ones arises because of a delicate balance between the ionic polarization contribution due to internal strain relaxation effects, and the contribution due to the electronic charge redistribution induced by macroscopic and internal strain.

cond-mat.mtrl-sci↗

arXiv2015

Atomistic analysis of the impact of alloy and well-width fluctuations on the electronic and optical properties of InGaN/GaN quantum wells

We present an atomistic description of the electronic and optical properties of $\text{In}_{0.25}\text{Ga}_{0.75}$N/GaN quantum wells. Our analysis accounts for fluctuations of well width, local alloy composition, strain and built-in field fluctuations as well as Coulomb effects. We find a strong hole and much weaker electron wave function localization in InGaN random alloy quantum wells. The presented calculations show that while the electron states are mainly localized by well-width fluctuations, the holes states are already localized by random alloy fluctuations. These localization effects affect significantly the quantum well optical properties,leading to strong inhomogeneous broadening of the lowest interband transition energy. Our results are compared with experimental literature data.

cond-mat.mes-hall↗

arXiv2013

Theory of local electric polarization and its relation to internal strain: impact on the polarization potential and electronic properties of group-III nitrides

We present a theory of local electric polarization in crystalline solids and apply it to study the case of wurtzite group-III nitrides. We show that a local value of the electric polarization, evaluated at the atomic sites, can be cast in terms of a summation over nearest-neighbor distances and Born effective charges. Within this model, the local polarization shows a direct relation to internal strain and can be expressed in terms of internal strain parameters. The predictions of the present theory show excellent agreement with a formal Berry phase calculation for random distortions of a test-case CuPt-like InGaN alloy and InGaN supercells with randomly placed cations. While the present level of theory is appropriate for highly ionic compounds, we show that a more complex model is needed for less ionic materials, in which the strain dependence of Born effective charges has to be taken into account. Moreover, we provide ab initio parameters for GaN, InN and AlN, including hybrid functional values for the piezoelectric coefficients and the spontaneous polarization, which we use to accurately implement the local theory expressions. In order to calculate the local polarization potential, we also present a point dipole method. This method overcomes several limitations related to discretization and resolution which arise when obtaining the local potential by solving Poisson's equation on an atomic grid. Finally, we perform tight-binding supercell calculations to assess the impact of the local polarization potential arising from alloy fluctuations on the electronic properties of InGaN alloys. In particular, we find that the large upward bowing with composition of the InGaN valence band edge is strongly influenced by local polarization effects. Furthermore, our analysis allows us to extract composition-dependent bowing parameters for the energy gap and valence and conduction band edges.

cond-mat.mtrl-sci↗

arXiv2008

A comparison of atomistic and continuum theoretical approaches to determine electronic properties of GaN/AlN quantum dots

In this work we present a comparison of multiband k.p-models, the effective bond-orbital approach, and an empirical tight-binding model to calculate the electronic structure for the example of a truncated pyramidal GaN/AlN self-assembled quantum dot with a zincblende structure. For the system under consideration, we find a very good agreement between the results of the microscopic models and the 8-band k.p-formalism, in contrast to a 6+2-band k.p-model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction and valence band states for the wide band gap materials GaN and AlN. Special attention is paid to the possible influence of the weak spin-orbit coupling on the localized single-particle wave functions of the investigated structure.

cond-mat.mtrl-sci↗

arXiv2005

Tight-Binding model for semiconductor nanostructures

An empirical $s_cp^3_a$ tight-binding (TB) model is applied to the investigation of electronic states in semiconductor quantum dots. A basis set of three $p$-orbitals at the anions and one $s$-orbital at the cations is chosen. Matrix elements up to the second nearest neighbors and the spin-orbit coupling are included in our TB-model. The parametrization is chosen so that the effective masses, the spin-orbit-splitting and the gap energy of the bulk CdSe and ZnSe are reproduced. Within this reduced $s_cp_a^3$ TB-basis the valence (p-) bands are excellently reproduced and the conduction (s-) band is well reproduced close to the $Γ$-point, i.e. near to the band gap. In terms of this model much larger systems can be described than within a (more realistic) $sp^3s^*$-basis. The quantum dot is modelled by using the (bulk) TB-parameters for the particular material at those sites occupied by atoms of this material. Within this TB-model we study pyramidal-shaped CdSe quantum dots embedded in a ZnSe matrix and free spherical CdSe quantum dots (nanocrystals). Strain-effects are included by using an appropriate model strain field. Within the TB-model, the strain-effects can be artifically switched off to investigate the infuence of strain on the bound electronic states and, in particular, their spatial orientation. The theoretical results for spherical nanocrystals are compared with data from tunneling spectroscopy and optical experiments. Furthermore the influence of the spin-orbit coupling is investigated.

cond-mat.other↗