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

Abstract

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, such as III-N materials, we show that a more complex model is needed for less ionic materials, such as GaAs, 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. *

Impact of cation-based localized electronic states on the conduction and valence band structure of Al1−xInxN alloys

“…(1), 5 but with GaInN showing some deviations from this simple description. 6,7 A similar behavior might therefore also be expected for Al 1Àx In x N. We note however that AlInN has been reported to have a very large and composition-dependent bowing parameter, with values of b ranging from $2.5 eV (high In content) 8 to 10.3 eV (low In content). 9 A large bowing parameter has to date generally been associated with the presence of isoelectronic states in a semiconductor alloy, such as ZnTe 1Àx Se x .…”

“…The structure is relaxed using a valence force field (VFF) model. 6,22 Figure 1 shows the calculated charge densities of (a) the CBE and (b) the first excited CB state (CBEþ1) at k ¼ 0. Figure 1(b) shows explicitly that a single, isolated In atom introduces a strongly localized state (CBEþ1) above the CBE.…”

Structural, electronic, and optical properties ofm-plane InGaN/GaN quantum wells: Insights from experiment and atomistic theory

“…The TB parameters and the TB model are discussed in detail in Ref. [52]. The application of the TB model to QW structures, including the coupling of the TB model to CI calculations to include excitonic effects, is discussed in detail in Ref.…”

“…Strain and built-in field fluctuations are included in the sp 3 TB model presented in Ref. [52]. The bulk TB parameters were determined from fitting TB band structures to hybrid functional (HSE) DFT band structures, showing a very good agreement between the TB and HSE-DFT band structures.…”

“…The strain field calculations are based on a modified valence force field model accounting for electrostatic corrections in addition to bond bending, bond stretching, and related cross-terms [35]. Local built-in field fluctuations are treated on the basis of our recently developed local polarization theory [52]. Strain and built-in field fluctuations are included in the sp 3 TB model presented in Ref.…”