Theory of local electric polarization and its relation to internal strain: impact on the 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, 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.

References in corpus (5)

• Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN
• Importance of second-order piezoelectric effects in zincblende semiconductors
• Interrelation of structural and electronic properties of InGaN/GaN quantum dots using an eight-band k.p model
• Composition dependent band gap and band edge bowing in AlInN: A combined theoretical and experimental study
• Spin-orbit coupling and crystal-field splitting in the electronic and optical properties of nitride quantum dots with a wurtzite crystal structure

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• Structural, electronic, and optical properties of $m$-plane InGaN/GaN quantum wells: Insights from experiment and atomistic theory
• Polar InGaN/GaN quantum wells: Revisiting the impact of carrier localization on the green gap problem
• Origin of non-linear piezoelectricity in III-V semiconductors: Internal strain and bond ionicity from hybrid-functional density functional theory
• 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
• Impact of cation-based localized electronic states on the conduction and valence band structure of AlInN alloys
• Impact of random alloy fluctuations on the electronic and optical properties of (Al,Ga)N quantum wells: Insights from tight-binding calculations
• Ga-polar (In,Ga)N/GaN quantum wells vs. N-polar (In,Ga)N quantum disks in GaN nanowires: Comparative analysis of carrier recombination, diffusion, and radiative efficiency
• Wigner-Weyl description of light absorption in disordered semiconductor alloys using the localization landscape theory
• Electronic structure of semiconductor nanostructures: A modified localization landscape theory
• Study of simulations of double graded InGaN solar cell structures