Bridging the gap between atomic microstructure and electronic properties of alloys: The case of (In,Ga)N

Abstract

The atomic microstructure of alloys is rarely perfectly random, instead exhibiting differently shaped precipitates, clusters, zigzag chains, etc. While it is expected that such microstructural features will affect the electronic structures ͑carrier localization and band gaps͒, theoretical studies have, until now, been restricted to investigate either perfectly random or artificial "guessed" microstructural features. In this paper, we simulate the alloy microstructures in thermodynamic equilibrium using the static Monte Carlo method and study their electronic structures explicitly using a pseudopotential supercell approach. In this way, we can bridge atomic microstructures with their electronic properties. We derive the atomic microstructures of InGaN using ͑i͒ density-functional theory total energies of ϳ50 ordered structures to construct a ͑ii͒ multibody cluster expansion, including strain effects to which we have applied ͑iii͒ static Monte Carlo simulations of systems consisting of over 27000 atoms to determine the equilibrium atomic microstructures. We study two types of alloy thermodynamic behavior: ͑a͒ under lattice incoherent conditions, the formation enthalpies are positive and thus the alloy system phase-separates below the miscibility-gap temperature T MG , ͑b͒ under lattice coherent conditions, the formation enthalpies can be negative and thus the alloy system exhibits ordering tendency. The microstructure is analyzed in terms of structural motifs ͑e.g., zigzag chains and In n Ga 4−n N tetrahedral clusters͒. The corresponding electronic structure, calculated with the empirical pseudopotentials method, is analyzed in terms of band-edge energies and wave-function localization. We find that the disordered alloys have no electronic localization but significant hole localization, while below the miscibility gap under the incoherent conditions, In-rich precipitates lead to strong electron and hole localization and a reduction in the band gap.

Distribution of cations in wurtzitic InxGa1−xN and InxCarvalho1, Schleife2, Furthmüller3 et al. 2012Phys. Rev. B251180View full textAdd to dashboardCite

“…19 The possible instability of In x X 1−x N layers (X=Ga, Al) against decomposition into two random alloys as well as the occurrence of fluctuations in a compositionally disordered system have been studied theoretically in a variety of papers. 10,[20][21][22][23][24][25][26] Many of these studies [20][21][22] consistently predict a miscibility gap for In x Ga 1−x N (mainly for the zinc-blende structure) in a broad temperature range and, hence, explain observations of precipitation or even spinodal decomposition. 27 More recently, minor component ordering and clustering in wz-In x Ga 1−x N but also wz-In x Al 1−x N has been studied by means of multiscale or ab initio methods.…”

“…27 More recently, minor component ordering and clustering in wz-In x Ga 1−x N but also wz-In x Al 1−x N has been studied by means of multiscale or ab initio methods. [23][24][25] Nevertheless, it has been found experimentally that the incorporation of small amounts of In leads to an enhancement of the light emission intensity in light-emitting diodes as well as laser diodes with respect to devices made from pure GaN or AlN. 28 This may be related to In clustering as well as composition fluctuations.…”

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)1−x(ZnO)x

“…Compositional fluctuations lead to surprisingly strong dependence of bond length on local chemical environment. Localization of states induced by disorder makes carrier transport in the alloy significantly different from the constituent semiconductors [3] [4]. Understanding the role of order and disorder in determining physical properties such as bond length, is complicated by the difficulty in modelling the numerous local chemical environments of the alloy.…”

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

“…The impact of SC size on localization effects has been discussed in detail, for example, in Ref. 20; it is common to find that a resonant localized state cannot be clearly identified for all SC sizes. However, since HSE-and LDA-DFT give similar results for CBE, LDA-DFT should also give reliable results for higher CB states.…”

“…10 Turning to the VB states, we note that several studies have shown how the highest valence states tend to become localized in GaInN alloys. [16][17][18][19][20] We show that the highest VB states can be strongly localized in AlInN, undertaking DFT studies both on ordered and on disordered supercells (SCs). We first consider ordered SCs in which each In atom only has Al atoms as second nearest neighbors.…”