Electron localization by a donor in the vicinity of a basal stacking fault in GaN

Abstract

We study the effects of the vicinity between a shallow donor nucleus and an I 1 -type basal stacking fault ͑BSF͒ in GaN. We propose a numerical calculation, in the "effective potential" formalism, of energies and envelope functions of electrons submitted to the conjunction of attractive potentials caused by the BSF and the donor. We show that the donor localizes the electron along the plane of the BSF, even when the donor lies as far as 10 nm from the BSF. Conversely, the presence of the BSF enhances the donor binding energy by up to a factor of 1.8, when the donor is placed exactly on the BSF. We briefly discuss the probability of occurrence of such a situation in, e.g., a-plane GaN, as well as its consequences on transport and optical properties of this material. DOI: 10.1103/PhysRevB.80.153309 PACS number͑s͒: 71.55.Eq, 73.21.Fg, 73.22.Dj The current interest in the growth of wurtzite GaN along the nonpolar ͓11-20͔ a-axis is fostered by the possibility of eliminating the internal electric fields that are induced in nitride-based quantum structures when grown along ͓0001͔, 1-3 the polar c-axis. In such a-plane GaN, however, large densities of a particular class of extended defects, namely, basal stacking faults ͑BSFs͒, are usually observed. After a number of theoretical and experimental studies, [4][5][6][7][8][9][10] these BSFs are generally considered to consist in ultrathin ͑three monolayers͒, perfectly smooth insertions of cubiclike GaN in a wurtzite GaN matrix. Electrons are confined in the cubiclike layer, but with significant spreading of the wave function in the surrounding barrier. On the other hand, the corresponding valence-band discontinuity has been predicted to be such that the cubiclike layer constitutes a potential barrier for holes, leading for the overall structure to a type-II band line-up. 7 In usual quantum wells ͑QWs͒ produced by epitaxy, potential fluctuations of diverse origins induce, especially at low temperatures, a natural in-plane localization of carriers ͑electrons, holes, or excitons͒. Quite generally, well-width fluctuations of typically one atomic monolayer occur during the epitaxial growth of QWs, leading to the localization of carriers where the QW is wider, i.e., with lower quantized energy. Moreover, even in nitride-based QWs with flat interfaces, the large effective mass of holes make them also sensitive to potential fluctuations due to alloy disorder in the well 11 or in the barriers. 12 In any case, the energy lost by, say, an exciton, when localized at such fluctuations, is larger than the energy that this exciton would lose by localizing onto a neutral donor in the bulk material. Donor-related excitonic transitions are consequently not observed in QWs: excitons are better localized by fluctuations than they are by donors. 13Given their intrinsic nature, BSFs represent the unprecedented situation of QWs without any well-width fluctuations. Consequently, and contrary to usual heterostructures produced by epitaxy, no in-plane exciton localization is expected. Now,...

Properties of the main Mg-related acceptors in GaN from optical and structural studies

“…32 The observed properties of the A2 acceptor discussed here may be understood in a similar way as for the BSFrelated PL in n-type GaN. 34 In that case, it was argued that the localization of electrons (and subsequently excitons) to BSFs in n-GaN is mainly induced by donor potentials in the vicinity of the BSF. 34 In the case of acceptor doping the acceptor potential is much more localized, within <1 nm, meaning that the acceptor hole may not easily delocalize to the BSF plane, but will distort the local potential at the BSF, thus assisting the BSF hole (and exciton) localization, so that the BSF luminescence is observed.…”

“…34 In that case, it was argued that the localization of electrons (and subsequently excitons) to BSFs in n-GaN is mainly induced by donor potentials in the vicinity of the BSF. 34 In the case of acceptor doping the acceptor potential is much more localized, within <1 nm, meaning that the acceptor hole may not easily delocalize to the BSF plane, but will distort the local potential at the BSF, thus assisting the BSF hole (and exciton) localization, so that the BSF luminescence is observed. 32 The acceptor will, in turn, be perturbed by the nearby BSF potential mainly governed by the spontaneous polarization field, 21 positioned on the average a few nm away in p-GaN with an Mg doping of 10 19 cm…”

One-dimensional exciton luminescence induced by extended defects in nonpolar GaN/(Al,Ga)N quantum wells

“…However, QW width fluctuation cannot account for the low-temperature redshift observed in figure 6, and the mechanisms localizing BSFbound QW excitons are therefore definitely more complex. The S-shaped behavior has already been observed for BSFbound excitons in a-plane GaN [33,34] and has been ascribed to the presence of donor nuclei in the vicinity of the BSF planes, as theoretically discussed in [35]. After a careful deconvolution procedure, Varshni fits reveal an intra-BSF localization energy of 33 meV for the 4 nm wide a-plane GaN/Al 0.05 Ga 0.95 N QW.…”

Luminescence associated with stacking faults in GaN

“…Such a coupling would influence the emission energy and lead to a localization of excitons within the plane of the BSF. Their calculations for electrons at I 1 BSFs suggest that donors with a distance of up to about 10 nm have an influence on the emission energy associated with the BSFs: The difference in electron localization energy with respect to a bare BSF ranges between 9 meV at 10 nm distance to 53 meV when the donor resides exactly on the BSF [83]. For the case of acceptors, Khromov et al [84] discuss the role of Mg impurities located within a few nm of BSFs.…”