Electronic and Optical Properties of the Group-III Nitrides, their Heterostructures and Alloys
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It thus appears necessary to re-examine the relation
between the UV optical response and the band structures. The LDA band structure has the disadvantage that strictly speaking it does not provide the quasiparticle excitation energies but merely intermediate results in obtaining the total energy of bonding between electrons and nuclei. Quasiparticle energies are the energies for extracting and electron from or adding an electron to the system as measured by photoemission and inverse photoemission. Fortunately, calculations of the self-energy corrections to the LDA band structure have been carried out for GaN and AIN using the GW 1 approach by a few groups [4, 5]. Furthermore, considerable insights in the magnitude, k-point, specific state and energy dependence of these corrections has accumulated from studies in other semiconductors. From these studies, we know that the main correction to the LDA band structure is an almost constant gap correction for the bands within at least about 5 eV from the gap. Before we can gauge the accuracy of these rather involved GW calculations, however, we need a better understanding of the experimental spectra which means that we need to re-examine the assignment of interband transitions. We [6] (and some other authors [7, 9]) have recently calculated the dielectric response function e2(w) within the random phase approximation (RPA) from LDA band structures. In addition, we have analyzed in detail how the latter is decomposed into its various interband transition contributions. Here, we briefly present these results for zincblende GaN and wurtzite AIN while for wurtzite GaN this analysis can be found in [6]. We compare our results with experimental reflectivity [6, 8] and spectroscopic ellipsometry data[9, 10, 11]. This is not trivial because optical response (which basically probes two-particle excitations) may involve further many-body corrections beyond the GW approach for 'GW stands for the first term in a perturbation theoretical expansion for the self-energy introduced by Lars Hedin and Stig Lundqvist in Solid State Physics, Vol. 23, p. 1 (1969), with G the one-electron Green's function and W the screened Coulomb interaction.
455 Mat. Res. Soc. Symp. Proc. Vol. 395 01996 Materials Research Society
single particle excitations. Our interpretation of the discrepancies between theory and experiment differs from that of other authors [9, 10, 11]. Further insights are gained by also comparing the occupied states to photoemission data. While the band structure probes on this large energy (several eV) scale are clearly strongly perturbed by many-body effects, the band structure details near the band edges should not suffer so much from these effects. Of course, excitonic effects are prominent but should not vary greatly with energy. We thus expect that the LDA band structures will account rather well for the excitonic fine structure related to the valence-band splittings near the valence-band maximum. The main issue here is whether the current calculations are sufficiently accurate
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