Comparison between the electronic dielectric functions of a GaAs/AlAs superlattice and its bulk components by spectroscopic ellipsometry using core levels.

Abstract

The dielectric functions of a GaAs/AlAs superlattice (SL) as well as it its bulk constituents GaAs and AlAs were determined at T=90 K by means of spectroscopic ellipsometry with rotating analyzer using synchrotron radiation in the photon-energy range between 3\ensuremath{\leqslant}\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\leqslant}25 eV. This broad spectral range gives access to excitations from the Ga 3d core levels lying approximately 20 eV below the conduction-band minimum. These levels are atomiclike with virtually no dispersion throughout the Brillouin zone (BZ). They can thus be used as an energy reference to investigate confinement effects and level splittings on interband transitions in heterostructures compared to their bulk counterparts. The samples were grown by molecular-beam epitaxy and maintained under ultrahigh vacuum conditions from growth to measurement, avoiding the effects of cap or oxide layers, especially for AlAs. The investigation concerns transitions at L- and X-related points in the BZ which is tetragonal in the case of the SL and face-centered-cubic for the bulk samples. For the latter it is found that the L-related ${\mathrm{E}}_{1}$ structure consists of two spin-orbit split groups of three transitions. For a (GaAs${)}_{\mathrm{m}}$(AlAs${)}_{\mathrm{n}}$SL with m=9, n=7 these two groups are blueshifted by about 200 meV compared with GaAs due to confinement effects. Similar shifts are not observed for transitions from the Ga 3d levels to the conduction-band valleys. Therefore, the confinement acts on the highest valence bands. The major part of the SL ${\mathrm{E}}_{1}^{\ensuremath{'}}$ structure is AlAs-like, but the minor one moves to higher energies by 165 and 80 meV compared to AlAs and GaAs, respectively. Since the two parts of the ${\mathrm{E}}_{1}^{\ensuremath{'}}$ structure exhibit a different confinement behavior, they cannot have a common origin in k space. The analysis of X-related ${\mathrm{E}}_{2}$ structures exhibits a blueshift for the SL transitions by about 55 meV compared with AlAs which is consistent with a confinement effect on the lowest conduction band. In correspondence to previous theoretical work a transition above the ${\mathrm{E}}_{2}$ critical point is found which was attributed to a SL specific transition due to the BZ folding. The comparison with the results for the bulk samples suggests a relation to the ${\mathrm{E}}_{2}$(${\mathrm{P}}_{2}$) critical point. Beyond that, an analysis of the interband transition line shapes reveals for all ${\mathrm{E}}_{1}$,${\mathrm{E}}_{1}^{\ensuremath{'}}$ structures, and the AlAs-${\mathrm{E}}_{2}$ one, that a modified Lorentzian profile indicating final-state interaction is more appropriate than two- or three-dimensional critical-point line shapes. This points to deviation from the one-electron band-structure picture even for transitions far above the fundamental absorption edge.