Continuous transition from multiple quantum-well regime to superlattice regime in GaAlAs/GaAs system as observed by spectroscopic ellipsometry with high lateral resolution

A multiple quantum-well structure grown by organometallic chemical vapor deposition and exhibiting a thickness gradient over the sample surface has been analyzed by spectroscopic and spatially resolved ellipsometry. The sample has been scanned in energy from 1.4 to 4.0 eV, with 5–10-meV resolution, and in position over a 46-mm line, with a 100-μm optical resolution. Using multilayer modeling we have first determined the structural parameters and particularly the aluminum concentration in the barrier, and the barrier and the quantum-well thicknesses. These two thicknesses vary from 95 to 10 Å along the 46-mm scanned line, while their ratio as well as the aluminum concentration (64%) remain constant. The ellipsometric spectra, namely, the effective dielectric function which can be deduced from the tan Ψ and cos Δ curves, allow for the determination of the multiple quantum-well optical transitions around Γ. In the thicker part of the wafer the optical spectra exhibit the well-known feature of a multiple quantum well associated to N=1, 2, and 3 heavy holes → electron transitions. As the thicknesses decrease, the coupling between quantum well increases, and the structure becomes a superlattice. For a barrier thickness of 30 Å, we observe the splitting of the fundamental level into two components: the first attributed to the symmetrical wave function and the second to the antisymmetrical wave function. The splitting is observed for both the heavy- and light-hole transitions. As the coupling between wells still increases, the dielectric function of the superlattice tends towards the one of the GaAlAs alloy with an average aluminum concentration of 32%. The evolution of the optical transitions versus barrier and quantum-well thickness has also been investigated theoretically by solving the Schrödinger equation for a periodic structure. The calculations have been done for two values of two conduction-band offsets: 60% and 85%. The overall agreement between theory and experiment is very good for the 60% conduction-band offset.