GaAs lower conduction-band minima: Ordering and properties

Synchrotron-radiation Schottky-barrier electroreflectance spectra from the $\mathrm{Ga} 3d^V$ core levels to the lower $s{p}^3$ conduction band have shown that the $L_6^C$ lower conduction-band minima are located 170 ± 30 meV in energy below the $X_6^C$ minima in GaAs. Here, we investigate the implications of this ordering, which is opposite to that commonly accepted as correct. We find that, without exception, the results of previous experiments that apparently supported the opposite ordering can be reinterpreted within the ${\Gamma }_6^C-L_6^C-X_6^C$ model. By performing a line-shape analysis, we resolve an apparent discrepancy between intraconduction band absorption measurements of the $X_6^C-{\Gamma }_6^C$ energy separation. By comparing these optical results with other modulation spectroscopic ($s{p}^3$ valence-conduction-band electroreflectance, high-precision reflectance) data, combining these with the results of photoemission, transport (high pressure and high temperature), semiconductor alloy, and luminescence measurements, nonlocal pseudopotential calculations $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ theory, the rigid-valence-band hypothesis, and using the systematics of other tetrahedrally bonded semiconductors with temperature and pressure, we obtain a set of consistent parameters describing the ${\Gamma }_6^C$, $L_6^C$, and $X_6^C$ lower conduction-band minima of GaAs. This model resolves the former contradictions in the apparent indirect threshold energy as determined previously by photoemission, transport, and optical measurements. Previous photoemission data for cesiated GaAs show clearly after structure reassignment that hot electrons thermalize in the $L_6^C$ minima. This implies that Gunn oscillator operation in GaAs involves the $L_6^C$, and not $X_6^C$, conduction-band minima. We obtain the variation of these minima with composition, $x$, in the $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ alloy series, and show that the increase in binding energy of the N isoelectronic trap with increasing As fraction in this series is in qualitative agreement with the prediction of a two-level model wherein a Koster-Slater isoelectronic trap potential interacts with the densities of states of both $L_6^C$ and $X_6^C$. These results have clear implications for the theory of operation of light-emitting diodes of GaAs and its alloys.