Schottky-Barrier Electroreflectance: Application to GaAs

We describe a Schottky-barrier electroreflectance (ER) technique for making high-resolution optical spectroscopic measurements on semiconducting materials. When combined with recent line-shape theories of low-field ER spectra, the method provides order-of-magnitude improvement in resolution of structure and accuracy in the determination of critical-point energies and broadening parameters as compared to previous spectroscopic work on higher interband transitions. The Schottky-barrier technique is applied to GaAs, where separate critical-point contributions of Γ and Δ symmetry in the E^'₀ triplet are resolved for the first time, together with all members of the quadruplet at X. We find the values of critical-point energies Eg and broadening parameters Γ for the following transitions at 4.2 ^∘{}K (all energies are in meV): E₀(1517.7±0.5,<0.3); E₀+Δ₀(1859±1,6±2); E₁(3043.9±1,28±1); E₁+Δ₁(3263.6±1,38±2); E^'₀ triplet, Γ symmetry: (4488 ±{} 10, 40 ±{} 5), (4659 ±{} 10, 30 ±{} 5), (5014 ±{} 15, 47 ±{} 10); E^'₀ triplet, M₁ transitions, Δ symmetry: (4529 ±{} 10, 36 ±{} 5) and (4712 ±{} 10, 34 ±{} 5); E₂ complex, Σ: (5137±10,104±10); E₂ complex, X quadruplet: (4937 ±{} 10, 47 ±{} 10), (5014 ±{} 10, 47 ±{} 10), (5339 ±{} 10, 48 ±{} 10), (5415 ±{} 15, 50 ±{} 15). These values enable us to determine the following spin-orbit-splitting energies: Δ₀=341±2 meV, Δ₁=220±2 meV, Δ^'₀ (at Γ)=171±15 meV, Δ^''₀(at Δ)=183±15 meV, and Δ₂=77±10 meV. The splitting of the lower conduction bands at X due to the antisymmetric potential is Δ^'₂=402±10 meV. The E^'₀ transitions of Δ symmetry are shown to lie about 10% of the way from Γ to X. By comparing the period of the large number of Franz-Keldysh oscillations observed at the E₁+Δ₁ transition with those of the E₀+Δ₀ transitions observed in the high-field measurements, we determine a value μT=(0.055±008)mₑ for the transverse reduced mass at E₁+Δ₁. These results are compared to previous experimental measurements and to calculated energy-band structures for GaAs. The determination of critical-point symmetry in surface-barrier geometries in terms of the transformation properties of the third- and fourth-rank low-field ER line-shape tensors is also discussed. Finally, the vanishing of an ER spectrum at a hyperbolic critical point, a reduced-mass effect predicted by the general theory of the Franz-Keldysh effect, is observed for the first time.