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 and 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 E₆ and broadening parameters for the following transitions at 4. 2 ^ (all energies are in meV): E₀ (1517. 70. 5, <0. 3) ; E₀+₀ (18591, 62) ; E₁ (3043. 91, 281) ; E₁+₁ (3263. 61, 382) ; {E^'}₀ triplet, symmetry: (4488 10, 40 5), (4659 10, 30 5), (5014 15, 47 10) ; {E^'}₀ triplet, M₁ transitions, symmetry: (4529 10, 36 5) and (4712 10, 34 5) ; E₂ complex,: (513710, 10410) ; 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: ₀=3412 meV, ₁=2202 meV, {^'}₀ (at) =17115 meV, {^''}₀ (at) =18315 meV, and ₂=7710 meV. The splitting of the lower conduction bands at X due to the antisymmetric potential is {^'}₂=40210 meV. The {E^'}₀ transitions of symmetry are shown to lie about 10% of the way from to X. By comparing the period of the large number of Franz-Keldysh oscillations observed at the E₁+₁ transition with those of the E₀+₀ transitions observed in the high-field measurements, we determine a value ₓ= (0. 055008) m₄ for the transverse reduced mass at E₁+₁. 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.