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 $\Gamma$ and $\Delta$ symmetry in the ${E^{\prime }}_0$ triplet are resolved for the first time, together with all members of the quadruplet at $X$. We find the values of critical-point energies $E_g$ and broadening parameters $\Gamma$ for the following transitions at 4.2 °K (all energies are in meV): $E_0(1517.7\mathrm{}\pm 0.5,<0.3)$; $E_0+{\Delta }_0(1859\mathrm{}\pm 1,6\pm 2)$; $E_1(3043.9\mathrm{}\pm 1,28\pm 1)$; $E_1+{\Delta }_1(3263.6\mathrm{}\pm 1,38\pm 2)$; ${E^{\prime }}_0$ triplet, $\Gamma$ symmetry: (4488 ± 10, < 40 ± 5), (4659 ± 10, 30 ± 5), (5014 ± 15, 47 ± 10); ${E^{\prime }}_0$ triplet, $M_1$ transitions, $\Delta$ symmetry: (4529 ± 10, < 36 ± 5) and (4712 ± 10, 34 ± 5); $E_2$ complex, $\Sigma : (5137\mathrm{}\pm 10,104\pm 10)$; $E_2$ 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: ${\Delta }_0=341\mathrm{}\pm 2$ meV, ${\Delta }_1=220\mathrm{}\pm 2$ meV, ${{\Delta }^{\prime }}_0 \left(\mathrm{at} \Gamma \right)=171\mathrm{}\pm 15$ meV, ${{\Delta }^{\prime \prime }}_0\left(\mathrm{at} \Delta \right)=183\mathrm{}\pm 15$ meV, and ${\Delta }_2=77\mathrm{}\pm 10$ meV. The splitting of the lower conduction bands at $X$ due to the antisymmetric potential is ${{\Delta }^{\prime }}_2=402\mathrm{}\pm 10$ meV. The ${E^{\prime }}_0$ transitions of $\Delta$ symmetry are shown to lie about 10% of the way from $\Gamma$ to $X$. By comparing the period of the large number of Franz-Keldysh oscillations observed at the $E_1+{\Delta }_1$ transition with those of the $E_0+{\Delta }_0$ transitions observed in the high-field measurements, we determine a value ${\mu }_T=(0.055\mathrm{}\pm 008)m_e$ for the transverse reduced mass at $E_1+{\Delta }_1$. 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.