Upstream modulation in photoreflectance

Photoreflectance is used for the characterisation of semiconductor samples, usually by sweeping the monochromatized probe beam within the energy range comprised between the highest value set by the pump beam and the lowest absorption threshold of the sample. There is, however, no fundamental upper limit for the probe beam other than the limited spectral content of the source and the responsivity of the detector. As long as the modulation mechanism behind photoreflectance does affect the complete electronic structure of the material under study, sweeping the probe beam upstream towards higher energies from that of the pump source is equally effective in order to probe high energy critical points. This fact, up to now largely overseen, is shown experimentally in this work. E1 and E0+{\Delta}0 critical points of bulk GaAs are unambiguously resolved using pump light of lower energy. Upstream modulation may widen further applications of the technique.

2 thereof by sweeping the monochromatized probe beam toward lower energies from the uppermost value set by the filter edge, recording changes in reflectance of the probe upon the action of the pump beam. Implicitly, the highest energy accessible to the experiment is therefore set by the optical edge of the LPF, normally chosen a few hundreds of meV below the nominal photon energy of the pump source. This small offset accounts for both the line broadening of the source (particularly if LEDs are used) as well as the finite width of the filter optical edge.
In contrast to this sort of standard PR, the so called "first derivative" modulation spectroscopies [9], like piezo-(PzR) or thermo-reflectance (TR), do not appear bounded at high energies as a result of the perturbing action. In the case of piezoreflectance [10], stress-strain cycles are imposed on the sample, usually by means of a piezoelectric actuator attached to the sample, whereas in thermoreflectance [11] the sample is subject to thermal cycles induced, e.g., by a Peltier element. The same applies to electroreflectance (ER), making use of an externally applied modulated electric field on the sample [12].
Even when each modulation mechanism is executed at a reference frequency thereby used for detection, the detection itself is in principle not constrained to a certain photon energy range of the probe beam. The only practical limitations are imposed by the spectral content of the source and the responsivity of the detector employed. The reason is that the perturbation used as modulation agent, independently of its origin, does affect the entire electronic structure of the sample under test. PR is not different from PzR, TR or ER in that respect. The generation of photovoltage upon pump illumination of a semiconductor, on which PR is based, is better illustrated as a change in band bending at those regions in the sample sustaining space charge (SCR), typically free surfaces or interfaces, as schematically shown in Figure 1. Even when photogeneration of free carriers upon appropriate illumination may just involve the first interband transitions allowed between occupied and empty states, the entire electronic structure of the material is thereby affected, as long as the modulation of the electric field associated to the SCR is active. It is thus expected that electronic transitions at energies higher than those directly accessible with the pump beam be equally subject to the modulating action and consequently not PR-silent, as schematically shown in Figure 1 illustrates the modulation mechanism at CPs, namely periodic SPV generation, upon illumination with a chopped pump beam of energy slightly above E g , inducing transitions at the fundamental gap. Notice that, although the E 0 +Δ 0 transition involves a valence state below the valence band edge (reference at zero energy), the corresponding energy is greater than the fundamental gap E g .
For this purpose, we have used a Si-doped GaAs wafer (AXT, n=1×10 18 cm -3 ). The reason is that n-type doped GaAs exhibits intense and broad signatures in PR at room temperature, particularly in the range of E 1 transitions, that are typically better resolved than in intrinsic material. PR was measured using the light beam of a quartz-tungsten-halogen lamp (operated at 150 W) as probe of intensity I 0 (λ). The light is passed through a monochromator (1/8 m Cornerstone-Newport) and focused with optical lenses on the sample. Light directly reflected with intensity I 0 (λ)R(λ) is focused on a solid-state Si-detector. The  E 0 +Δ 0 corresponds to the split-off valence band Γ 7 due to spin-orbit coupling, connecting to the same Γ 6 -conduction-band state; finally, E 1 is the next critical point in order of ascending energy and takes place along the Λ direction from the center of the Brioullin zone [13]. The filter edges can be identified in the spectra with the declining signals deviating from the LPF395nm spectrum. Perfect overlapping over the respective wavelength ranges with the measurement using just LPF395 is observed, confirming the absence of eventual second-order harmonics in the spectra.
The medium panel shows spectra obtained under 632.8 nm pump illumination. The short wavelength spectrum was obtained with SPF600nm, whereas the long wavelength one was obtained with LPF665nm. The nominal wavelength of the laser is indicated by the dotted line. As it can be observed, the spectra collected under 632.8 nm pump keep track of E 0 and E 1 signatures (E 0 +Δ 0 is affected by the filter edges), very much like the 325 nm pump does, even when E 1 is not directly accessible now under 632.8 nm illumination. Instead, upstream modulation of high energy critical points results from absorption involving lower energy transitions E 0 and E 0 +Δ 0 . The modified built-in potential and the associated field, due to photogenerated carrier screening at SCR, is the modulating mechanism affecting the entire electronic structure, including all high energy critical points. They can be probed thereof in a similar fashion as low energy critical points in downstream modulation. Finally, the lower panel of Figure 2 shows a PR spectrum obtained under 814 nm pump illumination using   Upstream photoreflectance is better understood when considering the character of modulation spectroscopies as absorptionbased techniques. As such, and contrarily to the case of luminescence, PR also probes unoccupied states which are accessible to the energy range of the photons in the probe beam. However, it is not necessary that the pump generating the periodic perturbation be absorbed in a process involving that particular transition to be probed in the experiment. This result has been recently reported in GaSb [14] and previously in sub-bandgap PR on GaAs [15]. The latter case illustrates the fact that upstream modulation can also be activated via optically active defect states in the bandgap. As a matter of fact, the upstream energy range in PR has largely been overseen in the past, as evidenced by the absence of related literature, with just a few exceptions mentioned. Even in such cases, results have oftentimes been presented in relation to certain specificities of the samples, rather than as an expected output.

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In summary, it has been shown that the information range accessible to PR can be extended to energies above that of the pump beam. Its practical implementation is simple, either replacing LPF with SPF or alternatively using notch or narrowband filters around the wavelength of the pump beam. Probing upstream is a direct consequence of the absorption-based nature of the technique and the intrinsic modulation mechanism involved, based on photovoltage generation upon the action of the pump beam affecting the entire electronic structure of the material under test. Accounting for this fact, apparently not much explored yet, may widen the current applicability of the technique.