Simple and direct estimation method for split-off hole effective mass from Franz–Keldysh oscillations appearing in photoreflectance spectra: a feasibility study using GaAs epitaxial layer structures at room temperature

We investigated the feasibility of directly estimating split-off hole effective mass m _so from Franz–Keldysh oscillations using non-destructive and non-invasive photoreflectance spectroscopy. We used an undoped/n-type GaAs epitaxial structure and two GaAs p–i–n diode structures. We observed the phenomenon that Franz–Keldysh oscillations, which originate both the E ₀ fundamental transition and from the E ₀ + Δ_so transition energy, appear in the photoreflectance spectra at room temperature. Initially, from the electro-optic constant ℏΘ _HH of the Franz–Keldysh oscillations originating from the E ₀ fundamental transition, we deduced the built-in electric field F in each sample with the use of the relation ℏΘ _HH = (e ²ℏ² F ²/2μ _HH)^1/3, where the quantity μ _HH is the reduced effective mass of the electron and heavy hole. In the next step, we calculated the reduced effective mass μ _so of the electron and split-off hole using the relation ℏΘ _so = (e ²ℏ² F ²/2μ _so)^1/3, where the quantity ℏΘ _so is the electro-optic constant of the Franz–Kelysh oscilations from the E ₀ + Δ_so transition. Finally, we estimated the split-off hole effective mass m _so from the reduced effective mass μ _so. The estimated split-off hole effective mass agrees with the reported value obtained experimentally. Thus, we conclude that the split-off hole effective mass is estimatable from analyzing the Franz–Keldysh oscillations in the photoreflectance spectra. We also compare the present hole effective masses to those theoretically known and discuss the appropriateness of the electronic-band calculations. (paper)