Theoretical analysis and experimental study of Fourier transformation of Franz–Keldysh oscillations in GaAs

Abstract

A study of the Franz-Keldysh oscillations in electromodulation reflectance of Si-delta-doped GaAs by a fast Fourier transformation Fourier transformation ͑FT͒ has been used in the theoretical line shape analysis of Franz-Keldysh oscillations ͑FKOs͒ in detail by numerical simulations. FKOs from the surface-intrinsic-n ϩ GaAs structure were obtained in photoreflectance ͑PR͒ measurements with various modulation light intensities and with different strengths of bias light illumination, which were used to change the static electric field in the intrinsic layer of the sample. The FT spectra of the PR spectra, including the real part, imaginary part, and the modulus, were very consistent with the theoretical line shapes. The ratio of the square root of the reduced mass (ͱ L /ͱ H ) and the ratio of transition strength of the electron heavy hole to the electron light hole were obtained from the FT spectra. In addition, the electric field in the intrinsic layer of the sample without and with bias illumination and the modulation field induced by photomodulation were also obtained.

Critical point energy as a function of electric field determined by electroreflectance of surface-intrinsic-n+ type doped GaAs

“…The thus obtained values of E c are plotted against F as shown in Fig. 13 This is reasonable because only the order of lifetime can be estimated from uncertainty principle. Instead of being a constant, which was taken as E g in previous works, the value of E c increases with F. In order to explain the dependence, the momentum gained in F was considered.…”

A comparison between contactless electroreflectance and photoreflectance spectra from n-doped GaAs on a semi-insulating GaAs substrate

“…The nominal epilayer thicknesses and the electron concentrations measured by the Hall effect at room temperature of these samples are summarized in table 1. The experiment set-ups of PR [9] and CER [10] were similar except for the signal modulation. A beam of light from a 0.5 m monochromator, which was illuminated by a 250 W tungsten halogen lamp, served as the probe light.…”

Gaussian and Faddeeva broadening of the Franz-Keldysh oscillations at three-dimensional critical-points

“…The relative error for ˜( ) H z A slightly improved to 48% versus 61% at h -= 1 for q G =  0.01 , as shown in figure 1(b). Contrastingly, the relative error for ˜( ) H z [60,61] in the analysis of FKOs. In future, the impact of previous errors on the PR spectra transition into low-field regime as it approaches the third-derivative regime may be investigated.…”

“…around eight FKO peaks away from the CP. Equation (15) and its region of validity had been fundamental for graphical techniques [57][58][59] and fast Fourier transforms [60,61] in the analysis of FKOs; hence, an assessment of its accuracy is essential. Figure 1(a) depicts the relative error (RE) for ˜( ) H z A in the dotted red line for Lorentzian broadening q G =  0.01 within FKO's moderate-field regime.…”