Third-derivative modulation spectroscopy with low-field electroreflectance

Abstract

The theoretical basis and experimental procedures are reviewed for third-derivative modulation spectroscopy, which is the same as low-field electroreflectance. The physical origin of the third-derivative behavior is discussed in terms of the effect of a uniform electric field on the translational symmetry of the unperturbed crystal. The relationship between the low-field and the Franz-Keldysh electroreflectance theories is discussed. In the lowfield range, both intraband and interband electric-field effects can be treated by first-order perturbation techniques, leading to great simplifications in the more general theory. By formulating the expression for the experimentally measured relative reflectivity change, ΔR R , in complex-variable form, effects due to experimental field inhomogeneities, the electron-hole interaction, and the optical constants of the material can be described by complex coefficients multiplying a theoretically calculated complex lineshape, thereby simplifying the analysis of experimental spectra. We also review the commonly used experimental configurations, and discuss procedures for determining experimentally the low-field range in a given experimental situation. The linearized third-derivative (LTD) technique, which makes use of specific properties of fully depleted space-charge regions, is discussed in detail. Finally, the application of third-derivative spectroscopy in the measurement of weak spectroscopic features and the determination of band structure parameters is demonstrated with specific examples.