text: Photo-reflectance is a particularly convenient type of modulation spectroscopy, as it may be performed at room temperature and only requires the sample have a reflecting surface.  It is an established tool for non-contact determination of material and electronic properties of semiconductor films. In photo-reflectance, a pump laser beam is used to modulate the free charge density in a semiconductor sample (via photo-injection), thereby modulating one or more physical quantities (e.g. the internal electric field).  The measured signal ΔR is the change in amplitude of the reflected probe light as the intensity modulated pump radiation interacts with the sample.  The normalized signal is ΔR/R, i.e. the pump-induced change in reflectance (AC) divided by the baseline reflectance (DC). The conventional photo-reflectance apparatus uses a spectroscopic source for the probe beam, such that the signal may be recorded as a function of the probe light's wavelength. Generally, the signal may be written:
  where ΔR/R is the normalized change in reflectance, α (≡1/R×∂R/∂ε) and β (≡1/R×∂R/∂ε) are the "Seraphin coefficients" which contain filmstack information, and Δε and Δε are the pump induced changes in the complex dielectric function. However, in conventional photo-reflectance analysis, it is not necessary to independently determine the refractive and absorptive components (the first and second terms in ΔR/R, respectively) of the signal. Rather, a fit to the overall signal is performed using the third derivative functional form given by Aspnes. This fit procedure yields the interband transition energies, amplitudes, and widths. However, because the signal depends on the uniformity of the perturbation, the extraction of such parameters must be treated with care.