This letter presents a simple A/D converter based on the circle map. The converter encodes a dc input into a binary output sequence and has the trapping window that extracts an available part of the output sequence. Using the available part, the decoder provides an estimation by a fraction with variable denominator: it can realize higher resolution. Theoretical evidences for the estimation characteristics are given.

We propose an analysis method for Franz-Keldysh (FK) oscillations appearing in photoreflectance (PR) spectra of heterojunction device structures, which enables precise and simultaneous evaluation of the built-in electric field strength and band-gap energy. Samples for PR measurements were n+-GaAs/n-Al0.3 Ga0.7 As/i-GaAs heterostructures with different Al0.3Ga0.7As-layer thickness. We have found that the phase of the FK oscillations originating from the i-GaAs buffer layer depends on the Al0.3 Ga0.7 As-layer thickness. We have derived a calculation model for FK oscillations that includes the interference of probe light. From the comparison of the calculated spectra with the measured spectra, we conclude that mixing of the real and imaginary parts of a modulated dielectric function, which is caused by the probe-light interference, gives rise to the phase shift of the FK oscillations. Our FK-oscillation analysis method reduces ambiguity in the estimation of band-gap energy that is considerable in a conventional analysis.