An optoelectronic notch (‘dip’) phenomenon in the heterodyne photocarrier radiometry frequency response of Si wafers: a route to quantitative trap-state dynamic processes in semiconductors

Abstract

An anomaly was observed in the heterodyne photocarrier radiometry (HePCR) frequency response of Si wafers in the form of a signal amplitude depression (‘dip’) accompanied by a 180° phase transition. This phenomenon resembles an electronic notch filter and was investigated experimentally and theoretically by invoking free-carrier-density-wave (CDW) kinetics in generic semiconductor systems. Both homodyne PCR and HePCR signals were obtained from n- and p-type wafers of different resistivities. Dynamic nonlinear rate-equation models with two bandgap carrier traps were introduced and analytical zeroth and first-order CDW solutions were obtained in the frequency domain. The experimental frequency responses of the HePCR optoelectronic notch phenomenon were found to be in very good agreement with the theory. Characteristic CDW recombination and trap capture and emission characteristic times were obtained and studied as functions of the illuminating laser intensity. The present newly observed HePCR notch phenomenon has revealed a new mechanism of nonlinear contributions due to trap-state-related CDW dynamics in semiconductors superposed on the well-known nonlinear electron-hole recombination interactions that give rise to non-zero HePCR signals. The implications of this notch phenomenon are discussed in terms of its importance in providing physical insights into photocarrier dynamic interactions with traps, leading to identification of active CDW trap-state numbers and precision measurements of their kinetic parameters, carrier capture and emission coefficients, and quantitative trap densities that determine the optoelectronic quality of semiconductors.