Time and frequency response of avalanche photodiodes with arbitrary structure

A method is developed for solving the coupled transport equations that describe the electron and hole currents in a double-carrier multiplication (DCM) avalanche photodiode (APD) of arbitrary structure. This solution makes it possible to determine the time and frequency response of the device. The injection can be localized to one or both ends of the multiplication region, or distributed throughout an extended region where multiplication can occur concurrently. The results are applied to conventional APDs with position-dependent carrier ionization rates (e.g., a separate-absorption-grading-multiplication APD) as well as to superlattice multiquantum-well (MQW) structures where the ionizations are localized to bandgap transition regions. The analysis may also be used to determine the dark current and include the carrier trapping at the heterojunction interfaces. The results indicate that previous time-dependent theories only account for the tail of the time response under high-gain conditions and are inaccurate for high-speed devices