Surface acoustic waves (SAWs) with a strong enough piezoelectric field can capture and transport electrons and holes. The presence of SAWs and their photo-generated carriers' transport properties in the GaAs/AlGaAs quantum well (QW) is a potential scheme to achieve single photon sources and single photon detectors. We numerically solve the system of coupled Schrödinger and Poisson equations and the carriers' radiative lifetime. A finite difference method of two-dimensional was developed as a conventional approach to the theoretical understanding of the presence in the QW through Python programs. The features of carriers' radiative lifetime are discussed as functions of the SAW wavelengths and SAW amplitudes. The spatial separation and radiative lifetime extension of the electrons and holes in the SAW-driven QW was explained by the method. © 2023 Society of Photo-Optical Instrumentation Engineers (SPIE).