A numerical method for describing the electrical response of a Back-Gated Metal-Semiconductor- Metal Photodetector (BGMSM-PD) to an impinging optical pulse on the active region of the device is presented. In the absence of external voltage, the main mechanism for the transport of photo-generated carriers is diffusion mechanism. Two nonlinear differential equations describe the behavior of photocarriers’ densities in the device medium with respect to time and position. Having linearized the parabolic partial differential equations, the time evolution of carrier densities is calculated using the Alternating Direction Implicit (ADI) method. The numerical results show good agreement with the experimental data. Both experimental and numerical findings confirm that the electrical response of the device to optical pulses with spatial FWHM comparable with the width of the active region is dependent on pulse position on the active region. This feature of the device makes it to be a good candidate as position sensors in places where micro-positioning is required.