Three-dimensional analytical simulation of self- and cross-responsivities of photovoltaic detector arrays

Decreasing dimensions, along with an increasing number of elements in imaging photodiode arrays, result in the degradation of spatial resolution and sensitivity due to lateral transport. This effect is modeled using a novel 3-D analytical solution of the continuity equation. The model enables the full 3-D analysis of lateral transport as manifested in excess carrier distribution, photocurrent, and self- and cross-responsivities. Three detector structures are investigated: the semi-infinite substrate, the perfectly collecting, and the perfectly reflecting backside. The front and rear illuminations are treated. The calculated results for the 3-D case deviate fundamentally from those predicted by the 1-D model. The 3-D model succeeds in explaining the reduced quantum efficiency of small-area detectors. It also predicts the limited effect diffusion length has on self-responsivity and cut-off wavelength. The calculated spectral responses fit extremely well data measured on InSb and HgCdTe test arrays. As a powerful design tool, the model enables optimizing responsivity and crosstalk by varying element geometry and spacing, optical aperture, lifetime, and spectral range. The model can be applied to any semiconductor photodiode array provided the relevant physical and geometrical parameters are known.