Dependence of zero-bias resistance-area product and quantum efficiency on perimeter-to-area ratio in a variable-area diode array

The dependence of the zero-bias resistance-area (RA) product and the quantum efficiency (η) of variable-area diode arrays is numerically calculated by solving the diffusion equation in a cylindrical, three-dimensional geometry in the thick base approximation. The calculation is done for long-wavelength IR HgCdTe n⁺-on-p diffusion-limited photodiodes at 77 K. The inverse resistance-area product 1/(RA) and the square root of the quantum efficiency, η^1/2, are plotted against the perimeter-to-area (P/A) ratio. The 1/RA results are fitted to a quadratic dependence on the P/A ratio. The dependence of the 1/RA on the minority carrier diffusion length, the junction depth and the surface recombination velocity (SRV) is evaluated. An empirical expression is proposed that largely accounts for the dependence of the coefficients of the quadratic on these parameters and is more general than those used in previous studies. The results are also in reasonable agreement with the results of Briggs, expressed in terms of the parameter f_3D, that are valid for zero junction depth and zero SRV. The slope of the quantum efficiency versus P/A plot, which is approximately a straight line, is related to an effective length L_opt, that also depends on the diffusion length, junction depth, SRV and the absorption coefficient α. The parameter L_opt varies as α^1/2.