Apparent band-gap narrowing doping functions for silicon in the Dhariwal and Ojhaʹs form facilitating solar cell modeling

It is shown that reported doping functions for apparent band-gap narrowing (ABGN) in silicon that are written in the Slotboom and De Graaffʹs form (Slotboom, De Graaff, Solid-State Electron. 19 (1976) 857) can be set in the Dhariwal and Ojhaʹs form (Dhariwal, Ojha, Solid-State Electron. 25 (1982) 909) at all dopings without any significant deviation in their capability of fitting the experimental data. The use of the Dhariwal and Ojhaʹs form is preferable because it allows for a straightforward application of the depletion approximation in the non-uniformly doped regions of silicon devices like ion-implanted and diffused solar cells, facilitating the device performance modeling and analysis. This is demonstrated by an application to the internal spectral responses of two ion-implanted silicon solar cells and a comparison with a modeling method which does not use the depletion approximation.