Current-voltage characteristics of surface barrier liquid-junction and metal-junction cells including recombination

A new expression for the current-voltage ($\mathrm{IV}$) characteristic is derived without assuming constant quasi-Fermi-levels in the depletion region of a surface barrier device, nor a constant surface minority-carrier density. Explicit expressions for recombination effects are discussed but are not involved directly in the treatment. However, the effects appear in the gradient of the excess-carrier transfer velocity. This velocity and its gradient can be obtained empirically by matching experimental curves. The expression is shown to match $\mathrm{IV}$ curves from CdSe photoelectrochemical cells and metal—Schottky-barrier cells based on GaAs. Some of the quasi-Fermi-level (QFL) treatment of Sah, Noyce, and Shockley is corrected to show larger QFL variations in $p-n$ junctions than previously supposed. The spacing of the minority-carrier QFL from the Fermi level is calculated at the surface for several semiconductors.