A simple theory of back surface field (BSF) solar cells

TLDR

A theory of an n‑p‑p+ junction based on Shockley’s depletion layer approximation explains the superior performance of BSF cells over ordinary n‑p cells, attributing it to two key effects. Assuming uniform doping, the model rapidly computes solar‑cell characteristics across parameters, showing that voltage sharing between the n‑p and p‑p+ junctions reduces dark current while the p‑p+ junction’s built‑in field boosts short‑circuit current. The model predicts that reducing cell thickness raises VOC while slightly lowering short‑circuit current, yet overall efficiency remains unchanged from 200 μm to 50 μm, a benefit for space missions demanding high power‑to‑weight ratios.

Abstract

A theory of an n-p-p+ junction is developed, entirely based on Shockley’s depletion layer approximation. Under the further assumption of uniform doping the electrical characteristics of solar cells as a function of all relevant parameters (cell thickness, diffusion lengths, etc.) can quickly be ascertained with a minimum of computer time. Two effects contribute to the superior performance of a BSF cell (n-p-p+ junction) as compared to an ordinary solar cell (n-p junction). The sharing of the applied voltage among the two junctions (the n-p and the p-p+ junction) decreases the dark current and the reflection of minority carriers by the builtin electric field of the p-p+ junction increases the short-circuit current. The theory predicts an increase in the open-circuit voltage (VOC) with a decrease in cell thickness. Although the short-circuit current decreases at the same time, the efficiency of the cell is virtually unaltered in going from a thickness of 200 μm to a thickness of 50 μm. The importance of this fact for space missions where large power-to-weight ratios are required is obvious.