Impact of Semiconductor Band Tails and Band Filling on Photovoltaic Efficiency Limits

TL;DR

This paper revises the theoretical efficiency limits of solar cells by accounting for non-ideal, tail-like band edges in semiconductors, revealing that these imperfections significantly reduce maximum efficiency.

Contribution

It introduces a modified detailed balance model incorporating band tail effects, showing how imperfect band edges lower photovoltaic efficiency limits.

Findings

Broader band edges than kT reduce efficiency.

Renormalized bandgap affects maximum efficiency.

Band tail effects create a Stokes shift impacting performance.

Abstract

The theoretical maximum efficiency of a solar cell is typically characterized by a detailed balance of optical absorption and emission for a semiconductor in the limit of unity radiative efficiency and an ideal step-function response for the density of states and absorbance at the semiconductor band edges, known as the Shockley-Queisser limit. However, real materials have non-abrupt band edges, which are typically characterized by an exponential distribution of states, known as an Urbach tail. We develop here a modified detailed balance limit of solar cells with imperfect band edges, using optoelectronic reciprocity relations. We find that for semiconductors whose band edges are broader than the thermal energy, kT, there is an effective renormalized bandgap given by the quasi-Fermi level splitting within the solar cell. This renormalized bandgap creates a Stokes shift between the onset of the absorption and photoluminescence emission energies, which significantly reduces the maximum achievable efficiency. The abruptness of the band edge density of states therefore has important implications for the maximum achievable photovoltaic efficiency.