Shockley-Queisser Model: Analytical Solution, Thermodynamics, and Kinetics

TL;DR

This paper provides an exact analytical solution to the Shockley-Queisser model, linking thermodynamics and kinetics to photovoltaic efficiency limits using the Lambert W function.

Contribution

It introduces a precise analytical formulation of the SQ model, revealing new thermodynamic relations and kinetic insights for photovoltaic efficiency.

Findings

Derived exact analytical solutions using Lambert W function

Established thermodynamic relation between efficiency and chemical potential

Linked photocarrier kinetics with PV conversion efficiency

Abstract

We derive exact analytical solution of the Shockley-Queisser (SQ) model and present all photovoltaic (PV) characteristics in compact and convenient form via the Lambert W function. We show that the SQ condition of chemical of equilibrium between photocarriers and emitted phonons leads to a new thermodynamic relation between the maximal conversion efficiency and the photo-induced chemical potential. Also, we consider kinetics of PV conversion and establish relation between the photocarrier collection time and photocarrier lifetime. We consider photonic and electronic requirements for approaching of SQ limit in semiconductor PV devices and highlight a role of photon reabsorption.