Fundamentals of PV efficiency interpreted by a two-level model

Muhammad A. Alam, Purdue University
Mohammad Ryyan Khan, Purdue University

Date of this Version



Am. J. Phys. 81, 655 (2013)


Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Am. J. Phys. 81, 655 (2013) and may be found at The following article has been submitted to/accepted by American Journal of Physics. Copyright (2013) Muhammad A. Alam, and M. Ryyan Khan. This article is distributed under a Creative Commons Attribution 3.0 Unported License.


We consider the physics of photovoltaic (PV) energy conversion in a two-level, atomic PV and explain the conditions for which the Carnot efficiency is reached and how it can be exceeded. The loss mechanisms—thermalization, angle entropy, and below-bandgap transmission—explain the gap between Carnot efficiency and the Shockley-Queisser limit. Techniques developed to reduce these losses (e.g., solar concentrators, tandem cells, etc.) are reinterpreted using a simple two-level model. Remarkably, this simple model captures the essence of PV operation and reproduces the key results and important insights that that have been previously obtained using more complicated derivations.


Power and Energy