Concentrated Photovotaics

Dong Liang
November 28, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010

Fig. 1: A schematic view of concentrated photovoltaic systems.

The Purpose of Concentration

The main reason for using concentrating systems is to minimize the use of expensive semiconductor components in favor of using cheaper optical components such as glasses and metallic mirrors. The concentration is characterized by the factor X = Optical area / solar cell area. Practical concentration factors of tens to thousands have been achieved.

Concentration Can Improve Cell Efficiency

For a p-n concentrator cell, assuming low carrier injection, the net current can be described as

J = Jsc - Jdark

in which Jsc is the short circuit current density, Jdark is the dark current density and J is the net current. Jsc is proportional to light intensity on the cell (P). If the incident light intensity is increased by a factor of X, Jsc increases by X times too. At any given bias that is below the open circuit voltage Voc, where the dark current vanishes, the net current is also increased by a factor of X. Voc is also larger if the light is more intensive, which increases logarithmically with X.

Voc' = Voc + m k T lnX / q

If the cell fill factor remains the same, then the power produced by the cell is increased by

X ( 1 + m k T lnX / qVoc )

and the efficiency is increased by

( 1 + m k T lnX / qVoc )
Fig. 2: A concentrated system with a parabolic reflector.

Practical Concerns

Based on the simple analysis above, the larger the concentration ratio X is, the higher efficiency the cell achieves. [1] However, in practice, there are other factors that limit this improvement. For example, high carrier densities lead to high injection conditions, which increase recombination losses. And increased temperature due to the accumulated heat will increase the dark current and make Voc smaller. Therefore, highest efficiency may be achieved with a 'medium' concentration ratio.

Series resistance is a major concern of concentrator cell design. It is very important because the current is large and the potential drop on the cell itself is also large. Increasing the doping level in the emitter will reduce series resistance significantly but will also be limited by recombination due to increased defects.


As the concentration ratio X increases, the concentrator itself begins to dominate system cost, therefore allowing expensive, high efficiency cells to be used economically with a high system efficiency. [2] In other words, for high efficiency solar cell such as III-V tandem cell, a concentrated system can maintain its high efficiency while keeping the total cost low.

© Dong Liang. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] J. Nelson, The Physics of Solar Cells (Imperial College Press, 2003).

[2] A. L.Fahrenbruch and R. H. Bube, Fundamentals of Solar Cells - Photovoltaic Solar Energy Conversion (Academic Press, 1983).