Shockley-Queisser analysis of Record Efficiency Solar Cells

The Shockley-Queisser Charts (S-Q charts) were introduced in Photovoltaic materials: Present efficiencies and future challenges, A. Polman, M. Knight, E.G. Garnett, B. Ehrler, and W.C. Sinke; Science, 352, (2016). They are updated biannually and can also be found here.

These charts identify and visualize two separate, equally crucial aspects of solar cell performance, namely electronic performance and optical performance. While electronic performance can be quantified by the open-circuit voltage (Voc) and the fill-factor (FF), the optical performance is associated with the short-circuit current density (Jsc). Such a distinction can be helpful for scientists as it identifies the current strengths and weaknesses of solar cell performance for specific semiconductors. The charts also classify materials according to how close they are to their S-Q limit, by separating them into three different categories, corresponding to potential fulfillment of >75% (blue), 75% to 50% (green), and less than 50% (red).

Fig. 1 shows the current record efficiencies for several well known solar cell materials as well how close they are to their SQ-limit. Fig. 2 attempts to distinguish the same materials a bit more, by looking at the Jsc and Voc-FF product of the corresponding record cells. This gives somewhat of an idea of where most of current research has been working on, but also about what it actually should focus on. As an example, while CdTe solar cells seem to have almost maximized their potential Jsc, there is much to gain regarding their electronic performance. GaAs on the other hand, is already pretty close to its theoretical limit, electronically and optically. Fig. 3 plots the three main solar cell parameters, Jsc, Voc and FF for all previously mentioned materials as a function of bandgap.


Efficiencies relative to Shockley-Queisser

SQ chart 1


Fraction of the Shockley-Queisser detailed-balance limit (black line) achieved by record-efficiency cells, gray lines showing 75% and 50% of the limit.

Optical and electrical fractions

SQ chart 3

The current ratio j = Jsc/ JSQ plotted versus the product of the voltage and fill factor fractions (v x f = FF Voc / FFSQ VSQ) for record-efficiency cells. The lines around some data points correspond to a range of band gaps taken in the S-Q calculations according to uncertainty in the band gap of the record cell.

Current, voltage, and FF

SQ chart 2

Single-junction solar cell parameters are shown as a function of band gap energy according to the Shockley-Queisser limit (solid lines) and experimental values for record-efficiency cells. Panel 1: Short-circuit current Jsc. Panel 2: Open-circuit voltage Voc. The voltage corresponding to the band gap is shown for reference, with the voltage gap Vg–VSQ indicated by the gray shaded region. Panel 3: Fill factor FF = (JmpVmp)/(VocJsc). All data are for standard AM1.5 illumination at 1000 W/m2.