Solar cell

A solar cell is a semiconductor p-n junction, usually silicon, operated as a power source: absorbed photons with energy above the bandgap create electron-hole pairs, the junction field separates them, and the resulting photocurrent flows through an external load at a forward voltage of a few hundred millivolts. It is the same device as a photodiode, operated in the fourth quadrant of its I–V curve and made as large as possible. Commercial silicon modules convert about 20–23% of standard sunlight to electricity; the best laboratory silicon cells are close to 28%, and the Shockley–Queisser limit for any single junction under the standard spectrum is about 33.7%, reached at a bandgap of 1.34 eV.

The I–V curve and its parameters

Under illumination the cell is described, to a first approximation, by the diode equation with a photocurrent subtracted:

$$J = J_0\left[e^{qV/nkT} - 1\right] - J_{sc},$$

where $J_0$ is the saturation current density, $n$ the ideality factor and $J_{sc}$ the short-circuit current density. Four numbers summarize the curve: $J_{sc}$, the open-circuit voltage $V_{oc}$ where the current is zero, the fill factor FF (the ratio of the maximum power to the product $J_{sc}V_{oc}$) and the efficiency $\eta$,

$$\eta = \frac{J_{sc}\,V_{oc}\,\mathrm{FF}}{P_{in}}.$$

Worked example. Standard test conditions specify the AM1.5G spectrum at 1000 W/m² (100 mW/cm²) and a cell temperature of 25 °C. A silicon cell with $J_{sc} = 40$ mA/cm², $V_{oc} = 0.70$ V and FF = 0.80 delivers 22.4 mW/cm², an efficiency of 22.4%; a 100 cm² cell then gives 2.24 W. Setting $J = 0$ in the diode equation with $n = 1$ and $kT/q = 25.7$ mV at 25 °C gives the corresponding saturation current density, about $5.9 \times 10^{-14}$ A/cm².

Because $V_{oc} = (nkT/q)\ln(J_{sc}/J_0 + 1)$, the open-circuit voltage rises by only about 59 mV for each tenfold increase in irradiance (for $n = 1$), which is why concentrator systems gain efficiency slowly with concentration. Series resistance from contacts and the emitter reduces the fill factor at high current; low shunt resistance from leakage paths reduces it at low light.

Spectral response

The current a cell produces at each wavelength is set by its external quantum efficiency, measured with a monochromator and a calibrated reference detector. Converted to responsivity, a quantum efficiency of 0.9 at 900 nm corresponds to 0.65 A/W. Integrating the measured quantum efficiency against the AM1.5G photon flux should reproduce the $J_{sc}$ measured under a solar simulator; disagreement points to spectral mismatch in the simulator or an error in the cell area.

The Shockley–Queisser limit and beyond

Shockley and Queisser (1961) treated a single junction that absorbs every photon above its bandgap and loses carriers only by radiative recombination. Two losses dominate: photons below the bandgap pass through unabsorbed, and photons far above it lose their excess energy as heat when the carriers relax to the band edges. The balance gives a maximum near 33.7% at 1.34 eV (a band edge near 925 nm) under AM1.5G. For silicon, with a 1.12 eV indirect gap and unavoidable Auger recombination, the practical limit is usually given as about 29.4%.

Multijunction cells stack junctions of decreasing bandgap so that each absorbs a slice of the spectrum with less thermalisation loss. III–V multijunctions dominate space power and have exceeded 47% under concentrated sunlight in the laboratory. Perovskite absorbers, with bandgaps tunable by composition, have reached single-junction laboratory efficiencies above 27%, and perovskite-on-silicon tandems have exceeded 35%; their long-term stability outdoors is still being established, and current records are tracked in the published solar cell efficiency tables.

Measurement pitfalls

• Temperature. Silicon $V_{oc}$ falls by roughly 2 mV/K, and module power by about 0.3–0.4% per kelvin. At −0.35%/K, a module at 60 °C produces about 12% less than its 25 °C rating.
• Area definition. Efficiency can refer to total area, aperture area or designated illumination area; small-cell records depend on a masked, well-defined area.
• Probing. Four-wire (Kelvin) contacts are needed so that probe and cable resistance do not appear as series resistance.
• Scan hysteresis. Perovskite cells can give different curves for forward and reverse voltage sweeps; stabilized maximum-power tracking is the accepted measurement.

Common questions

What is a good fill factor?

Good crystalline silicon cells reach about 0.80–0.85. Values well below 0.7 usually indicate high series resistance, low shunt resistance or a poor junction.

Why is silicon used if its bandgap is not optimal?

Silicon's 1.12 eV bandgap is close enough to the optimum that its theoretical efficiency is only a few points lower, and the material is abundant and processed at enormous scale. Its weak absorption near the band edge, a consequence of its indirect bandgap, is offset by light-trapping textures.

Does a solar cell work under indoor light?

Yes, at lower power. Indoor LED light has little infrared, so wider-bandgap absorbers such as amorphous silicon or perovskites are better matched to it than crystalline silicon, and the irradiance is hundreds of times lower than sunlight.

References: W. Shockley, H. J. Queisser, J. Appl. Phys. 32, 510 (1961); M. A. Green, Solar Cells: Operating Principles, Technology and System Applications (Prentice-Hall, 1982); J. Nelson, The Physics of Solar Cells (Imperial College Press, 2003); A. Richter, M. Hermle, S. W. Glunz, IEEE J. Photovoltaics 3, 1184 (2013); S. Rühle, Solar Energy 130, 139 (2016); ASTM G173, Standard Tables for Reference Solar Spectral Irradiances; M. A. Green et al., "Solar cell efficiency tables," Progress in Photovoltaics (published twice yearly).