This simulation shows how a single-junction solar cell converts sunlight into electrical power, and how the semiconductor band gap, light intensity, temperature, and resistive losses determine the cell's current, voltage, power, and efficiency. The cell is modeled with the one-diode equivalent circuit.
Select a semiconductor from the drop-down menu or set the band gap with its slider. The other sliders change the sunlight intensity, cell temperature, diode ideality factor, series and shunt resistances, and quantum efficiency. Cell performance values are listed below the sliders.
The current–voltage view plots current density and power density versus cell voltage. The red dot is the maximum power point. When the operating point is not at the maximum power point, the "move to maximum power point" button becomes red and clicking it moves the operating point to the maximum power point. The shaded rectangle has area \(V_{mp}J_{mp}\) and the dashed rectangle has area \(V_{oc}J_{sc}\); their ratio is the fill factor. Click or drag on the graph to move the operating point along the curve; the dotted line is the load line for the external resistance that gives that operating point. The dashed gray curve is the same cell at standard test conditions (1000 W/m², 25 °C).
The solar spectrum view shows how incident sunlight is divided: photons with energy below the band gap pass through the cell, and photons above the band gap are absorbed but lose their excess energy \(E - E_g\) as heat.
The efficiency vs. band gap view sweeps the band gap for the present settings and compares the result with an ideal cell.
The current density at cell voltage \(V\) satisfies
\[ J = J_{ph} - J_0\left[\exp\!\left(\frac{q\,(V + J R_s)}{n k_B T}\right) - 1\right] - \frac{V + J R_s}{R_{sh}} \]This equation is implicit in \(J\) and is solved numerically at each voltage.
Sunlight is approximated as a blackbody at \(T_s = 5778\) K, scaled so its total irradiance equals \(G\):
\[ \Phi(E) = A\,\frac{E^2}{\exp(E/k_B T_s) - 1} \] \[ \int_0^\infty E\,\Phi(E)\,dE = G \]Each absorbed photon with energy above the band gap contributes one electron with probability EQE:
\[ J_{ph} = q\,\mathrm{EQE}\int_{E_g}^{\infty} \Phi(E)\,dE \]The band gap decreases with temperature (Varshni relation, with the silicon constants used for every material):
\[ E_g(T) = E_g(300\ \mathrm{K}) - \alpha\left(\frac{T^2}{T+\beta} - \frac{300^2}{300+\beta}\right) \]For an ideal cell (\(R_s = 0\), \(R_{sh}\to\infty\)), the open-circuit voltage is
\[ V_{oc} = \frac{n k_B T}{q}\ln\!\left(\frac{J_{ph}}{J_0} + 1\right) \]The ideal cell in the efficiency vs. band gap view has \(n = 1\), \(R_s = 0\), \(R_{sh}\to\infty\), and EQE = 1.
Of the incident power, the part with \(E < E_g\) is not absorbed, the fraction
\[ \frac{1}{G}\int_{E_g}^\infty (E - E_g)\,\Phi\,dE \]is lost as heat (thermalization), and the fraction
\[ \frac{E_g}{G}\int_{E_g}^\infty \Phi\,dE \]remains at the band-gap energy. The cell efficiency is lower than this last fraction because \(qV_{oc} < E_g\), \(FF < 1\), and EQE < 1.
A blackbody spectrum is used instead of the AM1.5G reference spectrum, so short-circuit currents differ from measured values by several percent. The \(J_0\) expression is empirical, and all materials share the same temperature coefficients. The model shows trends; it does not predict the performance of a specific device.
| \(A\) | spectrum scaling constant |
| \(E\) | photon energy (eV) |
| \(E_g\) | semiconductor band gap (eV) |
| EQE | external quantum efficiency (electrons collected per absorbed photon) |
| \(FF\) | fill factor |
| \(G\) | irradiance, incident solar power per area (W/m²) |
| \(J\) | cell current density (A/cm²) |
| \(J_0\) | diode saturation current density (A/cm²) |
| \(J_{mp}\) | current density at maximum power (A/cm²) |
| \(J_{ph}\) | photocurrent density (A/cm²) |
| \(J_{sc}\) | short-circuit current density (A/cm²) |
| \(k_B\) | Boltzmann constant, \(8.617\times10^{-5}\) eV/K |
| \(n\) | diode ideality factor |
| \(P\) | power density (W/cm²) |
| \(P_{max}\) | maximum power density (W/cm²) |
| \(q\) | elementary charge (C) |
| \(R_s\) | series resistance (Ω·cm²) |
| \(R_{sh}\) | shunt resistance (Ω·cm²) |
| \(T\) | cell temperature (K) |
| \(T_s\) | sun surface temperature, 5778 K |
| \(V\) | cell voltage (V) |
| \(V_{mp}\) | voltage at maximum power (V) |
| \(V_{oc}\) | open-circuit voltage (V) |
| \(\alpha\) | Varshni constant, \(4.73\times10^{-4}\) eV/K |
| \(\beta\) | Varshni constant, 636 K |
| \(\eta\) | cell efficiency |
| \(\Phi\) | photon flux per unit photon energy (m⁻² s⁻¹ eV⁻¹) |
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.