Shockley–Queisser Efficiency Limit Calculator
Introduction: using the Shockley–Queisser detailed-balance calculator
This Shockley–Queisser limit calculator estimates the detailed-balance ceiling for a single-junction solar cell from three physical inputs: absorber band gap, source temperature, and cell temperature. It is built to answer the "what is the best possible efficiency?" question, not the "what will this real module do in the field?" question, so the result should be read as a theoretical benchmark.
That distinction matters because the Shockley–Queisser limit is most useful when you are comparing candidate band gaps, checking how much a hotter cell hurts the ceiling, or asking whether a material sits near the spectrum-matching sweet spot. A change that looks small on paper can move the detailed-balance result noticeably, especially when the absorber is already close to the optimum for the source spectrum.
The sections below explain what each field means, how the page turns those values into efficiency, and how to treat the output as a screening tool rather than a device guarantee. If you keep that boundary in mind, the calculator becomes a fast way to organize design choices without stepping through the radiative physics by hand every time.
What question does this Shockley–Queisser calculator answer?
The Shockley–Queisser calculator answers a narrow photovoltaic question: for a single absorbing junction under radiative-limit assumptions, how much power conversion efficiency is theoretically available? That helps when you are screening absorber materials, deciding whether a band gap is too narrow or too wide, or checking how much a hotter operating point may pull the ceiling downward.
It is also useful as a consistency check. If two designs differ only in band gap, the detailed-balance limit lets you see how the current-voltage tradeoff shifts before you spend time on a full device model. If the result surprises you, the first place to look is usually the assumptions behind the band gap and temperature inputs, not a hidden setting somewhere else on the page.
How to use this Shockley–Queisser calculator
- Enter Band gap energy E g (eV) using the unit shown beside the field.
- Enter Sun temperature T sun (K) as the source temperature for the incoming spectrum.
- Enter Cell temperature T cell (K) as the operating temperature of the junction.
- Submit the form to recalculate the detailed-balance ceiling and refresh the results panel.
- Read the current, voltage, fill factor, and efficiency together before comparing one absorber or operating point against another.
If you are checking several candidate materials, keep a note of the exact band gap and temperatures for each run. That makes it easier to return to the same Shockley–Queisser scenario later and confirm that you are comparing the same assumptions, not a slightly different setup.
Inputs: choosing Shockley–Queisser band-gap and temperature values
Choosing inputs for the Shockley–Queisser model is mostly about keeping the energy and temperature scales consistent with the physics of a single-junction solar cell. The calculator expects band gap in electronvolts and temperatures in kelvin, and the result can move quite a lot if you mix up the source spectrum, the device temperature, or the absorber threshold.
- Units: keep the band gap in eV and both temperatures in K so the detailed-balance expressions line up with the model.
- Ranges: stay within the field limits on the page; values far outside those limits may be mathematically entered but are not a helpful way to study a solar-cell ceiling.
- Defaults: the prefilled values are a starting point for the built-in example, not a substitute for your own absorber and temperature assumptions.
- Consistency: make sure the band gap, source temperature, and cell temperature all describe the same physical case before you compare results.
Common inputs for Shockley–Queisser limit studies include:
- Band gap energy E g (eV): the absorber threshold that decides which photons can contribute to current generation.
- Sun temperature T sun (K): the blackbody source temperature used to describe the incoming solar spectrum in this idealized model.
- Cell temperature T cell (K): the junction temperature that affects radiative loss and the voltage the device can sustain.
When you are unsure about an input, hold the temperatures fixed and change only the band gap first. That isolates the absorber effect, which is usually the quickest way to see whether the efficiency shift comes from better spectral matching or from a tradeoff that moves in the wrong direction.
Calculation method: how the Shockley–Queisser limit is estimated
The Shockley–Queisser calculation starts by counting photons above the band gap in the source spectrum and in the cell’s own thermal emission. That gives the model enough information to estimate short-circuit current and dark current without making you assemble the radiative integrals by hand.
From those currents, the calculator derives an open-circuit voltage, estimates the fill factor, and divides the output power by the incident power to produce efficiency. The result is the classic detailed-balance ceiling for a single junction: a best-case number that leaves out nonradiative losses, resistive losses, reflection, and other device-specific penalties.
Because the source and cell temperatures appear directly in the current balance, hotter cells usually lose voltage headroom, while band gaps that are too small or too large move the efficiency away from the optimum for the source spectrum. That is why the output is most useful as a design screen, not as a promise of real-world module performance.
Worked example: reading the default Shockley–Queisser setup
The prefilled values on this page form a quick baseline for the Shockley–Queisser model. Leave the band gap at 1.34 eV, the source temperature at 5778 K, and the cell temperature at 300 K, then submit the form to see the current, voltage, fill factor, and efficiency that the script calculates for that specific case.
Use that first run as a reference point. If you lower the band gap after that, you should expect the current side of the calculation to improve while the voltage side weakens; if you raise the band gap, the opposite tradeoff appears. That makes the worked example useful even before you change any values, because it shows how the model responds when only one physical lever moves.
Band-gap sensitivity: comparing Shockley–Queisser scenarios
The table below changes only the absorber band gap, so the temperatures stay fixed and the comparison stays focused on the current-voltage tradeoff. The point is not to invent a pseudo-score, but to show which direction the detailed-balance limit usually moves as the gap narrows or widens.
| Scenario | Band gap energy E g (eV) | Other inputs | What changes most | Interpretation |
|---|---|---|---|---|
| Conservative (-20%) | 1.072 | Unchanged | More current, less voltage | A narrower gap captures more photons, but the voltage ceiling usually drops. |
| Baseline | 1.34 | Unchanged | Reference case | Use this as the comparison point for nearby absorber choices. |
| Aggressive (+20%) | 1.608 | Unchanged | Less current, more voltage headroom | A wider gap can improve voltage, but the current loss can dominate if the spectrum no longer matches well. |
If your goal is to maximize current, the narrower-gap row may look tempting; if you need more voltage, the wider-gap row may be attractive. The calculator helps you see where the balance starts to flip, which is usually the most important question when you are screening candidate absorbers.
How to interpret a Shockley–Queisser efficiency result
The result panel condenses the detailed-balance run into four numbers: short-circuit current, open-circuit voltage, fill factor, and efficiency. Read them together. A high current with a weak voltage may still leave the efficiency below a slightly more balanced design.
After the calculator updates, verify that the temperatures are in kelvin, that the band gap is in electronvolts, and that the magnitude still makes sense for a single-junction theoretical ceiling. If the direction of change looks backwards, the most common cause is an input mix-up rather than a problem with the model.
For a quick record of the current run, use the Copy summary button after the calculation finishes. It captures the key values without adding another feature or export format to the page.
Limitations and assumptions in the Shockley–Queisser model
The Shockley–Queisser limit is intentionally idealized, so the calculator leaves out many effects that matter in real devices.
- Input interpretation: the band gap field refers to the absorber threshold in the detailed-balance model, not to a wiring parameter or an external control value.
- Unit conversions: convert any source measurements to eV and kelvin before entering them; the calculator does not infer Celsius, joules, or mixed-unit shortcuts.
- Linearity: the limit is highly sensitive near the band gap that best matches the source spectrum, so small changes can move the efficiency more than you expect.
- Rounding: displayed values are rounded for readability, so a tiny mismatch with hand calculations is normal.
- Missing factors: nonradiative recombination, optical reflection, series resistance, concentration effects, tandem stacks, and device-specific transport losses are outside this single-junction ceiling.
Treat the result as a theoretical benchmark. If you need a measured performance forecast, compare the calculator’s output with experimental data or a more detailed device model. The useful role of this page is to show the ideal upper bound clearly, so you can see how far a candidate band gap and operating temperature sit from the best case.