The Shockley–Queisser Limit

Introduction

Even a flawless single-band-gap solar cell cannot turn all sunlight into electricity. Sunlight contains photons of many energies, whereas one semiconductor has one principal absorption threshold. Photons below that threshold cannot make ordinary band-to-band carriers; energy well above it is mostly lost after excitation. A cell must also emit some light by radiative recombination. The Shockley–Queisser analysis combines these idealized constraints to set a benchmark, not a prediction that every real cell will reach it.

Core explanation

The Shockley–Queisser limit is a detailed-balance result for an idealized single-junction device under specified illumination and temperature. Common statements place the maximum near one third of incident power for unconcentrated terrestrial sunlight, with the precise number depending on spectrum and assumptions. DOE's multijunction research overview quotes about 33.5% for a single-band-gap cell under its stated non-concentrated conditions. The result is a model-bound limit, not an absolute law applying to all optical concentration, tandem, hot-carrier or multiple-exciton architectures.

The first major loss is sub-gap transmission . If photon energy E < E g, it cannot produce the ideal band-to-band excitation and generally passes through or is otherwise unusable. Lowering E g captures more of these photons, raising possible photocurrent. But a smaller gap usually lowers the energy scale of the output voltage. The second major loss is thermalization : above-gap photons generate a carrier pair, yet energy E − E g typically relaxes as heat before extraction. Raising E g reduces this excess-energy loss per absorbed high-energy photon, but rejects more low-energy light. An optimum gap balances current and voltage for the chosen spectrum.

The third essential loss is radiative recombination . An ideal absorber that absorbs light can also emit through the reverse process. At open circuit, generation is balanced by recombination; under load, recombination reduces collected carriers and voltage. Detailed balance connects absorption and emission, so an assumed cell with strong absorption but zero radiative emission is not a physically consistent ordinary ideal diode. DOE's solar-energy basic-research report describes the one-pair-per-photon and excess-energy-loss assumptions in its discussion of the single-junction limit.

The ideal model excludes many real-world losses: nonradiative defect recombination, incomplete absorption, reflection, series resistance, shunt leakage, contact barriers and parasitic absorption. Those lower actual efficiency below the ideal benchmark. Conversely, reporting that a tandem exceeds roughly 33% does not violate the limit, because a tandem uses more than one band gap and therefore changes the assumptions. DOE's photovoltaic research directions explains how different stacked layers collect different parts of the spectrum.

The limit applies to power conversion efficiency under defined illumination, not to fraction of photons counted or to an individual spectral response value. A cell can have near-100% external quantum efficiency at one wavelength yet much lower overall power efficiency across sunlight. A band gap alone does not give the efficiency; one needs the spectrum, temperature and a device model. The commonly quoted percentage is best used as a reference for diagnosing remaining avoidable losses, not as a universal comparison across unlike test conditions.

Several approaches aim beyond single-junction constraints. Tandems send high-energy photons to a higher-gap top cell and lower-energy photons to a lower-gap bottom cell, reducing both transmission and thermalization. Concentration changes the balance of photon flux and emission. Hot-carrier extraction or multiple-exciton generation would change how above-gap energy is used. Each requires additional materials and device engineering; an ideal-limit possibility does not prove a practical, durable module.

Step-by-step reasoning

State the illumination spectrum, concentration, temperature and one-junction assumption. Divide incident photons into below-gap and above-gap groups. For absorbed above-gap photons, count no more than one ordinary electron–hole pair and recognize thermalization of excess energy. Include radiative recombination required by detailed balance. Optimize E g for output power rather than maximum current alone. Compare a real cell with the ideal only after identifying its additional optical, transport and nonradiative losses.

Visual explanation

Draw the solar photon-energy spectrum and a vertical line at E g. Shade low-energy photons left of the line as transmitted and the excess energy above E g for high-energy photons as thermalized. A third arrow from the cell outward represents radiative emission. Next plot ideal conversion efficiency against band gap as a broad peak: small gaps lose voltage, large gaps lose current. A tandem sketch with two thresholds demonstrates why its ideal limit can differ.

Real-world analogy

Imagine a factory with one standard container size. Items too small cannot trigger its machine, while oversized items are trimmed to fit, wasting material. A different container size trades the two losses. A two-stage factory with different container sizes can use the input more efficiently. The analogy conveys spectral mismatch, but radiative recombination is a separate physical requirement that has no simple container equivalent.

Real-world example

A researcher measures a 27% single-junction cell under a calibrated standard spectrum. The number is below the ideal benchmark, but the remaining gap should not be attributed entirely to defects. Some loss is fundamental transmission, thermalization and radiative emission already included in the ideal limit; additional voltage and fill-factor deficits may come from nonradiative recombination and resistance. Measuring external quantum efficiency, luminescence and current–voltage response helps separate them.

Why?

Why does a lower band gap not always increase efficiency even though it absorbs more sunlight? It increases available photon count but lowers the voltage scale, and above-gap photons then lose more of their energy as heat. Power is current times voltage, so an increase in one can be outweighed by a decrease in the other. The optimal gap depends on the illumination spectrum and device assumptions.

Common misconception

“The Shockley–Queisser limit says no solar cell can exceed 33%.” It concerns a specified ideal single-junction architecture, not tandems or changed operating conditions. Another misconception says only manufacturing defects create the limit; spectral mismatch and radiative recombination remain even in the ideal model. A third treats the quoted percentage as exact regardless of spectrum, temperature or concentration.

Worked example

Consider a simplified two-photon illustration with a 1.4 eV gap. One 1.0 eV photon is below the gap and cannot make an ordinary band-to-band pair. One 2.4 eV photon can make one pair, but about 2.4 − 1.4 = 1.0 eV of its initial energy is above the gap and normally thermalizes. Total incident photon energy is 3.4 eV, and at most 1.4 eV is represented by the band-gap energy of one generated pair before voltage and recombination losses. That illustrative ratio is 1.4/3.4 ≈ 41% , not a Shockley–Queisser efficiency calculation; it simply shows two spectral-loss mechanisms in a tiny artificial spectrum.

Quick check

1. Does a two-junction tandem exceeding the usual single-junction benchmark contradict the Shockley–Queisser analysis? Answer: No. The tandem has two band gaps and therefore does not satisfy the single-junction assumptions behind that benchmark.

Exam focus

List sub-gap transmission, above-gap thermalization and radiative recombination as the main ideal mechanisms. State the one-pair-per-absorbed-photon and single-band-gap context. Explain the current–voltage trade-off when changing E g. Distinguish extra real-device losses from those already included in the ideal model, and qualify numerical limits by illumination conditions.

Advanced insight

Detailed balance links a strong absorber to an emitter through optical reciprocity. This means luminescence is not merely a nuisance: comparing measured emission and the radiative ideal can quantify avoidable nonradiative voltage loss. NREL analysis of solar-cell quality uses the radiative-limit concept in evaluating voltage. Optical concentration or photon recycling changes the photon balance and can modify the ideal outcome, so a single quoted percentage should never be detached from its boundary conditions.

Summary

The Shockley–Queisser benchmark captures the unavoidable spectral and radiative losses of an ideal single-junction solar cell under specified conditions. One gap cannot absorb low-energy photons and use all high-energy photon energy at once. Real cells have further losses, while tandems and other changed architectures can exceed the usual single-junction benchmark without contradiction.

Practice questions

1. What happens to an ideal 0.9 eV photon in a semiconductor with a 1.3 eV band gap? Answer: It is below the gap and normally cannot produce a band-to-band electron–hole pair.

2. What is thermalization loss for an absorbed 2.2 eV photon in an idealized 1.5 eV gap absorber? Answer: Approximately 0.7 eV of energy lies above the gap and normally relaxes as heat before extraction.

3. Why is radiative recombination included even in an ideal solar-cell limit? Answer: Absorption and emission are reverse optical processes; detailed balance requires radiative recombination in an ordinary absorbing junction.

4. Which change can allow a device to exceed the usual single-junction limit? Answer: Stacking two absorbers with different band gaps in a tandem changes the spectral-use assumptions.

5. Why is the usual approximate 33% value not a universal exact constant? Answer: It depends on illumination spectrum, concentration, temperature and ideal-model assumptions.