Solar Spectrum Simulator: Understand Photon Energy & PV Limits

simulator beginner ~8 min
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~33.7% Shockley-Queisser limit for Si at 1.12 eV

Silicon with a 1.12 eV bandgap can absorb roughly 65% of solar photons by number, but thermalization and sub-bandgap losses limit single-junction efficiency to about 33.7%. The peak solar wavelength at 5778 K is ~502 nm (green), explaining why the spectrum appears white.

Formula

Wien's displacement law: λ_max = 2.898 × 10⁶ / T (nm)
Photon energy: E = hc/λ = 1240/λ(nm) eV
Shockley-Queisser limit: η_SQ ≈ 33.7% at Eg = 1.34 eV under AM1.5

The Sun as a Blackbody

The sun radiates approximately as a blackbody at 5778 K, producing a broad spectrum that peaks in the green-yellow region around 502 nm. Wien's displacement law governs this peak: hotter stars peak at shorter wavelengths. The total power output follows the Stefan-Boltzmann law, delivering roughly 1361 W/m² at Earth's orbital distance before atmospheric absorption reduces it to about 1000 W/m² at sea level under standard conditions.

Bandgap and Spectral Mismatch

A semiconductor with bandgap Eg can only absorb photons carrying energy of at least Eg electron-volts. For silicon (Eg = 1.12 eV), this means wavelengths shorter than about 1100 nm. Photons with less energy sail through the material. Photons with more energy excite electrons far above the conduction band edge, but the excess energy is immediately lost as lattice heat. This double penalty — sub-bandgap transparency and above-bandgap thermalization — is the core physics behind the Shockley-Queisser limit.

Atmospheric Filtering

Earth's atmosphere absorbs and scatters sunlight selectively. Ozone blocks most UV below 300 nm. Water vapor and CO₂ carve deep absorption notches in the infrared. Rayleigh scattering removes short wavelengths preferentially, which is why direct sunlight reddens at sunrise and sunset (high air mass). The AM1.5 standard spectrum accounts for all these effects to give solar engineers a consistent reference for rating cell performance.

From Spectrum to Current

This simulation lets you adjust the semiconductor bandgap and atmospheric conditions to see how much of the solar spectrum a cell can actually harvest. Move the bandgap slider to watch the usable fraction change. Increase air mass to simulate low sun angles. The Shockley-Queisser limit readout shows the theoretical ceiling for each configuration, revealing why material scientists obsess over bandgap engineering and why multi-junction architectures exist.

FAQ

Why can't a solar cell use all sunlight?

A solar cell with bandgap Eg can only absorb photons with energy ≥ Eg. Photons with less energy pass through. Photons with more energy lose the excess as heat (thermalization). This spectral mismatch is the fundamental reason single-junction cells are limited to ~33.7% efficiency.

What is the AM1.5 solar spectrum?

AM1.5 (Air Mass 1.5) is the standard reference spectrum used to rate solar cells. It represents sunlight after passing through 1.5 atmospheres of air, corresponding to a solar zenith angle of about 48.2°. The total irradiance under AM1.5G (global) conditions is defined as 1000 W/m².

What is the optimal bandgap for a solar cell?

The Shockley-Queisser analysis shows the optimal single-junction bandgap is about 1.34 eV, yielding a theoretical maximum efficiency of 33.7%. Silicon at 1.12 eV is slightly below optimal but benefits from abundant material, mature manufacturing, and a theoretical limit of about 32%.

How do multi-junction cells beat the SQ limit?

Multi-junction cells stack semiconductors with decreasing bandgaps. The top cell captures high-energy photons, letting lower-energy ones pass through to cells beneath. A triple-junction cell (e.g., GaInP/GaAs/Ge) can exceed 47% in the lab by reducing both sub-bandgap transmission and thermalization losses.

Sources

Embed

<iframe src="https://homo-deus.com/lab/photovoltaics/solar-spectrum/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub