Solar Panels: From Photon to Watt

Silicon's 1.1 eV bandgap is (almost) optimal

The Sun radiates as a roughly 5778 K blackbody, delivering a solar constant of 1361 W/m² at the top of the atmosphere and about 1000 W/m² at the surface after passing through 1.5 atmospheres of air (the AM1.5 reference spectrum). A photon's energy is E = hc/λ: green light (550 nm) carries 2.3 eV, red light (700 nm) carries 1.77 eV, and roughly 52% of solar energy arrives at wavelengths longer than 700 nm, down in the infrared. Silicon's bandgap of E_g = 1.12 eV sits close to the sweet spot: photons with wavelength below ~1100 nm are absorbed and generate an electron-hole pair, while longer-wavelength photons simply pass through the crystal unabsorbed.

Photon absorption and the p-n junction

A photon with energy above the bandgap promotes an electron from the valence band to the conduction band, leaving a hole behind. How deep that absorption happens depends on the absorption coefficient α in the Beer-Lambert law I(x) = I₀·exp(−αx): silicon at 600 nm absorbs 90% of light within about 230 μm, but at 900 nm — close to its bandgap — it needs roughly 23 mm, which is why silicon cells rely on light-trapping textured surfaces. A solar cell itself is a large-area p-n junction: an electron-rich, phosphorus-doped n-type layer sits over a hole-rich, boron-doped p-type base. Diffusion across the junction leaves behind a depletion region roughly 0.5-1 μm wide and a built-in potential of about 0.6-0.7 V for silicon. When light generates an electron-hole pair near this junction, the built-in field sweeps electrons to the n-side and holes to the p-side — producing current with no external voltage applied.

I-V curve, fill factor and real-world efficiency

A cell under illumination follows the ideal diode equation, sweeping from short-circuit current I_sc down to open-circuit voltage V_oc. The fraction of that rectangle actually captured at the maximum power point is the fill factor, typically 0.75-0.85 for a good silicon cell.

I = I_L − I₀(exp(qV/nk_BT) − 1)
FF = P_max / (I_sc · V_oc)
η = (I_sc · V_oc · FF) / (1000 W/m² · A_cell)

Commercial silicon: η = 19–23%
Lab record silicon: η = 29.4% (LONGi, HJT, 2023)
Temperature coefficient: dη/dT ≈ −0.4%/°C — a 70°C rooftop panel
loses ~20% of its 25°C-rated efficiency

The Shockley-Queisser limit — a thermodynamic ceiling

In 1961 Shockley and Queisser derived the maximum possible efficiency of a single-junction cell under the AM1.5 spectrum: about 33%. This is not an engineering shortfall to be fixed with better manufacturing — it is thermodynamic, built from three unavoidable losses: roughly 23% of solar energy sits below the bandgap and is never absorbed; about 33% is lost to thermalisation, where photons far above the bandgap dump their excess energy as heat; and around 11% is lost to radiative recombination, which detailed balance requires and which caps V_oc. The optimal single-junction bandgap sits between 1.1 and 1.4 eV — silicon (1.12 eV) and gallium arsenide (1.42 eV) both land near the 33% ceiling, while germanium (0.67 eV) tops out around 23% because thermalisation dominates, and wide-gap GaN (3.4 eV) tops out near 15% because sub-bandgap loss dominates.

Multi-junction cells: stacking bandgaps to beat the limit

Stacking several p-n junctions of different bandgaps in series lets each subcell absorb the part of the spectrum it handles best. A triple-junction stack of InGaP (1.85 eV, absorbs UV/blue), GaAs (1.42 eV, absorbs visible) and germanium (0.67 eV, absorbs near-infrared) pushes the theoretical limit for three junctions to 63.8% under full concentration, with the limit rising toward 86.8% as junction count grows toward infinity. Real records already exceed single-junction physics: a two-junction GaAs/Si stack reaches 35.9%, and a three-junction III-V cell reaches 47.6% under 665x concentration. The trade-offs are lattice matching between layers, current matching in series (the stack is limited by its weakest subcell), and roughly 100x higher cost per area for epitaxial III-V growth than plain silicon — though perovskite/silicon tandems, which reached 33.9% in 2023, are narrowing that cost gap.

Economics: LCOE and the cost revolution

Levelised cost of energy (LCOE) — total lifetime cost divided by total lifetime energy produced — has fallen roughly 90% per decade since 1980, from about $20 per watt then to near $0.10 per watt in 2025, dragging utility-scale solar LCOE down from roughly $300/MWh in 2000 to $15-25/MWh at the best sites today. That makes solar the cheapest source of electricity in history at good locations. The trend is known as Swanson's Law: roughly a 20% cost reduction for every doubling of cumulative production, the solar-manufacturing equivalent of Moore's Law.

Frequently asked questions

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Everything above runs in your browser — open Solar Panel Simulator and sweep latitude, day of year, tilt and azimuth to see the daily power curve and the optimal-tilt readout update in real time. Nothing is installed, nothing is uploaded.