Solar Panels: From Photon to Watt

Every standard silicon solar cell converts sunlight using a 1.1 eV bandgap p-n junction — a choice that is near-optimal for the solar spectrum. But fundamental thermodynamics sets an absolute efficiency ceiling of 33% for single-junction cells. Understanding why requires following a photon from the moment it enters the silicon to the moment it drives current.

1. The Solar Spectrum and AM1.5

The Sun emits as a blackbody at ~5778 K. The total power reaching Earth's upper atmosphere is the solar constant: S₀ = 1361 W/m².

After passing through 1.5 atmospheres of air (AM1.5 standard), the surface irradiance is ~1000 W/m², with significant absorption bands from O₂, O₃, H₂O, and CO₂. The spectrum spans UV (300 nm) through visible to near-infrared (~2500 nm).

Photon energy: E_ph = hf = hc/λ UV (λ = 300 nm): E = 4.1 eV Green (λ = 550 nm): E = 2.3 eV Red (λ = 700 nm): E = 1.77 eV NIR (λ = 1100 nm): E = 1.13 eV \leftarrow near Si bandgap IR (λ = 2500 nm): E = 0.50 eV \leftarrow below Si bandgap ~52% of solar energy is in the infrared (λ > 700 nm)

2. Semiconductor Bandgap and Photon Absorption

A semiconductor has an energy gap E_g between the valence band (filled) and conduction band (empty). When a photon with energy E_ph > E_g is absorbed, it promotes an electron to the conduction band, leaving a hole in the valence band.

Silicon bandgap: E_g = 1.12 eV at 25°C (indirect gap). This means:

Photons with λ < 1100 nm → absorbed, generate electron-hole pairs
Photons with λ > 1100 nm → pass through — silicon is transparent to them
Photons with E_ph >> E_g → absorbed, but excess energy (E_ph − E_g) lost as heat (thermalisation)

Beer-Lambert absorption: I(x) = I₀ \cdot exp(-αx) α = absorption coefficient (depends strongly on λ and material) Si at 600 nm: α \approx 10⁴ cm⁻¹ \to 90% absorbed in ~230 μm Si at 900 nm: α \approx 10² cm⁻¹ \to 90% absorbed in ~23 mm (need light trapping!) GaAs (direct gap, E_g = 1.42 eV): At 850 nm: α \approx 10⁵ cm⁻¹ \to 90% absorbed in ~23 μm (far thinner)

3. The p-n Junction: Built-in Electric Field

A solar cell is a large-area p-n junction. The n-type layer (phosphorus-doped, electron-rich) sits on top of the p-type base (boron-doped, hole-rich). At the junction, electrons and holes diffuse across and recombine, leaving behind:

A depletion region (width W ≈ 0.5–1 μm) with no free carriers
A built-in electric field E pointing from n to p
A built-in potential V_bi ≈ 0.6–0.7 V for silicon

When light generates an electron-hole pair near the junction, the built-in field sweeps electrons toward n-side and holes toward p-side — creating a current without any external voltage.

Ideal diode (Shockley) equation: I = I_L - I₀(exp(qV/nk_BT) - 1) I_L = photogenerated current (\propto irradiance) I₀ = dark saturation current (~10⁻¹⁰ A for Si) n = ideality factor (1 for ideal, 1-2 real) q = electron charge, k_B = Boltzmann, T = temperature Open-circuit voltage (I = 0): V_oc = (nk_BT/q) \cdot ln(I_L/I₀ + 1) \approx (0.026 V) \cdot ln(I_L/I₀) at 300 K

4. I-V Curve, Fill Factor, and Efficiency

The I-V (current-voltage) curve of a solar cell under illumination sweeps from short-circuit current I_sc (at V=0) to open-circuit voltage V_oc (at I=0). Maximum power is extracted at the maximum power point (MPP).

Fill Factor: FF = P_max / (I_sc \cdot V_oc) = (I_mp \cdot V_mp) / (I_sc \cdot V_oc) FF for good Si cell: 0.75-0.85 Conversion efficiency: η = P_max / P_in = (I_sc \cdot V_oc \cdot FF) / (1000 W/m² \cdot A_cell) Commercial Si: η = 19-23% Lab record Si: η = 29.4% (LONGi, 2023, HJT) Multi-junction: η = 47.6% (under 665 suns concentration, III-V, 2022)

Temperature coefficient: Solar cell efficiency drops with temperature. For silicon: dη/dT ≈ −0.4%/°C relative. A panel at 70°C (typical rooftop) loses ~20% relative efficiency vs 25°C rating. This is why concentrator systems must cool their cells.

5. The Shockley-Queisser Limit (33%)

In 1961, Shockley and Queisser derived the fundamental efficiency limit for a single-junction solar cell under the AM1.5 spectrum: ~33%. This is not an engineering limit — it's thermodynamic, arising from three unavoidable losses:

−23%

Sub-bandgap photons — photons with E < E_g pass through unabsorbed (~23% of solar energy for Si 1.1 eV)

−33%

Thermalisation — photons with E >> E_g generate one electron-hole pair but excess energy E_ph − E_g lost as heat

−11%

Radiative recombination — detailed balance requires some photon re-emission (unavoidable); limits V_oc

Optimal single-junction bandgap: E_g ≈ 1.1–1.4 eV (maximises the SQ limit area) Si (1.12 eV) → SQ limit 33% GaAs (1.42 eV) → SQ limit 33% Ge (0.67 eV) → SQ limit 23% (too small: thermalisation wins) GaN (3.4 eV) → SQ limit 15% (too large: sub-bandgap loss wins) SQ efficiency: η_SQ = (∫_{E_g}^∞ N(E)dE · qV_oc_max · FF_ideal) / ∫₀^∞ E·N(E)dE

6. Why Real Cells Are Less Efficient

Commercial cells are well below the SQ limit due to additional loss mechanisms:

Loss Mechanism	Typical Impact	Mitigation
Reflection from front surface	~4% (bare Si) → ~1% (AR coated)	SiN₄ anti-reflection coating, textured surface
Surface recombination	High J₀ → lower V_oc	Passivation layers (SiO₂, Al₂O₃, amorphous Si)
Bulk recombination	Short minority carrier lifetime	Float-zone Si (purer), passivated emitter rear cell (PERC)
Series resistance	Lowers FF (0.85 → 0.75)	Fine grid fingers, silver paste sintering, laser doping
Shunt resistance	Low R_sh pulls down V_oc	Manufacturing cleanliness, avoid edge shorts
Metal shadowing	~5% of front surface	Fine-line printing, bifacial cells, transparent electrodes

7. Multi-Junction Cells: Breaking the Limit

Stack multiple p-n junctions with different bandgaps — each absorbs the part of the spectrum where it is most efficient. Subcells are connected in series; each absorbs progressively lower-energy photons.

Triple-junction example (InGaP/GaAs/Ge): Top subcell: InGaP E_g = 1.85 eV \to absorbs UV/blue Middle subcell: GaAs E_g = 1.42 eV \to absorbs visible Bottom subcell: Ge E_g = 0.67 eV \to absorbs NIR Theoretical limit for N junctions under full concentration: N=1: 40.7%, N=2: 55.0%, N=3: 63.8% N\to\infty: 86.8% (Carnot-like limit for full-spectrum concentration) Current records (NREL, 2026): Si single-junction: 29.4% (HJT, LONGi) 2-junction (GaAs/Si): 35.9% 3-junction (III-V): 37.9% (1 sun), 47.6% (665\times concentration)

Key challenges for multi-junction: lattice matching between layers (crystal defects at interfaces), current matching between subcells (series connection means limited by the lowest-current subcell), and cost of epitaxial III-V growth (~100× more expensive than Si per area).

Perovskites: ABX₃ compounds (e.g., MAPbI₃, E_g tunable 1.2–2.3 eV) are revolutionising multi-junction. A 2-terminal perovskite/Si tandem reached 33.9% (Helmholtz-Zentrum, 2023). Main challenge: stability under UV, moisture, and thermal cycling.

8. Economics: LCOE and the Cost Revolution

Levelised Cost of Energy (LCOE) = total lifetime costs / total lifetime energy produced. Solar LCOE has fallen ~90% per decade since 1980:

Year	Module cost ($/Wp)	LCOE utility solar
1980	~$20/Wp	—
2000	~$4.50/Wp	~$300/MWh
2010	~$1.80/Wp	~$150/MWh
2020	~$0.25/Wp	~$35/MWh
2025	~$0.10/Wp	$15–25/MWh (best sites)

Solar is now the cheapest source of electricity in history at good locations. The learning rate (Swanson's Law) is ~20% cost reduction per doubling of cumulative production — similar to Moore's Law but for manufacturing cost rather than transistor density.

LCOE (simplified): LCOE = (C_capex · CRF + C_opex) / (CF · 8760 h/yr) CRF = capital recovery factor = r(1+r)ⁿ / ((1+r)ⁿ − 1) CF = capacity factor (fraction of time at rated power) CF_solar ≈ 0.15–0.30 (location dependent) Example: 1 GW plant, $0.50/W installed, 25yr, 7% discount rate, CF=0.22: CRF = 0.086, LCOE ≈ $0.086 × 0.5B / (0.22 × 8760 × 1000 MWh) ≈ $22/MWh