How Solar Panels Work
A sheet of glass with no moving parts, sitting still on a roof, quietly pushing electrons around a circuit for thirty years. Here is the trick it is playing.
Sunlight in, electricity out
Junior level — plain language, no maths
A solar panel has no moving parts. Nothing spins, nothing burns, nothing is pushed. You put it in the sun and electricity comes out of the wire at the back - and it keeps doing that for three decades while you ignore it completely. It is the strangest machine on the house.
The trick happens inside a wafer of silicon thinner than a fingernail. Light does not arrive as a smooth stream; it arrives in tiny packets called photons. When a photon lands in the silicon it can knock an electron loose from its atom, the way one snooker ball knocks another off its spot. Now there is a loose electron and an empty space where it used to sit. Left alone, the two would wander about and settle back together, and nothing useful would happen at all.
So the cell is built with a one-way street inside it. The top of the wafer is treated with one impurity and the bottom with another, and where the two meet an electric field appears all by itself. Any electron freed near that boundary gets shoved upward - always upward, never back. Millions of them pile up on the metal fingers you can see printed across the front, push out along the wire, run through your fridge and your lights, and come back in at the bottom of the cell. That circulation is the current.
Two things decide how much of it you get. The first is how much light lands: full midday sun delivers about 1000 watts on every square metre, so a two-square-metre panel stands in roughly 2000 watts of sunshine and hands back about 400 of them. The rest turns into heat. The second is the angle. Light striking the glass at a slant spreads itself thinner, exactly the way your shadow stretches long and weak in the evening. Point the panel straight at the sun and you collect all of it; tilt it forty-five degrees away and a third is gone. That one fact settles most arguments about how to mount a roof.
Things worth knowing
- No fuel, no moving parts, nothing to service. Panels installed in the 1990s are typically still delivering over 80% of their original power today.
- Heat is the enemy. A panel on a hot roof can reach 65 °C, and every degree above 25 costs it about 0.35% of its output. A panel's dream weather is cold, bright and clear - not hot.
- The Sun drops about 170 million gigawatts on the Earth. All of humanity uses roughly 20 terawatts - some 8000 times less. The shortage was never sunlight; it was cheap silicon, and that price has fallen about 99.9% since 1976.
The I-V curve, and the single point on it worth having
Student level — the core equations
A solar cell is not a battery, and it is not a fixed current source either. What it gives you depends on how hard you pull. Short the terminals together and you draw the full short-circuit current \(I_{sc}\) at zero volts - which is zero power. Leave them open and you measure the full open-circuit voltage \(V_{oc}\) at zero current - also zero power. Between those two useless extremes runs a curve, and on it sits exactly one point where the product \(P = VI\) is as large as it can be: the maximum power point.
The two ends of that curve answer to sunlight in completely different ways. Current is essentially a photon count, so double the irradiance and you free twice as many electrons: \(I_{sc}\) is very nearly proportional to \(G\). Voltage hardly notices, because it climbs only with the logarithm of the light, \(V_{oc} = nV_T\ln(I_{ph}/I_0 + 1)\). A cell in one tenth of full sun has lost 90% of its current and maybe 12% of its voltage. That is why a panel under heavy overcast still shows an almost full reading on a multimeter while producing next to nothing.
Temperature runs the other way, and it is the fact that surprises everyone. Warmth does not help a solar panel; it hurts. As silicon heats, the reverse saturation current \(I_0\) climbs steeply and drags \(V_{oc}\) down with it, at roughly \(-0.3\%\) per degree. The current creeps up by about \(+0.05\%\) per degree, nowhere near enough to compensate. The net is close to \(-0.35\%\) of power per degree above the 25 °C at which panels are rated - so a module baking at 65 °C on an August roof has already given up about a seventh of its output before a single wire is connected.
Which means the operating point has to be hunted, continuously. That is the whole job of the MPPT stage inside every modern inverter: it nudges the voltage up and down a few times a second, watches which way the power moved, and walks the panel back onto the peak as sun, cloud and temperature shove it around. A system without one - a panel wired straight onto a battery, say - is pinned near the battery's voltage and routinely throws away a quarter of the harvest.
Key Formulas
| Power from sunlight | \(P = G\,A\,\eta\) | G in W/m², A in m² |
|---|---|---|
| Short-circuit current | \(I_{sc} \propto G\) | a photon count |
| Open-circuit voltage | \(V_{oc} = nV_T\ln\!\left(\dfrac{I_{ph}}{I_0}+1\right)\) | only logarithmic in G |
| Maximum power point | \(P_{mpp} = V_{mp}I_{mp}\) | |
| Fill factor | \(FF = \dfrac{P_{mpp}}{V_{oc}I_{sc}}\) | ≈ 0.80 for silicon |
| Efficiency | \(\eta = \dfrac{P_{mpp}}{G\,A}\) | |
| Temperature derate | \(P(T) = P_{STC}\left[1+\gamma(T-25)\right]\) | γ ≈ −0.35 %/°C |
| Cosine law | \(G_{\perp} = G\cos\theta\) | θ = angle of incidence |
Things worth knowing
- Fill factor measures how square the curve is: the best point divided by Voc times Isc. Good silicon modules reach about 0.80, and it is resistance in those printed metal fingers that stops them going higher.
- A panel's best minutes of the year are often in winter: cold, clear, low sun, with light bouncing off snow. Under those conditions a module can briefly exceed its nameplate rating.
- One silicon cell makes only about 0.65 V, so cells are wired in series - a 60-cell module sits near 40 V open-circuit. The catch is that a series string runs at the speed of its worst cell, which is exactly why bypass diodes exist.
The one-diode model, the Shockley-Queisser ceiling, and what a real roof gives back
Scholar level — full mathematical depth
01A photodiode in the fourth quadrant
A solar cell is a large-area pn junction operated exactly where it has no business being: illuminated, with the photocurrent running against the diode's own forward current, so the working point sits in the fourth quadrant of the I-V plane - positive voltage, negative current - which is the signature of a device delivering power instead of absorbing it. By convention we flip the sign and draw the first quadrant. Absorption creates electron-hole pairs throughout the wafer; the built-in field separates the ones that reach the junction before they recombine; and the entire engineering problem is keeping the minority-carrier diffusion length comfortably longer than the distance a carrier must travel to get there.
02The one-diode model
Nearly everything a module does in the field is captured by \(I = I_{ph} - I_0\left[\exp\frac{q(V+IR_s)}{nkT}-1\right] - \frac{V+IR_s}{R_{sh}}\). Note that it is implicit in \(I\) - which is why datasheets quote points rather than functions, and why extracting parameters is a fit rather than an algebra. Series resistance \(R_s\) - fingers, busbars, solder, contacts - rounds off the knee and eats fill factor. Shunt resistance \(R_{sh}\), from edge leakage and defects across the junction, tilts the flat portion of the curve and is what dominates the losses at low light, when there is little photocurrent left to lose. The ideality factor \(n\) sits near 1 when diffusion in the quasi-neutral regions dominates, and drifts toward 2 when depletion-region recombination takes over.
03Where the ceiling comes from
Shockley and Queisser's 1961 argument is one of the great pieces of physics-as-accounting. Assume a single band gap, a black-body Sun, and radiative recombination as the only unavoidable loss. Photons below \(E_g\) pass straight through and are lost completely; photons above it are absorbed, but everything beyond \(E_g\) thermalises into heat within picoseconds. Those two losses pull in opposite directions as \(E_g\) varies, so there is an optimum: about 1.34 eV, worth 33.7% under one sun. Silicon's 1.12 eV gap gives 33.2%, and because that gap is indirect, absorption is weak enough that a cell needs roughly 150 µm of thickness plus a textured, light-trapping surface to catch the red end of the spectrum at all. The laboratory record for a single silicon cell now stands at 27.3% - about 82% of its own thermodynamic ceiling - while commercial modules ship at 21-23%.
04Temperature, derived rather than measured
The temperature coefficient is not an empirical fudge factor. Differentiating the open-circuit condition gives \(\frac{dV_{oc}}{dT} = \frac{V_{oc}-E_g/q-\gamma kT/q}{T}\), which for silicon near 300 K lands around \(-2.2\ \text{mV/K}\) per cell, or about \(-0.3\%/\text{K}\). The physics underneath is \(I_0 \propto n_i^2 \propto T^3e^{-E_g/kT}\): the dark current is the cell competing against itself, and it grows explosively with temperature. Short-circuit current does rise, by +0.04 to +0.06 %/K, because a warmer gap is a slightly narrower gap and a few more red photons become absorbable - but the voltage loss wins comfortably. Module temperature itself is usually estimated from \(T_c = T_a + \frac{\text{NOCT}-20}{800}G\), a crude linear model that survives contact with the real world surprisingly well.
05Mismatch, or why one leaf matters
Cells in series share a common current, so a string performs at the pace of its worst member. Shade one cell in sixty down to 30% of full sun and the string current collapses toward that cell's - and worse, the shaded cell is now reverse-biased by the other fifty-nine and dissipates their power as heat in one small square of silicon. That is a hot spot, and it is how early modules occasionally caught fire. Bypass diodes, one per twenty-odd cells, offer the current a detour: you lose a third of the module rather than all of it. The same arithmetic explains why module-level electronics - optimisers and microinverters - sell so well on complicated roofs, and why half-cut cells wired as two parallel halves became the industry default.
06From datasheet to electricity meter
Nameplate power is quoted at STC: 1000 W/m², 25 °C, AM1.5G - a combination a real roof essentially never sees. What matters in the field is annual yield, \(E = P_{STC}\times H_{poa}\times PR\), where \(H_{poa}\) is plane-of-array insolation in kWh/m² per year divided by 1 kW/m², and the performance ratio \(PR\) absorbs temperature, soiling, mismatch, cabling, inverter efficiency and downtime. A well-built European rooftop lands at 0.80-0.85. Milan returns roughly 1250 kWh per installed kWp per year at optimum tilt and Rome about 1550 - numbers you look up in a validated irradiance database such as PVGIS rather than estimate. The frontier is the tandem: a perovskite top cell over silicon splits the spectrum between two gaps, sidesteps the single-junction ceiling entirely, and has already passed 34% in the laboratory.
Key Formulas
| One-diode model | \(I = I_{ph}-I_0\!\left[e^{\frac{q(V+IR_s)}{nkT}}-1\right]-\dfrac{V+IR_s}{R_{sh}}\) | |
|---|---|---|
| Thermal voltage | \(V_T = \dfrac{kT}{q} \approx 25.7\ \text{mV}\) | at 25 °C |
| Open-circuit voltage | \(V_{oc} = nV_T\ln\!\left(\dfrac{I_{ph}}{I_0}+1\right)\) | |
| Voltage coefficient | \(\dfrac{dV_{oc}}{dT} = \dfrac{V_{oc}-E_g/q-\gamma kT/q}{T}\) | ≈ −2.2 mV/K per cell |
| Dark current | \(I_0 \propto n_i^2 \propto T^3e^{-E_g/kT}\) | |
| Cell temperature | \(T_c = T_a + \dfrac{\text{NOCT}-20}{800}\,G\) | |
| Shockley-Queisser | \(\eta_{\max} \approx 33.7\%\) | one gap, 1.34 eV, one sun |
| Annual yield | \(E = P_{STC}\,H_{poa}\,PR\) | PR ≈ 0.80–0.85 |
Things worth knowing
- Module prices have obeyed Swanson's law for five decades - about 20% cheaper for every doubling of cumulative production. From roughly $100 per watt in 1976 to under $0.15 today, one of the steepest sustained cost declines ever recorded for a manufactured good.
- The Shockley-Queisser limit constrains single-junction cells, not solar cells. Split the spectrum across several band gaps and the ceiling rises: a six-junction concentrator cell has reached 47.6%.
- Bifacial modules over pale gravel or snow collect 5-20% extra through the back face - and because that light is diffuse and the module sits off the roof, they also run cooler, which quietly buys back some of the temperature penalty.