A solar panel, four pictures

Why do solar panels hate heat?

Under the same sun, a solar panel on a hot roof makes about 15% less power than on a cold, bright day. It delivers just as many electrons, but each one carries less energy. The reason: heat lets electrons leak back over the panel's one-way hill, and to keep that leak small, a hot panel has to run at a lower voltage.

Below are two identical panels under the same sun, simulated live in your browser: a cool one at 25 °C and a hot one at 65 °C. (That's the panels' own temperature: in full sun, panels run 25 to 40 °C hotter than the air.) The bar that sticks to the top of the screen sets their temperatures and the sun, and can hold both at the same voltage.

Picture 1

Two panels

Each panel is 60 silicon cells joined in a row. In each cell, sunlight knocks electrons loose, and a one-way junction just under the cell's front surface pushes them out round the circuit, at a voltage.

Top: each blue dot is a crowd of electrons (about 4 × 10¹⁸), delivered round the circuit, in real time. It climbs as high as the panel's voltage: the energy each electron carries away. Pink dots climb part way, leak back inside the panel and are lost. Bottom: each panel's power at every voltage it could run at; the dot is where it runs, at its peak.

The hot panel makes 233 watts, the cool one 275: 15% less. Now look at the meters. Both deliver the same current, about 8.1 amps: the same number of electrons each second. What the hot one has lost is voltage, 29.0 volts instead of 34.0. Power is current times voltage, so the voltage is what costs it. (Each panel runs at its peak because the inverter it's wired to hunts for the peak by itself.)

Why does it run at a lower voltage? Tick hold both at the left one's best voltage. At 34 volts (as it happens, about the most this hot panel can reach at all), it delivers nothing: its whole current leaks back inside. That leak is the whole story.

Shows

How much power each panel makes, and that heat takes it from the voltage, not the current.

Hides

What the leak is, and why heat makes it worse.

Picture 2

The hill

Here's the leak. The higher a panel's voltage, the lower the hill inside each cell, and the more electrons leak back over it.

This is the front of one cell, its first 1.6 thousandths of a millimetre, drawn as an energy map: up is more energy for an electron. Electrons move along the top band. The gaps they leave behind, called holes, act like positive charges and move along the bottom one. Between the cell's thin front layer and its base, the electrons' band climbs a hill. Electrons freed by light in the base wander about on its flat top until they happen to reach the edge of the slope (picture 4 shows the wandering). Then they roll down into the front layer and out round the circuit: that's the one-way push.

Energy across the front 1.6 µm of one cell in each panel, in electronvolts per electron. Thin lines are the edges of the bands: the least energy an electron can have (top), and the most a hole's missing electron can (bottom). The thick lines are the levels the electrons and holes fill to; their split is the cell's voltage. "Gets over" compares how many electrons there are at the top of the hill with how many at its foot (the Boltzmann factor, e−hill/kT). Holes leak too, the other way, into the front layer: in this cell, nearly half the leak. At the front contact, the holes' level drops to meet the electrons': holes that reach it are lost there.

The thick lines are the levels the electrons and holes fill up to, and the split between them is the cell's voltage (sixty cells make the panel's). Raise the voltage and the hill gets lower: more and more electrons in the front layer climb back over it into the base, and meet holes there or at the back of the cell, and are lost. That's the leak.

What lifts an electron over the hill is heat. Silicon's atoms jiggle, and pass their jiggling on to the electrons; only the luckiest few have the energy to climb. Hold both panels at 34 volts: in the cool one, for every electron at the top of the hill, about 900 000 wait at its foot. In the hot one, it's 36 000: about twenty-five times as many make it up. Heat does it twice over: the electrons jiggle harder, and at the same voltage, warm silicon's hill is lower (0.30 electronvolts, against 0.35).

So the hot panel backs off to 29 volts. A lower voltage means a higher hill, 0.39 electronvolts, which pulls its leak back down to about one in 600 000. The price: each electron it delivers carries 29 volts' worth of energy instead of 34.

Physicists who think in levels tell the same story another way. The cell's voltage is the split between the electrons' and holes' levels, the thick lines. Sunlight holds them apart by keeping far more electrons and holes in the cell than it would have in the dark. Every time an electron meets a hole, the split relaxes a little: that's the loss. The hill only sorts electrons and holes to their own contacts. Heat raises the number of free electrons the cell’s base holds in the dark, by almost a fifth for every degree, so the same sunlight holds the levels less far apart.

Shows

The one-way push, the leak back over the hill, and why heat helps it.

Hides

The other 178 µm of the cell, where the light frees most of its electrons.

Picture 3

How many, how high

A panel's power is how many electrons it delivers each second, times the energy each one carries: the area of a rectangle, current across and voltage up.

Left: each panel's power, as the area of its rectangle. Right: where every 100 pairs of charges the sunlight frees end up: delivered round the circuit, or lost at the front (mostly light absorbed in the thin front layer, two-thirds of it blue and violet), in the base, or at the back. The dashed mark is how many each panel delivers at 0 volts, where nothing leaks back.

The two rectangles are almost the same width; the hot one is shorter. On the right, the hot panel delivers 83 of every 100 pairs (an electron and its hole) that the light frees, and the cool one 85: just over one in a hundred fewer. In this simulated cell, about 12 more are lost whatever the voltage, mostly light absorbed in its bare front layer (real cells, with a treated front surface, lose fewer there, and lose some light to reflection instead): even at 0 volts, where nothing leaks back, each panel delivers 88. The rest leak back: 4 in the cool panel, 5 in the hot one. And the hot cell absorbs a little more of the sunlight, so its current is only half a percent lower. Heat costs the panel almost nothing in electrons, and 5 volts on every one.

Shows

Power as count times height, and where every pair goes.

Hides

Where in the cell the light frees its pairs.

Picture 4

The whole cell

Picture 2 zoomed in on the hill, in the first thousandth of a millimetre. Here's the whole cell, 0.18 millimetres deep, slowed down 30 million times. Most of the electrons are freed out in the base: 84 of every 100. Blue light is absorbed in the first thousandth of a millimetre, red within a few, and infrared all through the base.

A cut through one cell in each panel, front (left, where the light comes in) to back. Each blue dot is a fixed number of electrons, a sample of the simulation's own electron density, hopping at the rates it gives. Where electrons are too plentiful to draw (the front layer and the junction's edge, at the far left), they're shaded instead. Each trails a line of where it's been: electrons wander in all three directions, and the picture's height stands for the two it can't show. A yellow spark is a pair freed by light; a blue flash at the left is an electron landing in the junction; a pink ring is an electron meeting a hole, or lost at the back contact.

A freed electron has no field out in the base to push it anywhere. It just wanders at random, jostled by the atoms, until it happens to reach the edge of the junction at the front. There the hill sweeps it down into the front layer, and out round the circuit. Most of them make it, because an electron here can wander about 0.6 millimetres before it meets a hole: three times the cell's depth. A few meet a hole first, or wander to the back contact, and are lost.

The leak is here too, as a crowd. The higher the voltage, the lower the hill, and the more electrons come back over it from the front layer, so the base fills up. More of them then meet holes or reach the back. Tick hold both at the left one's best voltage: the hot panel's base floods with electrons, and every one of them is eventually lost inside.

Shows

Where the light frees electrons, how they get out, and where they're lost.

Hides

The holes, which outnumber the electrons in the base several hundred to one, and aren't drawn.

So

Why heat?

A solar panel's voltage is a balance. Sunlight pushes electrons across its junction one way; heat lets some climb back the other, and the higher the voltage, the more of them leak back. Heat makes the leak much worse: near a panel's working voltage, it doubles about every 8 °C. So a hot panel has to run at a lower voltage to hold the leak down. It still delivers about as many electrons, but each carries less energy. For silicon that's about 0.3 to 0.4% of the power for every degree: this simulation loses 0.38% per °C, and panel makers list about 0.25 to 0.45% (most 0.3 to 0.4).

And while we're here

Other questions the pictures answer

Is a cloudy day worse than a hot one?

Slide the sun down to 50%. The current halves, and so does the power, to 133 watts. But the voltage barely moves: the panel's best voltage drops by just 1 volt, from 34 to 33. Cloud starves a panel of electrons; heat makes it deliver them at a lower voltage. Halving the sun costs far more than heating the panel to 65 °C.

Why are panels rated at 25 °C?

A panel's rated power is measured under standard test conditions: full sun (1000 W/m²) with its cells at 25 °C. In full sun, cells typically run 25 to 45 °C hotter than the air (the high end on a roof in still air), so on a 30 °C day they're at 55 to 75 °C, and the panel makes about 11 to 19% less than its rating.

Where do panels work best?

Somewhere cold and bright. Slide a panel down to −10 °C (in full sun, that takes air at about −40 °C): it makes 312 watts, 13% more than at 25 °C. That's part of why panels on snowy mountains can beat their ratings: cold cells, and extra light from thin air and bright snow.

Under the hood

How a solar cell is simulated

The trend alone is textbook physics. A solar cell is a diode lit up, and the diode equation gives its voltage's fall with temperature: in Martin Green's form, dVoc/dT = −(Eg0/q − Voc + γkT/q)/T, about −2 millivolts per °C for each silicon cell. This page checks against it, and against real panels: its cell loses 2.0 millivolts per °C, and 0.38% of its power.

What this simulation adds is where: the bands and levels across the cell, the hill, and where every pair goes. It follows the electrons and holes through the depth of one cell as they diffuse and drift (the drift–diffusion model, the same rule that runs our lithium-ion battery and nerves), with silicon's properties at each temperature: its band gap narrowing as it warms, its electrons slowing as its atoms jiggle harder. The sunlight is the standard spectrum, in 90 bands of colour, each absorbed as deep as silicon's measured absorption says.

It leaves things out, to run live: no light is reflected or trapped; there's no wiring resistance; the contacts cover each face of the cell; and the panel is 60 identical cells, so its voltage is 60 times one cell's. Real panels make somewhat less. Heat costs them a similar share: the best of today's, with a higher voltage to start from, lose less, about 0.25 to 0.35% per degree.