Narration script

Unit four, photons. In the last unit, light was a wave. Here we meet its other face. Light travels like a wave, but it delivers its energy in packets called photons, and each photon's energy depends only on its wavelength. A solar cell works photon by photon. One absorbed photon, if it has enough energy, frees at most one electron. So the number of photons sets the current, and the energy of each photon, compared with the band gap, sets what is wasted.

You will learn to calculate photon energy from wavelength, explain the photoelectric effect, convert a light power into a photon flux and then into a maximum current, and explain why the solar spectrum counted in photons peaks at a redder wavelength than the same spectrum counted in watts.

This matters because the maximum current of a solar cell is literally a photon count. Silicon's theoretical maximum of about forty-three point eight milliamps per square centimetre is just the number of sunlight photons above its band gap, multiplied by the charge of one electron.

Around nineteen hundred, Max Planck and then Albert Einstein found that light energy comes in discrete packets. A photon's energy is Planck's constant times its frequency, or equivalently h c divided by the wavelength. In words, bluer light means more energetic photons. There is a shortcut you should memorise: photon energy in electron-volts equals twelve hundred and forty divided by the wavelength in nanometres.

This curve plots that relationship, and it turns band gaps into cutoff wavelengths. Silicon, with a gap of one point one two electron-volts, absorbs photons shorter than about eleven hundred and seven nanometres. Gallium arsenide, at one point four two, cuts off near eight hundred and seventy-three. Cadmium telluride, around one point five, near eight hundred and thirty. Photons on the long-wavelength side of the cutoff simply are not absorbed.

A few numbers to fix in your head. Blue light at four hundred and fifty nanometres: two point seven six electron-volts per photon. Red at seven hundred: one point seven seven. And silicon's band gap corresponds to eleven hundred and seven nanometres, in the near-infrared.

The evidence for photons came from the photoelectric effect. Shine light on a clean metal and electrons fly out, but only if the light's frequency is above a threshold. Below it, no matter how bright the light, nothing happens. Above it, brighter light gives more electrons, but not faster ones. Einstein explained this: each photon hands its whole energy to a single electron, which must pay an escape cost called the work function.

The graph shows that idea. Below the threshold frequency, zero electron energy. Above it, the electrons' maximum energy rises in a straight line whose slope is Planck's constant. The photovoltaic effect, discovered by Edmond Becquerel back in eighteen thirty-nine, is the semiconductor cousin. The photon lifts an electron across the band gap inside the material instead of knocking it out, but the logic is the same: one photon, one electron.

Photon flux is the number of photons per second per square metre. For single-colour light, it is the power density divided by the energy per photon. If every photon gave one electron to the circuit, the current density would be the electron charge times the photon flux.

Let's put numbers in. One thousand watts per square metre of six hundred nanometre light. Each photon carries about two point one electron-volts, so the flux is about three times ten to the twenty-one photons per second per square metre. The maximum current density is about forty-eight milliamps per square centimetre.

Now the same thousand watts, but at four hundred nanometres. Each photon carries more energy, so there are fewer of them, and the maximum current drops to about thirty-two milliamps per square centimetre. Same watts, fewer photons, less current. That is why even a perfect cell responds less, per watt, to blue light.

Here is the real standard sunlight spectrum plotted both ways. In red, power per nanometre, peaking near four hundred and ninety-five nanometres. In blue, photons per nanometre, peaking near six hundred and seventy. Red photons are cheaper, so counting photons shifts the weight toward longer wavelengths. In total, standard sunlight delivers about four point three times ten to the twenty-one photons per second on every square metre.

If we add up only the photons with enough energy for silicon, shorter than eleven hundred and seven nanometres, we get about two point seven times ten to the twenty-one per second per square metre. Multiply by the electron charge and you get forty-three point eight milliamps per square centimetre. The best real silicon cells reach roughly forty-one to forty-two, which is an estimate. The gap comes from reflection, shading by the metal fingers, and weak absorption near the band edge.

A related quantity is spectral responsivity: amps out per watt in, at each wavelength. For a perfect cell it is just the wavelength in nanometres divided by twelve hundred and forty. At one thousand nanometres, zero point eight one amps per watt. At four hundred, only zero point three two.

So, is light a wave or a particle? Both pictures are correct in their own domains. Waves explain interference and coatings. Photons explain absorption and current. You will use both, sometimes on the same device.

Three misconceptions to drop. Brighter light does not mean more energetic photons; it means more photons. A blue photon does not make more current than a red one; its extra energy becomes heat. And a photon below the band gap does not give a little bit of current; ideally it is not absorbed at all.

In industry, quantum efficiency tools measure electrons out per photon in at each wavelength, the standard way to diagnose where a cell loses current. Tandem cells must split photons fairly between two absorbers. And flash testers must be corrected for spectral mismatch, because a cell counts photons, not watts.

Try the review problems now. Next, we ask where the Sun's spectrum comes from in the first place: blackbody radiation.