## Antiparticles and Solar Cells: what’s the connection?

The answer is: the Dirac sea. Paul Dirac developed a quantum mechanical theory of the electron which is compatible with special relativity. In order to satisfy special relativity, the energy of the electron must satisfy the following equation:

$E^2 = m^2 + p^2$

where E is the energy, m is the rest mass of the electron and p is it’s momentum. (this is the correct version of $E=mc^2$ by the way). Dirac realized that there was something funny about this equation, when you take the square root to determine the energy of an electron it allows for both positive and negative roots. I am sure most of us would have just brushed these uncomfortable negative solutions under the carpet, but Dirac postulated that the negative solutions do in fact exist – except they are always occupied. The vacuum, in Dirac’s interpretation,  is teeming with these negative energy electrons. Dirac realised that if one of these negative energy electrons was excited to a positive energy state this would leave behind an empty state. This empty state would behave like a positive charged particle with inverse characteristics to a normal electron: the idea of positrons was born. In particular if a positron met an electron, the electron would simply return to its negative energy state liberating some energy, a process known as annihilation.

So what does this have to do with solar cells? The idea of the Dirac sea has now been abandoned in particle physics, but a close analogue is very important in the theory of solar cells. The figure below shows the energy levels in a semiconductor. There are a whole load

occupied (valence) states all full of electrons. Then there is a large sway of energy with no states (a band gap) and a whole load of empty (conduction) states. When a photon with energy greater than the band gap is absorbed, an electron is promoted to the empty states, leaving behind an empty space. Solid state physicists call this a “hole” rather than a positron, but the concept is exactly the same as Dirac’s. To a solid state physicist a hole is every bit as real as an electron, carrying current, holding a potential just as if it was an anti-electron.

It’s weird to think about “nothing” as something. Solar panels make half their current through absences of electrons. A beautiful  application of Dirac’s  seemingly abstruse idea!