Indirect Bandgap Semiconductors vs Direct Bandgap Semiconductors

Question

I have been looking into the foundational theory of solar cells, as a high school student. Due to this, a lot of the stereochemical and physical understanding I would need to specialise here completely eludes me. One particular doubt is that Silicon, as in indirect bandgap semiconductor, has a maximum and minimum bandgap value: 1.1 and 3.5 eV. I understand what this implies, however I still need to understand, in layman terms, what an indirect bandgap actually means, without reference to anything like k-vectors or brillouin zones. This will help me rationalise why Silicon solar cells are responsive to a range of wavelengths, instead of just a sharp cutoff wavelength. Could anybody help?

Answer 1

In an atom the energy levels are sharp and absorption and emission between energy levels are pretty easy to visualize. One atom gives a one allowed place for the electron.

It you have two atoms close together, then you have two electrons that could be excited individually, but the energy levels have to be split a little. You still have two places for the two electrons to be excited to.

In a semiconductor, you have lots of atoms, so you have some number of electrons that can go to some number of states that are in what we call bands, and usually we care the most about the nearest band the electrons can be excited to and move around easily in. So in a way you can think of a semiconductor as a giant molecule with two bands, the valence band where all the electrons that could be free are still bonded to atoms, and a conduction band where the electron can be excited to, and if it gets to the excited state it can move over to the next atom easily.

If you buy that, then you might also believe that the atoms in this giant molecule are also kept together by directional bonds and those bonds kind of act like springs. And the atoms vibrate with some energy depending on the temperature. The little quantum units of the vibration with some small energy are called phonons. Both your direct and indirect semiconductors will have phonons. Phonons don’t have a lot of energy, but they do have momentum. The vibrations like to travel along the directions of the bonds between atoms.

The electrons on the other hand can have a lot of energy, but don’t have much momentum.

When we are thinking about electrons and phonons in a crystal, because we use band structure theory to simplify things so we can treat them like billiard balls. Just like billiard balls

1. energy must be conserved
2. momentum must be conserved

In the direct band gap semiconductor, the conduction band minimum and the valence band maximum have the same momentum. So electrons can move from one energy to the excited energy state easily if there is enough energy provided by the incoming photon.

In the indirect band-gap like silicon, the electrons in lowest part of the conduction band have to have a different momentum that the electrons at the top of the valence band. So both an electron and one or more phonons need to be involved for the electron to be able to get to the new state in the conduction band. This is somewhat unlikely compared to not needing a photon.

So as as you increase the photon energy, in the indirect case start to get some absorption because of the phonons are helping conserve momentum but eventually once the photon energy is large enough you don’t need as many phonons for the electron to find an allowed energy state. At that point the absorption is strong like a direct bandgap semiconductor.

Answer 2

The difference between and indirect and direct band gap has to do with momentum. Recall that photons have nearly no momentum. So the absorption of a photon by an electron changes the momentum of the electron very little.

In a direct gap semiconductor the electrons and holes at the band gap have the same momentum in both the valence and conduction bands. Since no change in momentum is required, the energy of the photon alone is all that is required to make the transition of an electron from the valence band to the conduction band.

In an indirect band gap semiconductor the electrons and holes have different momentum in the valence band as opposed to the conduction band at the band gap. For a transition to occur, the electron must change momentum and it won't come from the photon alone. The change in momentum comes from the vibrations (called phonons) in the semiconductor. Where photons are all energy and no momentum, phonons are all momentum and no energy:

Direct gap transition: electron + photon

Indirect gap transition: electron + photon + phonon

The addition of a phonon means indirect optical transitions are slower and less efficient than direct transitions. Undesirable for lasers.