# How to understand exciton?

I know that exciton is an electron and hole orbiting around each other(at least that is what I have heard). So if the hole is a hypothetical particle with a plus sign, meaning that it is a lack of an electron jumping around in a certain material, how should I imagine hole jumping out to the gap in a semiconductor and there orbiting around with an electron. Is that the one-electron-less atom that does it or is that just made out idea like a hole?

An exciton really is a electron coupled to a hole, just as you said. A electron gets excited to a higher band, leaving a hole in the lower band behind (a bit like a bubble on top of a liquid). You can disregard the other electrons (and holes) in this picture, as they are smeared out and just form the background.

The electron and the hole are attracted to each other, and form a pair, just like a Hydrogen atom (electron+proton) or positronium (electron+positron). Since electrons are lighter than protons, the radius of the exciton is much larger than that of a Hydrogen atom. Actually, what counts are the effective masses of electron and hole.

Since you are talking about semiconductors, you are probably concerned with Wannier-Mott excitons. These have an especially large radius, larger than the lattice constant, since a screening effect reduces the coulomb attraction between electron and hole further.

Eventually, electron and hole will recombine, but it can take a while compared to other time scales. One reason is that the lattice has to carry away the exact excess energy and momentum of the exciton (its QM). Also, the wavefunctions of electron and hole don't overlap very much, further reducing the probability of recombination.

For further info, the Wikipedia article on Excitons seems not too bad.

• So the hole is really for example a proton? And why the radius is bigger than the one in Hydrogen? – KabaT Dec 9 '13 at 17:37
• Or what is the difference between the hole and the positron? – KabaT Dec 10 '13 at 8:49
• @KabaT: The hole is basically an atom that is missing an electron. But that picture is not quite accurate, since the atom is fixed in the lattice, but the hole moves around. A better picture would be to imagine a hole in the electron cloud that moves around as if it were a particle. Or think of it as an air bubble: When you excite an electon above the gap, you have a "droplet of water" in the upper band, and a "bubble of air" of same volume in the lower band. It is an absense of water, but behaves like a droplet... – jdm Dec 10 '13 at 8:59
• The radius of the exciton is larger because the eff. mass of the hole is smaller than the proton mass (The Bohr radius is $a_0 = \hbar\,/\,\mathbf{m_e}\, c \,\alpha$). And the difference between the hole and the positron is that the positron is a real particle ($e^+$), whereas the hole is a quasiparticle. It's a collective behavior of the material's electrons that looks like it is a particle. – jdm Dec 10 '13 at 9:04
• Thank you very much for answering! But I still have some doubts. I took part in a coursera's Nanotechnology The Basics course, and during it I started wondering more about the idea of a hole. Before the course I thought I understand it, that it is like electron is jumping from atom to atom leaving an atom behind it with a one electron less, so it "looks" like the lack of electron is moving in the opposite direction. But in one of the course surveys was the question: Do you think that holes are real? And 66% said they are not, so the professor answered on the forum why it is just as real as e. – KabaT Dec 11 '13 at 9:38