14 Dielectrics and Ferroelectrics
14.1 Excitons
14.1.1 Introduction
An exciton is a bound state of an electron and a hole in a semiconductor or an insulator. The
generation of an exciton is comparable to the principle of a solar cell. A photon comes in and creates
an electron-hole pair in the pn-junction. These electrons and holes get separated because of an electric
field and so an electric current starts to flow. If we just have a pure semiconductor (undoped) there
is no field to push the electrons and the holes away from each other, because there is just a coulomb
force which holds them together. What happens here, is comparable to the hydrogen atom, where we
have a light electron moving around a heavy proton. Here the mass of electrons and holes is almost
the same, but not exactly.
We remember that an incoming photon with an energy, which is higher than the band gap, can move
an electron to the conduction band and a hole is generated in the valence band. Now we think about
photons with energies less than the band gap. These are the photons that can create bound electron-
hole-pairs. Excitons are not very stable and so they will decay after a little amount of time and a
photon is emitted again. Another possibility to loose their energy is to interact with electrons or
phonons. This process can be seen in the optical absorption.
14.1.2 Mott Wannier Excitons
There are two types of excitons. One of them is called the Mott Wannier exciton. The important
thing about them is that their size is much bigger than the lattice constant.
To calculate the binding energy of excitons we can use the formula of the hydrogenic model with the
effective masses of electrons and holes.
En,K=Eg−μ∗e^4
32 π^2 ~^2 ^2 ^20 n^2+
~K^2
2(m∗h+m∗e)
︸ ︷︷ ︸
kinetic energy(237)
The quantum numbernagain defines the energy level and here an additional term appears, which
belongs to the kinetic energy of the exciton. When we calculate the energies, we draw them on the
same axis as the dispersion relationship with the valence band and the conduction band. The result
is, that there are additional states near the conduction band for the excitons, which can be seen in
fig. 114.
The result of an interesting experiment to see excitons is shown in fig. 115. Normally, light should
go right through a semiconductor, if the energy is less than the energy gap, so that no electrons are
taken from the valence to the conduction band, but in fig. 115 we see a number of absorption peaks.
These peaks appear when the incoming photons can excite excitons. Another experiment was done
with Gallium Arsenide (GaAs). In fig. 116 we see that the absorption has a peak, when the photon
energy is smaller than the energy gap. This happens again because of the excitation of excitons.