文档介绍：4
Excitons
The concept of excitons
Free excitons
Free excitons in external fields
Free excitons at high densities
Frenkel excitons
The concept of excitons
Exciton: bound electron – hole pair
Two basic types:
Wannier – Matt excitons (free exciton): mainly exist in semiconductors, have a large radius,
are delocalized states that can move freely throughout the crystal,
the binding energy ~ eV;
Frenkel excitons (tight bound excitons): found in insulator and molecular crystals, bound to
specific atoms or molecules and have to move by hopping from one
atom to another, the binding energy ~ -1 eV.
The maximum energy of a thermally excited phonon ~ kBT = eV (RT)
Wannier – Matt excitons:
stable at cryogenic temperature.
Frenkel excitons:
stable at room temperature.
General properties:
(补充)
Free excitons
Bing energy and radius
The eigenfunction and eigenvalue eq:
(Exciton Rydberg constant)
The binding energy and radius of exciton:
(Exciton Bore radius)
Table
Exciton absorption
Creating an electron-hole pair -> the same k vector;
Creating an exciton -> the same group velocity.
(high symmetry points)
(high symmetry lines)
At the zone centre: k=0 and zero gradient, strong excitons occur in the spectral region close to the fundamental band gap. The energy of exciton is:
Strong optical absorption line at energies equal to En that appear in the spectra at energies just below the fundamental band gap
Free excitons can only be observed in the absorption spectrum of very pure samples, because impurities release free elecrons and holes that can screen the Coulomb interaction in the exciton and thereby strongly reduce the binding froces.
Experimental data for free exciton in GaAs
Excitonic ansorption of GaAs among 21 K and 294 K. The dashed line is an attempt to fit the absorption edge with a value of Eg equal to eV which is appropriate for GaAs at 294 K
(a )
(b )
(a) The dissocia