Abstract
Optical band-to-band absorption can produce an electron and a hole in close proximity which attract each other via Coulomb interaction and can form a hydrogen-like bond state, the exciton. The spectrum of free Wannier–Mott excitons in bulk crystals is described by a Rydberg series with an effective Rydberg constant given by the reduced effective mass and the dielectric constant. A small dielectric constant and large effective mass yield a localized Frenkel exciton resembling an excited atomic state. Excitons increase the absorption slightly below the band edge significantly. The interaction of photons and excitons creates a mixed state, the exciton–polariton , with photon-like and exciton-like dispersion branches. An exciton can bind another exciton or carriers to form molecules or higher associates of excitons. Free charged excitons (trions ) and biexcitons have a small binding energy with respect to the exciton state. The binding energy of all excitonic quasiparticles is significantly enhanced in low-dimensional semiconductors. Basic features of confined excitons with strongest transitions between electron and hole states of equal principal quantum numbers remain similar. The analysis of exciton spectra provides valuable information about the electronic structure of the semiconductor.
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Notes
- 1.
This causes the breakdown of the adiabatic approximation. The error in this approximation is on the order of the fourth root of the mass ratio. For hydrogen this is \( {\left({m}_n/{M}_{\mathrm{H}}\right)}^{1/4}\cong 10\% \) and is usually acceptable. For excitons, however, the error is on the order of 1 and is no longer acceptable. This is relevant for the estimation of exciton molecule formation discussed in Sect. 1.4.
- 2.
When a quasi-free charge carrier (electron or hole) moves through a crystal with strong lattice polarization, it is surrounded by a polarization cloud. Carrier plus polarization form a polaron, a quasiparticle with an increased effective mass (see Sect. 1.2 of chapter “Carrier-Transport Equations”).
- 3.
It is, however, influenced by the gradient of an electric field or by strain; see, e.g., Tamor and Wolfe 1980.
- 4.
The ionization energy is also referred to as binding energy or Rydberg energy.
- 5.
\( {\phi}_n(0)\ne 0 \) applies only for S states.
- 6.
Strictly, such transitions cannot occur at k = 0; however, a slight shift because of the finite momentum of the photon permits the optical transition to occur because of a weak electric quadrupole coupling (Elliott 1961). Such transitions can also be observed under a high electric field using modulation spectroscopy (Washington et al. 1977). Dipole-forbidden transitions are easily detected with Raman scattering (Sect. 1.3) or two-photon absorption (for Cu2O, see Uihlein et al. 1981), which follow different selection rules.
- 7.
With a correspondingly large exciton Bohr radius of 1.04 μm for n = 25, compared to ~1 nm for n = 1.
- 8.
The analysis of the measured reflection spectrum as a function of the wavelength and incident angle is rather involved. A relatively simple method for measuring the central part of the exciton–polariton spectrum in transmission through a prismatic crystal was used by Broser et al. (1981) (see Fig. 13).
- 9.
A state close to an actual biexciton state (Sect. 1.4) which immediately decays into other states.
- 10.
Deviations from a pure quadratic dependence are due to the short radiative lifetime for the involved species in direct-bandgap semiconductors, preventing a thermal equilibrium of the population.
- 11.
Still a significant broadening of exciton transitions (of single quantum dots) well above the natural linewidth is observed due to the interaction of the quantum dot with its environment. The interaction with acoustic phonons (deformation potential coupling) and optical phonons (Fröhlich coupling) leads to broad transitions at increased temperature (Rudin et al. 1990); in addition, randomly fluctuating electrical fields of charged defects in the vicinity of the dots lead to a spectral jitter of the transitions on a very short time scale (spectral diffusion) even at low temperature (Türck et al. 2000).
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Böer, K.W., Pohl, U.W. (2015). Excitons. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_14-1
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