Abstract
The purpose of this chapter is to specialize some of the results and considerations of the previous chapter to the somewhat more complicated case of molecules and semiconductors. Particular emphasis will be given to semiconductors, either in bulk or quantum well form, since they play an increasingly important role as laser media.
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Notes
- 1.
While this statement is true for diatomic molecules, it is generally not true for polyatomic molecules. In the latter case (e.g., the SF 6 molecule) the spacing between vibrational levels is often appreciably smaller than 1000 cm − 1 (down to ∼ 100 cm − 1) and many excited vibrational levels of the ground electronic state may have a significant population at room temperature.
- 2.
When many vibrational levels of the ground electronic state are occupied, transitions may start from any of these levels. Absorption bands originating from v ′′ > 0 are referred to as hot bands.
- 3.
A simple example of infrared inactive transition is that of homonuclear diatomic molecules (e.g. H 2 ). Ro-vibrational transitions are not allowed in this case, because, on account of symmetry, the molecule cannot develop an electric dipole moment when it vibrates.
- 4.
Actually, this rapid decay results in a thermalization of the molecules in the upper electronic state. The probability of occupation of a given vibrational level of this state is thus given by (3.2.8). For simple molecules, therefore, the lowest vibrational level has the predominant populatation.
- 5.
To conform with the treatment of Chapt. 2, the interaction Hamiltonian is written in terms of an electric dipole interaction rather than in terms of the interaction of the vector potential with the electron momentum p, as commonly done in many textbooks on semiconductors. The two Hamiltonians can be shown however to lead to the same final results.
- 6.
Note that the concept of cross section as discussed in connection with Fig. 2.7 loses its meaning for a delocalized wavefunction such as the Bloch wavefunction. We nevertheless retain the same symbol σ for a semiconductor to make an easier comparison with the case of isolated atoms or ions. Here σ has the only meaning that the transition rate for a plane wave is W = σF, where F is the photon flux of the wave or, alternatively, \(W = \sigma \rho \ c/h\nu \), where ρ is the energy density and ν is the frequency of the wave.
- 7.
We recall that, in the parabolic band approximation, all the quantum details are essentially hidden in the values of the effective masses and energy gap.
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Svelto, O. (2010). Energy Levels, Radiative and Nonradiative Transitions in Molecules and Semiconductors. In: Principles of Lasers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1302-9_3
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