Lattice relaxation at defects

A defines the strength of the network vibrations and the equilibrium state is at = 0. The quantum mechanical solution to the harmonic oscillator gives the phonon energies ( -h ) (o with the frequency ro given by 2A/m). The model is readily extended to include more than one vibrational mode. 

The defect state has a potential minimum at q = B/2A, rather than at = 0, and the minimum energy of the defect state is Ef.—E — W, where, 

The potential well is indicated in Fig. 4.2. The electron-phonon coupling therefore causes the network to relax to a new equilibrium configuration at a lower energy. 

The main consequence of the lattice relaxation is that different types of excitation between the lower and upper levels measure apparently different energies. Thermal excitation of the electron requires an energy 

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