Central-cell correction

Defects with large central cell correction have very localized wave functions. The larger the correction, the more localized the wave function and the higher the probability of interaction between the core (or central cell) and the electron and/or the exciton bound to the defect. Hence the reason why the line is so much smaller than the Q line in the spectrum, as well as the reason why the phonon replicas to the Q-line, is simply a matter of probability, since the central cell correction is so much larger for a nitrogen defect on a cubic site than a hexagonal site. 

Interaction of electrons with phonons, and the fact that the presence of a trapped electron can deform the surrounding material, allows the radius of an empty localized state to change when the state is occupied. Also, in a condensed electron gas phonons lead to a mass enhancement near the Fermi energy, or in some circumstances to polaron formation. For the development of the theory, and comparison with experiment, it is therefore desirable to begin by choosing a system where these effects are unimportant. The study of doped semiconductors provides such a system. This is because the radius aH of a donor is given, apart from central cell corrections, by the hydrogen-like formula... 

The central cell correction results in a binding energy of 40 meV for phosphorus and 45 meV for arsenic in crystalline silicon and the boron acceptor energy is 45 meV. 

The shallow hydrogenlc donors, on the other hand, have small binding energies and also have small central-cell corrections. This makes the resolution of different donors resulting from different chemical impurities difficult to achieve. The early experiments from which different chemical donors were identified employed hlgh-resolutlon Fourier-transform infrared magnetospectroscopy (FTIR) which used the modulated photoconductivity detection technique to monitor the 1S-2P transition In a fixed magnetic field. 

For c-GaN, the effective Rydberg value calculated for mn = 0.19me and s = 9.5 is 28.6 meV. For w-GaN, a difference between mn// and mn would produce a splitting of the n = 2 level into 2s, 2po and 2pm 1 1 states. Calculations including central-cell corrections have been performed by [42], resulting in Table 5.11. 

A negative value of the central-cell correction indicates a central-cell potential which is repulsive for electrons. 

The presence of several lines associated with the same Zeeman component indicates the presence in the sample of several QHDs with different central-cell corrections. Figure 6.42 shows a spectrum of a high-purity GaAs sample at a lower resolution, but in a broader spectral domain, where more components are observed. 

A model of the spectral dependence of the photoionization spectrum of group-III acceptors in silicon has been presented by Edwards and Fowler [52]. This model uses hydrogenic continuum states and hydrogenic ground-state wave functions scaled to account for central-cell corrections, and it provides a good description of the energy dependence of the cross-sections, as can be seen from Fig. 7.8. 

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