ESR hyperfine interactions

The nuclear hyperfine interaction splits the paramagnetic states of an electron when it is close to a nucleus with a magnetic moment. For a random orientation of spins and nuclei, the tensor quantities in Eq. (4.11) are replaced by scalar distributions, and the resonance magnetic field is shifted from the Zeeman field // by 

The hyperfine ESR data are valuable because they are the best measure of the electron wavefunetion at the defeet. The form of the hyperfine spectrum, which contains two broad lines, implies that the defect state is highly localized on a single silicon atom. Further analysis makes use of an approach that is successful in analyzing the hyperfine interaction in crystalline materials and describes the defect wave-function, 4, by a linear combination of atomic orbitals. The wavefunetion of a single silicon valence electron is written in terms of s and p orbitals as 

The hyperfine interaction for a dilute system of localized states 

Based on this model, the hyperfine spectra for the defect can be related to the s- and p- components of the wavefunction (Stutzmann and Biegelsen, 1988). Table 4.1 shows the results and compares them with the silicon defects which are known to be of the dangling bond type in other materials. An sp dangling bond has J s-like and p-like character, so should have a = 0.5 and p = 0.87. In practice, all the defects in Table 4.1 have a slightly smaller s-character and larger p-character and also incomplete localization, compared to the sp dangling bond model. 

Both the g-value distribution and the hyperfine splittings of the g = 2.0055 defect are consistent with the expected properties of dangling bonds. Consistency, however, does not constitute proof of the structure, and other possibilities have been proposed, which are discussed below. The ESR parameters do provide quantitative constraints that must be met by alternative models and, at present, are the only specific experimental information that we have about the defect wavefunctions. 

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There is no sign of an ESR hyperfine interaction in boron-doped a-Si H, so that there is little information about the acceptor states. It may be that boron acceptors have an unexpectedly small hyperfine interaction. A more likely explanation is that virtually all the acceptors are ionized. The valence band tail is much broader than the conduction band and the Fermi energy remains further from the band edge, so that the probability that a hole occupies an acceptor is much smaller. The... 

Finally it must be emphasized that the empirical relation between proton chemical shifts and charge densities is not so firmly established as the corresponding relation for the ESR hyperfine interaction constant 15). Many theoretical and experimental points remain to be clarified. 

Cycloheptane-1,2-semidTone" is a rigid species (t>10 sec.) up to at least 90. From an analysis of the esr hyperfine interactions it can be concluded that the single populated conformation is the staggered conformation 4(5). 

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