Dangling bonds wavefunction

Atoms at solid surfaces have missing neighbors on one side. Driven by this asymmetry the topmost atoms often assume a structure different from the bulk. They might form dimers or more complex structures to saturate dangling bonds. In the case of a surface relaxation the lateral or in-plane spacing of the surface atoms remains unchanged but the distance between the topmost atomic layers is altered. In metals for example, we often find a reduced distance for the first layer (Table 8.1). The reason is the presence of a dipole layer at the metal surface that results from the distortion of the electron wavefunctions at the surface. 

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. 

Table 4.1. Wavefunction coefficients in Eq. (4.14) for silicon dangling bonds in different environments...

As compared to the molecules the wavefunction-based correlation methods for periodic systems are practically reliable only when the molecular cluster model is used. Unfortunately, the well-known problems of the cluster choice and the influence of the dangling bonds on the numerical results restricts the application range of the molecular cluster model to the essentially ionic systems. 

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