Hydrogen—Vibrational Frequencies

In this section, I will devote attention to the question how does H move in semiconductors One type of motion consists of vibrations around a particular site in the lattice. Another type of motion is involved in the migration of the impurity through the lattice, in which barriers have to be surmounted (or tunneled through). Once again, most of the available information concentrates on Si. 

Frequencies of the hydrogen stretching mode for H° at the bond-center site have been obtained from cluster calculations. Estreicher (1987) found the potential profile for displacements of H along the bond to be U-shaped and flat for small displacements (—0.1 A). Consequently, he found a very low vibrational frequency for such displacements ( that of single Si—H bonds). Other studies of the stretching mode have found 784 cm-1 (Deak et al., 1988) and 800 cm-1 (DeLeo et al., 1988). 

Calculations of vibrational frequencies in a three-center bond as a function of Si—Si separation were performed by Zacher et al. (1986), using linear-combination-of-atomic-orbital/self-consistent field calculations on defect molecules (H3Si—H—SiH3). The value of Van de Walle et al. for H+ at a bond center in crystalline Si agrees well with the value predicted by Zacher et al. for a Si—H distance of 1.59 A. 

For the neutral charge state, the situation is very similar the path through the region of high electron density is favored. However, the low-density path is only 0.2 eV higher now. This seems to indicate that neutral H would be able to move rather freely through the network with very small 

It is clear that the diffusion of H through semiconductors is a very complicated issue not only does the motion itself involve complex interactions between the impurity and the lattice, but the calculation of a diffusion coefficient requires the inclusion of different charge states plus the interaction of H with itself (molecule formation) and with other defects and impurities in the crystal. Chapter 10 of this volume discusses this problem in more detail. 

---

It was noted in the early study by Pankove et al. (1985) that the hydrogen vibrational frequency appropriate to the H—B pair was in the range consistent with a hydrogen bonded to a silicon but was in fact somewhat smaller than that expected for an isolated hydrogen connected to a single silicon. Generally, if an atom becomes more confined, the frequency is expected to increase. It was suggested that the frequency reduction was due to a three-body effect well known in molecules. 

In organic systems where a transfer of hydrogen is often between atoms for which the atom-hydrogen vibrational frequencies are similar, the concept of a symmetrical transition state can be readily visualized. It would appear that the most symmetrical TS is often viewed as one in which the H-C and H-B bonds in (21) are stretched to the same degree. More esoteric descriptions involving intersections of hypothetical potential surfaces are also used nevertheless, definitions of symmetrical in cases other than those in which C = B are obscure. An empirical approach has been proposed on the basis that the acidity of the C-H and B-H bonds should reflect the dissociation energy and, hence, a measure of the potential surfaces C-H and B-H bond breaking. The observation that maximum isotope effects are observed when the B-H and C-H acidities are similar... 

The hamionic oscillator of two masses is a model of a vibrating diatomic molecule. We ask the question, What would the vibrational frequency be for H2 if it were a hamionic oscillator The reduced mass of the hydrogen molecule is... 

Most of the movement occurs in the hydrogen attached to the oxygen atom, moving out of the plane of the molecule. This atom is positioned very differently in the two forms, and so it is not surprising that they generate substantially different vibrational frequencies in this normal mode. ... 

What would you expect to happen to the vibrational frequency of the C—H bond of methane if the hydrogen atoms, which are normally present as H, are replaced by 2H See Major Technique 1, Infrared Spectroscopy. 

Hirata and Iwata, 1998, extended these studies to linear oligomers and an infinite linear hydrogen fluoride polymer. Also this study substantiates the applicability of the BLYP and B3LYP functionals, for which reasonable agreement with experiment has been found with respect to structure, binding energies and vibrational frequencies of the species explored. 

Sokolov, N. D., Vener, M. V., Savel ev, V. A., 1990, Tentative Study of Strong Hydrogen Bond Dynamics. II. Vibrational Frequency Consideration , J. Mol. Struct. (Theochem), 222, 365. 

---