The calculated local vibrational modes (LVM's) for the neutral charge states of the VHn complexes and the effects of deuteration are compared with experiment in Table 1. The assignments of those vibrational modes arising from mixed isotopic defects are tentative.
Neutral VH gives rise to a partially occupied electronic doublet in the forbidden gap. The resulting Jahn-Teller distortion to C1h symmetry is effected by a rebonding by pairs of the Ge dangling bonds across the gap. The reconstructed bond length in the relaxed defect was calculated to be 2.78 Å in the relaxed structure (cf. 2.4 Å for bulk Ge). The high electron density in the region between the two paired atoms repels the H atom so that the Ge-H bond moves 4
out of the [111] axis. The Ge-H bond was found to be 1.541 Å as compared to 1.52 Å in molecular GeH4. The Ge atom bonded to the hydrogen moves outwards from the vacancy by 0.32 Å along [111].
The relaxed dihydrogen-vacancy defect was found to have C2v symmetry. The reconstructed Ge-Ge bond length was found to be 2.79 Å. The effect of the additional H atom in the defect results in a shortening of the Ge-H bond length to 1.531 Å.
The symmetry of the VH3 defect was assumed to be C3v. The relaxed defect then has three equivalent H atoms each with a Ge-H bond length of 1.536 Å. The angle made between the Ge-H bonds and the <111> directions was found to be 6.2.
An orbital-singlet level was found deep in the gap occupied by a single electron.
VH4 has four equivalent H atoms (Td symmetry) each bonded to a Ge atom with a bond length of 1.526 Å in VH4. The Ge atoms move outwards from the vacancy by 0.33 Å along [111] from their ideal sites. VH4 was found to possess an energy gap free from defect levels.
Also calculated were the vibrational modes for both VH3- and neutral V2H6. The effect of the addition of an electron to VH3 was to shorten all Ge-H bond lengths by 0.7% resulting in modest increases in the frequencies of the E and A symmetry vibrational modes by 6 and 25 cm-1 respectively. V2H6 was found to have the shortest Ge-H bond length of 1.52 Å. Two stretch modes of A2u and A1g symmetry were found at 2131 and 2129 cm-1 respectively. Two doublet Eu and Eg modes were found at 2128 and 2120 cm-1 respectively. The A1g and Eg modes are infrared inactive. The splitting between the I-R active A2u and Eu modes was found to be 3 cm-1, substantially smaller than that calculated difference between the A and E modes in VH3.
Preliminary calculations using a method described elsewhere[#!bob!#] were used to find the acceptor and donor levels. Acceptor levels were calculated for VH, VH2 , VH3 and were all found to lie within 0.35 eV of the valence band edge. The donor levels were calculated for VH and VH3 and lie close to the valence band .
The reorientation barrier was calculated by optimising the energy of a VH3 defect with one of the H atoms constrained to be equidistant from two unhydrogenated Ge atoms. The difference in energy between this configuration and the unconstrained VH3 was calculated to be 0.30 eV.
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