Diamond Transition Research Articles

Relative intensities of indirect transitions: Electron-phonon and hole-phonon interaction matrix elements in Si (TO) and GaP (LA,TA)

The electron-phonon ($e$-ph) and hole-phonon ($h$-ph) interaction matrix elements of the indirect transitions in Si and GaP can be evaluated individually by comparing their recently determined ratios together with experimental values of the absorption coefficient to the theoretical expressions for the absorption coefficient. We have obtained values of these matrix elements for the TO phonon of Si and the LA and TA phonons of GaP. For Si, ${S}_{{e\ensuremath{-}\mathrm{p}\mathrm{h}}_{\mathrm{TO}}}=15.3\ifmmode\pm\else\textpm\fi{}2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ Ry, ${S}_{{h\ensuremath{-}\mathrm{p}\mathrm{h}}_{\mathrm{TO}}}=\ensuremath{-}18.7\ifmmode\pm\else\textpm\fi{}2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ Ry, and in GaP ${S}_{{e\ensuremath{-}\mathrm{p}\mathrm{h}}_{\mathrm{TA}}}=19.2\ifmmode\pm\else\textpm\fi{}2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ Ry, ${S}_{{h\ensuremath{-}\mathrm{p}\mathrm{h}}_{\mathrm{TA}}}=17.4\ifmmode\pm\else\textpm\fi{}2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ Ry, and ${S}_{{e\ensuremath{-}\mathrm{p}\mathrm{h}}_{\mathrm{LA}}}=7.6\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ Ry, ${S}_{{h\ensuremath{-}\mathrm{p}\mathrm{h}}_{\mathrm{LA}}}=13.0\ifmmode\pm\else\textpm\fi{}2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ Ry. The magnitudes and signs of these matrix elements make it possible to understand more clearly the mechanisms responsible for the relative intensities of indirect transitions in diamond and zinc-blende (DZB) materials (excluding Ge). In Si, constructive interference between the $e$-ph and $h$-ph processes makes the TO phonon dominate, while in the other indirect DZB materials, the small ${\ensuremath{\Gamma}}_{1,c}$ to ${X}_{1,c}$ energy separation makes the longitudinal- (LA- or LO-) phonon-assisted transition with ${\ensuremath{\Gamma}}_{1,c}$ as an intermediate state, the most intense. By considering exact expressions for the coupling coefficient between ${\ensuremath{\Gamma}}_{1,c}$ and ${X}_{1,c}$ we are able to understand the behavior of ternary compounds whose fundamental gap can be adjusted from indirect to direct by alloying. We have also been able to explain why in DZB materials the longitudinal-phonon-assisted transition proceeding via ${\ensuremath{\Gamma}}_{15,c}$ is weak in intensity.

GR transitions in diamond: magnetic field measurements

The g-values of the GR1-GR8 levels are obtained from axial Zeeman and magnetic circular dichroism (MCD) measurements using a diamond sample which has minimal strain. The presence of large Zeeman interactions and the occurrence of doublets which are mixed by the magnetic field are not understood.

Calculation of linewidths of the GR2-8 transitions in diamond in a model where the energy levels are within the valence band

Linewidths of transitions between band gap states and localised energy levels within the valence band have been calculated. They show that it is possible to account for the small linewidths of the GR2-8 transitions about the vacancy in diamond provided the localised levels are very close within the valence band, but they are not consistent with Lowther's (1977) model of the GR2-8 transitions.

Selection rules for defect-activated lattice bands and vibronic transitions in face-centred cubic, diamond and zinc blende lattices

The presence of a single substitutional defect in an otherwise perfect crystal lattice reduces the symmetry group of the system from the crystal space group to the point group of a lattice site. The corresponding reduction of the space-group irreducible representations is tabulated for face-centred cubic, diamond and zinc blende lattices. The tables allow the easy determination of selection rules for defect-activated lattice bands. It is shown that all phonons can be defect activated for face-centred cubic and diamond lattices, but that some selection rules occur for rocksalt, calcium fluoride and zinc blende lattices. In the case of vibronic transitions, the selection rules for rocksalt and calcium fluoride are discussed. In favourable cases, both types of measurement lead to a knowledge of the phonon critical-point frequencies in a more direct way than measurement of lattice combination bands. The role of localized vibrations in vibronic spectra is briefly considered.

Luminescence as “forbidden” electronic transitions in diamond

Arguments are adduced to show that the doublet centred at 4152 A occurring in the spectrum of all fluorescing diamonds arises from ‘forbidden’ transitions analogous to the forbidden3P-1S transitions in the spectrum of C I. On the basis of this analogy, fluorescence lines are also expected to occur at about 8816 A and 7849 A, analogous to the3P-1D and1D-1S transitions in C I. Of these, the former should also occur in absorption, while the latter should not occur in absorption and should be emitted only if the exciting radiation has a wavelength shorter than 4152 A. A line has actually been found at 7930 A, satisfying the latter conditions. The former line could not be recorded being outside the limit of sensitivity of the photographic plate.