Intrinsic edge absorption in diamond

Abstract

The optical transmission spectra of several diamonds have been studied over the range 5.0 to 6.0 eV (2450 to 2000 $\overset{\circ}{\mathrm A}$) and at many temperatures between 90 and 600 $^\circ$K. The reflexion spectrum was also recorded between 5 and 14 eV (2450 to 900 $\overset{\circ}{\mathrm A}$) at 295 $^\circ$K and between 5 and 8 eV (2450 to 1550 $\overset{\circ}{\mathrm A}$) at 133 $^\circ$K. The intrinsic features of the absorption edge spectrum are discussed in terms of allowed indirect electronic transitions into exciton and free carrier states of the crystal. A weak absorption component, exhibited only by a p-type semiconducting specimen (type IIb), is tentatively identified with an exciton state bound to the acceptor centre. Analysis of the absorption data yields six phonon energies. Three of these are greater than the Raman energy ($\hslash\omega)_R$ and appear to represent combinations of two or more phonons having the following energies: $(1)\quad(\hslash\omega)_{\text{Raman}} = 0\cdot167 \pm 0\cdot 010 eV,$ $(2)\quad(\hslash\omega)_{\text{transverse optical}} = 0\cdot143 \pm 0\cdot002 eV,$ $(3)\quad (\hslash\omega)_{\text{longitudinal optical, acoustical}} = 0\cdot132 \pm 0\cdot002 eV,$ $(4)\quad (\hslash\omega)_{\text {transverse acoustical}} = 0\cdot 083 \pm 0\cdot003 eV.$ The classification of the phonons (2) to (4) given above is discussed in the light of the current knowledge of the lattice vibrational spectrum of diamond. The present results suggest that the lowest minima of the conduction band are near to the boundaries of the reduced zone in the $\langle100\rangle$ direction (symmetry point X$_1$), if the maximum of the valence bands lies at the zone centre. The binding energy of the indirect exciton, measured from the absorption spectra, is 0$\cdot$070 $\pm$ 0$\cdot$004 eV. The density of states effective mass of electrons at the lowest conduction-band minima, estimated from this result, is ca. 0$\cdot$2 m$_0$, where m$_0$ is the mass of a free electron. The indirect energy gap at 295 $^\circ$K and its rate of change of temperature between 135 and 295 $^\circ$K, obtained from the absorption data, are $E_g = 5\cdot470 \pm 0\cdot005 eV; & dE_g/dT = -5\cdot4 \pm 0\cdot5 x 10^{-5} eV/\deg K$ The corresponding values for the direct energy gap, obtained from the reflexion data, are $E_g = 7\cdot02 \pm 0.02 eV; & dE_g/dT = -6\cdot3 \pm 1\cdot8 x 10^{-4} eV/degK.$ Finally, a broad peak has been observed in the reflexion spectrum at the energy predicted for the direct transition at $\langle111\rangle$ zone boundaries in diamond (9.2 $\pm$ 0.1 eV).