~"~ Solid State Communications, Vol. 67, No. 5, pp. 49~ 498, 1988. <~Printed in Great Britain. 0038-1098/88 $3.00 + .00 Pergamon Press plc Electronic State of A C-is Core Exciton in Diamond H.W,L. Alves*, H. Chacham**, J.L.A. Alves**, and J.R. Leite* *Instituto de F{sica, Universidade de Sao Paulo, CP20516, Sao Paulo, 01498 SP, Brazil ~*Departamento de F{sica, Icex, UFMG, CP 702, Belo Horizonte, MG, Brazil (Received January I0, 1988 by R.C.C. Leite) The carbon-Is core exciton formation in diamond has been in- vestigated within the framework of the local density theory associated to a molecular cluster model. By using the multi- ple-scattering technique to solve the one-electron Schroedinger equation it has been shown that the electron state in the exciton is rather delocalized and quite similar to the single donor state induced by a substitucional on center nitrogen impurity. Therefore a hydrogenic-effective- mass theory description of a carbon-ls core exciton in diamond is expected to be highly appropriate. Introduction With the advent of synchrotron radiation, the characterization of core excitons has become a subject of experimental investigation during the last years. 1-6 Excitons, as a result of the formation of bound electron-hole pairs, play an important role in the fundamental understanding of the physical properties of insulators and semiconductors. In the core exciton the electron is bound to a hole in a core state. The core excitonic effects are detected by the enhancement of the absorption edge in optical absorption measurements and the excitonic binding energy is indirectly determined, i.e., it is obtained as the energy difference between the optical gap and the "photoemission energy gap".7, 8 A direct evaluation of the excitonic energies is usually not possible due to the lifetime broadening of the absorption llne. The only exception to our knowledge is the direct observation of the carbon-ls core exciton binding energy in diamond, 0.189 ± 0.015 eV, which was determined to a high degree of accuracy. 8 Most of the experimental data indicates that the excitonic binding energies of core excitons in semiconductors are generally about one order of magnitude larger than valence exciton binding energies or single isocoric donor energies in the same material. The well known hydrogenic-effective-mass theory 9 (HEMT), which has been successfully applied to describe the valence excitons or single isocoric donors, fails when applied to the core excitons, even when the dynamical effects are taken into account in the theory.10, II Recent attempts to obtain the core exciton spectra from rigourous first- principles self-consistent calculations enhanced our understanding of these systems considerably. 12,13 Results obtained for cationic core excitons in gallium arsenide 12 and II-VI compound semiconductors 13 show that the screening of the core hole state by the bound electron increases the core exciton binding energy. 12 It is also observed that the binding energy seems to be almost independent on the depth of the core level involved. 13 However, the measured binding energy of the carbon-ls core exciton in diamond is another typical puzzle among those usually found in the core exciton spectra of semiconductors. Recent application of HEMT to determine the ground-state C-is excitonic binding energy leads to the result 0.191 eV, in fairly good agreement with the measured value, 0.189 eV. 8 It is intriguing that we do not observe here the breakdown of the HEMT as it seems to occur for the description of core excitons in other semiconductors. 8 It is clear that the study of the core exciton problem in diamond by means of first- principles calculations is highly desirable. It would be interesting to verify whether the success of the HEMT in this case is fortuitous or is a real physical fact. In the present investigation we use the first principles self-consistent-field (SCF) multiple-scattering (MS) X~ molecular cluster model to carry out calculation of the 495