Excitation spectrum of point defects in semiconductors studied by time-dependent density functional theory
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A common fingerprint of the electrically active point defects in semiconductors is the transition among their localized defect states upon excitation, which may result in characteristic absorptionor photoluminescence spectrum. Identification of such point defects by means of density functional theory (DFT) calculations with traditional (semi) local functionals suffers from two problems: the “band gap error” and the many-body nature of the electron-hole interaction of the excited state. We show that non local hybrid density functionals may effectively mimic the quasiparticle correction of the band edges and the defect levels within the band gap in group-IV semiconductors, thus they can effectively heal the “band gap error.” The electron-hole interaction can be calculated by time-dependent DFT (TD-DFT) method. Here, we apply TD-DFT on three topical examples: nitrogen-vacancy defect in diamond, silicon-vacancy and divacancy defects in silicon carbide that are candidates in effective development of solid-state quantum bits. I. INTRODUCTION
Point defects often act as color centers in semiconductors where we use the phrase “semiconductor” in a broader context. For instance, it includes germanium crystal with small gap of 0.7 eV and diamond with large gap of 5.5 eV. Electrically active point defects introduce defect levels in the fundamental gap of semiconductors. An incident photon may excite an electron from the valence band (VB) into the defect level or from the occupied defect level to the conduction band (CB). This is the band-todefect level or defect level-to-band excitation. When two defect levels occur in the gap then defect level-to-defect level excitation may also take place, which can be more effective than transitions between defect levels and bands. In all these processes, the light absorbed is at lower energies (i.e., at larger wave lengths) than that in pristine semiconductors, so point defects can change the “color” of the host semiconductors, nevertheless, not necessarily in the visible range of the spectrum. Spectroscopy tools involve the use of very sensitive methods [such as absorption or photoluminescence (PL)] that can show the fingerprints of these color centers in the corresponding spectra even if the concentration of the point defects responsible for the signal is relatively low. Color centers are usually effective electron or hole traps that can seriously deteriorate the operation of semiconductor devices, thus the identification of these color centers is of high importance. Besides the traditional a)
Address all correspondence to this author. e-mail: [email protected] This paper has been selected as an Invited Feature Paper. DOI: 10.1557/jmr.2011.431 J. Mater. Res., Vol. 27, No. 6, Mar 28, 2012
application in electronic devices, there is a fast emerging field of quantum optics where paramagnetic isolated color centers or other point defects in semiconductors may play a crucial role: accomplishing the solid state quantum bit or qubit. The detailed knowledge about the ground and excited states of c
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