Breaking of Raman selection rules in Cu 2 O by intrinsic point defects
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Breaking of Raman selection rules in Cu2O by intrinsic point defects Thomas Sander1,*, Christian T. Reindl1, and Peter J. Klar1 1
I. Physikalisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, 35392 Gießen, Germany
*[email protected]
ABSTRACT The semiconductor cuprous oxide crystallizes in a simple cubic structure and reveals outstanding characteristics: Independent of the method and conditions of the synthesis of crystalline Cu2O its Raman spectra are dominated by infrared active, silent, and defect modes rather than by Raman allowed phonon modes only. A detailed group theoretical analysis demonstrates that point defects reduce the local symmetry, lift the Raman selection rules, and thus diminish the distinction between Raman allowed and Raman forbidden lattice vibrations. Of all intrinsic defects only the presence of the copper vacancy in the so called split configuration introduces possible Raman activity for all Cu2O extended phonon modes observed in experiment. INTRODUCTION Already in 1951, in a review article about copper oxide rectifiers, W. H. Brattain has described the origin of Cu2O as a semiconductor by "Copper oxide is a defect semiconductor. … The main impurity centers, acceptors in this case, are probably vacant copper ion lattice sites." [1]. Hardly anything has changed concerning the validity of this statement, nowadays it is well established that Cu2O is a natural p-type semiconductor, whose carrier concentration depends on the amount of cation deficiency (non-stoichiometry). Non-stoichiometry due to the formation of point defects such as vacancies, interstitials, or antisite defects has three major effects in Raman spectroscopy: On the one hand, perfect translational symmetry is broken leading to the breakdown of the wave vector selection rules allowing phonon momentum values from the whole Brillouin zone. Further, the Raman selection rules do no longer hold strictly, e.g. the point defects reduce the local symmetry such that the distinction between Raman allowed and forbidden lattice vibrations diminishes compared to the space symmetry of the crystal. On the other hand, depending on the point defect and its compatibility with the lattice, local vibrational modes may be introduced, which may also be Raman active. The Raman spectra of Cu2O are very good examples for these effects as the dominant Raman signals observed are actually due to infrared active, silent, or defect modes rather than due to the nominally Raman active mode.
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VIBRATIONAL CHARACTERISTICS OF Cu2O Three different phases CuO (cupric oxide), Cu2O (cuprous oxide), and Cu4O3 (paramelaconite) of the binary semiconductor are known. Each reveals unique Raman spectra due to their differences in crystal structure [2]. As depicted in figure 1a), cuprous oxide crystallizes in a simple cubic structure of space group O4h (Pn-3m) [3,4]. Its unit cell contains two Cu2O units, i.e. six atoms, yielding 18 phonon modes. Huang performed the first group theoretical analysis of the vibrational modes alrea
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