Excited Multiplets of Eu in GaN
- PDF / 751,801 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 92 Downloads / 273 Views
Excited Multiplets of Eu in GaN Ben Hourahine Department of Physics, SUPA, 107 Rottenrow, University of Strathclyde, Glasgow, Scotland, GL4 0NG, UK ABSTRACT A method to calculate the multiplet states of lanthanide impurities in solids is presented. This approach is based on a semi-empirical density functional method which includes corrections to account for the correlation and spin-orbit coupling of the 4f electrons. Specific multiplet states of the rare earth are produced by constraining the system. This approach is then used to investigate some of the properties of substitutional europium impurities in gallium nitride, reproducing the relative energy of two multiplets, and discussing a potential excitation mechanism for these centers. INTRODUCTION The optical spectra of trivalent rare-earth impurities in semiconductors are dominated by inter-f-shell transitions between multiplets of the ions, which themselves are labelled according to the atomic Russel-Saunder scheme [1]. These states are challenging to model theoretically for several reasons. In the general case of lanthanides with partly filled 4f shells, the typical choice of mean-field density functional theory (DFT) produces a qualitatively incorrect description of the levels. The states are also split by spin-orbit coupling, hence methods beyond the usual scalar relativistic correction of the energy levels of heavy atoms are also needed. Finally, conventional DFT is a ground state technique and while time-dependent DFT does allow access to excitation energies, the currently available functionals perform poorly for both ionic systems and charge transfer excitations. The experimental excitation processes of rare-earths are also contentious, with models based on either universal alignment of atomic energy levels to the semiconductor band-structure [2], or structured isoelectronic impurities (dopants which behave sufficiently similarly to a constituent element of the crystal, but posses further internal structure)[3]. The semi-empirical density-functional based tight binding (DFTB) method [4,5] has been extended to treat the gross physical effects present for lanthanide impurities in solids. The electronic properties of Eu have previously been investigated using DFTB[6], using a groundstate non-relativistic form of the current method. In this study, Sanna et al. found an acceptor level for europium, where the total number of 4f electrons changes from 6 (trivalent) to 7 (divalent) at Ev+2.70 eV, decreasing to Ev+1.58 eV if the negative charge state is structurally relaxed. This type of europium acceptor level has also been suggested on the basis of selfinteraction corrected DFT[7] in cubic GaN. A short description of the DFTB method and its extensions to treat 4f electrons is now given, followed by a discussion of the 7F0 ground and 5D0 excited states of subsitutional trivalent europium in GaN.
THEORY The DFTB[4] method is a form of non-orthogonal two center tight-binding where the onsite and hopping integrals are explicitly calculated from full DFT. A minimal
Data Loading...
