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Excitonic Effects In Core-Excitation Spectra Of Semiconductors

R. Buczko,1,2,3 G. Duscher,4 S. J. Pennycook1, S.T. Pantelides2,1

Full Article (PDF 168 KB)

Core-electron excitation spectra are used widely for structural and chemical analysis of materials, but interpretation of the near-edge structure has been controversial because electron-hole correlations may produce bound excitons below the band edge and also distort the continuum spectrum. For the important Si L2,3 edge, two mutually inconsistent interpretations have been used, in terms of effective-mass excitons and in terms of Bloch conduction-band final states. Ab-initio calculations show that neither interpretation is valid.

Calculations were performed using an all-electron energy-band code (Full-potential Linearized Augmented Plane Wave method). The resulting spectrum is shown in Fig. 1 using a threshold of 99.8 eV. The absolute magnitude of the absorption coefficient has not been adjusted. It is clear that spectra calculated without electron-hole interactions cannot reproduce the sharp onset of the experimental spectrum.  Core hole interactions were then included explicitly and the result showed good agreement with experiment (dotted line).  We also used the Z + 1 approximation, replacing the core hole with an additional proton, which reproduced the shape but not the absolute magnitude of the edge.  Finally we calculated the density of Bloch conduction-band final states multiplied by a matrix element extracted from the same calculation that produced the dotted curve (dash-dotted line).  This predicts a cross section about an order of magnitude too small.  Even adding effective-mass excitonic effects (long-dashed line) cannot account for the observed spectrum.

The calculations show that the common belief that energy loss spectra measure the conduction band density of states is not correct.  Accurate spectral shapes may be calculated through an all-electron code using the Z + 1 approximation or even a pseudopotential code provided matrix elements are calculated from an all electron code.  Such calculations enable experimental spectra to be inverted to deduce local bonding configurations at nanostructures and interfaces.

   
 
 
Figure 1
  Fig. 1. Experimental and theoretical X-ray absorption spectra of the Si L2,3 edge. Thick curve: experimental; solid curve: full calculation including electron-hole interactions with a self-consistent hole orbital; dashed curve: calculation using the Z+1 model; dotted curve: calculation of excitation spectrum without electron-hole interactions; dash-dot curve: effective-mass (parabolic band) spectrum without electron-hole interactions; long-dash curve: effective-mass spectrum with hydrogenic excitonic effects
   
 
  1. SSD ORNL
  2. Vanderbilt University, Nashville, TN.
  3. Polish Academy of Sciences, Warsaw, Poland
  4. North Carolina State University, Raleigh, NC

 Oak Ridge National Laboratory