Quantitative Analysis of Valence Electron Energy-Loss Spectra
of Aluminum Nitride
A. D. Dorneich *, R. H. French **, H.
Müllejans *, S. Loughin ***, M. Rühle *
- * Max-Planck-Institut für Metallforschung, Seestraße 92,
D-70174 Stuttgart, Germany
- ** DuPont Central Research, E356-384 Experimental Station,
Wilmington, DE 19880, USA
- *** Lockheed Martin, Mail Stop 29B12, PO Box 8555,
Philadelphia, PA 19101, USA
Abstract
The optical properties and electronic structure of aluminum
nitride are determined using valence electron energy-loss spectroscopy in a
dedicated scanning transmission electron microscope. Quantitative analysis of
the experimental valence electron energy-loss spectra to determine the
electronic structure encompasses: single scattering deconvolution of the valence
electron energy-loss spectra to calculate the energy-loss function,
Kramers-Kronig-analysis of the energy-loss function to reveal the complex
dielectric function, transformation of the dielectric function into the optical
interband transition strength via optical property relations and finally
critical point analysis of the interband transition strength. The influence of
both experimental and analytical parameters on the final result was
systematically studied to define and improve the understanding of the methods.
To check the reliability of this technique the interband transition strength
determined was compared to results of vacuum ultraviolet spectroscopy. Good
agreement was found if sample preparation was taken into account. The
preparation of the specimen for the transmission electron microscopy has an
effect on the electronic structure. Quantitative analysis of valence electron
energy-loss spectroscopy, using the methods presented, is an important and
capable method to determine the electronic structure of materials and it has the
benefit of high spatial resolution.
Kramers Kronig Dispersion Relation for the Energy Loss
Function
Index Sum Rule used to Scale the ELF
The Interband Transition Strength Jcv
The f Oscillator Strength Sum Rule
Figure 1. Energy-loss spectrum of single crystal
AlN covering the zero-loss (1), low-loss (2) and core-loss (3) regions. The
y-axis is on a logarithmic scale.
Figure 2. Single scattering
energy-loss spectrum (SSD) for single crystal AlN determined by single
scattering deconvolution of the multiple scattering energy-loss spectrum (MS).
Also shown is the zero-loss peak (ZL) with the fitted zero-loss peak wing
extension. Note the second plasmon peak evident at » 40 eV, which is not evident in the single scattering distribution.
Figure 3. Energy-loss function
(Im(-1/e) of single crystal AlN, on an absolute scale
determined using the index sum rule, and Re(1/e)
determined by Kramers-Kronig dispersion analysis.
Figure 4. Interband transition
strength of single crystal AlN, where the absorptive component is given by Re(JCV)
and the dispersive component is given by Im(JCV).
Figure 5. Comparison of the real
part of the Interband Transition Strength Re(JCV) of AlN determined
by VEELS and VUV-spectroscopy.
