Measurement of energy‐loss anisotropy along [001] in monoclinic hafnia and comparison with ab‐initio simulations
Authors: Guedj Cyril , Bernier Nicolas , Colliex Christian , Olevano Valerio 
Published: December 2016

Abstract‐
Monochromated aberration‐corrected STEM‐VEELS (Valence Electron Energy‐Loss Spectroscopy) measurements are performed on monoclinic hafnia. The maximum energy‐loss anisotropy is observed for the [001] orientation, in agreement with ab‐initio TDDFT simulations. From the fine structure of the energy loss spectra, the hypothesis of a possible Fano effect on the Hf 5p edge may be investigated.

1. Introduction

Nanoscopy inside a transmission electron microscope opens a large field of applications, in particular in the semiconductor industry. VEELS has been developed to map the opto‐electronic properties at a subnanometer scale inside a HR(S)TEM. A dielectric anisotropy in m‐HfO
2
has recently been observed
1
by energy‐filtered TEM. The agreement with
ab initio
simulations is nearly quantitative
2
but the anisotropy along [001] and the finest structures of the spectra have not been published yet. The motivation of this presentation is to compare STEM‐VEELS spectra recently recorded at high energy resolution with their
ab initio
simulations.

1. Methodology

STEM measurements are performed with the FEI Titan Ultimate aberration‐corrected STEM in monochromated mode with an energy resolution of 0.17 eV. The convergence and collection angles are 15.6 and 20 mrad respectively. The 25 nm‐thick samples are prepared with a dedicated
3
FIB, following a procedure optimized for VEELS measurements. The time‐dependent density‐functional theory (TDDFT) simulations are generated with the DP
4
code using the random phase approximation including local field effects.

1. Results and discussion

The structure of monoclinic hafnia is usually complex because of the presence of small overlapping nanocrystals separated by intermixed defective interfaces. Therefore it is rather difficult to find an isolated HfO
2
grain with the well‐defined [001] orientation, as checked by HRTEM focal series and associated JEMS simulations (fig. 1). The agreement between experimental and simulated diffraction patterns is also nearly perfect. The highest anisotropy in EELS spectra, is observed for the [001] orientation around the plasmon peak position (~ 16 eV, see fig. 2), when compared to random orientation spectra and with the reference spectrum of Couillard et al.
5
[A1] . The agreement with ab‐initio simulations is also remarkable (fig. 3), especially in terms of predicted peak positions, although measurements realized on a perfect single crystal of m‐HfO
2
would improve the comparison. With the high energy resolution of our instrument, the Fano effect suggested to be responsible for the spectral dip associated with the excitation of the Hf 5p electrons in m‐HfO
2
can be more finely investigated. The associated asymmetric line shape can be identified around 42.3 eV, with a resonance width of 0.8 eV and a coupling factor of 0.6. The optical absorption spectra deduced from a Kramers‐Krönig analysis also confirm the occurrence of such an effect in m‐HfO
2
.

1. CONCLUSIONS

Monochromated STEM experiments demonstrate a clear anisotropy between [001] and other crystal orientations in m‐HfO
2
. This anisotropy is mostly visible around the plasmon energy (16 eV). The statistical analysis of thousands of EELS spectra confirms the existence of a Fano effect around 42.3 eV to be associated with the excitation of the Hf 5p electrons.