Using a simplified in line holography method as a qualitative tool to detect local heterogeneities in
HfO2
layers
Authors: Alemany Mathias , Donnadieu Patricia , Chabli Amal , Rauch Edgar , Mayall Ben , Bernier Nicolas , Gros‐Jean Mickael , Barthe Marie‐France 
Published: December 2016

Oxygen vacancies in high‐k oxides are foreseen to have detrimental effects in devices like high‐k metal gate MOS transistors [1] and beneficial ones in RRAM [2]. In this context techniques capable to characterize defects in ultra‐thin (2 thin films and revealed the impact of the grain nanostructure on the electronic structures [4]. When traversing the sample electron waves experience a phase shift related to the local inner potential created by atoms. The reference technique to retrieve this phase shift is off axis electron holography. However as it is a delicate technique, the alternative in line holography based on the acquisition of a focal series can be of interest. The advantage of in line holography is to be easy to carry out in the course of a classical TEM study and to provide phase image on a large scale (up to several microns). The present work aims at examining the capabilities of a simplified approach of in line electron holography to evidence heterogeneities in a polycrystalline HfO
2
layer.

The
in line
holography method consists first in acquiring images at different defocus (‐D, 0, D) and then deriving the phase image using a post treatment that realizes the inversion of the phase transfer function. Various numerical treatments are possible, however a simple inversion process based on a small angle approximation can be achieved [5]. As a consequence of the approximation, the phase map has a limited spatial resolution, typically 1 nm for a 100 nm defocus. Also the inversion leads to a singularity at
q = 0
that can be dealt with using a Gaussian edge filtering or more efficiently a Tikhonov regularisation (i.e.

a q
2
/(q
2
+a
2
)
2

filter) [6]. Depending on the parameter
a
, long range fluctuations can be amplified or cancelled out which have a significant impact on the value of the phase output. However if only a qualitative information on the phase map is desired, this simplified
in line
holography can be used as a tool to point out chemical or charge fluctuations within the sample.

Figure 1 shows a HRTEM image of a FIB lamella from an HfO
2
layer grown by atomic layer deposition (ALD). A detailed analysis and FFT treatments have allowed to identify nanograins within the HfO
2
layer as illustrated by Figure 1b: the grain size is in the 5‐20 nm range. Focal series corresponding to the image in Figure 1 have been recorded. Using images at defocus of ±50 nm, the simplified
in line
holography treatment gives the phase images shown in Figure 2 (spatial resolution ~0.7 nm). Figure 2a and Figure 2b correspond to a parameter
a
equal to 0.07 nm
‐1
and 0.21 nm
‐1
respectively. As illustrated out by the marked areas in these figures, the phase images exhibit features independent from the numerical parameter
a
: here grain and grain boundary regions correspond to positive (blue and violet) or negative phase shift (green and red).

If diffraction effects are not involved, phase shifts of opposite sign should indicate effect of different nature on the local potential as can be expected from vacancies and chemical segregation. Of course, these defects will need further investigation by advanced TEM techniques to be identified. However the phase maps derived from the simplified
in line
holography approach can constitute a simple tool to evidence local heterogeneities in a complex microstructure.