Annual Report 2011 / 2012 - E21 - Technische Universität München

Chapter 3. Positron Physics 31
Quantum Confinement of Positrons in Au Clusters
P. Pikart 1, 2 , M. Horisberger 3 , Y. Matsukawa 4 , M. Hatakeyama 4 , T. Toyama 4 ,
Y. Nagai 4 , C. Hugenschmidt 1, 2
1 Physik-Department E21, Technische Universität München, D-85748 Garching, Germany.
2 Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II), Technische Universität München, D-85748 Garching, Germany.
3 PSI, Laboratory for Developments and Methods, CH-5232 Villingen PSI, Switzerland.
4 IMR, Tohoku University, 2145-2 Oarai, Ibaraki, Japan.
Introduction
Open-volume lattice defects and their chemical surrounding
can be studied non-destructively by coincident Doppler broadening
spectroscopy (CDBS) of the positron annihilation line.
Not only vacancy-like defects but also agglomerations
of atoms with a higher relative positron affinity ∆A + < 0
might form a trapping potential for positrons [1]. Due to its
elemental selectivity CDBS is particularly suited to detect
small metallic clusters or precipitates embedded in a matrix.
In addition, the application of a monoenergetic positron beam
allows one to adjust the positron implantation depth
which leads to a greatly enhanced sensitivity in a selected
depth.
Experimental
In the present study, defect-sensitive and element-selective
measurements on ultra-thin Cr, Cu, and Au layers embedded
in Al were performed by CDBS with the monoenergetic positron
beam at NEPOMUC [2]. The specimens, which were
grown by magnetron sputtering out of high-purity materials,
consist of an Al substrate, an intermediate layer of Cr, Cu or
Au, and a cover layer of 200 nm Al. Among these elements
Au has the highest positron affinity, i.e.∆A + =-1.82 eV with
respect to Al.
The obtained CDB spectra of Au layers with a nominal
thickness of 0.5, 2 and 100 nm embedded in Al and reference
spectra of pure Au and Al are shown in Figure 1. A clear Au
signature at the 100 nm layer was recorded which remained
almost the same even at a nominal thickness of only 2 nm
Au embedded in Al. The sample with an embedded Au layer
of only 0.5 nm showed no Au signature at all.
Figure 1: CDB spectra of Au layers with different nominal thickness
embedded in Al and reference spectra of pure Au and Al.
The Au signature is clearly visible at a Au layer of only 2 nm
embedded in Al.
Complementary TEM studies were performed in order to
image the buried layers as exemplified in Figure 2.
Aperture out
c
b
a
Area
c
b
d
a
Aperture in
20 nm
Figure 2: TEM image of the Au rich layer (b) embedded in Al
(a,c). The bright-field image (aperture in) reveals the grains and
grain boundaries of the Au clusters (d).
Positron trapping in Au clusters
The extremely high sensitivity, which was already achieved
for the 2 nm Au layer, is attributed to the highly efficient
positron trapping in the Au layer and Au clusters. Exceeding
a critical size, Au clusters in Al form a three dimensional
quantum well that confines the positron wave function. The
critical radius r c for positron trapping was calculated based
on the positron affinity difference ∆A + and amounts to
r c =0.23 nm. Consequently, Au clusters containing at least
14 Au atoms lead to efficient positron trapping. For the same
reason, no positron trapping sites are formed by Au at
the sample with a nominal thickness of 0.5 nm Au where no
Au signature was observed.
The positron behaviour was theoretically descirbed in two
steps: First, the psoitron implantation profile was calculated
using the Makhov-approximation. In a second step, a random
walk model was implemented to describe the positron
diffusion and the trapping in buried layers. The comparison
of the experimental results with Monte Carlo simulations of
the positron diffusion indicated a strong positron trapping
in the AlAu alloy layer in Al. Finally, the theoretically calculated
positron affinity was proofed to be a profound basis
for the understanding of a quantum confinement based model
of the positron trapping in Au clusters with a minimum
diameter of 0.46 nm surrounded by Al.
References
[1] C. Hugenschmidt et al., Physical Review B 77, 092105 (2008).
[2] P. Pikart et al., Physical Review B 84, 014106 (2011).