A Carnera

A Mazzolari

D De Salvador

D Lietti

E Bagli

E Vallazza

G Della Mea

G Maggioni

M Bazzan

M Dalla Palma

M Prest

N Argiolas

S Carturan

V Guidi

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Highly Bent (110) Ge Crystals for Efficient Steering of Ultrarelativistic Beams 
D. De Salvador1,2, G. Maggioni1,2, E. Bagli3, S. Carturan1,2, D. Lietti4, A. Mazzolari3, M. Dalla Palma2,5, N. Argiolas1, 
M. Bazzan1, V. Guidi3, A. Carnera1, M. Prest4, E. Vallazza6, G. Della Mea2,5 
1 Dipartimento di Fisica e Astronomia dell'Università di Padova, Padova, Italy. 
2 INFN, Laboratori Nazionali di Legnaro, Legnaro (Padova), Italy. 
3 Dipartimento di Fisica dell’Università di Ferrara and INFN, Sezione di Ferrara, Ferrara, Italy.  
4 Università dell’Insubria, Como, and INFN, Sezione di Milano Bicocca, Milano, Italy. 
5 Dipartimento di Ingegneria Industriale, Università di Trento, Trento, Italy. 6 INFN, Sezione di Trieste, Trieste, Italy. 
 
INTRODUCTION 
In a recent experiment De Salvador and co-workers [1,2] 
studied three different coherent interaction phenomena 
between a (111) Ge short strip crystal (1.85 mm long) and 
an ultra-relativistic proton beam: efficiencies of 72.5% and 
95.3% for channeling and VR, respectively, were obtained. 
The planar channeling efficiency for a nonparallel beam 
was higher than what reported for a similar Si sample and 
higher than previous experiments on Ge at similar 
energies. 
Though the experimental results presented in the 
previous paper are very promising and the ensemble of 
several key factors such as bending device strategy, careful 
choice of strip size and, most important, optimal crystal 
quality of the manufactured strip proved to be greatly 
beneficial for the final performances of the Ge crystal, 
nevertheless those results are not complete.  
In this work, an experimental investigation of channeling 
and VR phenomena with highly bent, thin (110) Ge strips 
is presented. In principle, (110) Ge lends itself better than 
(111) one to channeling, owing to the stronger coherent 
field generated by lattice atoms and to higher critical angle 
for incoming particles, as a result of longer inter-planar 
distance. 
EXPERIMENTAL 
Ge (110) strips can in principle be obtained by (110) 
wafers with the same procedures described in ref. [3,4]. On 
the other hand this particular orientation of Ge wafers is 
not of large interest for microelectronic applications and 
therefore much less available on the market.  
In order to circumvent this problem, some strips of (110) 
Ge were produced starting from a <100> Ge wafer 
(purchased by UMICORE) according to the procedure 
described in ref. [4].  
The ultrarelativistic channelling experiments were 
performed at the H8 extracted beam line of the SPS 
accelerator at CERN. A 400 GeV proton beam was used. 
RESULTS AND DISCUSSION 
Two Ge strips with two different curvature radii of the 
(110) planes were measured: Ra = 8.2 and 2.3 m. The strips 
were aligned in order to exploit (110) planar channeling. 
Fig. 1 presents the horizontal deflection angle in the case 
of the crystal with a 2.3 m radius (dashed line) and with a 
8.2 m one (continuous line) for particles impinging on the 
crystal in a spatial range of ± 0.2 mm in the horizontal 
direction and ± 0.5 mm in the vertical one, with a 
divergence range of ± 2 µrad in the horizontal direction. 
Fig. 1. Deflection angle for the Ge (110) planar channeling 
condition. 
The obtained efficiency and critical angle values for 
planar channeling cannot be easily compared with pristine 
previous experimental measurements with Ge crystals 
given the differences in the experimental setups. For 
instance, a maximum efficiency of 60% was reported for 
Ge (110) with a three-point bent 50 mm long crystals for 
450 GeV protons with an incoming divergence of 3 µrad. 
The efficiency measured by Biino et al. [5] was quickly 
decreasing at increasing curvature radius: at the values 
used in our experiment (Ra=8.2 m and 2.3 m) the 
efficiency was about 52% and 13% respectively for the 2 
radii. The results herewith reported improve this value: the 
maximum efficiency is higher than 74% at Ra=8.2 m and 
decreases to 56% at Ra=2.3 m. This significant efficiency 
improvement has been most likely obtained thanks to the 
short crystal bending strategy that we demonstrated to be 
applicable to Ge crystals. In fact, the shorter crystal 
reduces the effects of multiple scattering and the 
homogeneous curvature reduces dechanneling. Moreover 
our samples present a very low dislocation density 
reducing the dechanneling sources to those of an ideal 
crystal. 
Fig. 2. Planar channeling efficiency versus curvature radius for 
Ge and Si crystal strips as compared to simulated values. Si 
datum is from ref. [6], Ge (111) are from reference [1,2] and Ge 
(110) are from the present work. Simulations are obtained by 
semi-analytical calculation.  
In fig. 2 we report the efficiency results obtained as a 
function of the curvature radius. The data are compared 
with existing recent literature data for Ge and Si samples 
and with the efficiency obtained by semi-analytical 
calculation, on the basis of Moliere effective potential for 
(110) planes of Ge with the specific curvature radius. The 
method will be better described in a forthcoming paper. 
A very good agreement between the calculated and 
evaluated curves is obtained for all the data. This allows to 
conclude that the calculated curves are accurate 
extrapolations of the experimental trends at all the 
curvatures. Moreover, no parameter is introduced in the 
calculation to correct the data for possible defects neither 
in Si or in Ge, therefore we can conclude that both Si and 
Ge performs at the “ideal crystal” limit. The difference 
between the two kinds of crystals are only due to the 
difference in the potential shape.  
As expected, the deeper well in the Ge crystal allows for 
the retention of a higher efficiency also at higher curvature 
(low radius) with respect to Si.  
The volume reflection condition was obtained by 
rotating the goniometric sample holder of a fraction of the 
bending angle in such a way that the beam becomes 
tangent to the (110) strip planes in the bulk of the crystal. 
In this condition data were acquired for both curvatures. 
The deflection angle is shown in fig. 3 for both curvature 
radii.  
As can be noted, most of the particles are deflected to a 
negative angle in the opposite direction of the channeling 
one as typically reported for the VR phenomenon. A small 
fraction of particles is deflected at positive angles thanks to 
the volume capture phenomenon: some of the particles, 
after losing a fraction of their energy by multiple 
scattering, can be captured by the channel and can continue 
their path in a curved trajectory. Those particles which 
complete their trajectories in the bent channel cause the 
peak at large angles visible for both the curvature radii. 
Some of the captured particles may undergo dechanneling 
because of their large oscillating amplitude in the channel; 
those particles fill the tail that joins the main volume 
reflection peak to the small volume capture peak in the 
plot. In order to quantitatively estimate the VR 
phenomenon, we have fitted the main peaks with gaussian 
curves, determining the average deflection angles θVR of 
(17.3 ± 0.3) µrad and (11.4 ± 0.2) µrad for the larger and 
smaller curvature radii, respectively. The θVR values are 
consistent with theories expressing the present 
understanding of the VR phenomenon. We also estimated 
the VR efficiency according to assessed procedures. The 
obtained values are (96.6 ± 0.9) % and (99.5 ± 0.8) % for 
the larger and smaller curvature radii, respectively. The 
very low probability of volume capture at high curvature 
radius accounts for the exceptionally high efficiency value 
herein observed.  
Fig. 3. Horizontal deflection angle in the volume reflection 
condition. The thick line is relative to Ra=8.2 m, the dotted one to 
Ra = 2.3 m. Nonaligned beam deflection in the 8.2 m case is 
reported for comparison (dashed line). 
ACKNOWLEDGMENTS 
This work was funded by INFN, Vth Commission 
(experiment COHERENT) and by the Ministry of 
Research and University (PRIN Project 2009). 
 
 [1] D. De Salvador et al., Appl. Phys. Lett. 98 (2011) 234102. 
 [2] D. De Salvador et al., submitted to AIP Proc. IonBeams12 
Conf. (2012). 
 [3] S. Carturan et al., Mat. Chem. Phys. 132 (2012) 641. 
 [4] S. Carturan et al., LNL Ann. Rep. (2011) 85. 
 [5] C. Biino et al., Phys. Lett. B 403 (1997) 163. 
 [6] W. Scandale et al., Nucl. Instr. Meth. B 268 (2010) 2655.
 


Highly Bent (110) Ge Crystals for Efficient Steering of Ultrarelativistic Beams

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Highly Bent (110) Ge Crystals for Efficient Steering of Ultrarelativistic Beams

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