Modifications of the Meissner screening profile in YBa$_2$Cu$_3$O$_{7-\delta}$ thin films by gold nanoparticles

0.42 MB·

by  E. Stilp

Modifications of the Meissner screening profile in YBa Cu O thin films
2 3 7−δ
by gold nanoparticles
E.Stilp,1,2 A.Suter,1 T.Prokscha,1 Z.Salman,1 E.Morenzoni,1 H.Keller,2 C.Katzer,3 F.Schmidl,3 andM.D¨obeli4
1Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
2Physik-Institut der Universita¨t Zu¨rich, Winterthurerstrasse 190, CH-8057 Zu¨rich, Switzerland
3Institut fu¨r Festk¨orperphysik, Friedrich-Schiller-Universita¨t, Helmholtzweg 5, D-07743 Jena, Germany
4Laboratory of Ion Beam Physics, ETH-Zu¨rich, Schafmattstrasse 20, CH-8093 Zu¨rich, Switzerland
(Dated: January 27, 2014)
AddingAunanoparticlestoYBa Cu O thinfilmsleadstoanincreaseofthesuperconducting
2 3 7−δ
4 transitiontemperatureTc andthecriticalcurrentdensityjc. Whilethehigherjc canbeunderstood
1 in terms of a stronger pinning of the flux vortices at the Au nanoparticles, the enhanced Tc is
0 still puzzling. In the present study, we determined the microscopic magnetic penetration profiles
2 and the corresponding London penetration depths λL in the Meissner state of optimally doped
n YBa2Cu3O7−δ thinfilmswithandwithoutAunanoparticlesbylow-energymuonspinrotation. By
Rutherfordbackscatteringspectrometry,weshowthattheAunanoparitclesaredistributedoverthe
a
wholethicknessofthethin-filmsamples. Thesuperfluiddensityn ∝1/λ2 wasfoundtoincreasein
J s L
4 the films containing Au nanoparticles. We attribute this increase of ns to a reduction of the defect
density possibly due to defect condensation at the Au nanoparticles.
2

]
n The influence of disorder on cuprate systems is still films with different Au contents by means of low-energy
o an open issue. It is known that disorder directly af- muon spin rotation (LE-µSR) experiments and Ruther-
c fects the superconducting properties of these systems, ford backscattering spectrometry (RBS). The amount
- buttheunderlyingmechanismsarenotfullyclarified.1 In and the distribution of the Au nanoparticles were deter-
r
p YBa Cu O (YBCO), for instance, the charge carrier minedaswellasthemicroscopicchangesoftheMeissner
2 3 7−δ
u
transferfromtheCu-OchainstotheCuO planesiscru- screening profile and the London penetration depth λ .
s 2 L
cialfortheappearanceofsuperconductivity. Thischarge This is of special interest, since λ is related to the su-
. L
t
a transferdependsstronglyontheoxygenorderandonthe perfluid density ns:
m oxygenmobilitywithintheCu-Ochains.2 Substitutionof
m∗
d- csihoaninoCf uthbeysoutpheerrcomnedtuacltioinngslteraadnssigtieonnertaelmlypteoraatsuurpepTres.3- λ2L ∝ ns , (1)
c
n Surprisingly, this does not apply to Au. Superconduct- where m∗ is the effective mass of the supercarriers.
o
ing quantum interference device (SQUID) and neutron The optimally doped YBCO thin films studied in this
c
[ diffraction measurements performed by Cieplak et al.4,5 workwerepreparedbypulsed-laser-deposition(PLD)us-
showthatitispossibletoincorporate10at.%Auintothe ing a KrF excimer laser (λ = 248nm, τ = 25ns) at
1 structureofpolycrystallineYBCO,whereAuexclusively the Friedrich-Schiller-Universit¨at in Jena. Single-crystal
v
replacesthechainCu(1)atoms. Thisleadstoanincrease SrTiO 10×10×1mm3 in size and polished with the
5 3
9 of Tc of about 1.5K and to an increase of the c-axis lat- surface perpendicular to the [001] crystal axis was used
2 ticeconstant. TheCu-ObondlengthbetweenCu(1)and as substrate. In order to realize clustered Au nanoparti-
6 the oxygen in the Cu-O chains as well as between Cu(1) cles, an initial gold seed layer of 1.8nm thickness was
. and the bridging oxygen are enlarged. Previous studies sputtered on the substrates by dc-magnetron sputter-
1
0 revealedalsoalowernormalstateresistanceandaminor ing (I = 10mA, U = 215V, growth rate: 4nm/min,
4 influence on the normal state magnetization and on the p = 5mbar). Subsequently, the Au coated substrates
Ar
1 upper critical field.6 were heated to 780◦C to achieve a dewetting of the Au
: Recently, it has been demonstrated that Au nanopar- seed layer. The resulting nanoparticles were overgrown
v
i ticles, incorporated in YBCO thin films, lead to an in- by YBCO in an in situ process. The YBCO deposition
X
crease of T and the critical current density j (from was realized by a PLD process in an oxygen atmosphere
c c
r 4·107A/cm2 to6·107A/cm2 at10K).7,8 SinceYBCOis (repetition rate: 5Hz, laser fluence: 2.2J/cm2, growth
a
superconducting above the boiling temperature of nitro- rate: 20nm/min,p =0.5mbar). Inordertoobtainthe
O2
genthisisofspecialinterestforapplications. Astronger orthorhombicphase,theresultingYBCOthinfilmswere
fluxpinningofthevorticesattheAunanoparticlescauses cooled down to room temperature at a rate of 50K/min
a higher j , which is crucial in order to improve super- in pure oxygen (p = 800mbar). The resulting opti-
c O2
conductingmagneticfieldsensors8,9asusedindc-SQUID mally doped YBCO thin films have a typical thickness
gradiometers. of 120−200nm and are c-axis oriented. With the Au
Until now little is known about the effect of the in- seedlayerthicknessusedthetypicalAuparticlesizeisin
clusionofAunanoparticlesonthemicroscopicsupercon- the range 10−40nm.8 The area distribution of the Au
ductingparameters,suchasthesuperfluiddensityn . In nanoparticlesisquitehomogeneous,whereastheconcen-
s
thepresentstudyweinvestigatedtwosetsofYBCOthin trationwithinthedepthprofilevaries,aslaterdiscussed.
2
Moredetailsonthegrowthandthepropertiesoftheused saic of four samples from one set was glued with silver
samples can be found in Refs. 7 and 8. The mean dis- paintonanickelcoatedaluminumplate. Thelow-energy
tancebetweentheAunanoparticlesisabout50nm. The muons(µ+)areproducedatarateofabout104s−1 using
samples are therefore still in the clean limit, since the a solid Ar/N moderator. After reacceleration the final
2
correlation length is of the order of 2nm. energy of the muons is adjusted by a bias voltage at the
Here, we studied two sample sets with (YBCO ) and sample. By tuning the energy between 5 and 25keV the
Au
without(YBCO)Aunanoparticles. Asexpected,slightly mean stopping depth of the muons can be varied in a
higher T values were observed by resistivity measure- range of 25−106nm in YBCO (see Fig. 3).
c
ments for the YBCO compared to the pristine YBCO In condensed matter, muons act as local magnetic
Au
thin-film samples (see Fig. 1). In order to monitor pre- probes. Measuring the time difference t = t − t be-
e s
cisely the amount as well as the distribution of Au as a tween the implantation time t and the decay time t
s e
functionofdepthinthethin-filmsamples,RBSmeasure- of the µ+, detected via the decay positron, allows one
ments were performed at ETH Zu¨rich. For RBS a 4He to determine the temporal evolution of the muon-spin
beamwithanenergyof2−5MeVandasiliconPINdiode polarization P(t).16 This is possible due to the parity
detectoratascatteringangleof168◦wereused.10Theel- violation of the weak decay which results in a positron
ementalcompositionwasdeterminedbyusingtheRUMP emissionpreferentiallyalongtheµ+ spindirectionatthe
software.11 In the YBCO samples no Au peak is present time of decay. The positron count rate N(t) is given by:
intheRBSspectraasexpected. Thestoichiometryofop-
timallydopedYBCOwasconfirmedwithinexperimental N(t)=N0 e−t/τµ[1+AP(t)]+NBkg, (2)
uncertainty. The Au concentrations as function of depth
with a mean µ+ lifetime of τ =2.197µs, where N
were determined in the YBCO samples as depicted in µ 0
Au gives the scale of the counted positrons, N is a time-
Fig. 2. In these samples the Au nanoparticles are dis- Bkg
independentbackgroundofuncorrelatedevents,andAis
tributed over the whole superconducting region. On av-
the observable decay asymmetry.
erage there are about 4(1)·1015 Au atoms/cm2 in this
TheexperimentswereperformedintheMeissnerstate.
region. The so-called dead layer close to the substrate
After zero field cooling to 5K a magnetic field B =
interface d contains less nanoparticles and exhibits no ext
DL 8mT<µ H isappliedparalleltothethin-filmsurfaces
macroscopic Meissner screening. This is consistent with 0 c1
and perpendicular to the initial muon spin. In this case
the lower T generally observed in this region in these
c the muon-spin polarization P(t) is given by
thin-film samples.12
In order to determine the Meissner screening pro- (cid:90)
file B(z) and the temperature dependence of the mag- P (t)=e−σ2t2/2 n(z)cos[γµB(z)t+φ]dz, (3)
neticpenetrationdepthλ inastraightforwardwayLE-
L
µSRexperimentswereperformedattheµE4beamlineat with the initial phase φ, the muon gyromagnetic ra-
thePaulScherrerInstitut(PSI,Switzerland).13,14 Amo- tioγ =2π·135.5MHz/T,andthedepolarizationrateσ
µ
) S T O D L S C D L
1 0 0 2/nm 8
m
/c
)1 0 -1 ms 6
(100K1 0 -2 130 ato Y B C O A u
(cid:1)ab (1 4
(cid:1) (T)/ab1 0 -3 ntration
1 0 -4 Y B C O : T c= 9 0 .2 ( 2 ) K ce 2
n
Y B C O : T = 9 0 .8 ( 1 ) K o
A u c c d d z
1 0 -5 Au 0 D L sc 0
8 5 9 0 9 5 1 0 0 1 5 0 1 0 0 5 0 0
T ( K ) z (n m )
FIG. 1. (Color online) In-plane resistivity ρ normal- FIG. 2. (Color online) Gold concentration versus depth z
ab
ized at 100K versus temperature T of PLD-grown opti- alongthecrystallographicc-axisforaYBCO thin-filmsam-
Au
mally doped YBCO thin-film samples: YBCO (black dia- ple determined by RBS. The different regions are labeled:
monds) and YBCO (red circles). The listed values of the STOisthesubstrateregion(darkgray),DListhedeadlayer
Au
superconducting transition temperatures T are defined by atthesubstrate(d )andatthevacuum(z )interface(light
c DL 0
ρ (T )/ρ (100K)≤2.5·10−4. They are averaged over five gray), SC is the superconducting region with thickness d
ab c ab sc
measurement cycles (heating and cooling). (yellow). The red line is a guide to the eye.
3
TABLE I. Summary of the parameters determined for the investigated optimally doped YBCO thin-film samples with
(YBCO )andwithoutAunanoparticles(YBCO).ThesuperconductingtransitiontemperaturesT wereobtainedfromresis-
Au c
tivitymeasurements. TheaveragefilmthicknessesdwereextractedfromRBSmeasurements. FromaglobalfitoftheLE-µSR
data the superconducting thicknesses d , the dead layer thicknesses to the vacuum interface z , and the London penetrations
sc 0
depths λ (10K) were determined. λ (0K) and the superconducting gap ∆ were extracted from a linear fit in the range
ab ab 0
5−35K of λ (T) measured with LE-µSR. For comparison single crystal values20 are also presented.
ab
Sample T (K) d (nm) d (nm) z (nm) λ (10K) (nm) λ (0K) (nm) ∆ (meV)
c sc 0 ab ab 0
YBCO film 90.2(2) 150(8) 119(1) 0(2) 161(1) 158(1) 22(2)
YBCO film 90.8(1) 152(8) 133(1) 1(2) 154(1) 150(1) 24(2)
Au
YBCO bulk20 94.1(1) 10.3(5) 115(4) 20(4)
whichisameasureofanyinhomogeneouslocalmagnetic By the simultaneous analysis of the µSR spectra mea-
field distribution at the µ+ site. The muon stopping dis- sured at seven different implantation energies at 10K,
tributions n(z) for different energies are simulated using the Meissner screening profiles of the two sample sets
the Monte Carlo code TRIM.SP15 (see Fig. 3). The ap- YBCO and YBCO were determined (see Fig. 4). The
Au
plicability of the TRIM.SP code for low energy muons resulting values of the parameters are listed in Table I.
stopping in matter is demonstrated in Ref. 17. Since Thethicknessofthesuperconductinglayerd issubstan-
sc
the thin films have twinned a- and b-axes, the average tially smaller than the average film thickness d in both
magnetic penetration depth λ is determined with the sample sets. This confirms the presence of a dead layer
ab
present experimental set-up. To analyze the data, the at the substrate interface d of about 31nm for YBCO
DL
London model profile for thin films was used, resulting andabout18nmforYBCO . Theinterfacelayer(d )
Au DL
from an exponential decay of B from both interfaces: exhibits only weak superconductivity as mentioned be-
ext
fore. No macroscopic Meissner screening is observed in
 (cid:18)z−z −d /2(cid:19) this region. This could be explained by the presence of
B(z)=Bextcoshcosh(cid:18)d0λsca/b2(cid:19)sc ,z ≥z0 (4) gtoratihnebroeudnudcatrioiensdofueTctoinmtehchinanfiilcmalssctoraminp,a1r2eldeatdoinsginagllseo-
B λab ,z <z csarymsptalelsY,BinCdOica.tNinogtetthhaatttdhDeLAiussnmanalolperarfotircltehsemYaByCrOelAaxu
ext 0
the mechanical strain. The dead layers to the vacuum
where d is the thickness of the superconducting region,
sc
z is the depth along the c-axis, and z is the effective
0 1 .0 0
dead layer at the vacuum interface (see Fig. 2). This 1 0 K : Y B C O
dead layer may be due to the roughness of the surface18 1 0 K : Y B C O
A u
or to a reduction of the order parameter close to the 0 .9 8
surface.
ext0 .9 6
/B
Y B C O 5 .3 k e V >
5 B
7 .3 k e V < 0 .9 4
1 1 .3 k e V
4 1 4 .3 k e V
1 7 .3 k e V
0 .9 2
-1) 3 2 1 .3 k e V
m 2 4 .3 k e V
n 2 0 4 0 6 0 8 0 1 0 0
) (% 2 < z > (n m )
(z
n
FIG. 4. (Color online) The average local magnetic field nor-
1 malized to the applied field (cid:104)B(cid:105)/B versus the mean muon
ext
implantationdepth(cid:104)z(cid:105)measuredinanappliedmagneticfield
0 Bext = 8mT parallel to the film surface at 10K for thin-
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 film YBCO and YBCO . The solid lines represent the re-
Au
z (n m ) sults of the global fits obtained with musrfit,19 where seven
µSR spectra with different energies were analyzed simulta-
FIG. 3. (Color online) The normalized stopping distribution neously. The used parameter values are listed in Table I.
of positively charged muons n(z) for different implantation The data points are determined from single energy fits using
(cid:82)
energies (see inset) of a 150nm thick YBCO film simulated (cid:104)B(cid:105) = n(z)B(z)dz, where n(z) is the muon implantation
with TRIM.SP.15 The lines are guides to the eye. profile of the corresponding energy (see Fig. 3).
4
smaller, since most of the Au nanoparticles remained at
Y B C O : E = 1 1 .3 k e V
5 0 0 A u the interface to the substrate.
Y B C O : E = 1 4 .3 k e V
A u A possible explanation for the reduced magnetic pen-
etration depth in YBCO is the diffusion of Au from
Au
4 0 0 thenanoparticlesintotheCu-Ochains(likelyduringthe
YBCO deposition), since Au has a relatively high mo-
) bility at higher temperatures. A replacement of Cu(1)
m
(n 3 0 0 by Au in the Cu-O chains leads to an increase of the
(cid:1)ab oxygen mobility.23 An enhanced oxygen mobility favors
longer Cu-O chain segments leading to in increase of
the charge carrier transfer from the Cu-O chains to the
2 0 0
CuO planes.2 Since more charge carriers can contribute
2
to superconductivity, n increases while λ decreases.
s ab
0 2 0 4 0 6 0 8 0 In this case the c-axis lattice constant should be slightly
T ( K ) increased.4 This,however,wasnotobservedintheinves-
tigated samples.
FIG. 5. (Color online) The London penetration depth λab AnotherpossibilityisthatthepresenceofAunanopar-
versus temperature T for thin-film YBCO and YBCOAu. ticles in the superconducting region of YBCO lowers the
λ was determined from (cid:104)B(cid:105)/B (Gaussian fit to the µSR
ab ext defect density and leads therefore to the observed re-
spectra with musrfit19) by using the parameters from the
duction of λ in YBCO . A reduced defect density
globalfitdeterminedat10K.Theappliedmagneticfieldwas ab Au
could originate from a condensation of defects at the Au
B =8mT.TheimplantationenergiesE giveninthefigure
ext nanoparticles,sothattheCuO planesandthestructure
were selected according to the minimum in (cid:104)B(cid:105)/B . The 2
ext
arelessdisturbed. Toevaluatethedefectdensitywetake
corresponding solid lines are linear fits to the data in the
range 5−35K by means of Eq. (5). The parameter values thec-axislatticeconstantasanindication. InYBCOAu,
are listed in Table I. The dotted lines are fits to the power we observe a slightly smaller c-axis lattice constant
law λ (T)=λ (0)[1−(T/T )n]−1/2 with n(cid:39)2.7. (c = 1.1688(2)nm < c = 1.1699(2)nm).
ab ab c YBCOAu YBCO
YBCO single crystals have an even smaller c-axis lattice
constant (c = 1.167(1)nm).24 A lower defect den-
bulk
sity is generally expected in single-crystal YBCO com-
interface are surprisingly small in both sets (z ≈ 1nm)
0
compared to single-crystal YBCO (z (cid:39) 10nm)20 and pared to thin-film YBCO which is consistent with the
0
other YBCO thin-film measurements (z (cid:39)8nm).21 trend of the c-axis lattice constants. From this point of
0
view YBCO has a lower defect density than our pris-
YBCO screens the magnetic field better, and there- Au
Au tine YBCO, but a higher one compared to single-crystal
fore exhibits a smaller λ than our pristine YBCO
ab YBCO.Sincesingle-crystalYBCOhasalsoasmallerλ
(Fig. 4). The temperature dependence of λ of thin- ab
ab and a higher T compared to our YBCO and YBCO
film YBCO and YBCO is presented in Fig. 5. These c Au
Au samples, a reduced defect density is a possible reason for
values of λ were extracted from µSR spectra measured
ab the slightly different values of T and λ (0) in YBCO
attheenergycorrespondingtotheminimalaveragelocal c ab Au
compared to pure YBCO films.
magnetic field (cid:104)B(cid:105) at 10K. Both sample sets show a
min Insummary,wehaveshownbyusingLE-µSRthatthe
linear increase in λ up to 35K which is characteristic
ab increaseofT inthin-filmYBCOcontainingAunanopar-
for a d-wave pairing:22 c
ticles is accompanied by a reduction of the average mag-
netic penetration depth λ . We attribute this reduction
ab
λab(T)=λab(0K)·[1+ln(2)·kBT/∆0]. (5) to a lowered defect density. The diffusion of Au into the
Cu-Ochainsmayalsocontributetotheobservedchanges
The slopes for YBCO and YBCO are very similar of T and n . In previous studies on YBCO, Cu was ex-
Au c s
(≈0.4nm/K), so the superconducting gaps ∆ are the changed by Au within the Cu-O chains to obtain an en-
0
same within experimental uncertainty (see Table I). The hanced T . Our results indicate that the presence of Au
c
value of λ (0K) for YBCO is smaller compared to nanoparticles has a similar effect in thin-film YBCO.
ab Au
YBCO, but still larger than that one of single-crystal We acknowledge Hans-Peter Weber for his excellent
YBCO. If the amount of Au nanoparticles is higher (Au technical support. This work was partly supported by
seed layer of 3nm instead of 1.8nm) the same effects on the Swiss National Science Foundation and the Landes-
T and λ where observed. The nominal changes are graduiertenf¨oderung Thu¨ringen.
c ab
1 H.Alloul,J.Bobroff,M.Gabay,andP.J.Hirschfeld,Rev. 3 L. Shlyk, G. Krabbes, G. Fuchs, G. Sto¨ver, S. Gruss, and
Mod. Phys. 81, 45 (2009). K. Nenkov, Physica C 377, 437 (2002).
2 A. A. Aligia and J. Garces, Phys. Rev. B 49, 524 (1994). 4 M. Z. Cieplak, G. Xiao, C. L. Chien, J. K. Stalick, and J.
5
J. Rhyne, Appl. Phys. Lett. 57, 934 (1990). tions (Springer, Berlin, 1991).
5 M.Z.Cieplak,G.Xiao,C.L.Chien,A.Bakhshai,D.Arty- 16 A. Yaouanc and P. Dalmas de Reotier, Muon Spin Ro-
mowicz, W. Bryden, J. K. Stalick, and J. J. Rhyne, Phys. tation, Relaxation, and Resonance: Applications to Con-
Rev. B 42, 6200 (1990). densed Matter (Oxford University Press, Oxford, 2011);
6 U.Welp,S.Fleshler,W.K.Kwok,J.Downey,G.W.Crab- V. P. Smilga and Yu. M. Belousov, The Muon Method in
tree, H. Claus,A. Erb, and G. Mu¨ller-Vogt, Phys. Rev. B Science (Nova Science Publishers, New York, 1994).
47, 12369 (1993). 17 E. Morenzoni, H. Glu¨ckler, T. Prokscha, R. Khasanov, H.
7 C.Katzer,M.Westerhausen,I.Uschmann,F.Schmidl,U. Luetkens, M. Birke, E. M. Forgan, Ch. Niedermayer, and
Hu¨bner,andP.Seidel,Supercond.Sci.Technol.26,125008 M. Pleines, Nucl. Instr. Meth. B 192, 254 (2002).
(2013). 18 M. Lindstrom, B. Wetton, and R. Kiefl, J. Eng. Math.,
8 C. Katzer, M. Schmidt, P. Michalowski, D. Kuhwald, F. DOI 10.1007/s10665-013-9640-y.
Schmidl, V. Grosse, S. Treiber, C. Stahl, J. Albrecht, U. 19 A.SuterandB.M.Wojek,PhysicsProcedia30,69(2012).
Hu¨bner, A. Undisz, M. Rettenmayr, G. Schu¨tz, and P. 20 R.F.Kiefl,M.D.Hossain,B.M.Wojek,S.R.Dunsiger,G.
Seidel, EPL 95, 68005 (2011). D. Morris, T. Prokscha, Z. Salman, J. Baglo, D. A. Bonn,
9 C. Katzer, C. Stahl, P. Michalowski, S. Treiber, F. R.Liang,W.N.Hardy,A.Suter,andE.Morenzoni,Phys.
Schmidl, P. Seidel, J. Albrecht, and G. Schu¨tz, New J. Rev. B 81, 180502(R) (2010).
Phys. 15, 113029 (2013). 21 T.J.Jackson,T.M.Riseman,E.M.Forgan,H.Glu¨ckler,
10 M. Do¨beli, J. Phys.: Condens. Matter 20, 264010 (2008). T. Prokscha, E. Morenzoni, M. Pleines, Ch. Niedermayer,
11 L. R. Doolittle, Nucl. Instrum. Methods Phys. Res. B 15, G. Schatz, H. Luetkens, and J. Litterst, Phys. Rev. Lett.
227 (1986). 84, 4958 (2000).
12 H. Schneidewind, F. Schmidl, S. Linzen, and P. Seidel, 22 C.P.PooleJr.,H.A.Farach,R.J.Creswick,andR.Pro-
Physica C 250, 191 (1995). zorov, Superconductivity (Academic Press, London, 2007)
13 E.Morenzoni,T.Prokscha,A.Suter,H.Luetkens,andR. 23 H.Claus,S.Yang,H.K.Viswanathan,G.W.Crabtree,J.
Khasanov , J. Phys.: Cond. Matt. 16, S4583 (2004). W. Downey, and B. W. Veal, Physica C 213, 185 (1993).
14 T. Prokscha, E. Morenzoni, K. Deiters, F. Foroughi, D. 24 P.Benzi,E.Bottizzo,andN.Rizzi,J.Cryst.Growth269,
George, R. Kobler, A. Suter, and V. Vrankovic, Nucl. In- 625 (2004).
strum. Methods Phys. Res., Sect. A 595, 317 (2008).
15 W. Eckstein, Computer Simulation of Ion-Solid Interac-