Experimental determination and simulation of the angular ...

IOP PUBLISHINGJOURNAL OF PHYSICS D: APPLIED PHYSICSJ. Phys. D: Appl. Phys. 43 (2010) 075302 (7pp) doi:10.1088/0022-3727/43/7/075302Experimental determination andsimulation of the angular distributionof the metal flux during magnetronsputter depositionM Horkel 1 , K Van Aeken 2 , C Eisenmenger-Sittner 1 , D Depla 2 , S Mahieu 2and W P Leroy 21 Institute of Solid State Physics, E-138, Vienna University of Technology, Wiedner Hauptstrasse 8-10,Vienna A-1040, Austria2 Department for Solid State Sciences, Ghent University, Krijgslaan 281 (S1) 9000, Ghent 9000, BelgiumE-mail: m.horkel@gmx.atReceived 9 September 2009, in final form 11 January 2010Published 5 February 2010Online at stacks.iop.org/JPhysD/43/075302AbstractTo understand the film growth during magnetron sputter deposition a detailed knowledge ofthe flux of sputtered species from the target towards the substrate is vital. One importantparameter is the angular distribution of the impinging neutral target atoms on the substrate,since it is responsible for, for example, self-shadowing effects. The determination of theangular distribution of the metal flux at an arbitrary point in the deposition chamber isachieved by a pinhole camera, where the information of the angular distribution is convertedinto a thickness profile. This paper describes the construction of such a pinhole camera whichis capable of differential pumping, the determination of the angular distribution for a widevariety of target materials, and which can easily be inserted into a deposition chamber. Theangular distributions of different materials (Cu, W, Al, Ti, Mg) at different parameters(pressure, lateral position and vertical position) are experimentally determined and comparedwith simulations obtained from a newly developed Monte Carlo code. It was also investigatedwhether parameters derived from the angular distribution are related to the degree ofthermalization of the impinging particles.(Some figures in this article are in colour only in the electronic version)1. IntroductionThe angular distribution of the impinging neutral particlesduring magnetron sputtering, one of today’s most importantdeposition techniques, is an interesting parameter. First theangular distribution may have a direct relationship with theproperties of the deposited layers, e.g. the porosity of the filmcaused by self-shadowing effects [1, 2], mound formation [3],the step coverage in microelectronics [4] or the complex filmstructure caused by glancing angle deposition [5]. Besideits known influences, the angular distribution is an importantparameter for the simulation of film growth [6, 7]. In recentlydeveloped techniques such as the deposition of biaxiallyaligned layers [8, 9], the angle of the impinging atoms is evena vital parameter. Moreover, a detailed study of the angulardistribution can provide insight into the fundamental principlesof magnetron sputter deposition, such as the initial angulardistribution of the sputtered particles, the shape of the localsputter rate and transport of the sputtered particles throughthe gas phase as all these influence the angular distribution.In this context, a key aspect of magnetron sputter depositionis the energy of the particles arriving at the substrate whichis substantially higher than thermal energy. Of course thislatter has its impact on the thin film growth [8, 9], andhence the degree of thermalization of the arriving flux is animportant issue. As the angular distribution is influenced,0022-3727/10/075302+07$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK

J. Phys. D: Appl. Phys. 43 (2010) 075302 M Horkel et alFigure 1. (a) Sketch of the working principle of the pinhole camera with a cylindrical substrate holder. (b) Picture of the MFM, indicatedparts are housing (1), pinhole (2), gasket (3), cylindrical substrate holder (4), cylindrical bracket (5), coated slide (6), measuring barof 10 cm (7).together with the energy of the particles, by the gas transport,measurements of the angular distribution can give insight intothe thermalization process.To measure the angular distribution of the impingingparticles, a device called metal flux monitor (MFM) has beenconstructed. It is a pinhole camera [10–15], which converts theangular distribution of the arriving flux into a thickness profileof a layer on a substrate behind a pinhole. This informationcan briefly be described as an image of the local sputter ratemultiplied by the initial angular distribution, which is thenblurred by gas phase scattering. One difference of the MFMfrom the pinhole cameras in the previous papers [12, 13] isthat it can be inserted via a load lock and is not fixedlymounted in the deposition chamber. This allows a swiftchange of the position of the MFM, and a high experimentalthroughput. The methods to analyse the thickness profiles werealso designed with respect to the high experimental throughputand allow a large variety of materials (not only metallic butalso transparent materials) to be measured. The experimentswere performed for various materials (Cu, W, Al, Mg, Ti)at different parameters (lateral position; distance magnetron-MFM; pressure), and the results are compared with simulationsby the Monte Carlo (MC) code SIMTRA [16].Section 2 of this paper describes the design of the MFM, itsfundamental principles and the determination of the thicknessprofiles via optical methods. The experimental set-up andparameters are given in section 3, while section 4 gives abrief description of the MC-code SIMTRA. The experimentalresults in comparison with the simulations performed bySIMTRA are presented in section 5. A relationship betweenthe degree of thermalization and the properties of the obtainedangular distribution was studied.2. Metal flux monitorThe MFM is a pinhole camera which converts the informationof the angular distribution of the metal flux at the positionof the pinhole into a thickness profile on the substrate, eitherplanar or cylindrical, behind that pinhole. In this paper, thethickness profile T(x)along a strip of approximately 0.5 mmis measured and converted into the angular flux (ϕ) ofimpinging particles at the pinhole site using equation (3). Theworking principle (in this case for a cylindrical substrate) isTable 1. Technical data MFM.Radius pinhole rLength pinhole dMaximum angle error ϕCover plate thicknessRadius cylindrical substrate holderDistance pinhole to planar substrateAcceptance angle cylindricalAcceptance angle planar0.5 mm0.2 mm2.9 ◦2 mm10 mm10 mm75 ◦45 ◦sketched in figure 1(a). It is a sealed (except the pinhole)cylindrical chamber (figure 1(b)) connected to a stainless steelpipe with a KF40 linear feed-through.There is a MFM with the pinhole directed perpendicularto the feed-through axis (figure 1(b)), which can hold acylindrical or a planar substrate holder, and one with thepinhole directed parallel to the feed-through axis, which canonly hold a planar substrate holder.The direct connection of the MFM to a pipe and a linearfeed-through enhances its flexibility, as it can be mounted intoevery deposition chamber with a KF40 flange, and its positioncan be changed quickly. It also enables differential pumpingof the MFM via the pipe (to increase the mean free path ofparticles inside the MFM), and the inlet of reactants directlyinto the MFM from outside the recipient. Some important dataare given in table 1.To convert the thickness profile T(x)on the substrate intothe angular flux (ϕ) of impinging particles at the pinhole site,one has to take into account the geometry of the pinhole. Theeffective area of the pinhole decreases with increasing angle, aneffect called vignetting (V(ϕ))(figure 2), thus also decreasingthe number of passing particles.For a cylindrical pinhole (length d; radius r) V(ϕ) isdescribed as the ratio of effective area A eff seen by the tiltedbeam to the area of the pinhole A 0 . V(ϕ)can be expressed as[V(ϕ)= A ( )eff 2 cos (ϕ) π d tan (|ϕ|)=A 0 π 2 − arcsin 2r⎛ √⎞( ) ]− ⎝d tan (|ϕ|) d tan (|ϕ|) 21 −⎠ . (1)2r2r2

J. Phys. D: Appl. Phys. 43 (2010) 075302 M Horkel et alFigure 3. Grey scale image (green channel) of a scanned sample(Cu deposited on a flexible and transparent substrate).Figure 2. Vignetting: two particles are entering the MFM atdifferent angles ϕ; one perpendicular (ϕ = 0 ◦ ; aperture A 0 of r 2 π)and the second one at an angle ϕ 2 with a smaller aperture of A eff .The angle error ϕ decreases at higher angles because of thedecreasing aperture.For a substrate of cylindrical shape, T(x)can be converted into(ϕ) according to(ϕ) ∝ T (x(ϕ)) . (2)V(ϕ)Aside from cylindrical substrates, also planar substrates wereused. They were necessary, since the flexible substrates neededfor the cylindrical substrate holder prohibit certain surfaceanalysis techniques (e.g. thickness profile determination ofoxides; see below). Compared with the cylindrical substrate,planar substrates do have the disadvantage that the distancebetween pinhole and substrate is angle dependent, and that theincidence angle on the substrate is not perpendicular anymore.For planar substrates T(x) can be converted into (ϕ)according toT (x(ϕ))(ϕ) ∝V(ϕ)· cos 3 (ϕ) . (3)The resolution of the MFM is limited by two effects; one is theangular error ϕ caused by the aperture (figure 2), the otheris gas phase scattering inside the MFM, which can be loweredby differential pumping of the MFM.Another limiting factor might be that only those particleswhich stick contribute to film growth and can therefore bemeasured. The sticking probability is determined by energyand incidence angle [17]. For the cylindrically shapedsubstrate the incidence angle is always perpendicular, thereforethe sticking probability can be assumed to be 1, even at higherenergies. As mentioned above, the incidence angle on theplanar substrate is not perpendicular. However, the stickingprobability becomes angle dependent at higher angles (above45 ◦ , which is the maximum acceptance angle of the MFM).Moreover, in the described experiments the particles whichare not scattered, and therefore have higher energies, typicallyhave incidence angles of 20 ◦ and below. Therefore, even forthe planar substrate the sticking coefficient can be assumedto be 1.Due to the pinhole geometry, the deposition rate on thesubstrate is drastically reduced (by a factor of approximately0.01 and lower), thus increasing problems with residual gasincorporation. The reason is that the ratio of the impingementrates of the residual gas molecules v g [18] and of the sputteredparticles v d , given in (4), increases with decreasing depositionrate.v gv d=m d · pa w ρ √ 2πm g k B T , (4)where p is the residual gas pressure (Pa), m g is the molecularor atomic mass of the residual gas (kg), m d is the molecular oratomic mass of the sputtered material (kg), k B is the Boltzmannconstant (1.38 × 10 −23 JK −1 ), T is the temperature (K), a w isthe deposition rate (m s −1 ) and ρ is the density of depositedmaterial (kg m −3 ).If one assumes a residual oxygen pressure of 10 −5 Pa anda deposition rate of 5 × 10 −12 ms −1 of Al inside the MFMthe ratio v g /v d would be approximately 1. Knowing thatthe oxygen incorporation coefficient during sputter depositionof reactive metals such as Al and Mg can reach values upto 0.1–0.25 [19, 20], the formation of oxide layers seemsunavoidable, even for a low residual gas pressure.The thickness profiles on the substrates were determinedvia optical methods. For metallic layers the thickness wasdensitometrically determined via an optical scanner, as in theprevious papers [12, 13]. The transmissivity (figure 3) ofthe metallic layers was spatially resolved by a transmissionscanner (Reflecta CrystalScan 7200) and the transmissivity ofthe coated substrates was compared with that of an uncoatedsubstrate. With the known transmissivity, the thickness of eachpoint of the profile can be determined.The thickness profiles of the oxide layers were determinedvia a spatially resolved interferometric method especiallydesigned for this task, where the oxide layer is depositedon a reflective substrate (e.g. polished silicon wafer) andits interference patterns are captured by a digital camera(figure 4(a)). The image is then colour split (figures 4(b)–(d))and the profile determined for each colour individually(assuming a two beam interference). These three profiles arethen averaged. For the interferometric method an OlympusStylus 760 was used as digital camera.3. ExperimentalThe experimental set-up is depicted in figure 5. Experimentswere performed in different vacuum chambers with basepressures of about 10 −5 Pa. A planar disc shaped magnetronsource with a target diameter of 100 mm was used. Thedistance of the target centre to the area with the highestlocal sputter rate, called the racetrack, was 23 mm. Angular3

J. Phys. D: Appl. Phys. 43 (2010) 075302 M Horkel et alFigure 4. (a) Image of a sample (Al deposited on polished silicon wafer) captured by a digital camera. Grey scale images of the (b) blue;(c) green; (d) red colour channel. The interference patterns are clearly visible.Table 2. Parameters of the experiments.Pressures (Pa) x-positions (mm)Material (x = 0; z = 95 mm) (p = 0.5Pa,z = 95 mm)Cu 0.3; 0.5; 0.7; 1; 3 0; 11; 23; 35W 0.3; 0.5; 0.7; 1; 3Al 0.3; 0.5; 0.7; 1 0; 11; 23; 35Mg 0.1; 0.3; 0.5; 0.7; 1 0; 11; 23; 35Ti 0.3; 0.5; 0.7; 1 0; 11; 23; 35z-distances (mm) (eccentricity x = 5 mm; p = 0.5Pa)Cu 25; 50; 95; 125; 150Figure 5. Experimental set-up: vacuum chamber (1), MFM (withplanar substrate) movable in the x-axis (2), MFM (with planarsubstrate) movable in the z-axis (3), target and origin ofcoordinates in its centre (4), load-lock chamber (5), linearfeed-through for KF40 flange (6), pipe of the MFM leading outsidethe chamber, used for differential pumping and inlet of gas into theMFM (7).measurements were carried out for W, Cu, Ti, Al and Mgtargets sputtered with Ar as working gas (inlet via a needlevalve or a mass flow controller). Experiments were carriedout for different pressures with the monitor mounted 95 mmcentrally above the target, and also at a constant pressure of0.5 Pa for different lateral (x-positions) and target substrate (z)distances. For the experiments with a different z-distance asmall eccentricity of 5 mm was experimentally unavoidable,because the load lock was not right opposite the magnetron.A summary of the experimental parameters is given in table 2.The magnetron was operated at a constant dc dischargecurrent of 0.3 A (experiments with variable pressure and lateralposition) and 0.9 A (experiments with variable distance). Cuand W were deposited as metallic layers using the cylindricalsubstrate holder with transparent slides as substrates. Aland Mg were completely oxidized by the residual gas andwere therefore deposited on silicon wafers in the planarsubstrate holder, to enable the profile determination via theinterferometric method. Ti was only partially oxidized by theresidual gas, hence a very small amount of oxygen was inserteddirectly into the MFM (without influencing the sputteringprocess) to form an oxide layer, otherwise it was treated likeAl and Mg. Although the maximum acceptance angle of thecylindrical substrate is 75 ◦ , the experimental profiles were cutoffat45 ◦ , because the signal to noise ratio becomes large athigher angles.4. SimulationsThe metal flux towards the flux monitor was simulated usingthe MC-code SIMTRA [16], which tracks a representative setof individual particles in their movement through the vacuumchamber. By its working principle, first a sputtered particle isgenerated with initial position, energy and direction, sampledfrom given distribution functions. Here the ejection positionswere taken from a measured erosion profile, neglecting thesmall influence of the target material on the racetrack shape.The initial energy distribution resulted from simulations usingthe binary collision code SRIM [21] with a constant incidention energy corresponding to 75% of the discharge voltage[22, 23]. Although SRIM also provides the initial angulardistributions, these did not take the typical heart-like shapeobserved experimentally [24–28]. Hence, as was described4

J. Phys. D: Appl. Phys. 43 (2010) 075302 M Horkel et alFigure 6. Angular distribution (ϕ) of the metal flux at a substrate 95 mm above the target surface as a function of the discharge pressurefor (a) W,(b) Cu, (c) Ti, (d) Al . For W the angular distribution at p = 0 Pa (no gas phase scattering) is also shown. The angulardistributions have local minimum at the centre (ϕ = 0, value R min ), and a maximum at the racetracks (value: R max ).in [16], initial angular distributions for Cu, Al and Ti wereinstead reconstructed from deposition measurements, usingthe transport code in a reverse way. For W and Mg, on theother hand, having no data available, the SRIM initial angulardistributions were used. However, considering the geometryof the experimental set-up, this parameter was expected andfound to have a limited influence.In the next step of the model the collisional transport ofthe sputtered particle through the gas phase is described. Thebackground gas was assumed homogeneous at temperatureT = 350 K and specified pressure p. The assumptionof an homogeneous temperature distribution is valid, sincethe heating of the gas [29] and gas rarefaction [30, 31]are negligible at pressures below 1 Pa. Collisions weremodelled based on either quantum chemical (Cu–Ar, Al–Ar[32]) or screened Coulomb interaction potentials. Also thethermal motion of the background gas atoms was included.The sticking coefficient at the substrate was assumed tobe unity.The simulated configuration mimicked the experimentalset-up, including the inside of the MFM. The angulardistribution can be directly constructed from the particlesarriving at the pinhole. By continuing to track the particlesthrough the MFM and following the experimental procedure,i.e. calculation of the deposition profile and applying vignettingcorrection, it is possible to gauge the influence of scattering inthe flux monitor and the angular error due to the aperture.5. Results and discussionThe influence of the deposition pressure on the angulardistribution (ϕ) at a substrate positioned at z = 95 mmand x = 0 mm (central above the target) is shown infigures 6(a)–(d) for W, Cu, Ti and Al, respectively. Thecalculated angular distribution with neglected gas phasescattering (p = 0 Pa) is plotted for W. Clearly visible in figure 6is the broadening of the angular distribution with increasingpressure, reproduced well by the SIMTRA simulations. Withsome exceptions this is also the trend observed in the materialdependence. The lighter elements are averagely scattered overlarger angles, leading to an increase in the fraction of theflux arriving at higher incident angles. A good parameter toquantify the amount of gas scattering is the ratio R min /R max ofthe local minimum in the centre of the target and the maximumat the racetracks (indicated in figure 6(a) for 0.3 Pa). Since(ϕ) is symmetrical in this case, because the MFM is centrallyabove the target, the results are plotted from ϕ = 0 ◦ to ϕ = 45 ◦The influence of gas phase scattering inside the MFM wasinvestigated with simulations. Scattering inside the monitorbroadens the angular profile somewhat, although the effectis limited at all pressures. At low pressure the arrivingflux is directional, but the scattering probability remains lowso the profiles stay relatively intact. At higher pressuresimulations showed significant scattering in the monitor, butdue to scattering in the vacuum chamber, the arriving flux at5

J. Phys. D: Appl. Phys. 43 (2010) 075302 M Horkel et alFigure 7. Angular distribution (ϕ) of the metal flux at a substrate95 mm above the target surface as a function of the x(lateral)-position for Cu sputtered at a pressure of 0.5 Pa.Figure 9. Comparison between R min /R max (observed) and P therm(calculated) for all investigated target materials at differentdeposition pressures and for Cu with variable distances.and Valles-Abarca [33] asP therm (5). The analytical model ofthe calculation assumed a continuous slowing down of particlesalong straight line trajectories with a velocity proportionalenergy loss per unit path length.Figure 8. Angular distribution of copper as a function of thedistance z of the substrate from the target. Conditions werep = 0.5Pa,x = 0.5 mm (eccentricity).the pinhole is already randomized to such a degree that theextra scattering in the monitor only has a limited influenceon the resulting deposition profile. This indicates that, evenwithout differential pumping, the flux monitor allows accuratemeasurements of the arriving angular distribution.Figure 7 shows the influence of the x (lateral) positionon the angular distribution of the arriving metal flux for Cuas example. The angular distribution shifts and becomesasymmetric. Although the effect is mainly geometrical, anaccurate quantification can help in improving for instancethe uniformity of films deposited under conditions where thearriving angular distribution influences the microstructure.The results of the series with different z-distances (ata constant lateral eccentricity x = 5 mm) are shown infigure 8 with the MC-simulation for comparison. As expectedR min /R max increases with the distance. Since the distributionsare not symmetrical, due to the eccentricity, the results areplotted from −45 ◦ to +45 ◦ .Due to collisions with the working gas, the sputteredparticles will lose energy and direction. Hence, due tocollisions, the sputtered particles will get more and morethermalized. This degree of thermalization (the point wherethe sputtered particles can be treated as a Maxwellian gas, i.e.thermal energy and random direction) was given by Gras-Martix 2P therm =R(U) 2 + x , (5)2where x is the distance target-MFM, R(U)(6) is the path lengthof a particle with initial energy U (surface binding energy) untilthermalization is reached.R(U) = A · U 1/2 . (6)The energy independent coefficient A is given byA ∼ = 0.012 (Mg1/2 1+ 1 ) 1/2(1+µ2/3 ) 3/4 T (K)µp(Pa)withµ = M g /M swhere M g is the mass of gas (amu), M s is the mass of targetmaterial (amu), T is the temperature (300 K) and U is thesurface binding energy (eV).This probability of thermalization P therm can be comparedwith the ratio R min /R max of the local minimum in the centreof the target and the maximum at the racetracks (indicatedin figure 6(a)). Indeed, the flux in the centre should bezero when there is no gas scattering (R min /R max = 0) andshould be maximal when there is a lot of gas phase scattering(R min /R max = 1). This relation between P therm and R min /R maxis shown in figure 9. It can be concluded that the MFMallows measuring the degree of thermalization of the sputteredparticles.6. ConclusionsThe MFM allows measurement of the angular distributionof the metal flux. Also information on the number of(7)6

J. Phys. D: Appl. Phys. 43 (2010) 075302 M Horkel et althermalized neutrals can be obtained from the measuredangular distribution. The different methods presented forthickness determination with a good lateral resolution allowthe MFM to be used for a wide variety of target materials.It was demonstrated that (ϕ) is not isotropic for the usualdeposition parameters. The experimentally obtained resultswere compared with simulations and a good match was found.It was also shown that the ratio R min /R max is correlated withthe degree of thermalization of the metal flux. Therefore thedegree of thermalization can be estimated for given processparameters with one measurement.AcknowledgmentsThis work was supported by the Institute for the Promotionof Innovation by Science and Technology in Flanders (IWT)under Grant No SBO-060030.References[1] Bales G S, Bruinsma R, Eklund E A, Karunasiri RPU,Rudnick J and Zangwill A 1990 Science 249 264–8[2] Bales G S and Zangwill A 1991 J. Vac. Sci. Technol. A9 145–149[3] Pelliccione M, Karabacak T, Gaire C, Wang GCandLuTM2006 Phys. Rev. B 74 125420[4] Blech I A and Vander Plas H A 1983 J. Appl. Phys. 54 3489–96[5] Robbie K and Brett M J 1997 J. Vac. Sci. Technol. A15 1460–65[6] Lugscheider E and von Hayn G 1999 Surf. Coat. Technol.116–119 568–72[7] Wang L and Clancy P 2001 Surf. Sci. 473 25–38[8] Mahieu S, Ghekiere P, Depla D and De Gryse R 2006Thin Solid Films 515 1229–49[9] Mahieu S, Ghekiere P, Dewinter G, De Gryse R, Depla D andLebedev O I 2005 Solid State Phenom. 105 447–52[10] Thornton J A and Hoffman D W 1981 J. Vac. Sci. Technol.18 203–7[11] Swan S 1987 J. Vac. Sci. Technol. A 5 1750–4[12] Eisenmenger C, Bergauer A, Bangert H and Bauer W 1994J. Vac. Sci. Technol. A 12 536–41[13] Eisenmenger C, Beyerknecht R, Bergauer A, Bauer W andBetz G 1995 J. Vac. Sci. Technol. A 13 2435–43[14] Feddes B, WolkeJGC,Jansen J A and Vredenberg A M 2003J. Appl. Phys. 93 662–70[15] Panjan M, Cremer R, Fuss H G, Panjan P and Cekada M 2010The use of camera obscura in sputter deposition Vacuum84 45–48[16] Van Aeken K, Mahieu S and Depla D 2008 J. Phys. D: Appl.Phys. 41 205307[17] Zhou X W and Wadley HNG1999 Surf. Sci. 431 58–73[18] Maissel L and Glang R 1970 Handbook of Thin FilmTechnology (New York: McGraw-Hill) pp 1–21, ISBN978-0070397422[19] Leroy W P, Mahieu S, Persoons R and Depla D 2009 PlasmaProcess. Polym. 6 s342–s346[20] Leroy W P, Mahieu S, Persoons R and Depla D 2009 ThinSolid Films 518 1527–31[21] The Stopping and Range of Ions in Matter 2006 available athttp://www.srim.org/[22] Czekaj D, Goranchev B, Hollmann E K, Volpyas VAandZaytsev A G 1991 Vacuum 42 43[23] Goeckner M J, Goree J A and SheridanT E 1991 IEEE Trans.Plasma Sci. 19 301[24] Ramos R, Cunge G, Touzeau M and Sadeghi N 2008 J. Phys.D: Appl. Phys. 41 152003[25] Yamamura Y and Ishida M 1995 J. Vac. Sci. Technol. A 13 101[26] Goehlich A, Gillman D and Döbele H F 2001 Nucl. Instrum.Methods Phys. Res. B 179 351[27] Yamamura Y 1982 Nucl. Instrum. Methods 194 515[28] Tondu T 2005 PhD Thesis SUPAERO Engineering School,Toulouse, France[29] Depla D and Mahieu S 2008 Reactive Sputter Deposition(Berlin: Springer) pp 120, ISBN 978-3540766629[30] Palmero A, Rudolph H and Habraken FHPM2006Appl. Phys. Lett. 89 211501[31] Palmero A, Rudolph H and Habraken FHPM2007 J. Appl.Phys. 101 083307[32] Kuwata K T, Erickson R I and Doyle J R 2003 Nucl. Instrum.Methods Phys. Res. B 201 566–570[33] Gras-Marti A and Valles-Abarca J A 1983 J. Appl. Phys.54 1071–757