Size effect on electronic sputtering of LiF thin films

JOURNAL OF APPLIED PHYSICS 102, 083510 共2007兲

Size effect on electronic sputtering of LiF thin films Manvendra Kumara兲 Department of Physics, University of Allahabad, Allahabad 211 002, India

S. A. Khan Inter-University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110 067, India

Parasmani Rajput UGC-DAE Consortium for Scientific Research, University campus, Indore 452017, India

F. Singh, A. Tripathi, and D. K. Avasthi Inter-University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110 067, India

A. C. Pandey Department of Physics, University of Allahabad, Allahabad 211 002, India

共Received 20 February 2007; accepted 19 August 2007; published online 17 October 2007兲 Electronic sputtering in polycrystalline LiF thin film by 120 MeV Ag25+ is investigated. The sputter yields of Li and F for the different thicknesses 共10– 265 nm兲 of films are measured with online elastic recoil detection analysis technique. A reduction in sputter yield, from ⬃2.3⫻ 106 to 2.2 ⫻ 104 atoms/ion, is observed with increase in the film thickness. The trend in the experimental results can be explained in terms of size effect in thin film following inelastic thermal spike model. The confinement of energy in the film having smaller grains and lower thickness results in higher temperature causing higher sputtering yield. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2794694兴 I. INTRODUCTION

The bombardment of solid surfaces by ionizing radiation has attracted a great deal of attraction because of many interesting fundamental and technical aspects of ion beam induced effects. Irradiations are known for material modifications resulting in a variety of nonequilibrium events such as bond breaking, latent track formation, erosion of materials, etc. The removal of atoms from the surface due to impact of energetic ions is termed as sputtering.1 Depending on the projectile energy, different scenario of sputtering occurs, such as material ejection due to atomic collision cascade 共nuclear sputtering兲 at keV energies,1 electronic sputtering governed by electronic energy loss at higher energies 共⬎1 MeV/ u兲,2 and potential sputtering by slow highly charged ions.3,4 The nuclear sputtering has been studied on different materials and is well described by Sigmund’s theory.1 In the electronic energy loss regime, Sigmund’s theory fails to explain the large increase in sputtering yield.5 Although several mechanisms such as Coulomb explosion,6 thermal spike,7 shock wave model,8 and a combination of Coulomb explosion and thermal spike9 have been proposed for mass removal due to electronic energy loss, the electronic sputtering process is still to be understood and is, therefore, a fundamental research problem. The electronic sputtering process is a tool to understand the fundamentals of interaction of swift heavy ion 共SHI兲 with the matter and thus it has been studied in a number of materials.10–21 In case of metals, the yield is not so high but definitely larger than predicted by the Sigmund’s theory.14–16 High sputtering yield has also been observed in different insulating materials.16–22 However, a兲

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very little work exists on electronic sputtering in thin films of LiF.22 Sputtering process in a thin film due to irradiation is affected by several parameters such as substrate, grain size and thickness of the film, mass and energy of the incident ion, and irradiation temperature.15 Materials with reduced dimensions can have their properties modified due to size effect. This phenomenon is interesting both from scientific and technological aspect. In case of the film, the interface acts as a confinement barrier for the motion of the electrons perpendicular to the surface. The surface of the film and interface of film substrate scatter the electrons partially or completely and thus reduce their effective mean free path. Thickness dependence of electronic sputtering is complicated due to the fact that the sample structure changes with the increase in the film thickness. An example of this phenomenon is the increase in average grain size with the increasing film thickness.23 Debye temperature is also modified in a thin film with a high surface to volume ratio leading to change in the electron phonon interactions.24 In the present study, we report SHI induced removal of Li and F from the LiF thin films of different thicknesses deposited on Si substrates. LiF, due to its simple structure, chemical stability, almost nonhygroscopic nature, and easy production, is presently among the best known materials having numerous applications in the fields of optoelectronic devices, tunable color center lasers, radiation dosimeters, optical isolators, and can play an important role in the study of ion solid interaction processes. LiF is nonamorphizable by SHI irradiation and has shown larger electronic sputtering yield from its thick crystalline samples.18 To determine the stoichiometry and mass removal, on-line elastic recoil detec-

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tion analysis 共ERDA兲 technique was employed, which was first demonstrated by Avasthi et al.25 and had been subsequently used by several groups.19,26,27

II. EXPERIMENTAL

Electron beam evaporation at room temperature has been used to deposit LiF thin films of different thicknesses 共10, 20, 40, 80, 160, and 265 nm兲 on the Si具111典 under a vacuum of ⬃10−6 Torr.28 All the substrates were thoroughly cleaned before the deposition. Fused LiF pieces of 99.9% purity, from Sigma-Aldrich, were used as source material for deposition. The deposition rate was 0.2 nm/ s and the thickness of deposited film was monitored using a quartz crystal monitor. Pristine films were characterized by glancing angle x-ray diffraction 共GAXRD兲 to investigate their structural properties. GAXRD studies were performed using a Bruker AXS D8 advanced diffractometer with Cu K␣ 共1.54 Å兲 operated at 40 kV voltage and 40 mA current. All the GAXRD patterns were taken in the 2␪ range of 35°–46°. To examine the surface morphology of the pristine films, atomic force microscopy 共AFM兲 was performed using Digital Instrument Multimode SPM with Nanoscope IIIa controller. The sputtering was performed with 120 MeV Ag25+ ions at a glancing angle of incidence at 20°. For SHI induced surface and/or near surface modifications of materials, the charge state of the incident ions should be equilibrium charge state, i.e., of the order of effective charge defined in the electronic energy loss theory. To reach equilibrium charge state, all the projectiles from the accelerator having +9 charge states were passed through a thin carbon foil. The charge state +25, being the most probable in charge state distribution, is selected by dipole magnet for the experiment. The ion beam was collimated to a size of 1 ⫻ 3 mm2 by using a double slit placed before the chamber. The energy loss of these ions in LiF crystals is 15.4 keV/ nm and contribution of nuclear energy loss is only 0.34%. All the measurements were performed at room temperature and with a typical beam current of 0.44 pnA 共particle nanoampere, 1 pnA = 6.25⫻ 109 ions/ s兲 to minimize target heating. During irradiation, the layer thickness and stoichiometry of the sample were continuously monitored by ERDA in reflection geometry using a large area position sensitive detector telescope29 共LAPSDT兲 fixed at 45° port of a high vacuum chamber in Materials Science beam line of Inter-University Accelerator Centre 共IUAC兲, New Delhi. The data were collected in several steps at the same spot and electronic sputtering yield was estimated in lower fluence regime 共up to ⬃2 ⫻ 1012 ions/ cm2兲 in order to minimize the effect of surface modification. Typical two-dimensional recoil spectrum for 160 nm thin LiF film is shown in Fig. 1共a兲 which shows well-separated bands of the different elements, Si, F, O, C, and Li, present in the films/substrate. Figure 1共b兲 shows the recoil spectra of F at different fluences of 5 ⫻ 1010, 6 ⫻ 1011, and 1 ⫻ 1012 ions/ cm2. We note that the normalized yield of F decreases with the increase in fluence. The areal concentration of Li and F was deduced from ERDA data and the

FIG. 1. 共Color online兲共a兲 Primary ERDA spectrum of 160 nm thin LiF film showing bands of Si, F, O, C, and Li, recorded with LAPSDT. Channel number along X- and Y—axes represents the recoil energy and 共b兲 recoil spectra of F present in the corresponding film at different fluences.

sputtering yield was determined from the difference in areal concentration at two initial fluences divided by the corresponding difference in the fluences.22

III. RESULTS AND DISCUSSION

Figure 2共a兲 shows x-ray diffraction spectra of LiF thin films having different thicknesses. It is evident from the spectra that the films are polycrystalline in nature showing reflections at 2␪ angles of 38.5° and 45.6° corresponding to 共111兲 and 共220兲 planes, respectively. The crystallinity of film decreases with the decrease in film thickness. An increasing trend of the full width at half maximum 共FWHM兲 of 共111兲 reflection with the decrease in films thickness indicates reduction in the grain size of the films as shown in Fig. 2共b兲. A similar behavior has also been observed by Kaiser et al. for 共100兲 textured LiF film in the thickness range of 5 – 100 nm, deposited by thermal evaporation and analyzed by transmission electron microscopy.23 AFM images of 10 and 265 nm thin films are shown in Figs. 2共c兲 and 2共d兲, respectively. AFM analyses of these two films show that the films are continuous and uniform. Figure 3共a兲 represents the areal concentration of F, obtained by on-line ERDA, in two different films 共10 and 40 nm thin兲, which shows that the areal concentration decreases with the increase in fluence indicating sputtering of


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FIG. 2. 共Color online兲共a兲 Primary GAXRD spectra of LiF thin films for different thickness 共10– 265 nm兲 and 共b兲 variation of grain size with thickness of the films. Below a film thickness of 100 nm, sharp decrease in the grain size is observed. AFM images of 共c兲 10 and 共d兲 265 nm thin films, respectively.

the material from the films. The stoichiometry, Li to F concentration ratio, of the films was determined from the data and it was observed that Li and F were nearly equally present in the film before and after the sputtering as presented in Fig. 3共b兲, which is indication of stoichiometric sputtering of LiF. The sputtering yield estimated from the data is plotted against film thickness in Fig. 4. The y-axis 共on right hand side兲 of Fig. 4 represents the grain size variation of pristine films. The results of the sputtering are given in Table I which show that the electronic sputtering yield decreases with the increase in film thickness. A kink behavior in all the spectra is also observed as shown in Fig. 3共a兲 at a fluence of ⬃8 ⫻ 1010 and ⬃2 ⫻ 1011 ions/ cm2 for 10 and 40 nm thick films, respectively. The origin of such kink behavior can be correlated with fluence required for overlapping of cylindrical tracks. It seems that overlapping fluence is lower for thinner film and increases with film dimension because of the reduction in track radius of modified zone resulting in higher sputtering yield which is consistent with the observed results. Two distinct regimes of thickness dependence of electronic sputtering are observed. In the regime I, up to 50 nm thickness film, the yields are of the order of 106 atoms/ion, whereas beyond this thickness the yields are one order less 共105 atoms/ion兲. It is observed that the yield is more sensitive to thickness in regime I than in regime II. Larger sputtering yield in regime I may be due to combined effects of the reduced thickness and the grain size, whereas the change in

yield in regime II may be predominantly due to the change in grain size. Two distinct behaviors are also observed for the dependence of grain size with film thickness which indicates effective role of grain size on the sputtering as presented in Fig. 4 共on right hand side y-axis兲. The sputtering from LiF single crystal has been previously reported by Toulemonde et al. using catcher technique and the yields of Li and F were about 17 530 and 15 790 atoms/ion, respectively, for ions having electronic energy loss of 16.4 keV/ nm.18 Comparing the observed yield in previous studies with the present one, the yield 共2.2⫻ 104 atoms/ion for F兲 in case of thickest film is found to be comparable to the existing results, whereas the difference in the sputter yield of the film with lower thickness and grain size is huge. Among several theoretical approaches, Coulomb explosion and inelastic thermal spike models are the most commonly used models to understand the electronic sputtering phenomenon in different materials. According to the Coulomb explosion model, a highly ionized zone of charged particles is created along and in the vicinity of the ion path. If the charge neutrality is not re-established by target electrons on the time scale of lattice vibration, the electrostatic repulsion of ionized target atoms will force a rapid expansion of the material in the charged domain and will give rise to the erosion of material. On the other hand, according to the inelastic thermal spike model, the energy is deposited by the


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FIG. 4. Reduction in yields is observed with increase in the film thickness. Yields are enhanced by about one order of magnitude for the films less than 100 nm thickness. Right y-axis represents the grain size variation of pristine films with thickness. Two distinct regimes of sputtering as well as grain size with thickness of the film are observed.

g=

FIG. 3. 共a兲 Reduction in areal concentration of F with fluence for 10 and 40 nm films. 共b兲 The stoichiometry of the film is nearly same before and after sputtering. The Li and F are nearly equally present in the film.

projectile ions in the electronic subsystem of the target. This energy is shared among the electrons by electron-electron coupling and transferred subsequently to the lattice atoms via electron-lattice interactions. This leads to a transient increase in the temperature in a nanocylindrical zone along the ion path. Rapid quenching of thermal energy creates ion damage zone. The thermal energy gets converted into kinetic energy of the atoms and when this energy is more than the surface binding energy, ejection of material takes place from surface. In insulators, however, it is always possible that a Coulomb explosion precedes the thermal spike and is covered by the latter in the course of time.8 Therefore the possibility of Coulomb explosion for electronic sputtering in insulator cannot be ruled out. But, sputtering results can be explained only qualitatively with the help of Coulomb explosion model and no quantitative information can be extracted. As a quantitative approach to explain the observed sputtering yield, we applied inelastic thermal spike model. The electronic sputtering, according to thermal spike model, strongly depends on the efficiency of the transfer of the electronic energy to the lattice, which finally depends on electron phonon coupling strength 共g兲 given by the relation17

De共Te兲Ce共Te兲 , ␭2

共1兲

where De is the electronic thermal diffusivity, Ce is the electronic specific heat of the system, and ␭ is the mean diffusion length of the excited electrons. It is clear that ␭ is the key parameter for the sputtering process. In our case, there are two factors that may affect ␭ value. One is the thickness of the film and the other is grain size of the film, which in turn again depends on the film thickness. Thus the diffusion length of the electrons liberated in different directions from the ion track varies and is energy dependent. The diffusion length of slow electrons is about few nanometers, whereas that of the fast electron is several hundreds of nanometers.30 The scattering of fast electrons from the surface of the film and substrate interface is more prominent in thinner films. When the thickness of the film is less, the motion of the excited electrons will be restricted by the film surface and film-substrate interface because they act as confinement barrier for the motion of the electrons. The surface and interface scatter the electrons partially or completely resulting in reduction in electron mean free path. According to the theory of electron scattering from film surface,31 the effective mean free path of the electron can be given as ␭ = 共t / 2兲关ln共␭0 / t兲 + 共3 / 2兲兴, where ␭0 is background mean free path of the elecTABLE I. Results of simulation and sputtering experiment. The experiment was performed with 120 MeV Ag25+ ions at an angle of 20° with respect to the surface of LiF thin films having different thicknesses and grain sizes. Yield 共atoms/ion兲 Thickness 共nm兲

Grain size 共nm兲

Experimental

Simulated

10 20 40 80 160 265

11.2 17.5 26.8 30.7 34.2 38.1

2.3⫻ 106 1.1⫻ 106 4.1⫻ 105 8.1⫻ 104 3.8⫻ 104 2.2⫻ 104

79 657 48 039 24 554 16 967 11 495 6 937


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trons and t is the film thickness. Thus, as the thickness increases, the effective mean free path of the electrons increases. Consequently, the decrease in ␭ value results in higher electron-phonon coupling strength and hence increase in the temperature in thinner film is higher. Moreover, the motion of the electrons also gets affected by the smaller grain size due to grain boundary scattering. As the grain size decreases, scattering of electrons with grain boundaries influences the mean free path. The mean diffusion length 共␭兲 of the electrons in a grain of average diameter 共d兲 can be given as32 ␭=

␣d共1 − R兲 , R

共2兲

where ␣ is angle between velocity vector of electrons and the film plane and R is the reflection efficiency. Due to smaller grain size, the mean diffusion length will be smaller, resulting in the higher density of deposited energy. Also, since the dissipation of thermal energy in the lattice being less efficient due to smaller grain size and lower thickness, the duration of temperature spike increases, which can also enhance the sputtering yield. The sputtering yields for the films 共of different grain size兲 are simulated using inelastic thermal spike code.33 The solution of the equations17 provides the information about the evolution of the lattice temperature, Ta, with respect to time 共t兲 and space 共r兲. The total yield, Ytot, of sputtered particles from the surface is then given by the equations18 Y tot =

冕冕 dt

dr⌽关Ta共t,r兲兴

and ⌽关Ta共t,r兲兴 = N

冑

冋

册

kTa共t,r兲 −U exp , 2␲ M kTa共t,r兲

共3兲

where N is the atomic density, k is the Boltzmann constant, M is the molecular mass of the target, and U is the surface binding energy equal to sublimation energy per evaporated molecule. Numerical calculation of the sputtering yield for different films under normal ion incidence has been performed using 共i兲 the thermal spike code33 and 共ii兲 the scheme of Berthelot et al.34 A lower value of sublimation energy, i.e., 1.3 eV, was used in the calculation as suggested for sputtering in LiF to overcome the effect of modified interatomic binding conditions induced by electronic excitations or of cluster emission.18 For the calculation of ␭, we have made two assumptions: 共i兲 R and ␣ are constant for all the films and 共ii兲 the thickest film behaves like bulk LiF. Therefore, ␭ value for the bulk is treated as ␭ for the thickest film 共grain size d = 38.1 nm兲. For the thickest film, ␭ = 3.8 nm and d = 38.1 nm are taken. The constant part ␣共1 − R兲 / R in Eq. 共2兲 is nearly equal to 0.1. Putting this value in Eq. 共2兲, the ␭ values corresponding to different grain sizes are obtained. The ␭ varies from 3.8 nm 共the thickest film兲 to 1.1 nm for the thinnest film. All the other parameters used in the calculations are the same as used by Toulemonde et al.18 The yield calculated from thermal spike code has been then multiplied by sin−1.85 ␣ in order to correct for the grazing angle, ␣ of the

FIG. 5. Comparison of experimental and simulated sputtering yield as a function of grain size of the films. The corresponding film thicknesses are also shown. The experimental yields, from Ref. 22, depicting the variation with respect to grain size of the films having the same thickness 共160 nm兲 are also shown.

ion incidence.18 The experimental and calculated sputter yields as a function of grain size and the corresponding film thickness are shown in Table I and in Fig. 5. It is clear that the nature of the experimental yield follows the behavior of the simulated sputter yield; both show a reduction in the sputter yield with increase in the grain size and film thickness. Nevertheless, the calculated values are smaller 共one order of magnitude兲 than the observed sputtering yield. However, the experimental and predicted values are of the same order for LiF thin films of same thickness but of different grain size22 as shown in Fig. 5. The discrepancy observed in the experimental and simulated sputtering yields in the present case may be due to the following two reasons. First one is the fact that thermal spike code does not include the thickness of the film into account and the other reason is that the thermal spike model does not include the pressure pulse that arises due to the large local temperature in the excited region. Two different regimes of the electronic sputtering observed in the present study can be understood in terms of grain size and thickness effect. Below 50 nm thickness of the film, the grain size is comparable/equal to the film thickness resulting in strong grain boundaries scattering as well as electron scattering from surface and interface of the film and substrate. In case of thicker film the scattering from film surface and interface of the film and substrate is less effective, whereas the grain boundary scattering may still play an important role. In other words, high sputtering yield in regime I may be due to the combined effect of reduced thickness and grain size of the film, whereas in regime II, it may be due to smaller grain size of the film rather than the thickness of the films. Thus, the factors thickness and the grain size of the film may influence the sputtering yield. Thickness dependence of electronic sputtering has been studied in metals15 and organic materials,12 but the influence of grain size as well as that of thickness has never been observed simultaneously.


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IV. CONCLUSION

Electronic sputtering in polycrystalline LiF thin films of different thickness was studied using online ERDA technique. A strong dependence of sputter yield on grain size and thickness of the pristine film was observed. The experimental results are assessed within the framework of thermal spike model along with size effect in thin films. Smaller grain size and lower thickness of the films restrict the motion of excited electrons resulting in better confinement of the deposited energy, which finally enhances the temperature and duration of temperature spike, resulting in higher sputtering yield. ACKNOWLEDGMENTS

One of the authors 共M.K.兲 is thankful to CSIR, India for SRF award. The authors gratefully acknowledge Dr. M. Toulemonde, CIRIL, France for the helpful discussions on the experiments and allowing to use thermal spike code. IUAC is thankful to DST, India for IRHPA project for XRD/ AFM facilities. P. Sigmund, Phys. Rev. 184, 383 共1969兲. R. E. Johnson and B. U. R. Sundquist, Phys. Today 45共3兲, 28 共1992兲. 3 T. Neidhart, F. Pichler, F. Aumayr, M. Schmid, H. P. Winter, and P. Varga, Phys. Rev. Lett. 74, 5280 共1995兲. 4 F. Aumayr, P. Varga, and H. P. Winter, Int. J. Mass. Spectrom. 192, 415 共1999兲. 5 J. Chaumont, H. Bernas, A. Kusnetsov, C. Clerc, and L. Damoulin, Nucl. Instrum. Methods Phys. Res. B 129, 436 共1997兲. 6 R. L. Fleicher, P. B. Price, and R. M. Walker, Nuclear Tracks in Solids 共University of California Press, California, 1975兲. 7 Z. G. Wang, C. Dufour, E. Paumier, and M. Toulemonde, J. Phys.: Condens. Matter 6, 6733 共1994兲. 8 E. M. Bringa and R. E. Johnson, Phys. Rev. Lett. 88, 165501 共2002兲. 9 R. Behrisch, V. M. Prozesky, H. Huber, and W. Assmann, Nucl. Instrum. Methods Phys. Res. B 118, 262 共1996兲. 10 F. Pawlak, C. Dufour, A. Laurent, E. Paumier, J. Perriere, J. P. Stoquert, and M. Toulemonde, Nucl. Instrum. Methods Phys. Res. B 151, 140 共1999兲. 11 S. Ghosh, A. Tripathi, T. Som, S. K. Srivastava, V. Ganeshan, and D. K. Avasthi, Radiat. Eff. Defects Solids 154, 151 共2001兲. 12 S. Ghosh, D. K. Avasthi, A. Tripathi, S. K. Srivastava, S. V. S. Nageswara Rao, T. Som, V. K. Mittal, F. Gruner, and W. Assmann, Nucl. Instrum. 1 2

J. Appl. Phys. 102, 083510 共2007兲

Kumar et al.

Methods Phys. Res. B 190, 169 共2002兲. A. Tripathi, S. A. Khan, S. K. Srivastava, M. Kumar, S. Kumar, S. V. S. N. Rao, G. B. V. S. Lakshmi, A. M. Siddiqui, N. Bajwa, H. S. Nagaraja, V. K. Mittal, A. Szokefalvi, M. Kurth, A. C. Pandey, D. K. Avasthi, and H. D. Carstanjen, Nucl. Instrum. Methods Phys. Res. B 212, 402 共2003兲. 14 H. D. Mieskes, W. Assmann, F. Gruner, H. Kucal, Z. G. Wang, and M. Toulemonde, Phys. Rev. B 67, 155414 共2003兲. 15 A. Gupta and D. K. Avasthi, Phys. Rev. B 64, 155407 共2001兲. 16 M. Toulemonde, W. Assmann, C. Trautmann, F. Grüner, H. D. Mieskes, H. Kucal, and Z. G. Wang, Nucl. Instrum. Methods Phys. Res. B 212, 346 共2003兲. 17 M. Toulemonde, Ch. Dufour, A. Meftah, and E. Paumier, Nucl. Instrum. Methods Phys. Res. B 166–167, 903 共2000兲. 18 M. Toulemonde, W. Assmann, C. Trautmann, and F. Gruner, Phys. Rev. Lett. 88, 057602 共2002兲. 19 W. M. Arnoldbik, N. Tomozeiu, and F. H. P. M. Habraken, Nucl. Instrum. Methods Phys. Res. B 203, 151 共2003兲. 20 W. M. Arnoldbik, P. A. Zeijlmans van Emmichoven, and F. H. P. M. Habraken, Phys. Rev. Lett. 94, 245504 共2005兲. 21 S. Sugden, C. J. Sofield, and M. P. Murrell, Nucl. Instrum. Methods Phys. Res. B 67, 569 共1992兲. 22 M. Kumar, S. A. Khan, F. Singh, A. Tripathi, D. K. Avasthi, and A. C. Pandey, Nucl. Instrum. Methods Phys. Res. B 256, 328 共2007兲. 23 U. Kaiser, N. Kaiser, P. Weibbrodt, U. Mademann, E. Hacker, and H. Muller, Thin Solid Films 217, 7 共1992兲. 24 G. Kastle, H. B. Schroder, A. Plettl, and P. Ziemann, Phys. Rev. B 70, 165414 共2004兲. 25 D. K. Avasthi, W. Assmann, H. Huber, H. D. Mieskes, and H. Nolte, Nucl. Instrum. Methods Phys. Res. B 142, 171 共1998兲. 26 S. Ghosh, D. K. Avasthi, A. Tripathi, D. Kabiraj, P. Sugathan, G. K. Chaudhary, and P. Barua, Radiat. Eff. Defects Solids 161, 247 共2006兲. 27 S. V. S. Nageswara Rao, A. Kothari, G. B. V. S. Lakshmi, S. A. Khan, A. Tripathi, A. M. Siddiqui, A. P. Pathak, and D. K. Avasthi, Nucl. Instrum. Methods Phys. Res. B 212, 545 共2003兲. 28 M. Kumar, F. Singh, S. A. Khan, V. Baranwal, S. Kumar, D. C. Agarwal, A. M. Siddqui, A. Tripathi, A. Gupta, D. K. Avasthi, and A. C. Pandey, J. Phys. D 38, 637 共2005兲. 29 M. Kumar, Ph.D. thesis, University of Allahabad, 2007. 30 M. Jung, H. Rothard, B. Gervais, J. P. Grandin, A. Clouvas, and R. Wunsch, Phys. Rev. A 54, 4153 共1996兲. 31 M. Ohring, The Materials Science of Thin Films 共Academic, New York, 1991兲, Chap. 10. 32 A. F. Mayadas and M. Shatzkes, Phys. Rev. B 1, 1382 共1970兲. 33 M. Toulemonde, Ch. Dufour, and J. Stoquert, TSpike version 0.1 Copyright 2001. 34 A. Berthelot, S. Hémon, F. Gourbilleau, C. Dufour, E. Dooryhée, and E. Paumier, Nucl. Instrum. Methods Phys. Res. B 146, 437 共1998兲. 13
