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Guiding of highly charged ions through nanocapillaries in PET: Dependence on the projectile energy and charge
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 261 (2007) 149–152 www.elsevier.com/locate/nimb
Guiding of highly charged ions through nanocapillaries in PET: Dependence on the projectile energy and charge R. Hellhammer *, D. Fink, N. Stolterfoht Hahn-Meitner-Institut Berlin GmbH, Glienicker Strasse 100, D-14109 Berlin, Germany Available online 11 April 2007
Abstract We measured the energy and charge state dependence of the transmission of highly charged ions through nanocapillaries with a diameter of 200 nm and a length of 10 lm. The nanocapillaries were produced by etching ion tracks originating from 250 MeV krypton ions passed through PET polymer foils leading to a significant improvement in the parallelism of the capillaries to former used capillary foils. This improvement allowed us to investigate the guiding effect over a wider range in energy and charge state than done before. In accordance with model calculations, the experimental results show a scaling law describing the dependence of the integrated ion transmission on tilt angle, energy and charge state of the incident ions. The scaling law for capillaries with high parallelism are found to be applicable in a wide range of energies and charge states. New parameters describing the capability of a capillary foil to guide highly charge ions were derived. Ó 2007 Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 32.80.Fb Keywords: Nanocapillary; Ion transmission; Capillary guiding; Energy dependence; Charge state dependence; Scaling law
1. Introduction In recent years, the use of nanocapillaries in insulating materials like polyethylene terephthalate (PET) and oxides has received increasing attention. In contradiction to the experiments at nanocapillaries in metals [1,2], capillaries in insulating materials show the unexpected effect of guided transmission of slow highly charged ions. To investigate the effect of capillary guiding, we use nanocapillaries produced by etching ion tracks created with high-energy projectiles in PET [3,4]. This technique allows for the production of capillaries with large aspect ratios and high straightness for each capillary. The work in our laboratory with less aligned capillaries has been described before [5–9]. Using a higher projectile energy, i.e. a few MeV/u, for creating the ion tracks an alignment between all capillaries superior to former used ones could be achieved. This *
Corresponding author. Tel.: +49 308 062 3034; fax: +49 308 062 2293. E-mail address: [email protected] (R. Hellhammer).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.04.044
reduces the full width of half maximum (FWHM) of the distribution of the capillary inclination to a value much smaller than the opening angle of a capillary given by the aspect ratio. The present work is focused on the projectile energy and charge state dependence of the ion guiding. We used capillaries in highly insulating PET produced by etching ion tracks originating from 250 MeV krypton ions. Thus, we prepared capillaries with a diameter of 200 nm and a length of 10 lm. The transmission profiles of Ne7+ from 3 keV to 10 keV, Ar13+ from 7 keV to 13 keV and Xe25+ from 25 keV up to 40 keV as well as Ne9+ at 3 keV and Ar9+ at 9 keV were investigated in detail. 2. Experimental methods and results The experiments were carried out at the Ionenstrahllabor (ISL) of the Hahn-Meitner-Institut (HMI) Berlin using a 14.5 GHz electron cyclotron resonance (ECR) source [10]. The PET foil was irradiated by 250 MeV krypton ions.
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The irradiation experiments were performed at the Flerov Institute in Dubna and the ISL of the HMI in Berlin. By etching the ion tracks, we formed cylindrical capillaries with a diameter of 200 nm. We used scanning electron microscopy (SEM) to investigate the diameter, the density and the circularity of the capillaries. In the present case, the area of the capillary openings to the total surface is equal to about 4% with a track density of about 108 tracks per cm2. With these capillary foils, we investigated the transmission as a function of the charge state and the kinetic energy of the incident ions. In Fig. 1, we give examples for the transmission profiles for Ne7+ in an energy range from 3 keV to 10 keV and for Ar13+ in an energy range from 7 keV to 13 keV. In addition, we measured similar profiles for Xe25+ in an energy range from 25 keV to 40 keV as well as Ne9+ at 3 keV and Ar9+ at 9 keV. Here, it should be mentioned that all these profiles were measured after a saturation process leading to a constant transmission through the capillaries. This saturation process is necessary to reach equilibrium conditions for the deflection patch introduced in [5–7] and discharging processes through the bulk of the polymer and the surface of the capillary. In [11], we could show a strong nonlinear discharging behavior based on the Frenkel–Poole-process [12], which was also considered in [13]. This process causes a more or less constant equilibrium charge for the deflecting patch at different
beam intensities within the experimental uncertainties. Therefore, it suggests the same deposited charge for different tilt angles as well for different charge states and projectile energies. For each series of measurements with a given charge state, we observed a narrower width for the angular distribution of transmitted ions at higher energies, consistent with former experiments [9]. Moreover, we observed for a given charge state and projectile energy a tilt angle dependence of the width of the transmission profile. This dependence is more significant than seen in the former experiments [5–8], where the variation of the width could be ignored within uncertainties of the measurements and be treated as more or less constant for each energy. In addition, we found that even for higher projectile energies the maxima of the transmission profiles do not diverge from the tilt angle within the experimental uncertainties. This is in contradiction to former experiments with less well-aligned capillaries, where the maxima for higher energies were shifted to smaller observation angles. The present results can be attributed to the higher parallelism of the capillaries. In this case, the effect of capillary guiding for less tilted capillaries in the foil as the tilt angle of the capillary foil does not play such a strong role than in former experiments. We explain this findings as follows: for nonparallel capillaries a big fraction of less tilted capillaries showed a spurious maximum of the transmission caused by the strong tilt angle dependence of the transmission at high projectile energies. By contrast, the transmission through the very small fraction of misaligned capillaries in foils with a very high parallelism, as in the present case, can be ignored within the uncertainties of the measurement. As in [9], we calculate the quantity Itot representing the total intensity of transmitted ions with I tot ¼ Y max r2t
ð1Þ
obtained from the yield Ymax at the peak maximum and the width rt of the transmission profile. It is pointed out, that this quantity Itot gives only relative values for the integrated intensity. To compare the results of the total intensity for different projectiles, we normalized each quantity with the total intensity for the transmission under 0° tilt angle. This leads to the normalized transmission yield Ynor (Xq, E, W) with Y nor ðX q ; E; WÞ ¼
Fig. 1. Transmission profiles of Ne7+ in an energy range from 3 keV to 10 keV and for Ar13+ in the energy range from 7 keV to 13 keV.
I tot ðX q ; E; WÞ : I tot ðX q ; E; W ¼ 0Þ
ð2Þ
Here, Xq represents the projectile X with charge state q, E is the kinetic energy and W is the tilt angle of the capillary foil. Fig. 2 shows the normalized transmission yield Ynor for Ne7+ in the range from 3 keV to 10 keV and Xe25+ from 25 keV to 40 keV as a function of the tilt angle. For each projectile, we measured higher guiding efficiency for lower energies in consistency with the model previously developed in [7]. The lines were fitted by introducing the guiding
R. Hellhammer et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 149–152
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transmitted fraction of ions fp by the fraction of ions f0 propagated at W = 0° leads to the above introduced normalized transmission yield Ynor. Comparing the exponents in Eqs. (3) and (4) leads to the expression sin2 Wc ¼ U 1 Ep =q þ cs :
ð5Þ
In Fig. 3, the results for sin2Wc from the measurements in the range from Ne7+ at 3 keV up to Xe25+ at 40 keV are plotted over Ep/q. The plot shows that the results for sin2Wc are falling on a straight line within the experimental uncertainties, when the fit parameters in Eq. (5) are U = 1.75 V and cs = 130. This result confirms the assumption made in Eq. (4). It should be added, that previous results presented in [9] showed an inconsistency with Eq. (4), which we expect to be produced by the nonparallelism of capillaries in the foil caused by the primary irradiation and capillary production. The results reveal that Eq. (5) can be used as a scaling law for a single capillary foil to predict the guiding power for different charge states and projectile energies by knowing the parameters U and cs characteristic for the special foil material. It should be pointed out, that the representation of the data over a wide range of projectile energy and charge state by a straight line is an implicit confirmation of the finding, that the charge in the deflecting patch, and
Fig. 2. Normalized transmission yield Ynor for projectiles Ne7+ and Xe25+ at projectile energies from 3 keV up to 40 keV as a function of the tilt angle. The lines are plotted by using Eq. (3) as a fitting function.
power of a capillary, characterized by the guiding angle Wc in the following way: sin2 W : ð3Þ Y nor ¼ exp 2 sin Wc The guiding angle Wc is defined without any model assumption as the tilt angle for which the transmitted intensity drops to the value 1/e. With this expression, we are able to verify the model assumption for the transmitted fraction of ions through a capillary given by [7,9] Ep þ cs sin2 W ; ð4Þ fp ¼ f0 exp qU where fp is the propagated fraction of ions through the capillaries, f0 is the fraction for W = 0°, Ep is the projectile energy, q is the incident charge state, U is the potential of the deflecting field near the capillary entrance and cs is an adjustable correction parameter. This expression is based on the assumption, that the ions are lost by deposition in the entrance patch if the perpendicular energy E? = Ep sin2W exceeds the deflection energy qU. Normalizing the
Fig. 3. The quantity sin2Wc which characterizes the guiding power, shows a linear dependence on the ratio Ep/q of the projectile energy and charge. The straight line is plotted by using Eq. (5) with the parameters U = 1.75 V and cs = 130.
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therefore, the deflecting potential remains practically constant. In addition, one should keep in mind that the results for the parameters U and cs being dependent on the foil material and treatment. Therefore, we expect different results for each other types of foils. This expectation is due to the high sensitivity of the bulk and surface conductivity on the production processes of the PET-foils as well on the etching procedure to enlarge the ion tracks to nanocapillaries. On the other hand, other foil treatment at additional experiments with lower capillary density showed nearly the same values for the guiding angles Wc as those for the high density foils. For the capillary foils with lower density the etching process differs somewhat from the procedure used for the foils investigated here. This additional result gives rise to the assumption, that changes in the material treatment do not drastically change the transmission characteristics. 3. Conclusions In conclusion, we measured the guiding power for a wide range in charge state and projectile energies from 3 keV for Ne7+ up to 40 keV for Xe25+. We obtained a tilt angle dependence as well as a projectile energy dependence on the width of the angular distribution of the transmitted ions. Narrower transmission profiles were observed for smaller tilt angles as well as for higher projectile energies. Experimental guiding powers were determined from the transmission profiles for all investigated charge states and projectile energies within the uncertainties of the measurements. They are a confirmation of the model assumptions by comparing the results of the fits with the former assumptions. By comparing the model for capillary guiding with the experimental results, we could determine the constancy of the model parameter U as the average potential of the deflecting field in the scattering region of the capil-
lary for all charge states and projectile energies been measured. This finding is in agreement with the assumption of a constancy of the charge deposited in the deflecting patch under equilibrium conditions for different beam intensities, and therefore, predicted constancy for different charge states and projectile energies. Acknowledgements We thank P. Szimkowiak for preparing the PET capillary foils and J. Bundesmann for his technical support during the experiments. References [1] Y. Yamazaki, Phys. Scripta T 73 (1997) 293. [2] S. Ninomiya, Y. Yamazaki, F. Koike, H. Masuda, K. Komaki, K. Kuroki, M. Sekiguchi, Phys. Rev. Lett. 78 (1997) 4557. [3] C.R. Martin, Science 266 (1994) 1961. [4] R. Spohr, Ion Tracks and Microtechnology, Vieweg, Braunschweig, 1990. [5] N. Stolterfoht, J.H. Bremer, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, B. Sulik, Phys. Rev. Lett. 88 (2002) 133201. [6] N. Stolterfoht, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, Z.D. Pesˇic, B. Sulik, Nucl. Instr. and Meth. B 203 (2003) 246. [7] N. Stolterfoht, R. Hellhammer, Z.D. Pesˇic, V. Hoffmann, J. Bundesmann, A. Petrov, D. Fink, B. Sulik, Vacuum 73 (2004) 31. [8] N. Stolterfoht, R. Hellhammer, Z.D. Pesˇic, V. Hoffmann, J. Bundesmann, A. Petrov, D. Fink, B. Sulik, M. Shah, K. Dunn, J. Pedregosa, R.W. McCullough, Nucl. Instr. and Meth. B 225 (2004) 169. [9] R. Hellhammer, P. Sobocinski, Z.D. Pesˇic, J. Bundesmann, D. Fink, N. Stolterfoht, Nucl. Instr. and Meth. B 232 (2005) 235; R. Hellhammer, Z.D. Pesˇic, P. Sobocinski, D. Fink, J. Bundesmann, N. Stolterfoht, Nucl. Instr. and Meth. B 233 (2005) 213. [10] M. Grether, A. Spieler, D. Niemann, N. Stolterfoht, Phys. Rev. A 56 (1997) 3794. [11] R. Hellhammer, Thesis, TU Berlin, http://opus.kobv.de/tuberlin/ volltexte/2006/1415/. [12] J. Frenkel, Phys. Rev. 54 (1938) 647. [13] K. Schiessl et al., Nucl. Instr. and Meth. B 232 (2005) 228.
Nuclear Instruments and Methods in Physics Research B 261 (2007) 149–152 www.elsevier.com/locate/nimb
Guiding of highly charged ions through nanocapillaries in PET: Dependence on the projectile energy and charge R. Hellhammer *, D. Fink, N. Stolterfoht Hahn-Meitner-Institut Berlin GmbH, Glienicker Strasse 100, D-14109 Berlin, Germany Available online 11 April 2007
Abstract We measured the energy and charge state dependence of the transmission of highly charged ions through nanocapillaries with a diameter of 200 nm and a length of 10 lm. The nanocapillaries were produced by etching ion tracks originating from 250 MeV krypton ions passed through PET polymer foils leading to a significant improvement in the parallelism of the capillaries to former used capillary foils. This improvement allowed us to investigate the guiding effect over a wider range in energy and charge state than done before. In accordance with model calculations, the experimental results show a scaling law describing the dependence of the integrated ion transmission on tilt angle, energy and charge state of the incident ions. The scaling law for capillaries with high parallelism are found to be applicable in a wide range of energies and charge states. New parameters describing the capability of a capillary foil to guide highly charge ions were derived. Ó 2007 Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 32.80.Fb Keywords: Nanocapillary; Ion transmission; Capillary guiding; Energy dependence; Charge state dependence; Scaling law
1. Introduction In recent years, the use of nanocapillaries in insulating materials like polyethylene terephthalate (PET) and oxides has received increasing attention. In contradiction to the experiments at nanocapillaries in metals [1,2], capillaries in insulating materials show the unexpected effect of guided transmission of slow highly charged ions. To investigate the effect of capillary guiding, we use nanocapillaries produced by etching ion tracks created with high-energy projectiles in PET [3,4]. This technique allows for the production of capillaries with large aspect ratios and high straightness for each capillary. The work in our laboratory with less aligned capillaries has been described before [5–9]. Using a higher projectile energy, i.e. a few MeV/u, for creating the ion tracks an alignment between all capillaries superior to former used ones could be achieved. This *
Corresponding author. Tel.: +49 308 062 3034; fax: +49 308 062 2293. E-mail address: [email protected] (R. Hellhammer).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.04.044
reduces the full width of half maximum (FWHM) of the distribution of the capillary inclination to a value much smaller than the opening angle of a capillary given by the aspect ratio. The present work is focused on the projectile energy and charge state dependence of the ion guiding. We used capillaries in highly insulating PET produced by etching ion tracks originating from 250 MeV krypton ions. Thus, we prepared capillaries with a diameter of 200 nm and a length of 10 lm. The transmission profiles of Ne7+ from 3 keV to 10 keV, Ar13+ from 7 keV to 13 keV and Xe25+ from 25 keV up to 40 keV as well as Ne9+ at 3 keV and Ar9+ at 9 keV were investigated in detail. 2. Experimental methods and results The experiments were carried out at the Ionenstrahllabor (ISL) of the Hahn-Meitner-Institut (HMI) Berlin using a 14.5 GHz electron cyclotron resonance (ECR) source [10]. The PET foil was irradiated by 250 MeV krypton ions.
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R. Hellhammer et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 149–152
The irradiation experiments were performed at the Flerov Institute in Dubna and the ISL of the HMI in Berlin. By etching the ion tracks, we formed cylindrical capillaries with a diameter of 200 nm. We used scanning electron microscopy (SEM) to investigate the diameter, the density and the circularity of the capillaries. In the present case, the area of the capillary openings to the total surface is equal to about 4% with a track density of about 108 tracks per cm2. With these capillary foils, we investigated the transmission as a function of the charge state and the kinetic energy of the incident ions. In Fig. 1, we give examples for the transmission profiles for Ne7+ in an energy range from 3 keV to 10 keV and for Ar13+ in an energy range from 7 keV to 13 keV. In addition, we measured similar profiles for Xe25+ in an energy range from 25 keV to 40 keV as well as Ne9+ at 3 keV and Ar9+ at 9 keV. Here, it should be mentioned that all these profiles were measured after a saturation process leading to a constant transmission through the capillaries. This saturation process is necessary to reach equilibrium conditions for the deflection patch introduced in [5–7] and discharging processes through the bulk of the polymer and the surface of the capillary. In [11], we could show a strong nonlinear discharging behavior based on the Frenkel–Poole-process [12], which was also considered in [13]. This process causes a more or less constant equilibrium charge for the deflecting patch at different
beam intensities within the experimental uncertainties. Therefore, it suggests the same deposited charge for different tilt angles as well for different charge states and projectile energies. For each series of measurements with a given charge state, we observed a narrower width for the angular distribution of transmitted ions at higher energies, consistent with former experiments [9]. Moreover, we observed for a given charge state and projectile energy a tilt angle dependence of the width of the transmission profile. This dependence is more significant than seen in the former experiments [5–8], where the variation of the width could be ignored within uncertainties of the measurements and be treated as more or less constant for each energy. In addition, we found that even for higher projectile energies the maxima of the transmission profiles do not diverge from the tilt angle within the experimental uncertainties. This is in contradiction to former experiments with less well-aligned capillaries, where the maxima for higher energies were shifted to smaller observation angles. The present results can be attributed to the higher parallelism of the capillaries. In this case, the effect of capillary guiding for less tilted capillaries in the foil as the tilt angle of the capillary foil does not play such a strong role than in former experiments. We explain this findings as follows: for nonparallel capillaries a big fraction of less tilted capillaries showed a spurious maximum of the transmission caused by the strong tilt angle dependence of the transmission at high projectile energies. By contrast, the transmission through the very small fraction of misaligned capillaries in foils with a very high parallelism, as in the present case, can be ignored within the uncertainties of the measurement. As in [9], we calculate the quantity Itot representing the total intensity of transmitted ions with I tot ¼ Y max r2t
ð1Þ
obtained from the yield Ymax at the peak maximum and the width rt of the transmission profile. It is pointed out, that this quantity Itot gives only relative values for the integrated intensity. To compare the results of the total intensity for different projectiles, we normalized each quantity with the total intensity for the transmission under 0° tilt angle. This leads to the normalized transmission yield Ynor (Xq, E, W) with Y nor ðX q ; E; WÞ ¼
Fig. 1. Transmission profiles of Ne7+ in an energy range from 3 keV to 10 keV and for Ar13+ in the energy range from 7 keV to 13 keV.
I tot ðX q ; E; WÞ : I tot ðX q ; E; W ¼ 0Þ
ð2Þ
Here, Xq represents the projectile X with charge state q, E is the kinetic energy and W is the tilt angle of the capillary foil. Fig. 2 shows the normalized transmission yield Ynor for Ne7+ in the range from 3 keV to 10 keV and Xe25+ from 25 keV to 40 keV as a function of the tilt angle. For each projectile, we measured higher guiding efficiency for lower energies in consistency with the model previously developed in [7]. The lines were fitted by introducing the guiding
R. Hellhammer et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 149–152
151
transmitted fraction of ions fp by the fraction of ions f0 propagated at W = 0° leads to the above introduced normalized transmission yield Ynor. Comparing the exponents in Eqs. (3) and (4) leads to the expression sin2 Wc ¼ U 1 Ep =q þ cs :
ð5Þ
In Fig. 3, the results for sin2Wc from the measurements in the range from Ne7+ at 3 keV up to Xe25+ at 40 keV are plotted over Ep/q. The plot shows that the results for sin2Wc are falling on a straight line within the experimental uncertainties, when the fit parameters in Eq. (5) are U = 1.75 V and cs = 130. This result confirms the assumption made in Eq. (4). It should be added, that previous results presented in [9] showed an inconsistency with Eq. (4), which we expect to be produced by the nonparallelism of capillaries in the foil caused by the primary irradiation and capillary production. The results reveal that Eq. (5) can be used as a scaling law for a single capillary foil to predict the guiding power for different charge states and projectile energies by knowing the parameters U and cs characteristic for the special foil material. It should be pointed out, that the representation of the data over a wide range of projectile energy and charge state by a straight line is an implicit confirmation of the finding, that the charge in the deflecting patch, and
Fig. 2. Normalized transmission yield Ynor for projectiles Ne7+ and Xe25+ at projectile energies from 3 keV up to 40 keV as a function of the tilt angle. The lines are plotted by using Eq. (3) as a fitting function.
power of a capillary, characterized by the guiding angle Wc in the following way: sin2 W : ð3Þ Y nor ¼ exp 2 sin Wc The guiding angle Wc is defined without any model assumption as the tilt angle for which the transmitted intensity drops to the value 1/e. With this expression, we are able to verify the model assumption for the transmitted fraction of ions through a capillary given by [7,9] Ep þ cs sin2 W ; ð4Þ fp ¼ f0 exp qU where fp is the propagated fraction of ions through the capillaries, f0 is the fraction for W = 0°, Ep is the projectile energy, q is the incident charge state, U is the potential of the deflecting field near the capillary entrance and cs is an adjustable correction parameter. This expression is based on the assumption, that the ions are lost by deposition in the entrance patch if the perpendicular energy E? = Ep sin2W exceeds the deflection energy qU. Normalizing the
Fig. 3. The quantity sin2Wc which characterizes the guiding power, shows a linear dependence on the ratio Ep/q of the projectile energy and charge. The straight line is plotted by using Eq. (5) with the parameters U = 1.75 V and cs = 130.
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R. Hellhammer et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 149–152
therefore, the deflecting potential remains practically constant. In addition, one should keep in mind that the results for the parameters U and cs being dependent on the foil material and treatment. Therefore, we expect different results for each other types of foils. This expectation is due to the high sensitivity of the bulk and surface conductivity on the production processes of the PET-foils as well on the etching procedure to enlarge the ion tracks to nanocapillaries. On the other hand, other foil treatment at additional experiments with lower capillary density showed nearly the same values for the guiding angles Wc as those for the high density foils. For the capillary foils with lower density the etching process differs somewhat from the procedure used for the foils investigated here. This additional result gives rise to the assumption, that changes in the material treatment do not drastically change the transmission characteristics. 3. Conclusions In conclusion, we measured the guiding power for a wide range in charge state and projectile energies from 3 keV for Ne7+ up to 40 keV for Xe25+. We obtained a tilt angle dependence as well as a projectile energy dependence on the width of the angular distribution of the transmitted ions. Narrower transmission profiles were observed for smaller tilt angles as well as for higher projectile energies. Experimental guiding powers were determined from the transmission profiles for all investigated charge states and projectile energies within the uncertainties of the measurements. They are a confirmation of the model assumptions by comparing the results of the fits with the former assumptions. By comparing the model for capillary guiding with the experimental results, we could determine the constancy of the model parameter U as the average potential of the deflecting field in the scattering region of the capil-
lary for all charge states and projectile energies been measured. This finding is in agreement with the assumption of a constancy of the charge deposited in the deflecting patch under equilibrium conditions for different beam intensities, and therefore, predicted constancy for different charge states and projectile energies. Acknowledgements We thank P. Szimkowiak for preparing the PET capillary foils and J. Bundesmann for his technical support during the experiments. References [1] Y. Yamazaki, Phys. Scripta T 73 (1997) 293. [2] S. Ninomiya, Y. Yamazaki, F. Koike, H. Masuda, K. Komaki, K. Kuroki, M. Sekiguchi, Phys. Rev. Lett. 78 (1997) 4557. [3] C.R. Martin, Science 266 (1994) 1961. [4] R. Spohr, Ion Tracks and Microtechnology, Vieweg, Braunschweig, 1990. [5] N. Stolterfoht, J.H. Bremer, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, B. Sulik, Phys. Rev. Lett. 88 (2002) 133201. [6] N. Stolterfoht, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, Z.D. Pesˇic, B. Sulik, Nucl. Instr. and Meth. B 203 (2003) 246. [7] N. Stolterfoht, R. Hellhammer, Z.D. Pesˇic, V. Hoffmann, J. Bundesmann, A. Petrov, D. Fink, B. Sulik, Vacuum 73 (2004) 31. [8] N. Stolterfoht, R. Hellhammer, Z.D. Pesˇic, V. Hoffmann, J. Bundesmann, A. Petrov, D. Fink, B. Sulik, M. Shah, K. Dunn, J. Pedregosa, R.W. McCullough, Nucl. Instr. and Meth. B 225 (2004) 169. [9] R. Hellhammer, P. Sobocinski, Z.D. Pesˇic, J. Bundesmann, D. Fink, N. Stolterfoht, Nucl. Instr. and Meth. B 232 (2005) 235; R. Hellhammer, Z.D. Pesˇic, P. Sobocinski, D. Fink, J. Bundesmann, N. Stolterfoht, Nucl. Instr. and Meth. B 233 (2005) 213. [10] M. Grether, A. Spieler, D. Niemann, N. Stolterfoht, Phys. Rev. A 56 (1997) 3794. [11] R. Hellhammer, Thesis, TU Berlin, http://opus.kobv.de/tuberlin/ volltexte/2006/1415/. [12] J. Frenkel, Phys. Rev. 54 (1938) 647. [13] K. Schiessl et al., Nucl. Instr. and Meth. B 232 (2005) 228.