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Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy
Nuclear Instruments and Methods in Physics Research B xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy D. Keerthisinghe a,⇑, B.S. Dassanayake b, S.J. Wickramarachchi a, N. Stolterfoht c, J.A. Tanis a a
Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA Department of Physics, University of Peradeniya, Peradeniya, Sri Lanka c Helmholtz-Zentrum Berlin für Materialien und Energie, D-14109 Berlin, Germany b
a r t i c l e
i n f o
Article history: Received 5 November 2015 Received in revised form 22 February 2016 Accepted 19 April 2016 Available online xxxx Keywords: Electron transmission Electron guiding Nanocapillaries Charge deposition Elastic and inelastic transmission
a b s t r a c t Transmission of electrons through insulating polyethylene terephthalate (PET) nanocapillaries was observed as a function of charge deposition, angular and energy dependence. Two samples with capillary diameters 100 and 200 nm and pore densities 5 108/cm2 and 5 107/cm2, respectively, were studied for incident electron energies of 300, 500 and 800 eV. Transmission and steady state of the electrons were attained after a time delay during which only a few electron counts were observed. The transmission through the capillaries depended on the tilt angle with both elastic and inelastic electrons going through. The guiding ability of electrons was found to increase with the incident energy in contrast to previous measurements in our laboratory for a similar PET foil. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction The first measurement of slow highly charged ions (HCIs) passing through insulating polyethylene terephthalate (PET) foils with no energy loss or change in charge state was reported in 2002 [1]. This and subsequent studies [2–4] have shown that the transmission of HCIs through nanocapillaries is the result of a self-arranging process of the charge deposited near the capillary input, with possibly more charge patches formed further along the capillary [5,6].These charge patches deflect the ions and do not permit interactions with the capillary walls, a phenomenon referred to as guiding. The extension of the transmission of HCIs through insulating nanocapillaries to different materials including SiO2 [5,7], alumina [8] and polycarbonate (PC) [9] can be found in the literature. Further experimental work centered on electron transmission through insulating alumina [10,11] and PET [12] nanocapillaries. The alumina work [10,11] showed no evidence of energy loss for incident electron energies 200–350 eV, but it was found that the transmitted electron intensities were lower than ion transmission. This result was attributed to weaker charge patch formation by electrons passing through the capillaries as expected due to the greater mobility of these
⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (D. Keerthisinghe).
singly-charged projectiles. For the PET work [12], the transmission of electrons did show energy losses attributed to interactions with the capillary walls for incident energies 500 and 1000 eV. The transmission of HCIs [13] and electrons [14,15] through straight glass microcapillaries was reported, also with the transmission for ions being larger due to the stronger positive charge patch formation compared to electrons. More recently, ion [16,17] and electron [18,19] transmission through insulating tapered glass capillaries has been reported. It is found that the transmission of both ions and electrons is dependent on the shape of the capillary itself. In the present work, electron transmission through insulating PET capillaries focuses on the charge deposition, angular and energy dependence for two samples. The first sample, having capillaries of diameter 100 nm and a pore density of 5 108/cm2, was investigated for 300, 500 and 800 eV incident electrons with current densities of 1.6 nA/mm2, while the second sample with diameters of 200 nm and a pore density of 5 107/cm2, was studied for 500 and 800 eV incident electrons with current densities of 25 nA/cm2. The charge deposition dependence of the transmission of electrons was observed for both samples at 500 and 800 eV and found to be quite different, which is attributed to the higher input currents for the latter capillaries. For the angular dependence three different regions of transmitted electrons, referred to as direct, guiding and transition [20], were found. The guiding ability of electrons increased with the incident energy in
http://dx.doi.org/10.1016/j.nimb.2016.04.037 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
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D. Keerthisinghe et al. / Nuclear Instruments and Methods in Physics Research B xxx (2016) xxx–xxx
at angles 0.1°, 0.5° and 2.0°. The results are shown in Fig. 1(a and b), respectively, in which the resulting electron intensity is plotted against the charge deposited into the capillary, Qin. The black points in panels (a) and (b) represent the intensities of the integrated energy spectra for 64 s and 132 s, respectively, for samples 1 and 2 over the energy range 460–540 eV for each of the angles measured. The current densities of the incident beams were 1.6 nA/mm2 and 25 nA/mm2 as indicated. The red curves represent the exponential growth functions used to calculate the characteristic charging constants, Qc, and the blue curves in panel (b) represent the rates of decrease in intensity, Qb, for each angle. The characteristic charge constant Qc is the rate of change of charging as the charge grows shown in Fig. 1(a and b), and Qb is the rate of change of the decrease in intensity, i.e., the blocking constant, seen in Fig. 1(b). In panel (a) for 100 nm diameter capillaries and small input currents the transmission of electrons was observed after time periods when essentially no electrons were observed followed by a fast rise of transmission toward equilibrium. For the 200 nm capillaries with considerably larger input currents, panel (b) shows the transmission with essentially no time delay (except for 0.5°) decreasing rapidly to near zero. The different behavior of the transmissions is attributed to the incident beam current density difference of the two samples. The results for sample 1, which were collected for lower current densities, were reported in 2013 [24,25] for both 500 and 800 eV. It is observed that for angles away from zero degrees charge up of the sample takes a longer time than for the angles closer to zero degrees, as indicated by the smaller Qc values near zero and the larger values for angles away from zero. The results for sample 2 are mainly due to the higher current density of the incident beam, with the deposited charge blocking the incoming electrons [9], and, hence, the intensity decreases quite rapidly to near zero. The blocking constants, Qb, for the three angles, 0.1°, 0.5° and 2.0° are seen to have about the same values. Contour plots at 500 eV for tilt angles w = 0.0°, 1.5° and 2.4° for sample 1 and w = +0.3°, 0.3° and +4.5° for sample 2 are shown in Fig. 2(a, b). In this figure the energy variation is plotted against the observation angle with the color representing the electron intensity at each angle. A decrease in intensity is observed as the sample tilt angle goes away from zero agreeing with results for
agreement with results found for straight glass capillaries [14], but conflicts the previous HCI [21,22] and electron [12] data for PET capillaries. 2. Experiment The samples were prepared at the GSI laboratory in Darmstadt, Germany. High energy 2.2 GeV Au ions were incident on PET foils causing ion tracks following which a NaOH etching process was used to prepare straight capillaries of the desired diameters. The parallelism of the capillaries was stated [23] to be 0.2° and the 100 and 200 nm diameter capillaries had the same length of 12 lm. The experiment was conducted at Western Michigan University and has been described in detail previously [20]. Briefly, electrons emitted from the source were subsequently collimated before going through the capillary foil, which was followed by a parallel-plate electrostatic energy analyzer used to detect the transmitted electrons. The sample was mounted on a goniometer having two degrees of rotational freedom, one about the vertical (tilt angle) axis and the other about the horizontal (azimuthal angle) axis. The beam divergences for samples 1 and 2 were 0.4° and 0.6°, respectively, due to different distances from the electron source to the collimators used in the measurements. The current densities for the two samples were 1.6 nA/mm2 and 25 nA/mm2, respectively, for the 100 nm (sample 1) and 200 nm (sample 2) capillary foils. The experimental setups for the charge deposition, angular and energy dependence studies were the same and can be found elsewhere [20]. The incident beam was blocked for 24 h for the charge deposition dependence studies to allow sufficient time for the capillary to discharge with the measurements for transmitted electrons being carried out immediately after putting the beam onto the sample. The angular and energy dependence measurements were performed after allowing the beam to hit the sample for 6 h to attain equilibrium conditions. 3. Results and discussion
10 (a) 8 o 6 ψ =+0.3 4 2 0 16 12
0 1 ψ = 0.0o
8 4 0 3.0 2.5 ψ =0 -1.7o 1 2.0 1.5 1.0 0.5 0.0 6 7
(500 eV)
6000
100 nm
(b) 500 eV
200 nm ψ = 0.1o
4000 I ~ 1.5 nA/mm2 Qc= 0.032 (0.003) fC 2
3
4
5
I ~ 1.7 nA/mm2 Qc = 0.016 (0.003) fC 2
3
4
I ~ 22 nA/mm2
2000
Normalized Intensity
Normalized Intensity x 103
Charge (time) evolution studies for 500 eV were carried out for sample 1 at three tilt angles +0.3°, 0.0° and 1.7° and for sample 2
5
Qb= 1.3(0.6)fC
0
ψ = -0.5o
600 400
Qc = 2.9 (1.2) fC
200
Qb= 1.4(0.2)fC
0 300
ψ = -2.0o
200 2
I ~ 1.5 nA/mm
8
Qin (fC)
9
I ~ 23 nA/mm2
Qb= 1.6(0.4)fC
100
Qc= 0.024 (0.001) fC 10
I ~ 29 nA/mm2
0 11
0
10
20
30
40
50
60
70
Qin (fC)
Fig. 1. Normalized intensity vs. charge entering per capillary Qin (a) at w = +0.3°, w = 0.0° and w = 1.7° and (b) at w = +0.1°, w = 0.5° and w = 2.0° for the samples with 100 and 200 nm diameter capillaries, respectively, at 500 eV. The red curves in both the 100 and 200 nm panels represent an exponential growth function fitted to the fast rise of transmission and Qc is the characteristic charge constant, while the blue curves in panel (b) for the 200 nm sample represent the rate of decrease of the intensity, Qb, due to the blocking effect (see text). The numbers in parentheses immediately behind the charge and blocking constants represent the uncertainties in these values. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
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Energy (eV)
(a) 500 eV o 540 ψ = 0.0
560
100 nm
520 500 480 460
-0.5
0.0
0.5
(b) 500 eV o 540 ψ = 0.3
3
3.2x104 1.2x104 2.1x104 3.0x104 3.9x104 4.8x104 5.6x104 6.5x10
Energy (eV)
560
500 480 -2
-1
0
Energy (eV)
Energy (eV)
5.41 20.3 35.2 50.1 65.0 79.9 94.7 110
480
(e) 500 eV o 540 ψ = -2.4
1.9 7.0 12 17 22 28 33 38
500 480 -2
-1
1.7 6.5 11 16 21 25 30 35
520 500 480 -2
-1
0
560
100 nm
520
-3
200 nm
1
Observation Angle θ (deg)
0
Observation Angle θ (deg)
(f) 500 eV o 540 ψ = 4.5
Energy (eV)
560
(d) 500 eV o 540 ψ = -0.3
460
1
Observation Angle θ (deg)
Energy (eV)
500
560
100 nm
520
460
520
Observation Angle θ (deg)
560 (c) 500 eV 540 ψ = -1.5o
1.5 5.5 9.5 14 18 22 26 30
460 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
1.0
Observation Angle θ (deg)
460
200 nm
200 nm
0.4 1.6 2.7 3.9 5.1 6.2 7.4 8.5
520 500 480 460 3.5
4.0
4.5
5.0
5.5
6.0
Observation Angle θ (deg)
Fig. 2. Contour plots of the angular distributions for particular angles for the transmitted electrons at 500 eV. The vertical axis and the horizontal axis represent the transmitted energy and the observation angle h, respectively, and the color represents the intensity at each point. Panels (a), (c) and (e) are for sample 1 at tilt angles w = 0.0°, 1.5° and 2.4° and panels (b), (d) and (f) are for sample 2 at tilt angles w = +0.3°, 0.3° and +4.5°. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
500 eV
16
100 nm Direct
ψd= 0.59o(0.15o)
14
ln (Intensity)
HCIs [1], as well as previous electron studies [11,12,14] with insulating capillaries. In Fig. 2(a) at zero tilt angle for sample 1 and in Fig. 2(b) at w = +0.3° for sample 2 the intensity was found to be maximum in each case. The tilt angles w = 1.5° and 0.3° in panels (c) and (d) show two peaks at different observation angles, while angles further away from zero at w = 2.4° and +4.5° in panels (e) and (f) show one peak at an observation angle with the relation w = h. These findings for the transmission are attributed, respectively, to the direct region for the angles nearest zero degrees, the transition of the direct to the guiding region for the angles next farthest from zero, and the guiding region for the angles farthest from zero of the transmission. These regions can be explained by the overlapping of the capillary ends. The total overlap of capillary ends at angles close to zero allows electrons to transmit directly through the capillaries without surface collisions and with maximum intensity. For complete non-overlap of the capillary ends at angles away from zero degrees, electrons can be transmitted indirectly through the capillaries with lower intensity than for smaller angles. The transition region, i.e., the partial overlap of capillary ends, allows electrons to traverse both directly and indirectly giving rise to two maxima at different observation angles as reported in Ref. [20]. The transmitted energy at the maximum electron intensity for angles w = 0.0° in sample 1 (Fig. 2a) and w = +0.3° in sample 2 (Fig. 2b) is about 510 eV (this difference from 500 eV represents the uncertainty in setting the incident energy with the power supply used). This energy
300 eV 500 eV 800 eV
ψd= 0.50o(0.20o)
12
Guiding
ψc= 4.3o(1.6o)
10 ψc= 3.4o(0.8o)
8 6
ψc= 2.7o(0.9o) ψd= 0.33o(0.30o)
4 0
5
10
15
20
25
ψ2 (deg.) Fig. 3. Natural logarithm of intensity of the angular distribution variations plotted against the square of the tilt angle for sample 1 at 300, 500 and 800 eV. Circles, triangles and squares show the data for the three energies, respectively. The red and the black colors represent the direct and guiding regions. The direct region intensities at 800 eV have been shifted by +6 on the intensity axis scale for display purposes. The solid lines show linearity of the natural logarithm of intensity as a function of the square of the sample tilt angle. The uncertainties of the guiding angles are shown in parenthesis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
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Table 1 Characteristic guiding angles, wc, for HCIs through PET foils and electrons through PET and straight glass capillaries for different energies, 300 eV to 1000 eV. Energy (eV)
300 500 800 1000
wc HCIs
Electrons
PET [21,22]
PET-previous [12]
– 5° – 3°
Straight glass capillary [14]
PET- present [20]
Elastic
Inelastic
Direct
Indirect
Direct
Guiding
– 2.0° – 1.6°
– 2.8° – 2.1°
0.47° ± 0.07° 0.48° ± 0.19° 0.48° ± 0.12° 0.54° ± 0.10°
– 1.03° ± 0.14° 2.67° ± 0.07° 3.45° ± 1.06°
0.33° ± 0.30° 0.50° ± 0.20° 0.59° ± 0.15° –
2.7° ± 0.9° 3.4° ± 0.8° 4.3° ± 1.6° –
corresponds to the maximum electron energy in the transition region for both samples, while the guiding region shows the energy at maximum peak intensity to be 480 eV. These results, i.e., the energy loss of electrons for angles away from zero degrees, agree with the corresponding energy spectra [20]. The characteristic guiding angle wc, i.e., the angle at which the transmission falls to 1/e of its value at zero degree tilt angle, is a measure of guiding ability. The natural logarithm of the integrated intensity variation plotted against the square of the tilt angle for angles in both the direct and guiding regions for sample 1 at 500 eV is shown in Fig. 3. The wc values are found to be constant within the uncertainties for the direct region at all energies with values of 0.33° ± 0.30°, 0.50° ± 0.20° and 0.59° ± 0.15° at 300, 500 and 800 eV. These results are consistent with the beam divergence of sample 1 which has the value of 0.4° resulting from direct transmission and are the same as the results found in Ref. [14]. On the other hand, the guiding region values are seen to increase with increasing energy. This is in contrast with the results found for HCI studies [21,22] and for previous work with electrons on pffiffiffiffiffiffiffiffi PET [12], which show that wc / 1=E where E is the incident ion energy. The results for the present guiding angles agree with electron transmission for single straight glass capillaries [14] that also showed higher guiding ability at higher energies. The wc values found from the present work, however, are larger than the values found for single straight capillaries as shown in Table 1, attributed to the fact that the PET is more insulating than glass capillaries. 4. Conclusions Transmission of electrons through insulating PET nanocapillaries was observed with an initial time delay of the transmission followed by a fast rise and approach to equilibrium for sample 1 with 100 nm capillaries. The rate of change of charge becomes larger (takes longer) as the sample is tilted away from zero degrees. The results for sample 2 with 200 nm capillaries, which generally do not show a time delay (except for the data at 0.5°), are attributed to the larger incident current density for sample 2 compared to sample 1. Direct transmission was found to be in the vicinity of zero degrees with the guiding of electrons occurring for larger tilt angles. The region between direct and guiding transmission, i.e., the transition region, shows both behaviors as seen by two peaks in the spectra, giving rise to elastically transmitted and inelastically deflected electrons. The guiding ability of electrons was found to be larger at the higher energies measured than at the lower energies, a result which contradicted the previous PET work [12], but which was in agreement with results for glass capillaries [14]. In summary, it has been shown that the transmission of electrons through insulating nanocapillaries is dependent on the charge deposited as well as on the tilt angular and the incident energy.
Acknowledgments The research group of Dr. Christina Trautmann of the GSI laboratory, Darmstadt, Germany is acknowledged for providing the samples used in this work. Assistance with the experiment from Dr. A. Kayani and the accelerator engineer, A. Kern, of the physics department at Western Michigan University is greatly appreciated. References [1] N. Stolterfoht, J.-H. Bremer, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, B. Sulik, Phys. Rev. Lett. 88 (2002) 133201. [2] N. Stolterfoht, V. Hoffmann, R. Hellhammer, Z.D. Pešic´, D. Fink, A. Pretrov, B. Sulik, Nucl. Instr. Meth. B 203 (2003) 246. [3] N. Stolterfoht, R. Hellhammer, Z. Juhász, B. Sulik, V. Bayer, C. Trautmann, E. Bodewits, A.J. De Nijs, H.M. Dang, R. Hoekstra, Phys. Rev. A 79 (2009) 042902. [4] N. Stolterfoht, R. Hellhammer, Z. Juhász, B. Sulik, H.M. Dang, R. Hoekstra, Phys. Rev. A 82 (2010) 052902. [5] P. Skog, H.Q. Zhang, R. Schuch, Phys. Rev. Lett. 101 (2008) 223202. [6] N. Stolterfoht, R. Hellhammer, D. Fink, B. Sulik, Z. Juhász, E. Bodewitz, H.M. Dang, R. Hoekstra, Phys. Rev. A 79 (2009) 022901. [7] M.B. Sahana, P. Skog, Gy. Vikor, R.T.R. Kumar, R. Schuch, Phys. Rev. A 73 (2006) 040901. [8] H.F. Krause, C.R. Vane, F.W. Meyer, Phys. Rev. A 75 (2007) 042901. [9] N. Stolterfoht, R. Hellhammer, B. Sulik, Z. Juhász, V. Bayer, C. Trautmann, E. Bodewits, R. Hoekstra, Phys. Rev. A 83 (2011) 062901. [10] A.R. Milosavljevic´, Gy. Víkor, Z.D. Pešic´, P. Kolarzˇ, D. Ševic´, B.P. Marinkovic´, S. Mátéfi-Tempfli, M. Mátéfi-Tempfli, L. Piraux, Phys. Rev. A 75 (2007) 030901. [11] A.R. Milosavljevic´, J. Jureta, Gy. Víkor, Z.D. Pešic´, D. Ševic´, M. Mátéfi-Tempfli, S. Mátéfi-Tempfli, B.P. Marinkovic´, Europhys. Lett. 86 (2009) 23001. [12] S. Das, B.S. Dassanayake, M. Winkworth, J.L. Baran, N. Stolterfoht, J.A. Tanis, Phys. Rev. A 76 (2007) 042716. }kési, Nucl. Instr. Meth. B 267 (2009) [13] R.J. Bereczky, G. Kowarik, F. Aumayr, K. To 317. }kési, J.A. Tanis, Phys. Rev. A 81 [14] B.S. Dassanayake, S. Das, R.J. Bereczky, K. To (2010) 020701. }kési, J.A. Tanis, Phys. Rev. [15] B.S. Dassanayake, R.J. Bereczky, S. Das, A. Ayyad, K. To A 83 (2011) 012707. [16] T. Ikeda, T.M. Kojima, Y. Iwai, Y. Kanai, T. Kambara, T. Nebiki, T. Narusawa, Y. Yamazaki, J. Phys. Conf. Ser. 58 (2007) 68. [17] A. Cassimi, T. Ikeda, L. Maunoury, C.L. Zhou, S. Guillous, A. Mery, H. Lebius, A. Benyagoub, C. Grygiel, H. Khemliche, P. Roncin, H. Merabet, J.A. Tanis, Phys. Rev. A 86 (2012) 062902. [18] S.J. Wickramarachchi, B.S. Dassanayake, D. Keerthisinghe, A. Ayyad, J.A. Tanis, Nucl. Instr. Meth. B 269 (2011) 1248. [19] S.J. Wickramarachchi, T. Ikeda, D. Keerthisinghe, B.S. Dassanayake, J.A. Tanis, Nucl. Instr. Meth. B 317 (2013) 101; S.J. Wickramarachchi, B.S. Dassanayake, D. Keerthisinghe, T. Ikeda, J.A. Tanis, Phys. Scr. T156 (2013) 014057. [20] D. Keerthisinghe, B.S. Dassanayake, S.J. Wickramarachchi, N. Stolterfoht, J.A. Tanis, Phys. Rev. A 92 (2015) 012703. [21] R. Hellhammer, J. Bundesmann, D. Fink, N. Stolterfoht, Nucl. Instr. Meth. B 258 (2007) 159. [22] R. Hellhammer, D. Fink, N. Stolterfoht, Nucl. Instr. Meth. B 261 (2007) 149. [23] Christina Trautmann group, GSI, private communication. [24] B.S. Dassanayake, D. Keerthisinghe, S. Wickramarachchi, A. Ayyad, S. Das, N. Stolterfoht, J.A. Tanis, Nucl. Instr. Meth. B 298 (2013) 1. [25] D. Keerthisinghe, B.S. Dassanayake, S.J. Wickramarachchi, N. Stolterfoht, J.A. Tanis, Nucl. Instr. Meth. B 317 (2013) 105.
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy D. Keerthisinghe a,⇑, B.S. Dassanayake b, S.J. Wickramarachchi a, N. Stolterfoht c, J.A. Tanis a a
Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA Department of Physics, University of Peradeniya, Peradeniya, Sri Lanka c Helmholtz-Zentrum Berlin für Materialien und Energie, D-14109 Berlin, Germany b
a r t i c l e
i n f o
Article history: Received 5 November 2015 Received in revised form 22 February 2016 Accepted 19 April 2016 Available online xxxx Keywords: Electron transmission Electron guiding Nanocapillaries Charge deposition Elastic and inelastic transmission
a b s t r a c t Transmission of electrons through insulating polyethylene terephthalate (PET) nanocapillaries was observed as a function of charge deposition, angular and energy dependence. Two samples with capillary diameters 100 and 200 nm and pore densities 5 108/cm2 and 5 107/cm2, respectively, were studied for incident electron energies of 300, 500 and 800 eV. Transmission and steady state of the electrons were attained after a time delay during which only a few electron counts were observed. The transmission through the capillaries depended on the tilt angle with both elastic and inelastic electrons going through. The guiding ability of electrons was found to increase with the incident energy in contrast to previous measurements in our laboratory for a similar PET foil. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction The first measurement of slow highly charged ions (HCIs) passing through insulating polyethylene terephthalate (PET) foils with no energy loss or change in charge state was reported in 2002 [1]. This and subsequent studies [2–4] have shown that the transmission of HCIs through nanocapillaries is the result of a self-arranging process of the charge deposited near the capillary input, with possibly more charge patches formed further along the capillary [5,6].These charge patches deflect the ions and do not permit interactions with the capillary walls, a phenomenon referred to as guiding. The extension of the transmission of HCIs through insulating nanocapillaries to different materials including SiO2 [5,7], alumina [8] and polycarbonate (PC) [9] can be found in the literature. Further experimental work centered on electron transmission through insulating alumina [10,11] and PET [12] nanocapillaries. The alumina work [10,11] showed no evidence of energy loss for incident electron energies 200–350 eV, but it was found that the transmitted electron intensities were lower than ion transmission. This result was attributed to weaker charge patch formation by electrons passing through the capillaries as expected due to the greater mobility of these
⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (D. Keerthisinghe).
singly-charged projectiles. For the PET work [12], the transmission of electrons did show energy losses attributed to interactions with the capillary walls for incident energies 500 and 1000 eV. The transmission of HCIs [13] and electrons [14,15] through straight glass microcapillaries was reported, also with the transmission for ions being larger due to the stronger positive charge patch formation compared to electrons. More recently, ion [16,17] and electron [18,19] transmission through insulating tapered glass capillaries has been reported. It is found that the transmission of both ions and electrons is dependent on the shape of the capillary itself. In the present work, electron transmission through insulating PET capillaries focuses on the charge deposition, angular and energy dependence for two samples. The first sample, having capillaries of diameter 100 nm and a pore density of 5 108/cm2, was investigated for 300, 500 and 800 eV incident electrons with current densities of 1.6 nA/mm2, while the second sample with diameters of 200 nm and a pore density of 5 107/cm2, was studied for 500 and 800 eV incident electrons with current densities of 25 nA/cm2. The charge deposition dependence of the transmission of electrons was observed for both samples at 500 and 800 eV and found to be quite different, which is attributed to the higher input currents for the latter capillaries. For the angular dependence three different regions of transmitted electrons, referred to as direct, guiding and transition [20], were found. The guiding ability of electrons increased with the incident energy in
http://dx.doi.org/10.1016/j.nimb.2016.04.037 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
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D. Keerthisinghe et al. / Nuclear Instruments and Methods in Physics Research B xxx (2016) xxx–xxx
at angles 0.1°, 0.5° and 2.0°. The results are shown in Fig. 1(a and b), respectively, in which the resulting electron intensity is plotted against the charge deposited into the capillary, Qin. The black points in panels (a) and (b) represent the intensities of the integrated energy spectra for 64 s and 132 s, respectively, for samples 1 and 2 over the energy range 460–540 eV for each of the angles measured. The current densities of the incident beams were 1.6 nA/mm2 and 25 nA/mm2 as indicated. The red curves represent the exponential growth functions used to calculate the characteristic charging constants, Qc, and the blue curves in panel (b) represent the rates of decrease in intensity, Qb, for each angle. The characteristic charge constant Qc is the rate of change of charging as the charge grows shown in Fig. 1(a and b), and Qb is the rate of change of the decrease in intensity, i.e., the blocking constant, seen in Fig. 1(b). In panel (a) for 100 nm diameter capillaries and small input currents the transmission of electrons was observed after time periods when essentially no electrons were observed followed by a fast rise of transmission toward equilibrium. For the 200 nm capillaries with considerably larger input currents, panel (b) shows the transmission with essentially no time delay (except for 0.5°) decreasing rapidly to near zero. The different behavior of the transmissions is attributed to the incident beam current density difference of the two samples. The results for sample 1, which were collected for lower current densities, were reported in 2013 [24,25] for both 500 and 800 eV. It is observed that for angles away from zero degrees charge up of the sample takes a longer time than for the angles closer to zero degrees, as indicated by the smaller Qc values near zero and the larger values for angles away from zero. The results for sample 2 are mainly due to the higher current density of the incident beam, with the deposited charge blocking the incoming electrons [9], and, hence, the intensity decreases quite rapidly to near zero. The blocking constants, Qb, for the three angles, 0.1°, 0.5° and 2.0° are seen to have about the same values. Contour plots at 500 eV for tilt angles w = 0.0°, 1.5° and 2.4° for sample 1 and w = +0.3°, 0.3° and +4.5° for sample 2 are shown in Fig. 2(a, b). In this figure the energy variation is plotted against the observation angle with the color representing the electron intensity at each angle. A decrease in intensity is observed as the sample tilt angle goes away from zero agreeing with results for
agreement with results found for straight glass capillaries [14], but conflicts the previous HCI [21,22] and electron [12] data for PET capillaries. 2. Experiment The samples were prepared at the GSI laboratory in Darmstadt, Germany. High energy 2.2 GeV Au ions were incident on PET foils causing ion tracks following which a NaOH etching process was used to prepare straight capillaries of the desired diameters. The parallelism of the capillaries was stated [23] to be 0.2° and the 100 and 200 nm diameter capillaries had the same length of 12 lm. The experiment was conducted at Western Michigan University and has been described in detail previously [20]. Briefly, electrons emitted from the source were subsequently collimated before going through the capillary foil, which was followed by a parallel-plate electrostatic energy analyzer used to detect the transmitted electrons. The sample was mounted on a goniometer having two degrees of rotational freedom, one about the vertical (tilt angle) axis and the other about the horizontal (azimuthal angle) axis. The beam divergences for samples 1 and 2 were 0.4° and 0.6°, respectively, due to different distances from the electron source to the collimators used in the measurements. The current densities for the two samples were 1.6 nA/mm2 and 25 nA/mm2, respectively, for the 100 nm (sample 1) and 200 nm (sample 2) capillary foils. The experimental setups for the charge deposition, angular and energy dependence studies were the same and can be found elsewhere [20]. The incident beam was blocked for 24 h for the charge deposition dependence studies to allow sufficient time for the capillary to discharge with the measurements for transmitted electrons being carried out immediately after putting the beam onto the sample. The angular and energy dependence measurements were performed after allowing the beam to hit the sample for 6 h to attain equilibrium conditions. 3. Results and discussion
10 (a) 8 o 6 ψ =+0.3 4 2 0 16 12
0 1 ψ = 0.0o
8 4 0 3.0 2.5 ψ =0 -1.7o 1 2.0 1.5 1.0 0.5 0.0 6 7
(500 eV)
6000
100 nm
(b) 500 eV
200 nm ψ = 0.1o
4000 I ~ 1.5 nA/mm2 Qc= 0.032 (0.003) fC 2
3
4
5
I ~ 1.7 nA/mm2 Qc = 0.016 (0.003) fC 2
3
4
I ~ 22 nA/mm2
2000
Normalized Intensity
Normalized Intensity x 103
Charge (time) evolution studies for 500 eV were carried out for sample 1 at three tilt angles +0.3°, 0.0° and 1.7° and for sample 2
5
Qb= 1.3(0.6)fC
0
ψ = -0.5o
600 400
Qc = 2.9 (1.2) fC
200
Qb= 1.4(0.2)fC
0 300
ψ = -2.0o
200 2
I ~ 1.5 nA/mm
8
Qin (fC)
9
I ~ 23 nA/mm2
Qb= 1.6(0.4)fC
100
Qc= 0.024 (0.001) fC 10
I ~ 29 nA/mm2
0 11
0
10
20
30
40
50
60
70
Qin (fC)
Fig. 1. Normalized intensity vs. charge entering per capillary Qin (a) at w = +0.3°, w = 0.0° and w = 1.7° and (b) at w = +0.1°, w = 0.5° and w = 2.0° for the samples with 100 and 200 nm diameter capillaries, respectively, at 500 eV. The red curves in both the 100 and 200 nm panels represent an exponential growth function fitted to the fast rise of transmission and Qc is the characteristic charge constant, while the blue curves in panel (b) for the 200 nm sample represent the rate of decrease of the intensity, Qb, due to the blocking effect (see text). The numbers in parentheses immediately behind the charge and blocking constants represent the uncertainties in these values. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
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D. Keerthisinghe et al. / Nuclear Instruments and Methods in Physics Research B xxx (2016) xxx–xxx
Energy (eV)
(a) 500 eV o 540 ψ = 0.0
560
100 nm
520 500 480 460
-0.5
0.0
0.5
(b) 500 eV o 540 ψ = 0.3
3
3.2x104 1.2x104 2.1x104 3.0x104 3.9x104 4.8x104 5.6x104 6.5x10
Energy (eV)
560
500 480 -2
-1
0
Energy (eV)
Energy (eV)
5.41 20.3 35.2 50.1 65.0 79.9 94.7 110
480
(e) 500 eV o 540 ψ = -2.4
1.9 7.0 12 17 22 28 33 38
500 480 -2
-1
1.7 6.5 11 16 21 25 30 35
520 500 480 -2
-1
0
560
100 nm
520
-3
200 nm
1
Observation Angle θ (deg)
0
Observation Angle θ (deg)
(f) 500 eV o 540 ψ = 4.5
Energy (eV)
560
(d) 500 eV o 540 ψ = -0.3
460
1
Observation Angle θ (deg)
Energy (eV)
500
560
100 nm
520
460
520
Observation Angle θ (deg)
560 (c) 500 eV 540 ψ = -1.5o
1.5 5.5 9.5 14 18 22 26 30
460 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
1.0
Observation Angle θ (deg)
460
200 nm
200 nm
0.4 1.6 2.7 3.9 5.1 6.2 7.4 8.5
520 500 480 460 3.5
4.0
4.5
5.0
5.5
6.0
Observation Angle θ (deg)
Fig. 2. Contour plots of the angular distributions for particular angles for the transmitted electrons at 500 eV. The vertical axis and the horizontal axis represent the transmitted energy and the observation angle h, respectively, and the color represents the intensity at each point. Panels (a), (c) and (e) are for sample 1 at tilt angles w = 0.0°, 1.5° and 2.4° and panels (b), (d) and (f) are for sample 2 at tilt angles w = +0.3°, 0.3° and +4.5°. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
500 eV
16
100 nm Direct
ψd= 0.59o(0.15o)
14
ln (Intensity)
HCIs [1], as well as previous electron studies [11,12,14] with insulating capillaries. In Fig. 2(a) at zero tilt angle for sample 1 and in Fig. 2(b) at w = +0.3° for sample 2 the intensity was found to be maximum in each case. The tilt angles w = 1.5° and 0.3° in panels (c) and (d) show two peaks at different observation angles, while angles further away from zero at w = 2.4° and +4.5° in panels (e) and (f) show one peak at an observation angle with the relation w = h. These findings for the transmission are attributed, respectively, to the direct region for the angles nearest zero degrees, the transition of the direct to the guiding region for the angles next farthest from zero, and the guiding region for the angles farthest from zero of the transmission. These regions can be explained by the overlapping of the capillary ends. The total overlap of capillary ends at angles close to zero allows electrons to transmit directly through the capillaries without surface collisions and with maximum intensity. For complete non-overlap of the capillary ends at angles away from zero degrees, electrons can be transmitted indirectly through the capillaries with lower intensity than for smaller angles. The transition region, i.e., the partial overlap of capillary ends, allows electrons to traverse both directly and indirectly giving rise to two maxima at different observation angles as reported in Ref. [20]. The transmitted energy at the maximum electron intensity for angles w = 0.0° in sample 1 (Fig. 2a) and w = +0.3° in sample 2 (Fig. 2b) is about 510 eV (this difference from 500 eV represents the uncertainty in setting the incident energy with the power supply used). This energy
300 eV 500 eV 800 eV
ψd= 0.50o(0.20o)
12
Guiding
ψc= 4.3o(1.6o)
10 ψc= 3.4o(0.8o)
8 6
ψc= 2.7o(0.9o) ψd= 0.33o(0.30o)
4 0
5
10
15
20
25
ψ2 (deg.) Fig. 3. Natural logarithm of intensity of the angular distribution variations plotted against the square of the tilt angle for sample 1 at 300, 500 and 800 eV. Circles, triangles and squares show the data for the three energies, respectively. The red and the black colors represent the direct and guiding regions. The direct region intensities at 800 eV have been shifted by +6 on the intensity axis scale for display purposes. The solid lines show linearity of the natural logarithm of intensity as a function of the square of the sample tilt angle. The uncertainties of the guiding angles are shown in parenthesis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037
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D. Keerthisinghe et al. / Nuclear Instruments and Methods in Physics Research B xxx (2016) xxx–xxx
Table 1 Characteristic guiding angles, wc, for HCIs through PET foils and electrons through PET and straight glass capillaries for different energies, 300 eV to 1000 eV. Energy (eV)
300 500 800 1000
wc HCIs
Electrons
PET [21,22]
PET-previous [12]
– 5° – 3°
Straight glass capillary [14]
PET- present [20]
Elastic
Inelastic
Direct
Indirect
Direct
Guiding
– 2.0° – 1.6°
– 2.8° – 2.1°
0.47° ± 0.07° 0.48° ± 0.19° 0.48° ± 0.12° 0.54° ± 0.10°
– 1.03° ± 0.14° 2.67° ± 0.07° 3.45° ± 1.06°
0.33° ± 0.30° 0.50° ± 0.20° 0.59° ± 0.15° –
2.7° ± 0.9° 3.4° ± 0.8° 4.3° ± 1.6° –
corresponds to the maximum electron energy in the transition region for both samples, while the guiding region shows the energy at maximum peak intensity to be 480 eV. These results, i.e., the energy loss of electrons for angles away from zero degrees, agree with the corresponding energy spectra [20]. The characteristic guiding angle wc, i.e., the angle at which the transmission falls to 1/e of its value at zero degree tilt angle, is a measure of guiding ability. The natural logarithm of the integrated intensity variation plotted against the square of the tilt angle for angles in both the direct and guiding regions for sample 1 at 500 eV is shown in Fig. 3. The wc values are found to be constant within the uncertainties for the direct region at all energies with values of 0.33° ± 0.30°, 0.50° ± 0.20° and 0.59° ± 0.15° at 300, 500 and 800 eV. These results are consistent with the beam divergence of sample 1 which has the value of 0.4° resulting from direct transmission and are the same as the results found in Ref. [14]. On the other hand, the guiding region values are seen to increase with increasing energy. This is in contrast with the results found for HCI studies [21,22] and for previous work with electrons on pffiffiffiffiffiffiffiffi PET [12], which show that wc / 1=E where E is the incident ion energy. The results for the present guiding angles agree with electron transmission for single straight glass capillaries [14] that also showed higher guiding ability at higher energies. The wc values found from the present work, however, are larger than the values found for single straight capillaries as shown in Table 1, attributed to the fact that the PET is more insulating than glass capillaries. 4. Conclusions Transmission of electrons through insulating PET nanocapillaries was observed with an initial time delay of the transmission followed by a fast rise and approach to equilibrium for sample 1 with 100 nm capillaries. The rate of change of charge becomes larger (takes longer) as the sample is tilted away from zero degrees. The results for sample 2 with 200 nm capillaries, which generally do not show a time delay (except for the data at 0.5°), are attributed to the larger incident current density for sample 2 compared to sample 1. Direct transmission was found to be in the vicinity of zero degrees with the guiding of electrons occurring for larger tilt angles. The region between direct and guiding transmission, i.e., the transition region, shows both behaviors as seen by two peaks in the spectra, giving rise to elastically transmitted and inelastically deflected electrons. The guiding ability of electrons was found to be larger at the higher energies measured than at the lower energies, a result which contradicted the previous PET work [12], but which was in agreement with results for glass capillaries [14]. In summary, it has been shown that the transmission of electrons through insulating nanocapillaries is dependent on the charge deposited as well as on the tilt angular and the incident energy.
Acknowledgments The research group of Dr. Christina Trautmann of the GSI laboratory, Darmstadt, Germany is acknowledged for providing the samples used in this work. Assistance with the experiment from Dr. A. Kayani and the accelerator engineer, A. Kern, of the physics department at Western Michigan University is greatly appreciated. References [1] N. Stolterfoht, J.-H. Bremer, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, B. Sulik, Phys. Rev. Lett. 88 (2002) 133201. [2] N. Stolterfoht, V. Hoffmann, R. Hellhammer, Z.D. Pešic´, D. Fink, A. Pretrov, B. Sulik, Nucl. Instr. Meth. B 203 (2003) 246. [3] N. Stolterfoht, R. Hellhammer, Z. Juhász, B. Sulik, V. Bayer, C. Trautmann, E. Bodewits, A.J. De Nijs, H.M. Dang, R. Hoekstra, Phys. Rev. A 79 (2009) 042902. [4] N. Stolterfoht, R. Hellhammer, Z. Juhász, B. Sulik, H.M. Dang, R. Hoekstra, Phys. Rev. A 82 (2010) 052902. [5] P. Skog, H.Q. Zhang, R. Schuch, Phys. Rev. Lett. 101 (2008) 223202. [6] N. Stolterfoht, R. Hellhammer, D. Fink, B. Sulik, Z. Juhász, E. Bodewitz, H.M. Dang, R. Hoekstra, Phys. Rev. A 79 (2009) 022901. [7] M.B. Sahana, P. Skog, Gy. Vikor, R.T.R. Kumar, R. Schuch, Phys. Rev. A 73 (2006) 040901. [8] H.F. Krause, C.R. Vane, F.W. Meyer, Phys. Rev. A 75 (2007) 042901. [9] N. Stolterfoht, R. Hellhammer, B. Sulik, Z. Juhász, V. Bayer, C. Trautmann, E. Bodewits, R. Hoekstra, Phys. Rev. A 83 (2011) 062901. [10] A.R. Milosavljevic´, Gy. Víkor, Z.D. Pešic´, P. Kolarzˇ, D. Ševic´, B.P. Marinkovic´, S. Mátéfi-Tempfli, M. Mátéfi-Tempfli, L. Piraux, Phys. Rev. A 75 (2007) 030901. [11] A.R. Milosavljevic´, J. Jureta, Gy. Víkor, Z.D. Pešic´, D. Ševic´, M. Mátéfi-Tempfli, S. Mátéfi-Tempfli, B.P. Marinkovic´, Europhys. Lett. 86 (2009) 23001. [12] S. Das, B.S. Dassanayake, M. Winkworth, J.L. Baran, N. Stolterfoht, J.A. Tanis, Phys. Rev. A 76 (2007) 042716. }kési, Nucl. Instr. Meth. B 267 (2009) [13] R.J. Bereczky, G. Kowarik, F. Aumayr, K. To 317. }kési, J.A. Tanis, Phys. Rev. A 81 [14] B.S. Dassanayake, S. Das, R.J. Bereczky, K. To (2010) 020701. }kési, J.A. Tanis, Phys. Rev. [15] B.S. Dassanayake, R.J. Bereczky, S. Das, A. Ayyad, K. To A 83 (2011) 012707. [16] T. Ikeda, T.M. Kojima, Y. Iwai, Y. Kanai, T. Kambara, T. Nebiki, T. Narusawa, Y. Yamazaki, J. Phys. Conf. Ser. 58 (2007) 68. [17] A. Cassimi, T. Ikeda, L. Maunoury, C.L. Zhou, S. Guillous, A. Mery, H. Lebius, A. Benyagoub, C. Grygiel, H. Khemliche, P. Roncin, H. Merabet, J.A. Tanis, Phys. Rev. A 86 (2012) 062902. [18] S.J. Wickramarachchi, B.S. Dassanayake, D. Keerthisinghe, A. Ayyad, J.A. Tanis, Nucl. Instr. Meth. B 269 (2011) 1248. [19] S.J. Wickramarachchi, T. Ikeda, D. Keerthisinghe, B.S. Dassanayake, J.A. Tanis, Nucl. Instr. Meth. B 317 (2013) 101; S.J. Wickramarachchi, B.S. Dassanayake, D. Keerthisinghe, T. Ikeda, J.A. Tanis, Phys. Scr. T156 (2013) 014057. [20] D. Keerthisinghe, B.S. Dassanayake, S.J. Wickramarachchi, N. Stolterfoht, J.A. Tanis, Phys. Rev. A 92 (2015) 012703. [21] R. Hellhammer, J. Bundesmann, D. Fink, N. Stolterfoht, Nucl. Instr. Meth. B 258 (2007) 159. [22] R. Hellhammer, D. Fink, N. Stolterfoht, Nucl. Instr. Meth. B 261 (2007) 149. [23] Christina Trautmann group, GSI, private communication. [24] B.S. Dassanayake, D. Keerthisinghe, S. Wickramarachchi, A. Ayyad, S. Das, N. Stolterfoht, J.A. Tanis, Nucl. Instr. Meth. B 298 (2013) 1. [25] D. Keerthisinghe, B.S. Dassanayake, S.J. Wickramarachchi, N. Stolterfoht, J.A. Tanis, Nucl. Instr. Meth. B 317 (2013) 105.
Please cite this article in press as: D. Keerthisinghe et al., Transmission of electrons through insulating PET foils: Dependence on charge deposition, tilt angle and incident energy, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.04.037