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Optimization of an electrostatic quadrupole doublet focusing systems
Journal of Electron Spectroscopy and Related Phenomena 217 (2017) 11–15
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Optimization of an electrostatic quadrupole doublet focusing systems Oday A. Hussein a,∗ , Omer Sise b a b
Department of Physics, College of Science, Al-Nahrain University, Baghdad, Iraq Department of Science Education, Faculty of Education, Suleyman Demirel University, Isparta, Turkey
a r t i c l e
i n f o
Article history: Received 11 October 2016 Received in revised form 25 March 2017 Accepted 30 March 2017 Available online 4 April 2017 Keywords: Electrostatic lens Electrostatic quadrupole doublet lenses Charged particles optics Electron optics Optimization Aberration
a b s t r a c t The imaging properties of an electrostatic quadrupole doublet lens were analyzed with the aid of computer simulation. The optimal electrode voltages which lead to stigmatic image in both planes of the quadrupole doublet lens with minimum spot size at position sensitive detector (PSD) were found for two operation modes: point-to-point focusing and parallel-to-point focusing. The optical properties as: Magnifications, spot sizes in the image plane and aberration figures were discussed. The results showed that the focusing of the lens was strong in the xy-plane in comparison with the focusing in the xz-plane. The distortion of the image was greater when the image position will be close to the lens in comparison with object position. Also, the imaging properties were very sensitive to the lunching angle of the electron-beam. © 2017 Elsevier B.V. All rights reserved.
1. Introduction In quadrupole lens, the field has two perpendicular planes of symmetry and two planes of antisymmetry. Such a field can be made by four identical electrodes located symmetrically relative to the axis, to which alternating potentials and the potentials are applied. The quadrupole lens has zero axial potential. Note that the potentials are measured from the axial potential as the reference point [1,2]. Because of the wide range of using of quadrupole lenses in different fields of science and technology, many researchers studied briefly the theory and application of quadrupole lenses (see [3–6]). The stigmatic imaging is the property of axially symmetric fields in the first-order approximation. This property is absolutely important for the purposes of electron microscopy. While, there are many applications (as: mass spectrometers, particle accelerators, vacuum tubes, and also, even electron and ion probes) where stigmatic imaging is not required. In fact, in particle accelerators the role of beam optics is only to keep the beam together, analyze its parameters, and guide it to the experiments. In this case, no image has to be created [7]. It is necessary in some applications the departure from axial symmetry, particularly, when the strong focusing action is required. Quadrupole lenses are mostly used in high-energy
∗ Corresponding author. E-mail address: [email protected] (O.A. Hussein). http://dx.doi.org/10.1016/j.elspec.2017.03.018 0368-2048/© 2017 Elsevier B.V. All rights reserved.
beams because they are stronger focusing than rotationally symmetric lenses [8]. Subsequently, it is greatly improved to employ quadrupoles, whose fields are nearly perpendicular to the optical axis. Furthermore, a system of quadrupole can produce a stigmatic image [7]. One of the important applications of electrostatic quadrupole doublet lenses is in the focusing MeV heavy ions. In the case of MeV heavy ion beam there are two methods of lenses for focusing. The first is by using the magnetic quadrupole lens and the second via the electrostatic quadrupole lens. To select the lens type, the energy and mass of the primary ion should be considered. The most important parameter for MeV imaging is the secondary molecular ion yield [9]. The energy, mass and charge of the ion are the limits of quality of a magnetic quadrupole lens, and it is not easy to focus ion beams of high-energy and heavy mass. By difference; an electrostatic quadrupole lens is mass independent in the focusing process; therefore, it can be used to focus heavy ions with more efficiency in comparison [10]. Moreover, the selection of the electrostatic quadrupole lens to focus the heavy-ion beams of high energy because it is compact and light with respect to the magnetic quadrupole lens [9]. With the aid of magnetic storage rings and at rest in electrostatic traps, the high energies ions play a greater role in experiments to understand the complex nature of many particle systems. With these storage rings of high repetition rates and with the aid of new ability of imaging, the single particles could be analyzed with highaccuracy [11]. Despite these possibilities of magnetic storage rings,
12
O.A. Hussein, O. Sise / Journal of Electron Spectroscopy and Related Phenomena 217 (2017) 11–15
Fig. 1. 2D and 3D views of an electrostatic quadrupole doublet lens. Here, r = 1.14511R, R = D/2 [2].
its energy ranges not enough to cover many fields like selective fragmentation of heavy biomolecules. Therefore, electrostatic storage rings are developed to this role and became important part of new facilities [12–15]. The growth of the beam size is one of the important problems in storage rings due to initial divergence of an ion beam. Therefore, the electrostatic quadrupole lenses are used as counteracting force to prevent the particles hit the walls. Therefore, to produce overall focusing effects in both planes the combination of at least two quadrupole lenses must be used [11]. The aberration correctors are another application of the electrostatic quadrupole lenses where the electrostatic lenses were used to correct both spherical and chromatic aberration for scanning electron microscope (SEM) [16] and then the spherical aberration correction was achieved for TEM or scanning TEM (STEM) [17]. The electrostatic quadrupole lenses can be used into two methods in correcting both spherical and chromatic aberrations at low accelerating voltages for SEM, low-energy electron microscope (LEEM), photoelectron emission microscope (PEEM) and focused ion beam systems (FIB) [8]. The first, by creating negative chromatic aberration by combined magnetic and electrostatic quadrupoles and octupoles generate aperture [16]. The second, by producing the chromatic aberration via electrostatic quadrupoles and octupoles combined with retarding potential and negative spherical aberration is generated by using octupoles [18]. The computer simulations can be used to quickly understanding to the new designers in the field of charged particles optics and its applications [19,20]. In the present work, the characteristics of an electrostatic quadrupole doublet lens were investigated for pointto-point focusing and parallel-to-point focusing operation modes by using SIMION 8.1 [21]. The important point in the focusing of the electrostatic quadrupole double lens to find stigmatic image is finding the electrode voltages combinations of the lens which give this image. Therefore, the calculations were carried out to find these electrode voltages combinations which give the stigmatic image with minimum spot size on the image plane. The effects of changing the positions of the object plane (the position of the electron-beam source) and the image plane with respect to the lens position on the imaging properties of the focusing system were studied, and the comparisons between the aberration figures in the image plane were made. Also, the effects the lunching angle of the electronbeam on the imaging properties were investigated. 2. Computational methods 2.1. Geometry The charged particle optics simulation software 3D SIMION 8.1 [21] was used to study the characteristics of the symmetric electrostatic quadrupole doublet lens shown in Fig. 1. The system optically consists of two single quadrupole lenses with three apertures. The diameter of the lens (D) is 40 mm (the diameter of a circle with
the edges of electrodes). The electrode length (L) of each single quadrupole lens is 80 mm (L = 2D). The radius of the electrode (r) is chosen according to the equation: r = 1.14511R, R = D/2 [2]. The gap between two lenses (d) is 30 mm, and an aperture is putted at the middle distance between the two lenses. The distance between the first aperture and the first lens (t) is equal to the distance between the second lens and the third aperture (t) and equal to 15 mm. The diameter of all apertures is equal, and it is equal to the diameter of the lens (D). The object (O) was assumed to be at the left hand end of the first aperture and the image (I) at the right hand end of the third aperture. The reference plane (R) was chosen to be at the center of the lens. Also, we will refer to the distance between the object position and the reference plane of the lens (R) by P, while the distance between the image position and the reference plane of the lens (R) by Q. 2.2. Optimization The charged particles optics simulation package SIMION 8.1 [21] was used to study the behavior of the electrostatic quadrupole doublet lens. The geometry file was written to the lens system under investigation (Fig. 1). Code was written by using LUA language to search of the optimum electrode voltages which give the stigmatic image simultaneously in xy-plane and xz-plane, the computations were made for two operation modes: point-to-point focusing and for parallel-to-point focusing. The computations were achieved by variation the two lens voltages V1 and V2 to find the minimum spot size at position sensitive detector (PSD). In present calculations for the point-to-point focusing mode, the maximum radius of the stigmatic image (rm ) on PSD was considered to be rm = 0.1 mm for initial electron-beam with the lunching angle ˛ = 0.1◦ and initial energy 100 eV. While, in the case of parallel-to-point focusing mode, the maximum radius of the stigmatic image (rm ) on PSD was considered to be rm = 0.1 mm for initial circular electron-beam with radius 1 mm and initial energy 100 eV. Also, one must notice that the maximum radius of the stigmatic image (rm ) was considered on the assumption that the shape of the image is circular, but in the fact, because there is a distortion in the image, the shape will not be circularly. Therefore, rm = z/2 for z-direction and rm = y/2 for y-direction, where z and y are the widths of the image in yz-plane for z-direction and y-direction, respectively. Therefore, the conditions will be z/2 <1 mm for z-direction y/2 <1 mm for y-direction, for non-circularly image shape. The electrons were used in this work for simulation, but one can use the positive ions by changing the signs of electrode voltages in Fig. 1. 3. Results and discussion In an electrostatic quadrupole doublet lens, there are two adjustable voltages that should be optimized to fix image position and magnification. For point-to-point focusing mode, Fig. 2 shows the optimized voltages of the lens for the point-to-point focusing. In this figure, the calculations of optimized voltages combinations took into account the effects of changing the object position (electron-beam source position) and image position with respect to the lens position. These effects are important in some applications, especially; when one need to find addition distance to doing the experiment. These calculations were achieved by choosing unequal distance for object and image planes. Therefore, the search for optimum electrode voltages was made for different cases; P/D = 4 and Q/D = 6, P/D = 5 and Q/D = 5, and P/D = 6 and Q/D = 4; and the behavior through the lens was studied in each case with constant launching angle of an electron-beam (˛ = 0.1◦ ) and the initial energy = 100 eV with maximum image radius at the PSD rm = 0.1 mm. Fig. 2a, c and
O.A. Hussein, O. Sise / Journal of Electron Spectroscopy and Related Phenomena 217 (2017) 11–15
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Table 2 Fixed parameters of an electrostatic quadrupole doublet lens for three combinations at parallel-to-point focusing mode. The initial circular electron-beam radius = 1 mm and an initial energy = 100 eV. No
V1 (V) V2 (V) P/D Q/D y (mm) z (mm)
Fig. 2. Optimized voltages and corresponding magnifications for both planes at point-to-point focusing mode, with initial energy = 100 eV, ˛ = 0.1◦ and rm = 0.1 mm. Here P4Q6 means that P/D = 4, and Q/D = 6. Table 1 Fixed parameters of an electrostatic quadrupole doublet lens for three combinations at point-to-point focusing mode for launching angle of an electron-beam ˛ = 0.1◦ . No
V1 (V) V2 (V) P/D Q/D y (mm) z (mm)
1
2
3
8.038 8.038 5 5 0.00048 0.00001
9.800 7.321 4 6 0.00126 0. 0086
7.321 9.800 6 4 0.00476 0.0242
e, shows the relation between V1 and V2 , and in these figures; we have two curves, one for focusing in xy-plane and the other in the xz-plane. The cross point between two curves gives the values of voltages combination, which lead to stigmatic image or focusing in both planes simultaneously, and these values are listed in Table 1. The dependence of the magnification (M) on the voltage V1 is shown in Fig. 2b, d and c for the focusing in xy-plane and xz-plane focusing and the results appear that the magnification in xz-plane is less than the magnification in xy-plane. The results show that the calculated electrode voltages combinations give the stigmatic image coincide with initial criteria and consideration in the present work about the dimensions of the image, where the image radius is less than rm = 0.1 mm (z/2 <1 mm and y/2 <1 mm) for all cases as is shown in Table 1
1
2
3
3.299 6.054 5 5 0.0068 0.038
3 5 5 6 0.0664 0. 07
3.55 8 5 4 0.177 0.085
and Fig. 5. Therefore, the calculations satisfied the initial condition of the design. In the case of parallel-to-point focusing, only the position of the image was changed because that the alignment of the parallel beam is independent on the object position and the beam enters the lens with the same radius whether it came from near distance or far distance from the lens. Therefore, the calculations were carried out for the object position P/D = 5 and an initial circular electron-beam with radius = 1 mm and initial energy = 100 eV. Fig. 3 shows the optimum voltages for different values of the image distance: Q/D = 6, Q/D = 5, and Q/D = 4. The optimum voltages combinations which lead to a stigmatic image in the image plane with radius less than rm are shown in Table 2. From this Table and Fig. 6, the values of z and y show that the initial condition of the dimensions of the image was satisfied. By comparison between Figs. 2 and 3, the required applied voltage in the case of parallel-to-point focusing is less than that in the case of point-to-point focusing. The electron trajectories in both planes for two operation modes: point-to-point focusing and parallel-to-point focusing at P = Q = 5D are shown in Fig. 4. In general, the figure appears that y is less than z for the electron-beam along the path inside the lens for both focusing mode. Also, in this figure, one must note that the figure was extended or was scaled for y-axis and z-axis to show the behavior of the electron beam along the optical axis (x-axis). The effect of changing the lunching angles of the electron beam on the imaging properties of the focusing system was investigated for point-to-point focusing mode. Fig. 5 shows the aberration figures in the image plane of the quadrupole doublet lens for three lunching angles of an electron-beam ˛ = 0.1◦ , 0.8◦ and 1◦ . These figures are a reflection to the results Tables 1 and 3, where the distortion of the image in xz-plane is greater than that in xy-plane and that due to the strong focusing of the quadrupole doublet lens in the xy-plane. The shapes of aberration figures are similar that to the work of Branova [22]. Moreover, the distortion of the image increases when the object distance (P) is greater than the image distance (Q), i.e. the image is close to the lens than the object, and reversed. More results were listed in Table 3, where the results for cases of P/D = 3 and Q/D = 7, and P/D = 7 and Q/D = 3 were included, and the calculations were made for lunching angle of an electron beam ˛ = 1◦ . For the parallel-to-point focusing mode, the effects of changing the image position with respect to the lens position on the imaging properties of the focusing system were studied. Fig. 6 illustrates these effects on the aberration figures for different values of the image distance: Q/D = 6, Q/D = 5 and Q/D = 4. In this figure, the results show that the minimum distortion or aberration occurs when the object and image have the same distance with respect to the lens, i.e. in the case of P/D = 5 and Q/D = 5. While the maximum distortion in the image occurs when the image was close to the lens in comparison with the object, i.e. P/D = 5 and Q/D = 4.
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O.A. Hussein, O. Sise / Journal of Electron Spectroscopy and Related Phenomena 217 (2017) 11–15
Fig. 3. Optimized voltages for both planes for parallel-to-point focusing with the object position P/D = 5, an initial energy = 100 eV, an initial electron-beam radius = 1 mm and rm = 0.1 mm.
Fig. 4. Simulations of the electron trajectories at both planes for P = Q = 5D. (a) V1 = V2 = 8.038 V. (b) V1 = 3.299 V, V2 = 6.054 V. The voltages in (a) and (b) were obtained from the crossing points in Fig. 2(c) and in Fig. 3(b), respectively. The energy is 100 eV for all cases, rm = 0.1 mm ␣ = 0.1◦ and for point-to-point focusing mode ␣=0.1◦ .
Fig. 5. Aberration figures in the image plane of an electrostatic quadrupole doublet lens at point-to-point focusing mode for different values of P and Q. Here; P4Q6 means that P/D = 4, and Q/D = 6. The results are shown for three values of launching angles: 0.1◦ , 0.8◦ and 1◦ .
O.A. Hussein, O. Sise / Journal of Electron Spectroscopy and Related Phenomena 217 (2017) 11–15
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Table 3 Fixed parameters of an electrostatic quadrupole doublet lens at point-to-point focusing mode for five combinations. ˛ = 1◦ was used for the z and y calculations. No
V1 (V) V2 (V) P/D Q/D My Mz y (mm) z (mm)
1
2
3
4
5
8.038 8.038 5 5 4.127 0.239 0.027 0.54
9.800 7.321 4 6 6.423 0.348 0.032 0.402
7.321 9.800 6 4 2.845 0.152 0.061 0.786
7.222 14.443 3 7 11.048 0.471 0.014 0.318
14.443 7.222 7 3 2.052 0.089 0.06 1.30
ages combinations for each lunching angle of the electron-beam to guarantee the more accurate lens performance. References
Fig. 6. Aberration figures in the image plane of an electrostatic quadrupole doublet lens for different values of the image position (Q) for parallel-to-point focusing mode. The initial circular electron-beam radius = 1 mm and the initial energy = 100 eV. Here; P5Q6 means that P/D = 5 and Q/D = 6.
4. Summary and conclusion The SIMION 8.1 was used to find the optimum combination of lens voltages, which gives the stigmatic image in xz-plane and xy-plane, simultaneously with minimum image spot size on PSD. The results in both focusing mode show that the calculated electrode voltages combinations lead to stigmatic image, with spot size satisfies the conditions in the present work. Furthermore, the calculations show that under the conditions of the investigation, the focusing in xy-plane is greater than that the focusing in xz-plane. The required applied voltages in the case of point-to-point focusing are greater than that in the parallel-to-point focusing. In the case of point-to-point focusing, the distortion in the image is greater when the object position is far from the lens and the image position is close to the lens as it appears clearly in aberration figures, where this distortion in the case of P6Q4 is larger than that in cases of P4Q6 and P5Q5. While, in the case of parallel-to-point focusing, the distortion in the image is greater when the image position is close to the lens, i.e. P5Q4. Therefore, in both cases the aberration figures are very susceptible to the image position. Also, the results show that the imaging properties are very sensitive to the lunching angle of the electron-beam. Therefore, to find the best imaging properties of the focusing system, one must find the electrode volt-
[1] L.A. Baranova, S.Ya. Yavor, Advances in Electronics and Electron Physics, vol. 76: The Optics of Round and Multipole Electrostatic lenses, 1989. [2] M. Yavor, Advances in Imaging and electron Physics – vol. 157: Optics of Charged Particles Analyzers, 2009. [3] F.U. Naab, O.F. Toader, G.S. Was, Ion Beam Transport Simulations for the 1.7 MV Tandem Accelerator at the Michigan Ion Beam Laboratory, Phys. Procedia (2015) 632–640. [4] A.J. Kreiner, Accelerator-based BNCT, Appl. Radiat. Isot. 88 (2014) 185–189. [5] D. Barna, Field simulations and mechanical implementation of electrostatic elements for the ELENA transfer lines, in: Proceedings of IPAC2014, Dresden, Germany, 2014. [6] O.A. Hussein, Determination of the most favorable shapes for the cylindrical concave electrostatic quadrupole lens, J. Al-Nahrain Univ. Sci. 12 (3) (2009) 86–93. [7] M. Szilagyi, Electron and Ion Optics, Plenum Press, New York, 1988, pp. 461. [8] J. Orloff, Handbook of Charged Particle Optics, CRC Press, Boca Raton, 2009, pp. 131. [9] T. Seki, S. Shitomoto, S. Nakagawa, T. Aoki, J. Matsuo, An electrostatic quadrupole doublet focusing system for MeV heavy ions in MeV-SIMS, Nucl. Instrum. Methods Phys. Res. B 315 (2013) 356–359. [10] G. Grime, F. Watt, Beam Optics of Quadrupole Probe-Forming Systems, Adam Hilger Ltd., Bristol, 1984. [11] C.P. Welsch1, M. Grieser, J. Ullrich, An electrostatic quadrupole doublet with an integrated steerer, in: Proceedings of EPAC 2004, Lucerne, Switzerland, 2004, pp. 1234–1236. [12] T. Tanabe, K. Noda, M. Saito, S. Lee, Y. Ito, H. Takagi, Resonant neutral-particle emission in collisions with peptide ions in a storage ring, Phys. Rev. Lett. 90 (2003) 193201. [13] C.P. Welsch, A. Schempp, J. Wolfgang, Layout of an electrostatic storage ring at IAP, in: Particle Accelerator Conference, Chicago, USA, 2001, pp. 2551–2553. [14] M.O.A. El Ghazaly, S.M. Alshammari, C.P. Welsch, H.H. Alharbi, Design of a novel electrostatic ion storage ring at KACST, Nucl. Instrum. Methods Phys. Res. A 709 (2013) 76–84. [15] F.W. Martin, Cc, Cs, and parasitic correction in quadrupole probe-forming lenses, Optik 125 (2014) 1311–1315. [16] J. Zach, M. Haider, Aberration correction in a low voltage SEM by a multipole corrector, Nucl. Instrum. Methods Phys. Res. A 363 (1995) 316–325. [17] M. Haider, G. Braunshausen, E. Schwan, Correction of the spherical aberration of a 200 kV TEM by means of a hexapole-corrector, Optik 99 (1995) 167–179. [18] unlabelleda C. Weibacker, H. Rose, Electrostatic correction of the chromatic and of the spherical aberration of charged-particle lenses (part I), J. Electron Microsc. 50 (2001) 383–390; unlabelledb C. Weibacker, H. Rose, Electrostatic correction of the chromatic and of the spherical aberration of charged-particle lenses (part II), J. Electron Microsc. 51 (2002) 45–51. [19] O. Sise, G. Martínez, I. Madesis, A. Laoutaris, A. Dimitriou, M. Fernández-Martín, T.J.M. Zouros, The voltage optimization of a four-element lens used on a hemispherical spectrograph with virtual entry for highest energy resolution, J. Electron Spectrosc. Relat. Phenom. 211 (2016) 19–31. [20] Q. Wu, Y. Tian, A. Li, D.E. Austin, Simulations of electrode misalignment effects in two-plate linear ion traps, Int. J. Mass Spectrom. 393 (2015) 52–57. [21] SIMION 3D v8.1, Scientific Instrument Services Inc. (www.simion.com). [22] L.A. Baranova, F.H. Read, Minimisation of the aberrations of electrostatic lens systems composed of quadrupole and octupole lenses, Int. J. Mass spectrom. 189 (1) (1999) 19–26.
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Optimization of an electrostatic quadrupole doublet focusing systems Oday A. Hussein a,∗ , Omer Sise b a b
Department of Physics, College of Science, Al-Nahrain University, Baghdad, Iraq Department of Science Education, Faculty of Education, Suleyman Demirel University, Isparta, Turkey
a r t i c l e
i n f o
Article history: Received 11 October 2016 Received in revised form 25 March 2017 Accepted 30 March 2017 Available online 4 April 2017 Keywords: Electrostatic lens Electrostatic quadrupole doublet lenses Charged particles optics Electron optics Optimization Aberration
a b s t r a c t The imaging properties of an electrostatic quadrupole doublet lens were analyzed with the aid of computer simulation. The optimal electrode voltages which lead to stigmatic image in both planes of the quadrupole doublet lens with minimum spot size at position sensitive detector (PSD) were found for two operation modes: point-to-point focusing and parallel-to-point focusing. The optical properties as: Magnifications, spot sizes in the image plane and aberration figures were discussed. The results showed that the focusing of the lens was strong in the xy-plane in comparison with the focusing in the xz-plane. The distortion of the image was greater when the image position will be close to the lens in comparison with object position. Also, the imaging properties were very sensitive to the lunching angle of the electron-beam. © 2017 Elsevier B.V. All rights reserved.
1. Introduction In quadrupole lens, the field has two perpendicular planes of symmetry and two planes of antisymmetry. Such a field can be made by four identical electrodes located symmetrically relative to the axis, to which alternating potentials and the potentials are applied. The quadrupole lens has zero axial potential. Note that the potentials are measured from the axial potential as the reference point [1,2]. Because of the wide range of using of quadrupole lenses in different fields of science and technology, many researchers studied briefly the theory and application of quadrupole lenses (see [3–6]). The stigmatic imaging is the property of axially symmetric fields in the first-order approximation. This property is absolutely important for the purposes of electron microscopy. While, there are many applications (as: mass spectrometers, particle accelerators, vacuum tubes, and also, even electron and ion probes) where stigmatic imaging is not required. In fact, in particle accelerators the role of beam optics is only to keep the beam together, analyze its parameters, and guide it to the experiments. In this case, no image has to be created [7]. It is necessary in some applications the departure from axial symmetry, particularly, when the strong focusing action is required. Quadrupole lenses are mostly used in high-energy
∗ Corresponding author. E-mail address: [email protected] (O.A. Hussein). http://dx.doi.org/10.1016/j.elspec.2017.03.018 0368-2048/© 2017 Elsevier B.V. All rights reserved.
beams because they are stronger focusing than rotationally symmetric lenses [8]. Subsequently, it is greatly improved to employ quadrupoles, whose fields are nearly perpendicular to the optical axis. Furthermore, a system of quadrupole can produce a stigmatic image [7]. One of the important applications of electrostatic quadrupole doublet lenses is in the focusing MeV heavy ions. In the case of MeV heavy ion beam there are two methods of lenses for focusing. The first is by using the magnetic quadrupole lens and the second via the electrostatic quadrupole lens. To select the lens type, the energy and mass of the primary ion should be considered. The most important parameter for MeV imaging is the secondary molecular ion yield [9]. The energy, mass and charge of the ion are the limits of quality of a magnetic quadrupole lens, and it is not easy to focus ion beams of high-energy and heavy mass. By difference; an electrostatic quadrupole lens is mass independent in the focusing process; therefore, it can be used to focus heavy ions with more efficiency in comparison [10]. Moreover, the selection of the electrostatic quadrupole lens to focus the heavy-ion beams of high energy because it is compact and light with respect to the magnetic quadrupole lens [9]. With the aid of magnetic storage rings and at rest in electrostatic traps, the high energies ions play a greater role in experiments to understand the complex nature of many particle systems. With these storage rings of high repetition rates and with the aid of new ability of imaging, the single particles could be analyzed with highaccuracy [11]. Despite these possibilities of magnetic storage rings,
12
O.A. Hussein, O. Sise / Journal of Electron Spectroscopy and Related Phenomena 217 (2017) 11–15
Fig. 1. 2D and 3D views of an electrostatic quadrupole doublet lens. Here, r = 1.14511R, R = D/2 [2].
its energy ranges not enough to cover many fields like selective fragmentation of heavy biomolecules. Therefore, electrostatic storage rings are developed to this role and became important part of new facilities [12–15]. The growth of the beam size is one of the important problems in storage rings due to initial divergence of an ion beam. Therefore, the electrostatic quadrupole lenses are used as counteracting force to prevent the particles hit the walls. Therefore, to produce overall focusing effects in both planes the combination of at least two quadrupole lenses must be used [11]. The aberration correctors are another application of the electrostatic quadrupole lenses where the electrostatic lenses were used to correct both spherical and chromatic aberration for scanning electron microscope (SEM) [16] and then the spherical aberration correction was achieved for TEM or scanning TEM (STEM) [17]. The electrostatic quadrupole lenses can be used into two methods in correcting both spherical and chromatic aberrations at low accelerating voltages for SEM, low-energy electron microscope (LEEM), photoelectron emission microscope (PEEM) and focused ion beam systems (FIB) [8]. The first, by creating negative chromatic aberration by combined magnetic and electrostatic quadrupoles and octupoles generate aperture [16]. The second, by producing the chromatic aberration via electrostatic quadrupoles and octupoles combined with retarding potential and negative spherical aberration is generated by using octupoles [18]. The computer simulations can be used to quickly understanding to the new designers in the field of charged particles optics and its applications [19,20]. In the present work, the characteristics of an electrostatic quadrupole doublet lens were investigated for pointto-point focusing and parallel-to-point focusing operation modes by using SIMION 8.1 [21]. The important point in the focusing of the electrostatic quadrupole double lens to find stigmatic image is finding the electrode voltages combinations of the lens which give this image. Therefore, the calculations were carried out to find these electrode voltages combinations which give the stigmatic image with minimum spot size on the image plane. The effects of changing the positions of the object plane (the position of the electron-beam source) and the image plane with respect to the lens position on the imaging properties of the focusing system were studied, and the comparisons between the aberration figures in the image plane were made. Also, the effects the lunching angle of the electronbeam on the imaging properties were investigated. 2. Computational methods 2.1. Geometry The charged particle optics simulation software 3D SIMION 8.1 [21] was used to study the characteristics of the symmetric electrostatic quadrupole doublet lens shown in Fig. 1. The system optically consists of two single quadrupole lenses with three apertures. The diameter of the lens (D) is 40 mm (the diameter of a circle with
the edges of electrodes). The electrode length (L) of each single quadrupole lens is 80 mm (L = 2D). The radius of the electrode (r) is chosen according to the equation: r = 1.14511R, R = D/2 [2]. The gap between two lenses (d) is 30 mm, and an aperture is putted at the middle distance between the two lenses. The distance between the first aperture and the first lens (t) is equal to the distance between the second lens and the third aperture (t) and equal to 15 mm. The diameter of all apertures is equal, and it is equal to the diameter of the lens (D). The object (O) was assumed to be at the left hand end of the first aperture and the image (I) at the right hand end of the third aperture. The reference plane (R) was chosen to be at the center of the lens. Also, we will refer to the distance between the object position and the reference plane of the lens (R) by P, while the distance between the image position and the reference plane of the lens (R) by Q. 2.2. Optimization The charged particles optics simulation package SIMION 8.1 [21] was used to study the behavior of the electrostatic quadrupole doublet lens. The geometry file was written to the lens system under investigation (Fig. 1). Code was written by using LUA language to search of the optimum electrode voltages which give the stigmatic image simultaneously in xy-plane and xz-plane, the computations were made for two operation modes: point-to-point focusing and for parallel-to-point focusing. The computations were achieved by variation the two lens voltages V1 and V2 to find the minimum spot size at position sensitive detector (PSD). In present calculations for the point-to-point focusing mode, the maximum radius of the stigmatic image (rm ) on PSD was considered to be rm = 0.1 mm for initial electron-beam with the lunching angle ˛ = 0.1◦ and initial energy 100 eV. While, in the case of parallel-to-point focusing mode, the maximum radius of the stigmatic image (rm ) on PSD was considered to be rm = 0.1 mm for initial circular electron-beam with radius 1 mm and initial energy 100 eV. Also, one must notice that the maximum radius of the stigmatic image (rm ) was considered on the assumption that the shape of the image is circular, but in the fact, because there is a distortion in the image, the shape will not be circularly. Therefore, rm = z/2 for z-direction and rm = y/2 for y-direction, where z and y are the widths of the image in yz-plane for z-direction and y-direction, respectively. Therefore, the conditions will be z/2 <1 mm for z-direction y/2 <1 mm for y-direction, for non-circularly image shape. The electrons were used in this work for simulation, but one can use the positive ions by changing the signs of electrode voltages in Fig. 1. 3. Results and discussion In an electrostatic quadrupole doublet lens, there are two adjustable voltages that should be optimized to fix image position and magnification. For point-to-point focusing mode, Fig. 2 shows the optimized voltages of the lens for the point-to-point focusing. In this figure, the calculations of optimized voltages combinations took into account the effects of changing the object position (electron-beam source position) and image position with respect to the lens position. These effects are important in some applications, especially; when one need to find addition distance to doing the experiment. These calculations were achieved by choosing unequal distance for object and image planes. Therefore, the search for optimum electrode voltages was made for different cases; P/D = 4 and Q/D = 6, P/D = 5 and Q/D = 5, and P/D = 6 and Q/D = 4; and the behavior through the lens was studied in each case with constant launching angle of an electron-beam (˛ = 0.1◦ ) and the initial energy = 100 eV with maximum image radius at the PSD rm = 0.1 mm. Fig. 2a, c and
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Table 2 Fixed parameters of an electrostatic quadrupole doublet lens for three combinations at parallel-to-point focusing mode. The initial circular electron-beam radius = 1 mm and an initial energy = 100 eV. No
V1 (V) V2 (V) P/D Q/D y (mm) z (mm)
Fig. 2. Optimized voltages and corresponding magnifications for both planes at point-to-point focusing mode, with initial energy = 100 eV, ˛ = 0.1◦ and rm = 0.1 mm. Here P4Q6 means that P/D = 4, and Q/D = 6. Table 1 Fixed parameters of an electrostatic quadrupole doublet lens for three combinations at point-to-point focusing mode for launching angle of an electron-beam ˛ = 0.1◦ . No
V1 (V) V2 (V) P/D Q/D y (mm) z (mm)
1
2
3
8.038 8.038 5 5 0.00048 0.00001
9.800 7.321 4 6 0.00126 0. 0086
7.321 9.800 6 4 0.00476 0.0242
e, shows the relation between V1 and V2 , and in these figures; we have two curves, one for focusing in xy-plane and the other in the xz-plane. The cross point between two curves gives the values of voltages combination, which lead to stigmatic image or focusing in both planes simultaneously, and these values are listed in Table 1. The dependence of the magnification (M) on the voltage V1 is shown in Fig. 2b, d and c for the focusing in xy-plane and xz-plane focusing and the results appear that the magnification in xz-plane is less than the magnification in xy-plane. The results show that the calculated electrode voltages combinations give the stigmatic image coincide with initial criteria and consideration in the present work about the dimensions of the image, where the image radius is less than rm = 0.1 mm (z/2 <1 mm and y/2 <1 mm) for all cases as is shown in Table 1
1
2
3
3.299 6.054 5 5 0.0068 0.038
3 5 5 6 0.0664 0. 07
3.55 8 5 4 0.177 0.085
and Fig. 5. Therefore, the calculations satisfied the initial condition of the design. In the case of parallel-to-point focusing, only the position of the image was changed because that the alignment of the parallel beam is independent on the object position and the beam enters the lens with the same radius whether it came from near distance or far distance from the lens. Therefore, the calculations were carried out for the object position P/D = 5 and an initial circular electron-beam with radius = 1 mm and initial energy = 100 eV. Fig. 3 shows the optimum voltages for different values of the image distance: Q/D = 6, Q/D = 5, and Q/D = 4. The optimum voltages combinations which lead to a stigmatic image in the image plane with radius less than rm are shown in Table 2. From this Table and Fig. 6, the values of z and y show that the initial condition of the dimensions of the image was satisfied. By comparison between Figs. 2 and 3, the required applied voltage in the case of parallel-to-point focusing is less than that in the case of point-to-point focusing. The electron trajectories in both planes for two operation modes: point-to-point focusing and parallel-to-point focusing at P = Q = 5D are shown in Fig. 4. In general, the figure appears that y is less than z for the electron-beam along the path inside the lens for both focusing mode. Also, in this figure, one must note that the figure was extended or was scaled for y-axis and z-axis to show the behavior of the electron beam along the optical axis (x-axis). The effect of changing the lunching angles of the electron beam on the imaging properties of the focusing system was investigated for point-to-point focusing mode. Fig. 5 shows the aberration figures in the image plane of the quadrupole doublet lens for three lunching angles of an electron-beam ˛ = 0.1◦ , 0.8◦ and 1◦ . These figures are a reflection to the results Tables 1 and 3, where the distortion of the image in xz-plane is greater than that in xy-plane and that due to the strong focusing of the quadrupole doublet lens in the xy-plane. The shapes of aberration figures are similar that to the work of Branova [22]. Moreover, the distortion of the image increases when the object distance (P) is greater than the image distance (Q), i.e. the image is close to the lens than the object, and reversed. More results were listed in Table 3, where the results for cases of P/D = 3 and Q/D = 7, and P/D = 7 and Q/D = 3 were included, and the calculations were made for lunching angle of an electron beam ˛ = 1◦ . For the parallel-to-point focusing mode, the effects of changing the image position with respect to the lens position on the imaging properties of the focusing system were studied. Fig. 6 illustrates these effects on the aberration figures for different values of the image distance: Q/D = 6, Q/D = 5 and Q/D = 4. In this figure, the results show that the minimum distortion or aberration occurs when the object and image have the same distance with respect to the lens, i.e. in the case of P/D = 5 and Q/D = 5. While the maximum distortion in the image occurs when the image was close to the lens in comparison with the object, i.e. P/D = 5 and Q/D = 4.
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Fig. 3. Optimized voltages for both planes for parallel-to-point focusing with the object position P/D = 5, an initial energy = 100 eV, an initial electron-beam radius = 1 mm and rm = 0.1 mm.
Fig. 4. Simulations of the electron trajectories at both planes for P = Q = 5D. (a) V1 = V2 = 8.038 V. (b) V1 = 3.299 V, V2 = 6.054 V. The voltages in (a) and (b) were obtained from the crossing points in Fig. 2(c) and in Fig. 3(b), respectively. The energy is 100 eV for all cases, rm = 0.1 mm ␣ = 0.1◦ and for point-to-point focusing mode ␣=0.1◦ .
Fig. 5. Aberration figures in the image plane of an electrostatic quadrupole doublet lens at point-to-point focusing mode for different values of P and Q. Here; P4Q6 means that P/D = 4, and Q/D = 6. The results are shown for three values of launching angles: 0.1◦ , 0.8◦ and 1◦ .
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Table 3 Fixed parameters of an electrostatic quadrupole doublet lens at point-to-point focusing mode for five combinations. ˛ = 1◦ was used for the z and y calculations. No
V1 (V) V2 (V) P/D Q/D My Mz y (mm) z (mm)
1
2
3
4
5
8.038 8.038 5 5 4.127 0.239 0.027 0.54
9.800 7.321 4 6 6.423 0.348 0.032 0.402
7.321 9.800 6 4 2.845 0.152 0.061 0.786
7.222 14.443 3 7 11.048 0.471 0.014 0.318
14.443 7.222 7 3 2.052 0.089 0.06 1.30
ages combinations for each lunching angle of the electron-beam to guarantee the more accurate lens performance. References
Fig. 6. Aberration figures in the image plane of an electrostatic quadrupole doublet lens for different values of the image position (Q) for parallel-to-point focusing mode. The initial circular electron-beam radius = 1 mm and the initial energy = 100 eV. Here; P5Q6 means that P/D = 5 and Q/D = 6.
4. Summary and conclusion The SIMION 8.1 was used to find the optimum combination of lens voltages, which gives the stigmatic image in xz-plane and xy-plane, simultaneously with minimum image spot size on PSD. The results in both focusing mode show that the calculated electrode voltages combinations lead to stigmatic image, with spot size satisfies the conditions in the present work. Furthermore, the calculations show that under the conditions of the investigation, the focusing in xy-plane is greater than that the focusing in xz-plane. The required applied voltages in the case of point-to-point focusing are greater than that in the parallel-to-point focusing. In the case of point-to-point focusing, the distortion in the image is greater when the object position is far from the lens and the image position is close to the lens as it appears clearly in aberration figures, where this distortion in the case of P6Q4 is larger than that in cases of P4Q6 and P5Q5. While, in the case of parallel-to-point focusing, the distortion in the image is greater when the image position is close to the lens, i.e. P5Q4. Therefore, in both cases the aberration figures are very susceptible to the image position. Also, the results show that the imaging properties are very sensitive to the lunching angle of the electron-beam. Therefore, to find the best imaging properties of the focusing system, one must find the electrode volt-
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