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Dynamic focusing of microprobe lens system during scanning process
Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Dynamic focusing of microprobe lens system during scanning process K.I. Melnik ⇑ Institute of Applied Physics, National Academy of Sciences of Ukraine, Sumy, Ukraine, Petropavlovskaya Str., 58, Sumy 40030, Ukraine
a r t i c l e
i n f o
Article history: Received 20 July 2012 Received in revised form 13 December 2012 Accepted 20 December 2012 Available online 18 January 2013 Keywords: Nanoprobe Probe-forming system Quadrupole lens Scanner Deflector Dynamic focusing
a b s t r a c t Highly excited quadrupole lenses have significant spherical aberrations and they are very sensitive to the beam entrance angle, and microprobe size may vary considerably during scanning if the scanner is placed before or inside the focusing system. The effect of probe blurring while moving away from the optical axis can be partially compensated by adopting a dynamic focusing procedure to systems of magnetic quadrupole lenses like it is in electron beam devices. Dynamic focusing implies changing of quadrupole lens currents synchronously with the beam deflection on the certain rule such that probe size remains minimal in any raster point. A quadruplet of magnetic quadrupole lenses was considered. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction It is commonly known that an originally focused beam blurs while scanning over a sample surface because of deflection aberrations and because it leaves a focus of a lens system. These challenges are solved in electron-beam facilities by combined application of several optical elements correcting some aberrations and by a dynamic focusing. The dynamic focusing allows the focus depth of the optical system to be changed quickly and interactively; it permits to focus the beam on the target surface all the time, be it CRT screen or a specimen in SEM (TEM), even when measurements are performed on tilted objects. There is some information that the dynamic focusing could work in ion-beam lithography facilities (FIB) but for the Ga+ beam energy of some tens of keV [1]. Microprobe forming systems (PFS), in comparison to the above-mentioned facilities, are less flexible; the theory of their optics is incomplete. Apart from some former systems of axial geometry, focusing is usually performed by a system of magnetic quadrupole lenses (MQL), a beam divergence is limited by a set of slits; system adjustment and current control in quadrupoles are mostly manual while beam yield profiles are analyzed. Neither aberration correctors nor lenses with time-variable field that are widely used in electron facilities have not been applied yet (see review [2]). Meantime a time-variable field distribution may be realized in the principal focusing elements, i.e. in MQL. Modern power ⇑ Address: Institute of Applied Physics, Petropavlovskaya Str., 58, Sumy 40030, Ukraine. Tel.: +380 542 640953. E-mail address: [email protected] 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.12.048
supplies allow lens excitations to be regulated during the experiment so the focus depth can be changed synchronously with the beam deflection. The following motivates a consideration of this possibility. As to [3], a space between the last lens and the target is the most suitable to install the scanner in order to minimize perturbations. The length g of this space is called a working distance; it specifies a focal distance of the whole system. Recent trends lie in constant reduction of g, and in raised demands to process repeatability, scanning frequency and positional accuracy of submicron probes. An electrostatic scanner meets all these demands but it should be placed at the space in front of the whole PFS or between the lenses where the probe is formed. An additional element is therewith incorporated; the scanner becomes an additional source of perturbations, which involve unbalancing of the probe formation process. Stigmatic focusing is preserved in the presence of deflection fields if the deflection is insufficient to violate the paraxial nature of the beam. Should the deflection field be strong enough paraxial approximation is not valid. Since strong quadrupoles are characterized by considerable spherical aberrations and sensitivity to the beam entrance angle, the probe size can change greatly during the scanning. Recently it was regarded as insignificant, e.g., in classical arrangement of the triplet with a pre-lens scanning [4] for a 1.25 mm deviation a beam spread was found to be 10 lm to a base size of the probe about 6–7 lm. But ignoring this factor is unacceptable with a view of submicron probe. This challenge will become relevant, primarily, for the latest PFS with considerable demagnifications (>100). This work is aimed at the analysis of perturbations caused by the electrostatic scanner installed between the second and the
22
K.I. Melnik / Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
third MQL of the quadruplet and at the study of how the dynamic focusing can be used to preserve probe size during the scanning. Here the dynamic focusing means synchronous change of the lens excitations and the voltage at the deflectors under some law in such a way that the spot remains the smallest in every raster point. Recently this task was not considered for the ion microprobes. 2. Dynamics of a beam at the PFS The study is based on the evaluation of the beam spread in various raster points. The similar task was examined in [3], however, scanning in the [ direction only was considered there and with the following simplifications: a mono-energetic beam, a deflection field assumed to be uniform inside the scanner and zero outside it (sharp cut-off fringe field or SCOFF model), the first-order trajectory equations in the scanner. Here I used the trajectory equations along the z axis, each particle of the beam was described through the x, y coordinates counted off the optical z axis, and the path inclinations x0 , y0 , where x0 = dx/dz, y0 = dy/dz. In contrast to [3], within the SCOFF model I have taken into account the third-order terms and chromatic phenomena caused by a discontinuous jump of the field derivative at the edge of the deflector using the d = (p p0)/p0 term which is a relative divergence between the p particle impulse and the p0 average particle impulse at the moment of passing through the plane of the object collimator. The deflector was assumed to be two plates parallel to the xz plane (similar equations would be for yz plane if exchange x and y) with the r distance between them, with the Du potential difference; the beginning of the plates was taken as 0 and their effective length was Lc. Limiting conditions for the boundary value problem before the deflector were yjz¼0 ¼ yi ; y0 jz¼0 ¼ y0i . The solution of this problem with the thirdorder terms was found as
y ¼ yi þ Lc y0i þ Lc =2 Dy0
ð1Þ
y0 ¼ y0i þ Dy0
ð2Þ 2
2
Dy0 ¼ Lc a ðð1 2dÞð1 þ x0 þ y0 Þ þ 3d2 4d3 Þ
a¼
Du 2Vr
Eqs. (1) and (2) do not take into account the focusing effect that is proportional to the ratio of r/Lc, that may be determined by the method in [5]. At the same time Eqs. (1) and (2) account a change of a particle energy at the entrance and the exit of the deflector through the terms of the d kind. More recent works [6,7] provide all aberration coefficients for quadrupoles and the rules for the calculation of the whole system coefficients using the coefficients of individual elements. The study was performed within the project on construction of proton beam writing channel in the institute. The PFS of this channel is developed as a quadruplet with four independent power supplies [8], with demagnifications 133.2 164.1 (horizontally and vertically), the length L is 6.681 m, g is 70 mm. Geometric parameters are planned to be: the distance from the object to the first lens is 358.2 cm; the distances between lenses in doublets are as follows: 3.94 cm between the first and the second and 3.18 cm between the third and the fourth lenses; the distance between doublets (between the second and the third lenses) is 270.2 cm; the working distance is 70 mm; the effective lens lengths are L1,eff = 5.068 cm, L2,eff = 7.141 cm, L3,eff = L4,eff = 6.825 cm; the lens bore radii are ra1 = ra2 = 6.5 mm, ra3 = ra4 = 7.5 mm; the distance between the object and the angular collimators is 195 cm, the deflector on x is the first after the second lens and is of 70 mm
length with 5 mm distance between the plates, then the deflector on y that is of 280 mm length with 4 mm distance between the plates is placed in the distance 5 mm, and then in 344 mm distance the third lens is placed. Arrangement of excitations is C1D2C3D4, where Cn or Dn denotes connection to a supply with number n (n = 1. . .4) thus the lens focuses the beam on [ or y direction, correspondingly. Energy of the beam assumed to be 1.5 MeV, dmax is 5 104. Basic probe size d0 is 512 518 nm2 (0.27 lm2), object aperture is of size 36 80 lm2 and angular aperture is 48 130 lm2. The aperture sizes remain the same during calculations because there is not any way to change them quickly and precisely during the experiment. For the practical tasks at this channel the scanning raster should be about 1 mm2. Distribution of beam current density at the system entrance was taken from [9]. The electrostatic scanner for the separated quadruplet is incorporated between two lens doublets. Such an arrangement is said in [3] to provide smaller broadening of the probe in comparison to that in case of the scanner placed in front of the whole system and it should give an opportunity to scan without considerable blurring up to 1 mm2 for the systems where g = 180 mm. Focus depth is shifted by the third and the fourth lenses that are not coupled by power to the first doublet [8], otherwise the dynamic focusing is meaningless to speak of because it is not possible to re-adjust the whole lens system considering the hysteresis loops of four lenses in an instant. 3. Dynamic focusing in a quadruplet Fig. 1 shows the effect from the dynamic focusing usage. Because of the task symmetry, only one fourth of the raster was considered. The G focus depth was varied about g0 = 70 mm, the current in the first two lenses remained constant, the current in the third and the fourth lenses was changed to provide the focusing in the G plane. If G is optimally chosen (Fig. 1d), the FWHM probe size is reduced (compare Fig. 1a and b) from dNx dNy to dx dy. In Fig. 1c the ratio (dx dy)/(dNx dNy) is shown. For deflections on y < 100 lm the dynamic focusing is not required, but its significance stably increases further. Compensation of blurring is mainly effected on the y direction; the optimal focus depth neatly correlates with the deflection on y. It is from Fig. 1a that the conclusion of [3] that the quadruplets without considerable spreading may perform scanning within 2–3 mm is wrong when more accurate model is used and both principal directions x and y are considered. The paraxial approximation is no longer valid at the raster of 500 200 lm2. The process in the selected point with (0.25;0.25) mm coordinates away from the optical axis is shown in details in Fig. 2. Initial probe 512 518 nm2 deflected by (0.238;0.203) mm grew to 33.9 24.1 lm2 (FWHM) for G = g0. The necessary deflection (0.25;0.25) mm therewith could not be attained, the spherical aberrations limited the deflection with (0.238; 0.203) mm, on further increase of Du the beam deflection on the target even reduced but the probe size still enlarged. On focusing at G = 72.2 mm the probe size in the plane g0 = 70 mm reduced to 1.4 9.0 lm2 (FWHM), the deflection on the target could be made the specified (0.25;0.25) mm. The probe area was 65 times decreased. Fig. 3 explains the correlation between the beam characteristics and the deflection on y. Asymmetry of the optics of the quadrupole system causes the beam to stay close to the optical axis in the x plane; but the beam is deflected by y to a great extent where the beam gets to the zone of spherical aberration influence. The similar data were published for the triplet [4, fig. 6] too but there the beam suffers from a greater degradation in the x direction. The focus depth increasing by 3.1% of the 1.5 MeV ion beam was provided by the change of the magnetic induction in the third lens
K.I. Melnik / Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
23
Fig. 1. Results of the dynamic focusing in the quadruplet at one fourth of the raster from zero to 0.25 mm. a) The probe area (dNx dNy) lm2, the focus depth unchanged; b) the area (dNx dNy) lm2, with the optimal focus depth; c) relative change of the probe area (dx dy)/(dNx dNy); d) the G optimal focus depth, mm.
Fig. 2. The probe size d vs. the G focus depth at the point of (0.25;0.25) mm away from the optical axis. dx – the probe size on x, dy – the probe size on y.
onto 0.1738 T instead of 0.1748 T; in the fourth lens onto 0.3486 T instead of 0.3550 T. For windings in number of 101 in the lens coils the currents should change in the following way: in the third lens onto 5.129 A instead of 5.158 A; in the fourth lens onto 12.545 A instead of 14.752 A (for energy of 1.5 MeV this lens is saturated so a thorough analysis is required). It is evident that it is possible to change the focus depth for this raster point. Fig. 4 shows a dependency between relative changes in currents exciting the third and the fourth lenses and the resulting focus depth. Thus, if power supplies are capable to change the current by 0.1% of the initial value, then the next discreet value of the focus depth is 70.35 mm, i.e. almost all the required range as to Fig. 1d can be covered. Characteristics in Fig. 4 are relevant only for the
Fig. 3. The path of the originally axial particle deflected on a target to (0.25;0.25) mm away from the optical axis.
linear area where the magnetic field is current-proportional. Dynamic focusing will be difficult in the saturation zone. Conditions for the lens power supplies are rather severe. Thus our GwInstek PSM-2010 with the maximum current of 10 A, accuracy adjustment of 0.2%, the change increment of 1 mA, the noise level of 2 mA are capable to run only if the necessary magnetic induction change is greater than 4 mT, that corresponds to the current change by 3 mA. For the 1.5 MeV proton beam, zone of dynamic focusing possibility starts from deflection by 175 lm. Time for current setting is 100 ms, thus operation is possible in regimes where frequency is lower than 10 Hz. The magnetic lens hysteresis is a vital issue also. The hysteresis may be taken into account only for typical tasks like a square
24
K.I. Melnik / Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
Fig. 4. Relative change of currents exciting the third and the fourth lenses vs. the focus depth.
scanning with the constant scanning step and pattern size. Here the procedure similar to that from [1] may be used, where before operation with real samples, the aberration coefficients were analyzed from the results of scanning over the referenced mark, then input into the computer memory and used for the scanning control. Here we may proceed in the same manner. Since a variety of sizes and scanning steps is limited in tasks of material analysis, there is a typical set of control programs. Thus, for each program it is quite possible to do several experiments on a step-by-step adjustment of the lens system and to determine the correction factors to the calculated currents. The things may be simpler in the case of the electrostatic quadruplet. From the principal point of view, the difference of the optics in magnetic and electrostatic quadrupole systems is insignificant, because the major aberrations are the same and equations of the particle motion are very similar. Even when the chromatic aberrations of the electrostatic quadrupole are twice that of the magnetic one, but the absence of hysteresis and existence of easy controlled high-frequency voltage supplies make the idea applicable to the electrostatic quadruplet. 4. Conclusions For the submicron probe forming systems the paraxial approximation is no longer valid at the scanning raster of some hundreds
of micrometers. In the examined quadruplet, for example, ignoring perturbations that occur because of the deflection is tolerable only for the scanning patterns of 500 200 lm2. This restriction is significant, as microprobe applications require a larger range of scanning, up to 1–2 mm. Beam broadening while deflecting away from the optical axis may be partially compensated by using the dynamic focusing of the lens system. For this purpose synchronous change of the lens exciting currents and voltage at the deflectors is required that allows the spot to be minimized near the raster edges. The dynamic focusing is not required in the studied system for deflections on y < 100 lm but for the greater deflections it makes possible reducing the probe area (up to 100 times on 250 lm deflection). This technique can help in controlling the probe parameters, but its practical application requires the high-current power supplies, which can precisely change the current by 0.1% of the initial value, and which can operate with the frequency of the scanning system, otherwise the scanning frequency will be very limited. Some special experiments will be necessary for each scanning program to determine the correction factors to the calculated currents and thus to consider the hysteresis loops in the lenses. References [1] M. Kinokuni, H. Sawaragi, R. Mimura, R. Aihara, A. Forchel, J. Vac. Sci. Technol. B 16 (4) (1998) 2484. [2] C.G. Ryan, Nucl. Instr. Meth. B 269 (2011) 2151. [3] A.D. Dymnikov, G.A. Glass, B. Rout, Nucl. Instr. Meth. B 239 (2005) 250. [4] G.W. Grime, M. Dawson, M. Marsh, I.C. McArthur, F. Watt, Nucl. Instr. Meth. B 54 (1991) 52. [5] G.A. Doskeyev, O.A. Edenova, I.F. Spivak-Lavrov, Nucl. Instr. Meth. A 645 (2011) 163. [6] A.D. Dymnikov, G.M. Osetinskiy, Sov. J. Part. Nucl. 20 (1989) 293. [7] A.G. Ponomarev, K.I. Melnik, V.I. Miroshnichenko, V.E. Storizhko, B. Sulkio-Cleff, Nucl. Instr. Meth. B 201 (2003) 637. [8] A.A. Ponomarova, K.I. Melnik, G.S. Vorobjov, A.G. Ponomarev, Nucl. Instr. Meth. B 269 (2011) 2202. [9] A.A. Ponomarov, V.I. Miroshnichenko, A.G. Ponomarev, Nucl. Instr. Meth. B 267 (2009) 2041.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Dynamic focusing of microprobe lens system during scanning process K.I. Melnik ⇑ Institute of Applied Physics, National Academy of Sciences of Ukraine, Sumy, Ukraine, Petropavlovskaya Str., 58, Sumy 40030, Ukraine
a r t i c l e
i n f o
Article history: Received 20 July 2012 Received in revised form 13 December 2012 Accepted 20 December 2012 Available online 18 January 2013 Keywords: Nanoprobe Probe-forming system Quadrupole lens Scanner Deflector Dynamic focusing
a b s t r a c t Highly excited quadrupole lenses have significant spherical aberrations and they are very sensitive to the beam entrance angle, and microprobe size may vary considerably during scanning if the scanner is placed before or inside the focusing system. The effect of probe blurring while moving away from the optical axis can be partially compensated by adopting a dynamic focusing procedure to systems of magnetic quadrupole lenses like it is in electron beam devices. Dynamic focusing implies changing of quadrupole lens currents synchronously with the beam deflection on the certain rule such that probe size remains minimal in any raster point. A quadruplet of magnetic quadrupole lenses was considered. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction It is commonly known that an originally focused beam blurs while scanning over a sample surface because of deflection aberrations and because it leaves a focus of a lens system. These challenges are solved in electron-beam facilities by combined application of several optical elements correcting some aberrations and by a dynamic focusing. The dynamic focusing allows the focus depth of the optical system to be changed quickly and interactively; it permits to focus the beam on the target surface all the time, be it CRT screen or a specimen in SEM (TEM), even when measurements are performed on tilted objects. There is some information that the dynamic focusing could work in ion-beam lithography facilities (FIB) but for the Ga+ beam energy of some tens of keV [1]. Microprobe forming systems (PFS), in comparison to the above-mentioned facilities, are less flexible; the theory of their optics is incomplete. Apart from some former systems of axial geometry, focusing is usually performed by a system of magnetic quadrupole lenses (MQL), a beam divergence is limited by a set of slits; system adjustment and current control in quadrupoles are mostly manual while beam yield profiles are analyzed. Neither aberration correctors nor lenses with time-variable field that are widely used in electron facilities have not been applied yet (see review [2]). Meantime a time-variable field distribution may be realized in the principal focusing elements, i.e. in MQL. Modern power ⇑ Address: Institute of Applied Physics, Petropavlovskaya Str., 58, Sumy 40030, Ukraine. Tel.: +380 542 640953. E-mail address: [email protected] 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.12.048
supplies allow lens excitations to be regulated during the experiment so the focus depth can be changed synchronously with the beam deflection. The following motivates a consideration of this possibility. As to [3], a space between the last lens and the target is the most suitable to install the scanner in order to minimize perturbations. The length g of this space is called a working distance; it specifies a focal distance of the whole system. Recent trends lie in constant reduction of g, and in raised demands to process repeatability, scanning frequency and positional accuracy of submicron probes. An electrostatic scanner meets all these demands but it should be placed at the space in front of the whole PFS or between the lenses where the probe is formed. An additional element is therewith incorporated; the scanner becomes an additional source of perturbations, which involve unbalancing of the probe formation process. Stigmatic focusing is preserved in the presence of deflection fields if the deflection is insufficient to violate the paraxial nature of the beam. Should the deflection field be strong enough paraxial approximation is not valid. Since strong quadrupoles are characterized by considerable spherical aberrations and sensitivity to the beam entrance angle, the probe size can change greatly during the scanning. Recently it was regarded as insignificant, e.g., in classical arrangement of the triplet with a pre-lens scanning [4] for a 1.25 mm deviation a beam spread was found to be 10 lm to a base size of the probe about 6–7 lm. But ignoring this factor is unacceptable with a view of submicron probe. This challenge will become relevant, primarily, for the latest PFS with considerable demagnifications (>100). This work is aimed at the analysis of perturbations caused by the electrostatic scanner installed between the second and the
22
K.I. Melnik / Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
third MQL of the quadruplet and at the study of how the dynamic focusing can be used to preserve probe size during the scanning. Here the dynamic focusing means synchronous change of the lens excitations and the voltage at the deflectors under some law in such a way that the spot remains the smallest in every raster point. Recently this task was not considered for the ion microprobes. 2. Dynamics of a beam at the PFS The study is based on the evaluation of the beam spread in various raster points. The similar task was examined in [3], however, scanning in the [ direction only was considered there and with the following simplifications: a mono-energetic beam, a deflection field assumed to be uniform inside the scanner and zero outside it (sharp cut-off fringe field or SCOFF model), the first-order trajectory equations in the scanner. Here I used the trajectory equations along the z axis, each particle of the beam was described through the x, y coordinates counted off the optical z axis, and the path inclinations x0 , y0 , where x0 = dx/dz, y0 = dy/dz. In contrast to [3], within the SCOFF model I have taken into account the third-order terms and chromatic phenomena caused by a discontinuous jump of the field derivative at the edge of the deflector using the d = (p p0)/p0 term which is a relative divergence between the p particle impulse and the p0 average particle impulse at the moment of passing through the plane of the object collimator. The deflector was assumed to be two plates parallel to the xz plane (similar equations would be for yz plane if exchange x and y) with the r distance between them, with the Du potential difference; the beginning of the plates was taken as 0 and their effective length was Lc. Limiting conditions for the boundary value problem before the deflector were yjz¼0 ¼ yi ; y0 jz¼0 ¼ y0i . The solution of this problem with the thirdorder terms was found as
y ¼ yi þ Lc y0i þ Lc =2 Dy0
ð1Þ
y0 ¼ y0i þ Dy0
ð2Þ 2
2
Dy0 ¼ Lc a ðð1 2dÞð1 þ x0 þ y0 Þ þ 3d2 4d3 Þ
a¼
Du 2Vr
Eqs. (1) and (2) do not take into account the focusing effect that is proportional to the ratio of r/Lc, that may be determined by the method in [5]. At the same time Eqs. (1) and (2) account a change of a particle energy at the entrance and the exit of the deflector through the terms of the d kind. More recent works [6,7] provide all aberration coefficients for quadrupoles and the rules for the calculation of the whole system coefficients using the coefficients of individual elements. The study was performed within the project on construction of proton beam writing channel in the institute. The PFS of this channel is developed as a quadruplet with four independent power supplies [8], with demagnifications 133.2 164.1 (horizontally and vertically), the length L is 6.681 m, g is 70 mm. Geometric parameters are planned to be: the distance from the object to the first lens is 358.2 cm; the distances between lenses in doublets are as follows: 3.94 cm between the first and the second and 3.18 cm between the third and the fourth lenses; the distance between doublets (between the second and the third lenses) is 270.2 cm; the working distance is 70 mm; the effective lens lengths are L1,eff = 5.068 cm, L2,eff = 7.141 cm, L3,eff = L4,eff = 6.825 cm; the lens bore radii are ra1 = ra2 = 6.5 mm, ra3 = ra4 = 7.5 mm; the distance between the object and the angular collimators is 195 cm, the deflector on x is the first after the second lens and is of 70 mm
length with 5 mm distance between the plates, then the deflector on y that is of 280 mm length with 4 mm distance between the plates is placed in the distance 5 mm, and then in 344 mm distance the third lens is placed. Arrangement of excitations is C1D2C3D4, where Cn or Dn denotes connection to a supply with number n (n = 1. . .4) thus the lens focuses the beam on [ or y direction, correspondingly. Energy of the beam assumed to be 1.5 MeV, dmax is 5 104. Basic probe size d0 is 512 518 nm2 (0.27 lm2), object aperture is of size 36 80 lm2 and angular aperture is 48 130 lm2. The aperture sizes remain the same during calculations because there is not any way to change them quickly and precisely during the experiment. For the practical tasks at this channel the scanning raster should be about 1 mm2. Distribution of beam current density at the system entrance was taken from [9]. The electrostatic scanner for the separated quadruplet is incorporated between two lens doublets. Such an arrangement is said in [3] to provide smaller broadening of the probe in comparison to that in case of the scanner placed in front of the whole system and it should give an opportunity to scan without considerable blurring up to 1 mm2 for the systems where g = 180 mm. Focus depth is shifted by the third and the fourth lenses that are not coupled by power to the first doublet [8], otherwise the dynamic focusing is meaningless to speak of because it is not possible to re-adjust the whole lens system considering the hysteresis loops of four lenses in an instant. 3. Dynamic focusing in a quadruplet Fig. 1 shows the effect from the dynamic focusing usage. Because of the task symmetry, only one fourth of the raster was considered. The G focus depth was varied about g0 = 70 mm, the current in the first two lenses remained constant, the current in the third and the fourth lenses was changed to provide the focusing in the G plane. If G is optimally chosen (Fig. 1d), the FWHM probe size is reduced (compare Fig. 1a and b) from dNx dNy to dx dy. In Fig. 1c the ratio (dx dy)/(dNx dNy) is shown. For deflections on y < 100 lm the dynamic focusing is not required, but its significance stably increases further. Compensation of blurring is mainly effected on the y direction; the optimal focus depth neatly correlates with the deflection on y. It is from Fig. 1a that the conclusion of [3] that the quadruplets without considerable spreading may perform scanning within 2–3 mm is wrong when more accurate model is used and both principal directions x and y are considered. The paraxial approximation is no longer valid at the raster of 500 200 lm2. The process in the selected point with (0.25;0.25) mm coordinates away from the optical axis is shown in details in Fig. 2. Initial probe 512 518 nm2 deflected by (0.238;0.203) mm grew to 33.9 24.1 lm2 (FWHM) for G = g0. The necessary deflection (0.25;0.25) mm therewith could not be attained, the spherical aberrations limited the deflection with (0.238; 0.203) mm, on further increase of Du the beam deflection on the target even reduced but the probe size still enlarged. On focusing at G = 72.2 mm the probe size in the plane g0 = 70 mm reduced to 1.4 9.0 lm2 (FWHM), the deflection on the target could be made the specified (0.25;0.25) mm. The probe area was 65 times decreased. Fig. 3 explains the correlation between the beam characteristics and the deflection on y. Asymmetry of the optics of the quadrupole system causes the beam to stay close to the optical axis in the x plane; but the beam is deflected by y to a great extent where the beam gets to the zone of spherical aberration influence. The similar data were published for the triplet [4, fig. 6] too but there the beam suffers from a greater degradation in the x direction. The focus depth increasing by 3.1% of the 1.5 MeV ion beam was provided by the change of the magnetic induction in the third lens
K.I. Melnik / Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
23
Fig. 1. Results of the dynamic focusing in the quadruplet at one fourth of the raster from zero to 0.25 mm. a) The probe area (dNx dNy) lm2, the focus depth unchanged; b) the area (dNx dNy) lm2, with the optimal focus depth; c) relative change of the probe area (dx dy)/(dNx dNy); d) the G optimal focus depth, mm.
Fig. 2. The probe size d vs. the G focus depth at the point of (0.25;0.25) mm away from the optical axis. dx – the probe size on x, dy – the probe size on y.
onto 0.1738 T instead of 0.1748 T; in the fourth lens onto 0.3486 T instead of 0.3550 T. For windings in number of 101 in the lens coils the currents should change in the following way: in the third lens onto 5.129 A instead of 5.158 A; in the fourth lens onto 12.545 A instead of 14.752 A (for energy of 1.5 MeV this lens is saturated so a thorough analysis is required). It is evident that it is possible to change the focus depth for this raster point. Fig. 4 shows a dependency between relative changes in currents exciting the third and the fourth lenses and the resulting focus depth. Thus, if power supplies are capable to change the current by 0.1% of the initial value, then the next discreet value of the focus depth is 70.35 mm, i.e. almost all the required range as to Fig. 1d can be covered. Characteristics in Fig. 4 are relevant only for the
Fig. 3. The path of the originally axial particle deflected on a target to (0.25;0.25) mm away from the optical axis.
linear area where the magnetic field is current-proportional. Dynamic focusing will be difficult in the saturation zone. Conditions for the lens power supplies are rather severe. Thus our GwInstek PSM-2010 with the maximum current of 10 A, accuracy adjustment of 0.2%, the change increment of 1 mA, the noise level of 2 mA are capable to run only if the necessary magnetic induction change is greater than 4 mT, that corresponds to the current change by 3 mA. For the 1.5 MeV proton beam, zone of dynamic focusing possibility starts from deflection by 175 lm. Time for current setting is 100 ms, thus operation is possible in regimes where frequency is lower than 10 Hz. The magnetic lens hysteresis is a vital issue also. The hysteresis may be taken into account only for typical tasks like a square
24
K.I. Melnik / Nuclear Instruments and Methods in Physics Research B 306 (2013) 21–24
Fig. 4. Relative change of currents exciting the third and the fourth lenses vs. the focus depth.
scanning with the constant scanning step and pattern size. Here the procedure similar to that from [1] may be used, where before operation with real samples, the aberration coefficients were analyzed from the results of scanning over the referenced mark, then input into the computer memory and used for the scanning control. Here we may proceed in the same manner. Since a variety of sizes and scanning steps is limited in tasks of material analysis, there is a typical set of control programs. Thus, for each program it is quite possible to do several experiments on a step-by-step adjustment of the lens system and to determine the correction factors to the calculated currents. The things may be simpler in the case of the electrostatic quadruplet. From the principal point of view, the difference of the optics in magnetic and electrostatic quadrupole systems is insignificant, because the major aberrations are the same and equations of the particle motion are very similar. Even when the chromatic aberrations of the electrostatic quadrupole are twice that of the magnetic one, but the absence of hysteresis and existence of easy controlled high-frequency voltage supplies make the idea applicable to the electrostatic quadruplet. 4. Conclusions For the submicron probe forming systems the paraxial approximation is no longer valid at the scanning raster of some hundreds
of micrometers. In the examined quadruplet, for example, ignoring perturbations that occur because of the deflection is tolerable only for the scanning patterns of 500 200 lm2. This restriction is significant, as microprobe applications require a larger range of scanning, up to 1–2 mm. Beam broadening while deflecting away from the optical axis may be partially compensated by using the dynamic focusing of the lens system. For this purpose synchronous change of the lens exciting currents and voltage at the deflectors is required that allows the spot to be minimized near the raster edges. The dynamic focusing is not required in the studied system for deflections on y < 100 lm but for the greater deflections it makes possible reducing the probe area (up to 100 times on 250 lm deflection). This technique can help in controlling the probe parameters, but its practical application requires the high-current power supplies, which can precisely change the current by 0.1% of the initial value, and which can operate with the frequency of the scanning system, otherwise the scanning frequency will be very limited. Some special experiments will be necessary for each scanning program to determine the correction factors to the calculated currents and thus to consider the hysteresis loops in the lenses. References [1] M. Kinokuni, H. Sawaragi, R. Mimura, R. Aihara, A. Forchel, J. Vac. Sci. Technol. B 16 (4) (1998) 2484. [2] C.G. Ryan, Nucl. Instr. Meth. B 269 (2011) 2151. [3] A.D. Dymnikov, G.A. Glass, B. Rout, Nucl. Instr. Meth. B 239 (2005) 250. [4] G.W. Grime, M. Dawson, M. Marsh, I.C. McArthur, F. Watt, Nucl. Instr. Meth. B 54 (1991) 52. [5] G.A. Doskeyev, O.A. Edenova, I.F. Spivak-Lavrov, Nucl. Instr. Meth. A 645 (2011) 163. [6] A.D. Dymnikov, G.M. Osetinskiy, Sov. J. Part. Nucl. 20 (1989) 293. [7] A.G. Ponomarev, K.I. Melnik, V.I. Miroshnichenko, V.E. Storizhko, B. Sulkio-Cleff, Nucl. Instr. Meth. B 201 (2003) 637. [8] A.A. Ponomarova, K.I. Melnik, G.S. Vorobjov, A.G. Ponomarev, Nucl. Instr. Meth. B 269 (2011) 2202. [9] A.A. Ponomarov, V.I. Miroshnichenko, A.G. Ponomarev, Nucl. Instr. Meth. B 267 (2009) 2041.