Feasibility of a 90° electric sector energy analyzer for low energy ion beam characterization C. L. S. Mahinay, M. Wada, and H. J. Ramos Citation: Review of Scientific Instruments 86, 023306 (2015); doi: 10.1063/1.4908307 View online: http://dx.doi.org/10.1063/1.4908307 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/86/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A simple double-focusing electrostatic ion beam deflector Rev. Sci. Instrum. 81, 063304 (2010); 10.1063/1.3433485 High resolution energy analyzer for broad ion beam characterization Rev. Sci. Instrum. 79, 093304 (2008); 10.1063/1.2972175 Electrostatic ion beam trap for electron collision studies Rev. Sci. Instrum. 76, 013104 (2005); 10.1063/1.1832192 Design of a parallel-plate energy spread analyzer Rev. Sci. Instrum. 69, 1194 (1998); 10.1063/1.1148663 A tandem parallel plate analyzer Rev. Sci. Instrum. 68, 2020 (1997); 10.1063/1.1148090
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REVIEW OF SCIENTIFIC INSTRUMENTS 86, 023306 (2015)
Feasibility of a 90◦ electric sector energy analyzer for low energy ion beam characterization C. L. S. Mahinay,1,a),b) M. Wada,2 and H. J. Ramos1 1
National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Metro Manila, Philippines 2 Graduate School of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
(Received 25 October 2014; accepted 5 February 2015; published online 24 February 2015) A simple formula to calculate refocusing by locating the output slit at a specific distance away from the exit of 90◦ ion deflecting electric sector is given. Numerical analysis is also performed to calculate the ion beam trajectories for different values of the initial angular deviation of the beam. To validate the theory, a compact (90 mm × 5.5 mm × 32 mm) 90◦ sector ESA is fabricated which can fit through the inner diameter of a conflat 70 vacuum flange. Experimental results show that the dependence of resolution upon the distance between the sector exit and the Faraday cup agrees with the theory. The fabricated 90◦ sector electrostatic energy analyzer was then used to measure the space resolved ion energy distribution functions of an ion beam with the energy as low as 600 eV. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4908307] I. INTRODUCTION
A sector deflection type instrument is an energy/charge analyzer that uses a static electric or magnetic field, or a combination of both. There are various types of sector instruments and one of the types utilizes trajectory deflection of a charged particle travelling in a radial electrostatic field. Electric sectors are commonly used to guide ions to a specific trajectory thus electric sectors have geometries compatible to an angled chamber.1–3 One of the earliest applications of an electric sector is by Bainbridge and Jordan4 which uses a 127.3◦ sector angle electric sector with no initial drift length that refocuses the ion beam just at the exit, and it is coupled with a 60◦ magnetic sector that filters and refocuses for a specific ion mass. Mattauch and Herzog5,6 utilized a 31.2◦ electric sector with an initial and exit drift length that lead to a 90◦ magnetic sector. Nier7 and Johnson8 were the first to develop a 90◦ electric sector but with an initial and exit drift length that also lead to a magnetic sector with a 60◦ geometry. Diaz9 also developed a compact 90◦ electric sector which was sandwiched by two magnets to produce magnetic fields that are perpendicular to the electric fields within the electric sector. Takeshita10 used two electric sectors with the initial electric sector having a bending angle of 54.43◦ and the secondary having 121.33◦. Matsuda11 developed a mass spectrograph which eliminated second order aberrations by using an 85◦ electric sector that lead to a quadrupole mass analyzer and a 72.5◦ magnetic sector. These configurations are being used primarily for mass spectroscopy and not for energy analysis of ion beams. The dimensions of these geometries are also quite large and cannot
be applied to any compact ion beam system. In this study, the performance of a compact electric sector energy analyzer or sector electrostatic energy analyzer (ESA) with a 90◦ bending angle is investigated. It has been established that a 127◦ sector ESA enables refocusing of the dispersion of the ion beam.2,4 At 90◦ bending, the beam does not refocus at the exit of the sector. However, if paired with a uniform magnetic field, it can be used to enable refocusing on a 90◦ geometry.9 For the sector ESA in this study, only the electric field is being generated and the output slit is placed at a distance away from the exit of the sector to create an exit drift length and realize refocusing when the beam enters the detector. A simple formula is given and experimental confirmation that a 90◦ sector ESA can still realize refocusing follows. The fabricated 90◦ sector ESA is designed in such a way that it is small enough to fit to a conflat (CF) 70 flange which should enhance ease of use on most chambers with right angle port structures.
II. REFOCUSING FOR A 90◦ ELECTRIC SECTOR
It is assumed that no electric field exists in the azimuthal direction and that the edge effect is negligible. Consider an ion passing through the electric sector. It experiences an electrostatic force directed radially inwards and its equation of motion in cylindrical coordinates is given by ( )2 dθ −qEr d 2r −r = . (1) 2 dt m dt The conservation of angular momentum gives the equation dθ = L. (2) dt Here, m is the ion mass, r is the radial distance from the center, θ is the angular position, Er is the magnitude of the radial electric field, q is the ion charge, and L is the angular momentum. Consider the case wherein the radial forces are mr 2
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]
b)This research was performed while C. L. S. Mahinay was initially at the
Graduate School of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan and finished at National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Philippines.
0034-6748/2015/86(2)/023306/6/$30.00 86, 023306-1 © 2015 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.179.16.201 On: Thu, 04 Jun 2015 14:21:10
023306-2
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Rev. Sci. Instrum. 86, 023306 (2015)
in equilibrium and the ion travels in a constant radius of r 0, hence d 2r/dt 2 = 0. From Eq. (1), this case will then yield to the expression ( ) dθ qE0 = . (3) dt 0 mr 0 Here, E0 is the radial electric field during equilibrium, and r 0 is the equilibrium radius. Assuming two-dimensional symmetry at the center of the sector ESA, the electric field can be expressed as in Eq. (4) using Gauss Law, where λ is the line electrical charge density of the semicircular arc. The right hand side of Eq. (1) can then be expressed as follows: ( ) q λ qE0 r 0 qEr r0 = = · . (4) · m m 2πε 0r 0 r m r Due to the conservation of angular momentum, L will remain constant. From Eq. (2), the angular speed can be expressed as in Eq. (6) ( )2 2 r 03 L2 L + dθ * = 2 3= r · , (5) r 0 2 dt mr r3 , mr 0 ( )2 ( )2 r 3 qEr r 03 dθ dθ (6) r = r 0 · 03 = · . dt dt 0 m r3 r Assuming a small deviation from the equilibrium radius r 0, r can then be written as r = r 0 + δ, where δ is the distance of perturbation from the equilibrium radius. Fig. 1 illustrates the diagram of the sector ESA which shows these parameters. Taking the second derivative of δ i will then result into the following: ( ) d 2δ δ qE0 = −2 . (7) r0 m dt 2 Substituting the expression of dt taken from Eq. (3) into Eq. (7), the 2nd derivative of δ with respect to θ can then be expressed as follows: d 2δ = −2δ. (8) dθ 2 In the region between the two electrodes, the distance travelled by the ion in the equilibrium radius is given by z = r 0θ. Hence, the 2nd derivative of δ with respect to z is given in Eq. (9) and the solution is given in Eq. (10) d 2δ δ = −2 2 , (9) dz 2 r0 √ √ 2 2 δ = C1 sin z + C2 cos z. (10) r0 r0 Given the conditions that at z = 0, dδ/dz = tan χ χ using a linear approximation. Here, χ is the angle of deviation from the equilibrium trajectory of the perturbed ion. If the initial position is displaced by a distance d i from z = 0, then δ = δ i + χd i , where δ i is the initial perturbed distance from the equilibrium radius. The final solution is then the following: √ √ r0 χ 2 2 δse = √ sin z + (δ i + χd i ) cos z. (11) r0 r0 2 Here, δse is the perturbed distance at the exit of the electric sector. The perturbed distance δ after the exit of a
FIG. 1. Theoretical diagram of the electric sector. Inset is the diagram of the region between the input slit and the entrance of the electric sector.
90◦ (z/r 0 = π/2) sector ESA is given as follows: δ = δse +
dδ · z ′. dz z=r0 π
(12)
2
Here, z ′ is the distance along the axis from the exit of the electric sector. The distance of the focal point from the exit of the electric sector is given by z ′ = d o . At this point, δ should be constant against change with respect to the incident angle χ, dδ = 0, (13) dχ z ′=d o ( ) √ di do di + do π 1 π * + 0 = √ − 2 2 sin √ + cos √ , (14) r r0 0 2 2 , 2 √ π 2 r 0 tan √ 2 + 2r 0d i do = . (15) √ 2d i tan √π2 − 2r 0 The fabricated sector ESA has a radius of r 0 = 25 mm and an initial drift length of d i = 1.0 mm. Substituting these values into Eq. (15), the distance of the focal point from the exit of the electric sector is calculated to be 20.68 mm.
III. BEAM IMAGE MAGNIFICATION AND ENERGY RESOLUTION
At the focal point where z ′ = d o , the ion beam with an initial perturbed radial deviation of δ i will produce an image height δ o , which is also the perturbed distance from the equilibrium beam trajectory at the focal point. Using Eq. (12), the image height at the focal distance d o will yield
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023306-3
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Rev. Sci. Instrum. 86, 023306 (2015)
the following equation: √ δi d o π π δ o = δ i cos √ − 2 (16) sin √ . r o 2 2 Equation (15) is substituted to Eq. (16) to express δ o in terms of the initial drift length d i . The following equation will then give the equation of the image magnification M, where M = − (δ o /δ i ), M=−
−1 δo = × δi cos √π2 1 −
1 2d i r0
tan √π2
.
(17)
For the setup used in the experiment, where d i = 1.0 mm and r 0 = 25 mm, the magnification is calculated to be M = 1.49. The fabricated sector ESA has an entrance slit width of 0.3 mm, thus δ i = 0.3 mm/2 = 0.15 mm. Using the calculated value of M and Eq. (17), the beam image height at the focal point is approximately δ o = 0.22 mm. The resolution, E0/∆E can also be calculated. Substituting Eq. (2) into Eq. (1) will yield the equation L2 qEr d 2r = − . (18) 2 3 m dt mr Using the linear approximation, the expression for the radial electric field Er = E0 + ∆E becomes Er = E0 + ∆E − δE0/r 0, where δ = r − r 0. Substituting this and the expression for the angular momentum in Eq. (6) into Eq. (18) and linearizing the equation will yield the expression v02 v02 ∆E d 2δ = − 2δ − . r 0 E0 dt 2 r 02
(19)
Here, v0 = qEr 0/m is the equilibrium speed of the ion. Letting dz = r 0dt, and taking into account the condition that δ z=0 = δ i + χd i , the solution to Eq. (19) is the expression √ ) ( ∆Er 0 2 cos δ = δ i + χd i + z 2E0 r0 √ dδ ∆Er 0 r0 2 √ sin + z− . (20) dz r0 2E0 2 z=0
As the ion beam enters the input slit, the beam is collimated which makes the coefficient of the 2nd term in Eq. (20) equal to zero. The δ at the focal point z ′ = d o can then be calculated from Eq. (12) using the function in Eq. (20). The expression for the resolution R can then be calculated from Eq. (22) √ ( ) 2 ∆Er 0 ∆Er 0 * π π cos √ − sin √ + − , δ o = δ i + χd i + 2E0 , r 2E0 0 2 2(21) ( ) √ do 2 π π r 0 1 − cos √ 2 + r sin √ 2 E0 0 ( √ ) . = R= ∆E 2 δ + (δ + χd ) d o 2 sin √π − cos √π o i i r 2 2
IV. NUMERICAL ANALYSIS OF THE ION BEAM TRAJECTORY
To illustrate the refocusing of the 90◦ sector ESA at a certain distance away from the exit of the sector, numerical calculation using finite difference method was made. The two-dimensional cylindrical equations of motion, with linear approximation, of an ion travelling inside the electric sector are given as ( ) 2 (r − r 0) qE0 d 2r =− , (23) r0 m dt 2 dθ qE0 = . (24) dt m Using the initial conditions r t=0 = r 0, and r˙t=0 = r˙0 the solutions to both Eqs. (23) and (24) are calculated as follows: r˙0 sin χ 2qE0 + sin *t r= + r 0, (25) r 0m 2q E 0 , r0m ) ( qE0 t cos χ + θ 0. (26) θ= m Here, χ is the initial angular deviation of the beam trajectory from the equilibrium trajectory, r˙0 is the initial radial velocity, and r 0, θ 0 are the initial radial and angular positions of the ion, respectively. A time element ∆t is introduced for each iteration that runs from i = 0 to 1000, hence t i+1 = t i + ∆t. The initial beam kinetic energy is set to KEion = 1000 eV and the initial radial distance of the ion is r 0 = z0 = 2.5 cm. For these parameters, the equilibrium electric field is calculated to be E0 = −8000 V / m. The distance from the entrance of the electric sector is set to d i = 0 mm. To see if the numerical calculation is valid, the beam trajectories inside a 127◦ electric sector are first calculated to see if refocusing is realized right at the 127◦ angular position. Figure 2 shows the beam trajectory of an ion traveling through a 127◦ electric sector with χ ranging from χ = ±0.001 rad to χ = ±0.002 rad. From Fig. 2, it is clearly shown that refocusing is realized since all trajectories converge at one point which is at θ = 127◦. This validates the numerical method being used to calculate the beam trajectory. The same numerical method is then used for a 90◦ electric sector. For this configuration, the electric field within the angles from θ = 0◦ to 90◦ is set to the equilibrium
0
(22) At the focal point d o = 20.68 mm, with the parameters r 0 = 25 mm, d i = 1.0 mm, δ o = δ i = 0.15 mm, and assuming χ ≈ 0 rad, the theoretical resolution from Eq. (22) is then calculated to be 83.33.
FIG. 2. Beam trajectories of Ar1+ ions in a 127◦ electric sector with varying angular deviations. The value of δ = r − r 0 is multiplied by 100 to better show the deviation from the equilibrium trajectory. Refocusing is evident even for the different χ values. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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Mahinay, Wada, and Ramos
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FIG. 3. Beam trajectories of Ar1+ ions in a 90◦ electric sector with different angular deviations χ = ±0.03 rad, ±0.02 rad, and n = 1000. The inset indicates the beam trajectories for the positive and negative χ converging on the equilibrium beam trajectory.
electric field E0 and every other region is a field free region. The same parameters from the 127◦ electric sector beam trajectory are used for the 90◦ electric sector. Using Eq. (15) with d i = 0 and r o = 25 mm, the resulting theoretical focal point is located at d o ≃ 23.2 mm away from the exit of the sector. Figure 3 shows the non-equilibrium beam trajectories refocus and intersect with the equilibrium beam trajectory at a distance from the exit of the 90◦ electric sector. Several beam trajectories were calculated for a range of χ from χ = ±0.02 rad to χ = ±0.03 rad, and the points of intersection of the non-equilibrium beam trajectory with the equilibrium trajectory are plotted. The non-equilibrium beam trajectories travelling through the 90◦ sector ESA intersect with the equilibrium beam trajectory at different points, as shown in Figs. 3 and 4. At + χ = 0.03 rad, the point of intersection is at 25.7 mm, and at − χ = 0.03 rad, the point of intersection is at 21.1 mm. Both points though are very close to the theoretical point of refocusing which is at 23.2 mm and the average between the two is 23.4 mm. When the angular deviation is very small, χ ≪ 0.01, the point of intersection between the positive and negative angular deviated trajectories is very far apart. For this value though, the angular deviation is so small that the non-equilibrium trajectories are approximately the same to the equilibrium trajectory that refocusing is not that significant. Increasing the number of iterations n does make the + χ and − χ beam trajectories converge closer to each other since a large n
FIG. 5. Distance of the point of intersection of the perturbed beam trajectories (χ = ±0.02 rad) with the equilibrium beam trajectory from the exit of the sector ESA as calculated from the numerical analysis for different n values.
would indicate a more accurate result for a finite difference numerical calculation. As shown in Fig. 5, as n is increased by a large amount more than 105 iterations, the points of intersection converge until they reach the theoretical focal point of d o ≃ 23.2 mm. Thus, the shift of the points of intersection is attributed to the inherent error of the finite difference method which can be remedied by increasing the number of iterations. This validates the formula used to calculate the focal point at a distance away from the exit of a 90◦ sector ESA.
V. EXPERIMENTAL METHODOLOGY
In order to test experimentally the feasibility of a 90◦ electric sector, a compact 90◦ sector ESA was fabricated with a movable output aperture and a Faraday cup assembly, as seen in Fig. 6. It has a radius of 25 mm which is the maximum
FIG. 4. Ion beam trajectory at the field free region after exiting the 90◦ sector FIG. 6. Diagram of the 90◦ sector ESA with (a) side view and (b) cross ESA. The theoretical focal point, d o ≃ 23.2 mm, is shown and the nonsectional view. equilibrium beam trajectories are off slightly from that point. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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Rev. Sci. Instrum. 86, 023306 (2015)
FIG. 7. Normalized IEDF for each overall distance of the output slit. FIG. 9. FWHM and energy resolutions of the IEDF for each distance of the output slit. Geometric curves are fitted to illustrate the trend.
allowable dimension in order for the device to fit through a CF 70 flange. It has an input and output slit width of 0.3 mm. The dimensions of the device are small enough to fit inside the inner diameter of a CF 70 flange, with an inner diameter of 34 mm. The 90◦ electric sector was being tested on a hot cathode ion source producing Ar+ ions. The base pressure was at 4–5 × 10−6 Pa and the operating pressure was set to 0.11 Pa inside the ion source and 1.7 × 10−4 Pa within the downstream chamber where the electric sector is located. The discharge voltage and current are 50 V and 0.5 A, respectively.
VI. EXPERIMENTAL RESULTS AND DISCUSSION
The ion energy distribution functions (IEDFs) were measured with respect to the distance of the output slit from the exit of the electric sector. The detector was moved manually with a sub-millimeter interval. An extraction voltage (Vext) of 400 V was applied which translates to ions extracted with energies at around 400 eV. Due to the manual adjustment of the distance of the detector, the precision is only limited to 1 mm. The distance of the input slit from the entrance of the sector is measured as d i = 1.0 mm. Figure 7 shows the normalized IEDF taken using the 90◦ sector ESA as the overall distance of the output slit is changed. From Fig. 8, the peak intensity position varies from 286 eV to 391 eV. The peak position gets closer to the theoretical energy as the faraday cup is moved away from the electrodes. At the region between the electrodes and the exit
slit, the electric field intensity becomes more prominent as the exit slit and the electrodes are closer together which bends the beam and gives a higher deviation, hence as the exit slit is moved farther the deviation also decreases. The energy spread was then taken by fitting a Gaussian function over the IEDF and taking the full-width-at-halfmaximum (FWHM). The energy resolution is then calculated by dividing the ion energy by the FWHM (E/∆E). Figure 9 shows the FWHM and energy resolution versus the output slit distance plot. Using the Microsoft Word trend line function that utilizes the method of least squares, a curve is fitted into the FWHM plot and it has a coefficient of determination, R2, value of 0.5 and for the energy resolution, R2 = 0.4. From Eq. (22), the resolution is constant with respect to the output slit distance d o but the results show an increasing trend. This may be due to the collimating effect of the sector region of the ESA, in which the beam intersects with the sector walls at larger deflection angle χ and bounces towards a new trajectory. Increasing the distance d o would collect data as the beam trajectory approaches the linear theory and thus the resolution is increased. Further increasing the slit distance would result to losing the beam current however since the magnification, as suggested in Eq. (17) increases with increasing slit distance but the output slit width remains fixed thus the signal intensity decreases. The IEDF’s are also measured as the extraction potential or the ion energy is changed, as seen in Fig. 10. These were
FIG. 8. Peak position of the IEDF scaled to the deviation from E ion = FIG. 10. Ion energy distribution functions taken using the 90◦ sector ESA 400 eV, (E ion − E peak) versus the distance of the output slit. for each extraction voltage. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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Rev. Sci. Instrum. 86, 023306 (2015)
energy resolution where it is increasing and tapers off as the extraction potential is increased. VII. CONCLUSION
FIG. 11. Energy spread and resolution of the IEDF taken for each extraction potential. Geometric curves are fitted to illustrate the trend.
measured at the output slit distance of 14.5 mm which is not the optimum distance but yields an energy resolution which is within the range of the energy resolution at the optimum output slit distance. As expected, the intensity increased as the extraction potential is also increased. There are several peaks appearing before the more prominent peak. These may be attributed to the charge exchange component at the beam extraction region, and/or the inherent design of the cylindrical electric sector. The ions travelling inside the electric sector may hit the electrodes as it diverges due to the space charge effect and as it hits the walls of the electrodes, it loses some energy. If these ions, escape through the exit aperture, they may register as noise of smaller peaks at lower energies compared to the more prominent peak. Their intensities are small compared to the more prominent peak thus they are neglected when calculating the FWHM. The energy spread and energy resolution was then calculated, as shown in Fig. 11. Fitted curves are then displayed with an R2 of 0.7 for the FWHM and 0.9 for the energy resolution. The fitted curve energy spread is decreasing until it tapers off and increases slightly as the extraction potential is increased above 500. This would indicate that the ion beam focal point is at or near the sector ESA entrance slit at the extraction potentials where the FWHM appears to taper off. This is also evident in the
A simple formula is given to prove the validity of using a 90◦ sector ESA based on a perturbation method. A linear approximation of the equation of motion for an ion inside an electric sector predicts the focal point and the resolution of an analyzer with a bending angle. Numerical analysis was made to plot the trajectory of the ion beam. The numerical calculation was able to show the refocusing of a 127◦ electric sector. For the 90◦ electric sector however, it showed the points of intersection of the non-equilibrium and equilibrium beam trajectories vary by a small amount but increasing the number of iterations fixes this deviation. A small compact 90◦ sector ESA was also fabricated to test its feasibility. As the distance of the output slit approaches the optimum value, the energy resolution increases which may be due to the collimating effect of the electrode region of the ESA. The output slit width remains fixed in this experiment, and the energy resolution has not been demonstrated maximum when the output slit is placed at the focal point. An ESA with the variable slit width may increase the resolution further, but the system should require more complexity in fabrication and operation. Using the 90◦ sector ESA, to measure the IEDF as the extraction potential of the ion source is increased, the energy resolution appears to taper at greater than 400 V which indicates the ion beam focal point is at the entrance slit at these energies. 1A.
Nier, J. Am. Soc. Mass Spectrom. 2, 447 (1992). W. Burgoyne and G. M. Hieftje, Mass Spectrom. Rev. 15, 241 (1996). 3A. Klemm, Z. Naturforsch. A 1(3), 137–141 (1946). 4K. T. Bainbridge and E. B. Jordan, Phys. Rev. 50, 282 (1936). 5J. Mattauch and R. Herzog, Z. Phys. 89, 786 (1934). 6J. Mattauch, Phys. Rev. 50, 617 (1936). 7A. O. Nier and T. R. Roberts, Phys. Rev. 81, 507 (1951). 8E. G. N. Johnson and A. O. Nier, Phys. Rev. 91, 10 (1953). 9J. A. Diaz, C. F. Giese, and W. R. Gentry, J. Am. Soc. Mass Spectrom. 12, 619 (2001). 10I. Takeshita, Rev. Sci. Instrum. 38, 1361 (1967). 11H. Matsuda, Int. J. Mass Spectrom. Ion Phys. 14, 219 (1974). 2T.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.179.16.201 On: Thu, 04 Jun 2015 14:21:10
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.179.16.201 On: Thu, 04 Jun 2015 14:21:10
REVIEW OF SCIENTIFIC INSTRUMENTS 86, 023306 (2015)
Feasibility of a 90◦ electric sector energy analyzer for low energy ion beam characterization C. L. S. Mahinay,1,a),b) M. Wada,2 and H. J. Ramos1 1
National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Metro Manila, Philippines 2 Graduate School of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
(Received 25 October 2014; accepted 5 February 2015; published online 24 February 2015) A simple formula to calculate refocusing by locating the output slit at a specific distance away from the exit of 90◦ ion deflecting electric sector is given. Numerical analysis is also performed to calculate the ion beam trajectories for different values of the initial angular deviation of the beam. To validate the theory, a compact (90 mm × 5.5 mm × 32 mm) 90◦ sector ESA is fabricated which can fit through the inner diameter of a conflat 70 vacuum flange. Experimental results show that the dependence of resolution upon the distance between the sector exit and the Faraday cup agrees with the theory. The fabricated 90◦ sector electrostatic energy analyzer was then used to measure the space resolved ion energy distribution functions of an ion beam with the energy as low as 600 eV. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4908307] I. INTRODUCTION
A sector deflection type instrument is an energy/charge analyzer that uses a static electric or magnetic field, or a combination of both. There are various types of sector instruments and one of the types utilizes trajectory deflection of a charged particle travelling in a radial electrostatic field. Electric sectors are commonly used to guide ions to a specific trajectory thus electric sectors have geometries compatible to an angled chamber.1–3 One of the earliest applications of an electric sector is by Bainbridge and Jordan4 which uses a 127.3◦ sector angle electric sector with no initial drift length that refocuses the ion beam just at the exit, and it is coupled with a 60◦ magnetic sector that filters and refocuses for a specific ion mass. Mattauch and Herzog5,6 utilized a 31.2◦ electric sector with an initial and exit drift length that lead to a 90◦ magnetic sector. Nier7 and Johnson8 were the first to develop a 90◦ electric sector but with an initial and exit drift length that also lead to a magnetic sector with a 60◦ geometry. Diaz9 also developed a compact 90◦ electric sector which was sandwiched by two magnets to produce magnetic fields that are perpendicular to the electric fields within the electric sector. Takeshita10 used two electric sectors with the initial electric sector having a bending angle of 54.43◦ and the secondary having 121.33◦. Matsuda11 developed a mass spectrograph which eliminated second order aberrations by using an 85◦ electric sector that lead to a quadrupole mass analyzer and a 72.5◦ magnetic sector. These configurations are being used primarily for mass spectroscopy and not for energy analysis of ion beams. The dimensions of these geometries are also quite large and cannot
be applied to any compact ion beam system. In this study, the performance of a compact electric sector energy analyzer or sector electrostatic energy analyzer (ESA) with a 90◦ bending angle is investigated. It has been established that a 127◦ sector ESA enables refocusing of the dispersion of the ion beam.2,4 At 90◦ bending, the beam does not refocus at the exit of the sector. However, if paired with a uniform magnetic field, it can be used to enable refocusing on a 90◦ geometry.9 For the sector ESA in this study, only the electric field is being generated and the output slit is placed at a distance away from the exit of the sector to create an exit drift length and realize refocusing when the beam enters the detector. A simple formula is given and experimental confirmation that a 90◦ sector ESA can still realize refocusing follows. The fabricated 90◦ sector ESA is designed in such a way that it is small enough to fit to a conflat (CF) 70 flange which should enhance ease of use on most chambers with right angle port structures.
II. REFOCUSING FOR A 90◦ ELECTRIC SECTOR
It is assumed that no electric field exists in the azimuthal direction and that the edge effect is negligible. Consider an ion passing through the electric sector. It experiences an electrostatic force directed radially inwards and its equation of motion in cylindrical coordinates is given by ( )2 dθ −qEr d 2r −r = . (1) 2 dt m dt The conservation of angular momentum gives the equation dθ = L. (2) dt Here, m is the ion mass, r is the radial distance from the center, θ is the angular position, Er is the magnitude of the radial electric field, q is the ion charge, and L is the angular momentum. Consider the case wherein the radial forces are mr 2
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]
b)This research was performed while C. L. S. Mahinay was initially at the
Graduate School of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan and finished at National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Philippines.
0034-6748/2015/86(2)/023306/6/$30.00 86, 023306-1 © 2015 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.179.16.201 On: Thu, 04 Jun 2015 14:21:10
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Rev. Sci. Instrum. 86, 023306 (2015)
in equilibrium and the ion travels in a constant radius of r 0, hence d 2r/dt 2 = 0. From Eq. (1), this case will then yield to the expression ( ) dθ qE0 = . (3) dt 0 mr 0 Here, E0 is the radial electric field during equilibrium, and r 0 is the equilibrium radius. Assuming two-dimensional symmetry at the center of the sector ESA, the electric field can be expressed as in Eq. (4) using Gauss Law, where λ is the line electrical charge density of the semicircular arc. The right hand side of Eq. (1) can then be expressed as follows: ( ) q λ qE0 r 0 qEr r0 = = · . (4) · m m 2πε 0r 0 r m r Due to the conservation of angular momentum, L will remain constant. From Eq. (2), the angular speed can be expressed as in Eq. (6) ( )2 2 r 03 L2 L + dθ * = 2 3= r · , (5) r 0 2 dt mr r3 , mr 0 ( )2 ( )2 r 3 qEr r 03 dθ dθ (6) r = r 0 · 03 = · . dt dt 0 m r3 r Assuming a small deviation from the equilibrium radius r 0, r can then be written as r = r 0 + δ, where δ is the distance of perturbation from the equilibrium radius. Fig. 1 illustrates the diagram of the sector ESA which shows these parameters. Taking the second derivative of δ i will then result into the following: ( ) d 2δ δ qE0 = −2 . (7) r0 m dt 2 Substituting the expression of dt taken from Eq. (3) into Eq. (7), the 2nd derivative of δ with respect to θ can then be expressed as follows: d 2δ = −2δ. (8) dθ 2 In the region between the two electrodes, the distance travelled by the ion in the equilibrium radius is given by z = r 0θ. Hence, the 2nd derivative of δ with respect to z is given in Eq. (9) and the solution is given in Eq. (10) d 2δ δ = −2 2 , (9) dz 2 r0 √ √ 2 2 δ = C1 sin z + C2 cos z. (10) r0 r0 Given the conditions that at z = 0, dδ/dz = tan χ χ using a linear approximation. Here, χ is the angle of deviation from the equilibrium trajectory of the perturbed ion. If the initial position is displaced by a distance d i from z = 0, then δ = δ i + χd i , where δ i is the initial perturbed distance from the equilibrium radius. The final solution is then the following: √ √ r0 χ 2 2 δse = √ sin z + (δ i + χd i ) cos z. (11) r0 r0 2 Here, δse is the perturbed distance at the exit of the electric sector. The perturbed distance δ after the exit of a
FIG. 1. Theoretical diagram of the electric sector. Inset is the diagram of the region between the input slit and the entrance of the electric sector.
90◦ (z/r 0 = π/2) sector ESA is given as follows: δ = δse +
dδ · z ′. dz z=r0 π
(12)
2
Here, z ′ is the distance along the axis from the exit of the electric sector. The distance of the focal point from the exit of the electric sector is given by z ′ = d o . At this point, δ should be constant against change with respect to the incident angle χ, dδ = 0, (13) dχ z ′=d o ( ) √ di do di + do π 1 π * + 0 = √ − 2 2 sin √ + cos √ , (14) r r0 0 2 2 , 2 √ π 2 r 0 tan √ 2 + 2r 0d i do = . (15) √ 2d i tan √π2 − 2r 0 The fabricated sector ESA has a radius of r 0 = 25 mm and an initial drift length of d i = 1.0 mm. Substituting these values into Eq. (15), the distance of the focal point from the exit of the electric sector is calculated to be 20.68 mm.
III. BEAM IMAGE MAGNIFICATION AND ENERGY RESOLUTION
At the focal point where z ′ = d o , the ion beam with an initial perturbed radial deviation of δ i will produce an image height δ o , which is also the perturbed distance from the equilibrium beam trajectory at the focal point. Using Eq. (12), the image height at the focal distance d o will yield
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the following equation: √ δi d o π π δ o = δ i cos √ − 2 (16) sin √ . r o 2 2 Equation (15) is substituted to Eq. (16) to express δ o in terms of the initial drift length d i . The following equation will then give the equation of the image magnification M, where M = − (δ o /δ i ), M=−
−1 δo = × δi cos √π2 1 −
1 2d i r0
tan √π2
.
(17)
For the setup used in the experiment, where d i = 1.0 mm and r 0 = 25 mm, the magnification is calculated to be M = 1.49. The fabricated sector ESA has an entrance slit width of 0.3 mm, thus δ i = 0.3 mm/2 = 0.15 mm. Using the calculated value of M and Eq. (17), the beam image height at the focal point is approximately δ o = 0.22 mm. The resolution, E0/∆E can also be calculated. Substituting Eq. (2) into Eq. (1) will yield the equation L2 qEr d 2r = − . (18) 2 3 m dt mr Using the linear approximation, the expression for the radial electric field Er = E0 + ∆E becomes Er = E0 + ∆E − δE0/r 0, where δ = r − r 0. Substituting this and the expression for the angular momentum in Eq. (6) into Eq. (18) and linearizing the equation will yield the expression v02 v02 ∆E d 2δ = − 2δ − . r 0 E0 dt 2 r 02
(19)
Here, v0 = qEr 0/m is the equilibrium speed of the ion. Letting dz = r 0dt, and taking into account the condition that δ z=0 = δ i + χd i , the solution to Eq. (19) is the expression √ ) ( ∆Er 0 2 cos δ = δ i + χd i + z 2E0 r0 √ dδ ∆Er 0 r0 2 √ sin + z− . (20) dz r0 2E0 2 z=0
As the ion beam enters the input slit, the beam is collimated which makes the coefficient of the 2nd term in Eq. (20) equal to zero. The δ at the focal point z ′ = d o can then be calculated from Eq. (12) using the function in Eq. (20). The expression for the resolution R can then be calculated from Eq. (22) √ ( ) 2 ∆Er 0 ∆Er 0 * π π cos √ − sin √ + − , δ o = δ i + χd i + 2E0 , r 2E0 0 2 2(21) ( ) √ do 2 π π r 0 1 − cos √ 2 + r sin √ 2 E0 0 ( √ ) . = R= ∆E 2 δ + (δ + χd ) d o 2 sin √π − cos √π o i i r 2 2
IV. NUMERICAL ANALYSIS OF THE ION BEAM TRAJECTORY
To illustrate the refocusing of the 90◦ sector ESA at a certain distance away from the exit of the sector, numerical calculation using finite difference method was made. The two-dimensional cylindrical equations of motion, with linear approximation, of an ion travelling inside the electric sector are given as ( ) 2 (r − r 0) qE0 d 2r =− , (23) r0 m dt 2 dθ qE0 = . (24) dt m Using the initial conditions r t=0 = r 0, and r˙t=0 = r˙0 the solutions to both Eqs. (23) and (24) are calculated as follows: r˙0 sin χ 2qE0 + sin *t r= + r 0, (25) r 0m 2q E 0 , r0m ) ( qE0 t cos χ + θ 0. (26) θ= m Here, χ is the initial angular deviation of the beam trajectory from the equilibrium trajectory, r˙0 is the initial radial velocity, and r 0, θ 0 are the initial radial and angular positions of the ion, respectively. A time element ∆t is introduced for each iteration that runs from i = 0 to 1000, hence t i+1 = t i + ∆t. The initial beam kinetic energy is set to KEion = 1000 eV and the initial radial distance of the ion is r 0 = z0 = 2.5 cm. For these parameters, the equilibrium electric field is calculated to be E0 = −8000 V / m. The distance from the entrance of the electric sector is set to d i = 0 mm. To see if the numerical calculation is valid, the beam trajectories inside a 127◦ electric sector are first calculated to see if refocusing is realized right at the 127◦ angular position. Figure 2 shows the beam trajectory of an ion traveling through a 127◦ electric sector with χ ranging from χ = ±0.001 rad to χ = ±0.002 rad. From Fig. 2, it is clearly shown that refocusing is realized since all trajectories converge at one point which is at θ = 127◦. This validates the numerical method being used to calculate the beam trajectory. The same numerical method is then used for a 90◦ electric sector. For this configuration, the electric field within the angles from θ = 0◦ to 90◦ is set to the equilibrium
0
(22) At the focal point d o = 20.68 mm, with the parameters r 0 = 25 mm, d i = 1.0 mm, δ o = δ i = 0.15 mm, and assuming χ ≈ 0 rad, the theoretical resolution from Eq. (22) is then calculated to be 83.33.
FIG. 2. Beam trajectories of Ar1+ ions in a 127◦ electric sector with varying angular deviations. The value of δ = r − r 0 is multiplied by 100 to better show the deviation from the equilibrium trajectory. Refocusing is evident even for the different χ values. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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FIG. 3. Beam trajectories of Ar1+ ions in a 90◦ electric sector with different angular deviations χ = ±0.03 rad, ±0.02 rad, and n = 1000. The inset indicates the beam trajectories for the positive and negative χ converging on the equilibrium beam trajectory.
electric field E0 and every other region is a field free region. The same parameters from the 127◦ electric sector beam trajectory are used for the 90◦ electric sector. Using Eq. (15) with d i = 0 and r o = 25 mm, the resulting theoretical focal point is located at d o ≃ 23.2 mm away from the exit of the sector. Figure 3 shows the non-equilibrium beam trajectories refocus and intersect with the equilibrium beam trajectory at a distance from the exit of the 90◦ electric sector. Several beam trajectories were calculated for a range of χ from χ = ±0.02 rad to χ = ±0.03 rad, and the points of intersection of the non-equilibrium beam trajectory with the equilibrium trajectory are plotted. The non-equilibrium beam trajectories travelling through the 90◦ sector ESA intersect with the equilibrium beam trajectory at different points, as shown in Figs. 3 and 4. At + χ = 0.03 rad, the point of intersection is at 25.7 mm, and at − χ = 0.03 rad, the point of intersection is at 21.1 mm. Both points though are very close to the theoretical point of refocusing which is at 23.2 mm and the average between the two is 23.4 mm. When the angular deviation is very small, χ ≪ 0.01, the point of intersection between the positive and negative angular deviated trajectories is very far apart. For this value though, the angular deviation is so small that the non-equilibrium trajectories are approximately the same to the equilibrium trajectory that refocusing is not that significant. Increasing the number of iterations n does make the + χ and − χ beam trajectories converge closer to each other since a large n
FIG. 5. Distance of the point of intersection of the perturbed beam trajectories (χ = ±0.02 rad) with the equilibrium beam trajectory from the exit of the sector ESA as calculated from the numerical analysis for different n values.
would indicate a more accurate result for a finite difference numerical calculation. As shown in Fig. 5, as n is increased by a large amount more than 105 iterations, the points of intersection converge until they reach the theoretical focal point of d o ≃ 23.2 mm. Thus, the shift of the points of intersection is attributed to the inherent error of the finite difference method which can be remedied by increasing the number of iterations. This validates the formula used to calculate the focal point at a distance away from the exit of a 90◦ sector ESA.
V. EXPERIMENTAL METHODOLOGY
In order to test experimentally the feasibility of a 90◦ electric sector, a compact 90◦ sector ESA was fabricated with a movable output aperture and a Faraday cup assembly, as seen in Fig. 6. It has a radius of 25 mm which is the maximum
FIG. 4. Ion beam trajectory at the field free region after exiting the 90◦ sector FIG. 6. Diagram of the 90◦ sector ESA with (a) side view and (b) cross ESA. The theoretical focal point, d o ≃ 23.2 mm, is shown and the nonsectional view. equilibrium beam trajectories are off slightly from that point. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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FIG. 7. Normalized IEDF for each overall distance of the output slit. FIG. 9. FWHM and energy resolutions of the IEDF for each distance of the output slit. Geometric curves are fitted to illustrate the trend.
allowable dimension in order for the device to fit through a CF 70 flange. It has an input and output slit width of 0.3 mm. The dimensions of the device are small enough to fit inside the inner diameter of a CF 70 flange, with an inner diameter of 34 mm. The 90◦ electric sector was being tested on a hot cathode ion source producing Ar+ ions. The base pressure was at 4–5 × 10−6 Pa and the operating pressure was set to 0.11 Pa inside the ion source and 1.7 × 10−4 Pa within the downstream chamber where the electric sector is located. The discharge voltage and current are 50 V and 0.5 A, respectively.
VI. EXPERIMENTAL RESULTS AND DISCUSSION
The ion energy distribution functions (IEDFs) were measured with respect to the distance of the output slit from the exit of the electric sector. The detector was moved manually with a sub-millimeter interval. An extraction voltage (Vext) of 400 V was applied which translates to ions extracted with energies at around 400 eV. Due to the manual adjustment of the distance of the detector, the precision is only limited to 1 mm. The distance of the input slit from the entrance of the sector is measured as d i = 1.0 mm. Figure 7 shows the normalized IEDF taken using the 90◦ sector ESA as the overall distance of the output slit is changed. From Fig. 8, the peak intensity position varies from 286 eV to 391 eV. The peak position gets closer to the theoretical energy as the faraday cup is moved away from the electrodes. At the region between the electrodes and the exit
slit, the electric field intensity becomes more prominent as the exit slit and the electrodes are closer together which bends the beam and gives a higher deviation, hence as the exit slit is moved farther the deviation also decreases. The energy spread was then taken by fitting a Gaussian function over the IEDF and taking the full-width-at-halfmaximum (FWHM). The energy resolution is then calculated by dividing the ion energy by the FWHM (E/∆E). Figure 9 shows the FWHM and energy resolution versus the output slit distance plot. Using the Microsoft Word trend line function that utilizes the method of least squares, a curve is fitted into the FWHM plot and it has a coefficient of determination, R2, value of 0.5 and for the energy resolution, R2 = 0.4. From Eq. (22), the resolution is constant with respect to the output slit distance d o but the results show an increasing trend. This may be due to the collimating effect of the sector region of the ESA, in which the beam intersects with the sector walls at larger deflection angle χ and bounces towards a new trajectory. Increasing the distance d o would collect data as the beam trajectory approaches the linear theory and thus the resolution is increased. Further increasing the slit distance would result to losing the beam current however since the magnification, as suggested in Eq. (17) increases with increasing slit distance but the output slit width remains fixed thus the signal intensity decreases. The IEDF’s are also measured as the extraction potential or the ion energy is changed, as seen in Fig. 10. These were
FIG. 8. Peak position of the IEDF scaled to the deviation from E ion = FIG. 10. Ion energy distribution functions taken using the 90◦ sector ESA 400 eV, (E ion − E peak) versus the distance of the output slit. for each extraction voltage. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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energy resolution where it is increasing and tapers off as the extraction potential is increased. VII. CONCLUSION
FIG. 11. Energy spread and resolution of the IEDF taken for each extraction potential. Geometric curves are fitted to illustrate the trend.
measured at the output slit distance of 14.5 mm which is not the optimum distance but yields an energy resolution which is within the range of the energy resolution at the optimum output slit distance. As expected, the intensity increased as the extraction potential is also increased. There are several peaks appearing before the more prominent peak. These may be attributed to the charge exchange component at the beam extraction region, and/or the inherent design of the cylindrical electric sector. The ions travelling inside the electric sector may hit the electrodes as it diverges due to the space charge effect and as it hits the walls of the electrodes, it loses some energy. If these ions, escape through the exit aperture, they may register as noise of smaller peaks at lower energies compared to the more prominent peak. Their intensities are small compared to the more prominent peak thus they are neglected when calculating the FWHM. The energy spread and energy resolution was then calculated, as shown in Fig. 11. Fitted curves are then displayed with an R2 of 0.7 for the FWHM and 0.9 for the energy resolution. The fitted curve energy spread is decreasing until it tapers off and increases slightly as the extraction potential is increased above 500. This would indicate that the ion beam focal point is at or near the sector ESA entrance slit at the extraction potentials where the FWHM appears to taper off. This is also evident in the
A simple formula is given to prove the validity of using a 90◦ sector ESA based on a perturbation method. A linear approximation of the equation of motion for an ion inside an electric sector predicts the focal point and the resolution of an analyzer with a bending angle. Numerical analysis was made to plot the trajectory of the ion beam. The numerical calculation was able to show the refocusing of a 127◦ electric sector. For the 90◦ electric sector however, it showed the points of intersection of the non-equilibrium and equilibrium beam trajectories vary by a small amount but increasing the number of iterations fixes this deviation. A small compact 90◦ sector ESA was also fabricated to test its feasibility. As the distance of the output slit approaches the optimum value, the energy resolution increases which may be due to the collimating effect of the electrode region of the ESA. The output slit width remains fixed in this experiment, and the energy resolution has not been demonstrated maximum when the output slit is placed at the focal point. An ESA with the variable slit width may increase the resolution further, but the system should require more complexity in fabrication and operation. Using the 90◦ sector ESA, to measure the IEDF as the extraction potential of the ion source is increased, the energy resolution appears to taper at greater than 400 V which indicates the ion beam focal point is at the entrance slit at these energies. 1A.
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