UNIVERSITY OF CINCINNATI

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1 UNIVERSITY OF CINCINNATI Date: I,, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair:

2 Micromachined Magnetic Devices for Electron Beam Control in the Electron Beam Microcolumn A dissertation submitted to the Division of Research and Advanced Studies of the University of Cincinnati In partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY In the Department of Electrical and Computer Engineering of the College of Engineering April, 007 By Rong Rong B.E., Shanghai Jiaotong University, China 1995 M.E., Shanghai Jiaotong University, China 1998 M.E., Nanyang Technological University, Singapore 001 Committee Chairman: Dr. Chong H. Ahn

3 ABSTRACT This research studies an innovative micromagnetic method for electron beam control in the electron beam microcolumn. In order to realize the magnetic electron beam control in the electron beam microcolumn, three new micromachined magnetic devices have been designed, fabricated and characterized in this work. First, a magnetic microdeflector has been designed, fabricated, and characterized for the electron beam deflection/scanning in the EBMC. Experimental results showed that the developed magnetic microdeflector with a pole distances 0.5 mm linearly deflected the electron beam (80 ev) a distance of 10 µm with an electrical power of 3 mw. The realized magnetic microdeflector shows an excellent dynamic property with the reponse time of 5 ns for a step signal of 50 ma. The developed magnetic microdeflector has excellent capability of deflecting/scanning the electron beam in the electron beam microcolumn system with large scanning linearity and low power consumption. Second, a magnetic microstigmator has been designed, fabricated, and characterized for the electron beam astigmatism correction in the EBMC. Experimental results showed that the astigmatism of an electron beam (00 ev) was effectively corrected by the fabricated magnetic microstigmator with a low power consumption. Third, a magnetic microlens has been designed, simulated, fabricated, and tested for the electron beam focusing in an EBMC. The experimental results showed

4 that, with a driving current of 150 ma, an electron beam of 1 kev was effectively focused by the developed magnetic microlens. Finally, the magnetic interference within the miniaturized magnetic electron beam control system consisting of the three developed magnetic devices has been modeled and simulated. The span range of the magnetic field distribution generated by each individual device has also been simulated and investigated. In summary, an innovative magnetic method for the electron beam control in the electron beam microcolumn has been introduced and fully demonstrated in this work. For the realization of the magnetic control method, three micromachined magnetic devices such as the magnetic microdeflector, the magnetic microstigmator, and the magnetic microlens have been successfully realized in this work for a miniaturized magnetic electron beam control system.

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6 ACKNOWLEDGMENT First of all, I would like to express my greatest appreciation to my advisor, Dr. Chong H. Ahn for his advice, inspiration, guidance and support throughout my graduate study. He has been and would be the role model for my research and career life. I am indebted to his constant encouragement and mentoring throughout my graduate study. I would like to convey my sincere thanks to Dr. Kenneth Roenker, Dr. Joseph Nevin, Dr. Ian Papautsky, and Dr. Sang Young Son for their helpful suggestions, comments, and guidance on my research and dissertation study. I would express my sincere appreciation to Dr. Ho Soeb Kim and his group at CEBT Company for their tremendous effort and assistance in testing of my devices. This research is a collaboration work with CEBT Company. The developed magnetic devices in this work were assembled in the electron beam microcolumn developed by the CEBT Company for testing. I cannot imagine the achievement of this research without their technical support in testing of my devices. I would like to thank all the former and current members of the Microsystems and BioMEMS Lab for their tremendous support and help during my stay. Many thanks to Dr. Jin-Woo Choi, Dr. Hyoung-Jin Cho, Dr Kwang-Wook Oh, Dr. Daniel J. Sadler, Dr. Aniruddha Puntambekar, Dr. Xiaoshan Zhu, Dr. Chuan Gao, Dr. Chien Chong Hong, Dr. Junhai Kai, Dr. Jungyoup Han, Dr. Jaephil Do, Se Hwan Lee, SooHyun Lee, Chunyan Li, Andrew Browne, Michael Rust, Matthew Estes, Zhiwei

7 Zou, Pei-Ming Wu, Joon Sub Shim, and Kang Kug Lee for their various contributions to my study and research. I would also like to thank Ron Flenniken, Jeff Simkins, and Robert Jones for their remarkable technical support they have always offered me for the tasks related to devices fabrication in the clean room. Without their prompt and important help and suggestions on my devices fabrication, my research would not have been going through so smoothly. Finally I would like to express my great appreciation to my family and friends, especially my wife. She has always been by my side. I cannot think of my achievement without their love and support.

8 TABLE OF CONTENTS Table of Contents 1 List of Figures 3 List of Tables 14 List of Symbols 15 Chapter 1. Introduction 1.1 Research Motivation Review of Previous Work Electrostatic Octupole Stigmator/Deflector Electrostatic Einzel Lens Research Objectives 36 Chapter. Magnetic Microdeflector for Electron Beam Deflection/Scanning.1 Introduction 40. Design and Simulation of the Magnetic Microdeflector 43.3 Fabrication of the Magnetic Microdeflector Experimental Results and Discussion of the Magnetic Microdeflector 5.5 Conclusion 56 Chapter 3. Magnetic Microstigmator for Electron Beam Astigmatism Correction 3.1 Introduction Design and Simulation of the Magnetic Microstigmator Fabrication of the Magnetic Microstigmator Experimental Results and Discussion of the Magnetic Microstigmator Conclusion. 81 1

9 Chapter 4. Magnetic Microlens for Electron Beam Focusing 4.1 Introduction Design and Simulation of the Magnetic Microlens Fabrication of the Magnetic Microlens Experimental Results and Discussion of the Magnetic Microlens Conclusion 10 Chapter 5. Miniaturized Magnetic Electron Beam Control System 5.1 Introduction Modeling and Simulation of the Miniaturized Magnetic Electron Beam Control System Magnetic Field Distribution of the Magnetic Microdeflector Magnetic Field Distribution of the Magnetic Microstigmator Magnetic Field Distribution of the Magnetic Microlens The Miniaturized Magnetic Electron Beam Control System Conclusion Chapter 6. Conclusion 6.1 Summary Research Contributions Suggestions for Future Work References 140 Publications Appendix.. 15

10 LIST OF FIGURES Figure 1.1 Photograph of an electron beam lithography system (Raith 150) at the University of Cincinnati... 1 Figure 1. Schematic of a typical electron beam lithography system (Etec System Inc).. Figure 1.3 Arrayed microcolumn lithography system using one or more microcolumn per chip [35] 3 Figure 1.4 Schematic diagram of an electron beam microcolumn Figure 1.5 Photographs of the electron beam microcolumns developed by: (a) H.S. Kim, et al. 005 [45]; (b) S.S. Park, et al. 004 [46] and H.S. Kim et al., 003 [47]; (c) L.P. Muray, et al., 000 [48]; (d) I. Honjo, et al., 1997 [49]; and (e) E. Kratshmer, et al., 1996 [50]. 7 Figure 1.6 Photographs of the x arrayed electron beam microcolumn systems developed by (a) L.P.Muray, et al., 000 [48] and (b) J.W. Jeong, et al., 005 [51]... 7 Figure 1.7 Schematic diagram of an electrostatic microcolumn.. 9 Figure 1.8 Operational principle of the electrostatic octupole working as: (a) deflector; (b) stigmator; and (c) stigmator/deflector.. 31 Figure 1.9 Photographs of the electrostatic octupoles developed by different research groups: (a) M.M. Gomati, et al [66]; (b) E. Yin, et al. 000 [67]; (c) H.S. Gross, et al [68]; (d) H. Kim, et al

11 [69]; (e) L.P. Muray, et al. 000 [54]; and (f) J.W. Jeong, et al. 005 [51]. 33 Figure 1.10 Principle of the electrostatic Einzel lens 34 Figure 1.11 (a) Fabrication process of the individual electrode of the Einzel lens [47] and (b) a fabricated electrode with round lens aperture [46]. 34 Figure 1.1 Fabrication of the electrostatic Einzel lens: (a) multi-layer anodic bonding process and (b) the photograph of an Einzel lens [78]. 35 Figure 1.13 Magnetic microcolumn consisting of the magnetic microdeflector, magnetic mirostigmator, and magnetic microlens, in substitution of the present electrostatic microcolumn 37 Figure.1 Schematic diagram of the designed magnetic microdeflector: (a) 3-D view and (b) cross sectional view.. 41 Figure. Operational principle: (a) magnetic field distribution and (b) cross section view of the electron beam deflection.. 4 Figure.3 (a) 3-D model of the magnetic microdeflector and (b) B field distribution with a driving current of 50 ma 45 Figure.4 Simulation results of the designed microdeflector: (a) B field distribution at XY plane (Z=0) and (b) B field distribution at XZ plane (Y=0).. 46 Figure.5 Simulation results: (a) B x field distribution in the central bore region (100 µm 100 µm) at XY plane (Z=0) and (b) B x field distribution 4

12 along the Z axis at the center (X=0 and Y=0).. 47 Figure.6 Simulation results of the microdeflector with 0.5 mm pole-distance: (a) Electron deflection and (b) deflection angle with driving current varying from 10 ma to 50 ma.. 48 Figure.7 Schematic diagram of the fabrication steps for magnetic microdeflector. 50 Figure.8 Microphotographs of the two fabricated magnetic microdeflectors: (a) 0.5mm and (b) 1mm between the magnetic poles. 50 Figure.9 Measured electrical parameters of the fabricated magnetic microinductors with respect to the driving frequency: (a) resistance and (b) inductance.. 51 Figure.10 Measured step response of the fabricated microinductor.. 5 Figure.11 The electron beam microcolumn (EBMC) used for testing: (a) schematic diagram and (b) microphotograph of EBMCS assembled with the fabricated magnetic microdeflector. 53 Figure.1 Measurement results of the magnetic microdeflector (1.0 mm poledistance) with driving current varying from 0 ma to 50 ma: (a) Current images of the copper grid specimen and (b) electron beam deflection vs. driving current. 54 Figure.13 Measurement results of the magnetic microdeflector (0.5 mm poledistance) with driving current varying from 0 ma to 50 ma: (a) Current images of the copper grid specimen and (b) electron beam 5

13 deflection vs. driving current 55 Figure.14 Measurement and simulation results of the electron beam deflection of the two magnetic microdeflectors with 0.5 mm and 1.0 mm bore diameters Figure 3.1 Astigmatic electron beam results when passing through an electron lens with different focal lengths in X and Y direction: (a) circular beam and (b) elliptical image of least confusion.. 58 Figure 3. Schematic diagram of an electron beam microcolumn. 59 Figure 3.3 Schematic diagram of the designed magnetic microstigmator: (a) 3- D view and (b) top view 60 Figure 3.4 Electron beam passing by a pair of microinductors element: (a) the electron beam pulled toward the element and (b) the electron beam pushed away from the element due to action of the Lorentz force 6 Figure 3.5 Operational principle of the proposed magnetic microstigmator: (a) uncorrected astigmatic electron beam and (b) corrected circular electron beam. 63 Figure 3.6 (a) 3-D model of the proposed magnetic microstigmator with a bore diameter of 1 mm and B field distributions of the microstigmator with a driving current of (b) 50 ma and (c) 500 ma. 65 Figure 3.7 (a) Vector plot of the B field and (b) contour plot of the B field distribution at XY plane (Z=0) around the poles of the 6

14 microstigmator (I=50mA). 66 Figure 3.8 Simulation results: (a) B field distribution along the radial direction (Z=0) with driving currents varying from 50 ma to 300 ma, and (b) B field distribution along the Z axis at different radial with a driving current of 50 ma 67 Figure 3.9 Schematic diagram of the astigmatism correction of an elliptical electron beam passing through the magnetic field produced by the microstigmator 69 Figure 3.10 Simulation results of the traces of the electrons at different radial locations: (a) electrons on the X axis and (b) electrons on the Y axis.. 71 Figure 3.11 Simulation results of the astigmatism correction of an elliptical electron beam with a semimajor axis of 10 µm and a semiminor axis of 8 µm: (a) the schematic and (b) top view.. 71 Figure 3.1 Simulation results of the variation of the stigmatic points with driving current varying from 50 ma to 300 ma: magnetic microstigmators with bore diameters of (a) 1 mm and (b) 0.5mm. 7 Figure 3.13 Stigmatic point vs. driving currents applied to the two microstigmators with bore diameters of 1 mm and 0.5 mm, respectively 73 Figure 3.14 The fabrication steps for the magnetic microstigmator. 74 7

15 Figure 3.15 Microphotographs of the fabricated magnetic microstigmators with bore diameters of (a) 1 mm and (b) 0.5 mm. 74 Figure 3.16 Electron beam microcolumn (EBMC): (a) schematic diagram and (b) microphotograph of EBMC assembled with the fabricated magnetic microstigmator. 75 Figure 3.17 Experimental setup for testing the fabricated magnetic microstigmator. 75 Figure 3.18 Phosphor screen image of the electron beam probe: (a) no driving current applied to the magnetic microstigmator; 50 ma driving current applied to (b) the pairs of 1 and 3; (c) the pairs of and 4; and (d) all four pairs of the microinductors. 77 Figure 3.19 (a) Current images of the copper grid specimen and (b) variation of the deviation angle of the copper grid image for the magnetic microstigmator with a bore diameter of D = 1 mm and the driving current varying from 0 to 300 ma Figure 3.0 (a) Current images of the copper grid specimen and (b) variation of the deviation angle of the copper grid image for the magnetic microstigmator with a bore diameters of D = 0.5 mm and the driving current varying from 0 to 300 ma.. 79 Figure 3.1 Measured deviation angles of the copper grid image and the simulation results of the stigmatic points varying with driving currents applied to the magnetic microstigmators with bore diameters 8

16 of 1.0 mm and 0.5 mm 81 Figure 4.1 (a) Trajectory of the electron in an axially symmetrical magnetic field and (b) magnetic field strength along the off-axis flux line 83 Figure 4. Schematic diagram of the designed magnetic microlens: (a) 3D view and (b) cross sectional view 85 Figure 4.3 Operational principle of the proposed magnetic microlens: (a) axially symmetrical magnetic field produced within the central bore area; (b) electron beam focused by the lens field.. 86 Figure 4.4 (a) 3-D model of the proposed magnetic microlens and (b) magnetic field (B) distribution of the microlens with a driving current of 50 ma Figure 4.5 Simulation results of the magnetic microlens with a driving current of 50 ma: (a) vector plot of the magnetic field B; the contour plot of B field at planes of (b) Z=L/=50 µm and (c) Z=0 within the aperture of the magnetic microlens. 91 Figure 4.6 Simulation results of the magnetic field distribution along the length of the magnetic microlens with a driving current of 50 ma: (a) vector plot and (b) contour plot.. 9 Figure 4.7 Magnetic field (B) varying along the Z-direction of the magnetic microlens (r = 10 µm and I = 50 ma): (a) Bz and (b) Br Figure 4.8 B zmax vs. lens diameter with lens length of 00 µm, 300 µm, and 400 µm. (driving current I = 50 ma) 94 9

17 Figure 4.9 B zmax vs. driving current with different lens diameters (D).. 95 Figure 4.10 Trajectories of the electrons at different energy levels (Lens diameter D= 00 µm and B zmax = 50 mt). 96 Figure 4.11 Simulation results of the focal length and demagnification percentage ratio of the magnetic microlens with a lens diameter of 00 µm at different electron energy level. 96 Figure 4.1 Schematic diagram of the fabrication steps for the magnetic microlens 98 Figure 4.13 Microphotograph of a micromachined planar spiral coil 99 Figure 4.14 Microphotographs of the fabricated magnetic microlens 99 Figure 4.15 Electron beam microcolumn (EBMC): (a) schematic diagram and (b) microphotograph of EBMC assembled with the fabricated magnetic microlens 100 Figure 4.16 Experimental setup for testing the fabricated magnetic microlens Figure 4.17 Measured current images of the copper grid with different driving currents applied to the fabricated magnetic microlens. 101 Figure 5.1 Schematic diagram of an electrostatic electron beam microcolumn 103 Figure 5. Schematic diagram of the electron beam microcolumn with magnetic electron beam control devices Figure 5.3 (a) No magnetic field interference and (b) magnetic field 10

18 interference among the three magnetic electron beam control devices. 105 Figure 5.4 3D model of the three vertically stacked magnetic electron beam control devices. 107 Figure 5.5 Simulation results of the magnetic field B distribution of the designed the magnetic microdeflector with a pole distance of 1mm and a driving current of 50 ma 109 Figure 5.6 Simulation results of the magnetic field B distribution of the microdeflector at XZ plane (Y=0) with a pole distance of 1 mm and a driving current of 50 ma Figure 5.7 (a) Magnetic field B distributions along the Z axis at the center (X=0 and Y=0) of the microdeflector with a pole distance of 1 mm and (b) the variation of the span range with the driving currents applied to the microdeflector 111 Figure 5.8 (a) Magnetic field B distributions along the Z axis (X=0 and Y=0) with a driving current of 50 ma and (b) the variation of the span range with different pole distances of the microdeflectors.. 11 Figure 5.9 Simulation results of the magnetic field B distribution of the designed the magnetic microstigmator with a bore diameter of 1mm and a driving current of 100 ma Figure 5.10 Simulation results of the magnetic field B distribution of the microstigmator at XZ plane (Y=0) with a bore diameter of 1 mm 11

19 and a driving current of 100 ma. 115 Figure 5.11 (a) Magnetic field B distributions along the Z direction (r =10 µm) with a bore diameter of 1 mm and (b) the variation of the span range with the driving currents applied to the microstigmator. 116 Figure 5.1 (a) Magnetic field B distributions along the Z direction (r = 10 µm) with a driving current of 300 ma and (b) the variation of the span range with different pole distances of the microstigmators 118 Figure 5.13 Simulation results of the magnetic field B distribution of the designed the magnetic microlens with a lens diameter of 00 µm and a driving current of 50 ma.. 10 Figure 5.14 Simulation results of the magnetic field B distribution along the Z axis (X=0 and Y=0) of the magnetic microlens with a bore diameter of 00 µm and a driving current of 100 ma 11 Figure 5.15 (a) Magnetic field B distributions along the Z axis (r =0) of the microlens with a bore diameter of 00 µm and (b) the variation of the span range with the driving currents applied to the microlens.. 1 Figure 5.16 (a) Magnetic field B distributions along the Z axis (r = 0) with a driving current of 50 ma and (b) the variation of the span range with different bore diameters of the microlens 14 Figure D models of the three magnetic electron beam control devices stacked vertically: (a) schematic and (b) side view

20 Figure 5.18 FEA simulation results of the magnetic electron beam control system with magnetic interference among the three devices (L 1 =L =1.5 mm) 18 Figure 5.19 Magnetic field magnetic B distribution (a) at XZ plane (Y=0) and (b) along the central axis (X=10 µm and Y=0) with L 1 = L = 1.5 mm. 19 Figure 5.0 FEA simulation results of the magnetic electron beam control system without magnetic interference among the three devices (L 1 =L =3.5 mm) 130 Figure 5.1 Magnetic field magnetic B distribution (a) at XZ plane (Y=0) and (b) along the Z direction (X=10 µm and Y=0) with L 1 = L =3.5 mm

21 LIST OF TABLES Table 1.1 Electron beam microcolumns reported in the literature. 8 Table 5.1 The three devices with largest calculated field span range

22 LIST OF SYMBOLS E Electric field F e Electrostatic force q Electron charge ( C) F m Lorentz force v B L r r& The electron speed Magnetic flux density The Lagrangian of the electron The displacement vector of the electron The first order derivative of the displacement, i.e., the velocity of the electron m 0 The rest mass of the electron ( kg) c v A B x, B y, B z The speed of light ( m/s) The electron speed The magnetic vector potential Three components of the magnetic flux density B x(t),y(t),z(t) The time dependence of the electron motion x(z), y(z) B H r and H z The trajectory of electron moving along the z axis The magnitude of the magnetic flux density (B) The radial and axial magnetic fields µ The permeability H (H x,h y,h z ) The magnetic field strength 15

23 r, θ, and z Coordinates of the cylindrical coordinate system B r and B z Magnetic field components in the cylindrical coordinate system B zmax The maximum B z DM The demagnification percentage ratio r 0 The initial radial distance of the electron r min The minimum radial distance the electron obtains 16

24 CHAPTER 1 INTRODUCTION The objective of this research is to develop micromachined magnetic devices for electron beam control in the electron beam microcolumn (EBMC). The EBMC has a variety of applications for an electron beam nanolithography, a portable electron microscope, a metrology and defect inspection, a non-contact testing, material analysis, and a biomedical instrument. The magnetic devices to be developed in this work include the magnetic microdeflector, magnetic microstigmator, and magnetic microlens. The three magnetic microdevices, which can be assembled for an electron beam microcolumn, can achieve the goals of electron beam deflection/scanning, electron beam astigmatism correction, and electron beam focusing. In this work, the new magnetic electron beam control devices are proposed, designed and fabricated using MEMS (Micro Electro Mechanical System) technology and fully characterized for an electron beam microcolumn. 1.1 Research Motivation This research is motivated by the rapidly growing demands for high throughput and low-cost nanofabrication technology and tools. The origination of nanoscience and nanotechnology can be dated back to 1960s. The Nobel Prizewinning physicist Richard Feynman first introduced the nanotechnology concept in 17

25 his famous 1959 lecture [1], There is plenty of room at the bottom, in which he pointed out that the properties of materials and devices at the nanometer range would present future opportunities. In recent years, research on nanodevices and nanomaterials has drawn tremendous worldwide interests [-4]. The significance of nanoscience and nanotechnology is their potential impact on nearly every industry, for example, manufacturing, medicine, scientific research, communication, and computing. As mentioned in [], the importance of nanoscience and nanotechnology to our human activities is comparable to the steam engine in the 18 th century, electricity in the 0 th century, and the internet in contemporary society. Nanotechnology is the science of fabricating, characterizing, and utilizing structures with dimensions of approximately nm [3]. The fabrication of the nanostructures is of most interest and fundamental to the entire field of the nanoscience and nanotechnology. Lithography is one of the most important and widely used nanofabrication methods. Based on the exposure sources, lithography can be categorized into four major types: ultraviolet (UV) optical lithography, X-ray lithography, ion beam lithography, and electron beam lithography (EBL) [5]. Currently in the semiconductor industry, the optical lithography is exclusively used for fabricating the integrated chip (IC) in a massively parallel mode. The wavelength of the ultraviolet (UV) light used in the optical lithography is usually in the range of nm. Therefore, the line width limit of optical lithography lies near 400 nm, although 00 nm features may eventually be printed under carefully 18

26 controlled conditions. When the feature sizes fall down to the range of 100 nm, alternative lithography methods are required. X-ray lithography [6], in which a mask is in close proximity of less than 10 µm for sub-100 nm lithography, is one of the nanofabrication techniques being explored. Even though features as small as 0 nm can be obtained with a vanishingly small contact gap, the accurate gap control needed for exposure still presents a big challenge. In addition, the availability of masks for X-ray lithography with sufficient quality is also limited. X-ray lithography requires a 1x mask made by EBL. It remains a challenge to achieve accurate large aspect ratio 1x masks with sub-100 nm dimensions. Another disadvantage of X-ray lithography at present is its extremely high cost. It requires either a custom-built X-ray source and stepper or access to a synchrotron storage ring to perform the exposure. The third type of lithography is ion beam lithography (IBL) [7]. The resolution, throughput, cost, and complexity of an ion beam system are comparable to those of electron beam lithography. However, the high-energy ion beam used for writing in IBL may cause the broadening of the ion beam due to the space-charge effect. Thus the thickness of the electron resist that can be exposed is limited. In addition, the high-energy ion beam could possibly damage the sample due to ion bombardment. Electron beam lithography (EBL) is considered as one of the most advanced and most reliable nanofabrication technologies. It is a lithography process in which a focused electron beam is used to produce the features or patterns on the substrate wafer through a layer of electron resist. The EBL system was originally derived from 19

27 the scanning electron microscopes (SEM) [8-10]. In EBL, a focused electron beam probe (< 100 nm) scans across a substrate surface and transports the electron energy into the electron resist which is an organic polymer of high molecular weight, such as PMMA (polymethyl methacrylate) [11]. After exposure, with a suitable developing process, sub-100 nm features are produced on the substrate wafer. Unlike the optical lithography that requires a mask for exposure, EBL does not need any mask, but rather draws the pattern directly on the substrate wafer coated with the electron resist. EBL offers higher resolution than the optical lithography because of the smaller wavelength (-5 nm) of the electron beam used for the lithography. The resolution of the optical lithography is limited by the diffraction related to the wavelength of the UV light used for the exposure. In summary, the major advantages of EBL over the other three lithography approaches are as follows: (1) Sub-100 nm resolution (0 nm resolution can even be achieved); () Direct patterning without a mask; (3) Greater depth of focus; (4) Highly automated and precisely controlled; (5) Flexible technique that can work with a variety of materials. Because of these advantages, EBL remains the most established method for complex nanofabrication in the sub-100 nm regime today. Figure 1.1 shows a commercially available EBL system (Raith 150) at the University of Cincinnati. 0

28 Figure 1.1 Photograph of an electron beam lithography system (Raith 150) at the University of Cincinnati. The first electron beam lithography machine based on the scanning electron microscope (SEM) was developed in the late 1960s [1]. A schematic of a typical EBL system is shown in Figure 1.. The major component of the EBL system is the electron beam column (EBC) [13-18], which mainly consists of two parts. The first part is an electron gun source in which the electron beam is extracted from the electron field emission (FE) tip and is then accelerated by the lens of the electron beam source. The second part of the EBC is the electron beam control unit. The electron beam emitted from the electron gun source is deflected/scanned, astigmatism-corrected, and focused in this electron beam control unit. The electron beam control unit mainly consists of three types of electron beam control devices: (1) deflectors that deflect/scan the electron beam [19-3], () stigmators that correct the electron beam astigmatism [4-6]; and (3) lenses that focus the electron beam [7-3]. These electron beam control devices play a key role in the EBC and determine the ultimate performance of the electron beam lithography. 1

29 Although EBL is most widely used in nanofabrication, it has two major problems. First, since the EBL system produces the nanometer scale patterns on the substrate surface using a serial operation manner, the throughput is very low. Second, the EBL system is extremely expensive due to its high manufacturing and maintenance costs. As a result of these problems, the use of EBL is mainly limited to mask-making and experimental device prototyping. Electron gun source Electron beam control system Figure 1. Schematic of a typical electron beam lithography system [17]. To overcome the two major problems associated with a conventional EBL system, the use of the electron beam microcolumn fabricated by MEMS technology was proposed in the late 1980s [33, 34]. MEMS technology is a low-cost and mass fabrication technique, and it allows the electron beam columns to achieve a desired precision and a high degree of miniaturization. By using MEMS technology, the

30 conventional bulky electron beam column system can be miniaturized and massfabricated, so the manufacturing cost is significantly reduced. Additionally, the miniaturization of the column system allows an arrayed structure to be formed. Chang, et al. first proposed an arrayed microcolumn system based on semiconductor microfabrication and MEMS technology [35, 36]. Figure 1.4 shows the basic concept of this arrayed microcolumn approach. Figure 1.3 Arrayed microcolumn lithography system using one or more microcolumn per chip [35]. As shown in Figure 1.3, multiple electron beams with energies of 1- kev are generated with an array of closely-spaced miniaturized electron columns. The arrayed microcolumns print the different regions of the wafer in a parallel mode, which largely reduces the total stage moving distance and the printing time. The electron beam generated by each microcolumn is designed at low 1- kev to avoid the proximity and beam-heating effects [36]. By using the parallel writing scheme, the 3

31 arrayed microcolumn system has great potential to significantly improve the EBL productivity. In addition to being used as arrayed electron beam microcolumn system for high-throughput electron beam nanolithography, the electron beam microcolumn has many other important applications, such as portable electron microscopes, metrology and defect inspection, non-contact testing, material analysis, and biomedical instruments. As is known, two mechanisms can be used to control the electron beam, i.e., electrostatic and magnetic. Presently, all of the developed microcolumns employ the electrostatic devices to control the electron beam. As described in detail in Section 1., the electrostatic electron beam control devices employed in the current electron beam microcolumn have many problems. First, the fabrication cost for these electrostatic devices is high. Second, the complicated fabrication process of these devices remains a challenging issue. Finally, the electrical breakdown for these electrostatic devices becomes a major concern especially when the size of the microcolumn is further scaled down. Therefore, to overcome the problems associated with the present electrostatic devices, this thesis presents the development of micromachined magnetic devices for the electron beam control in the electron beam microcolumn. Compared to their electrostatic counterparts, the proposed magnetic devices possess the advantages of low-cost and reliable fabrication process, no concern on the electrical breakdown, and inherently higher sensitivity and smaller aberrations. 4

32 1. Review of Previous Work Electron beam lithography is one of the most promising next-generation lithography (NGL) technologies for use in nanofabrication with a feature size of 100 nm or less. In order to enhance the low productivity and reduce the high manufacturing cost associated with the current conventional electron beam nanolithography machine, the research on developing a miniaturized electron beam microcolumn (EBMC) using MEMS technology has drawn much interest and has achieved significant progress [37-4]. Field emission (FE) tip Extractor and limiting aperture Field emission source Stigmator Focusing lens X- and Y-deflector Electron beam control Wafer stage Figure 1.4 Schematic diagram of an electron beam microcolumn Figure 1.4 shows the typical structure of an electron beam microcolumn. As is shown, an electron beam microcolumn is mainly composed of two parts. One part is the field emission (FE) microsource system, or electron gun, which includes the field emission tip and the source lens. In this part, the electron beam is extracted from the FE tip and accelerated by the source lens. The other part is an electron beam control 5

33 unit which usually consists of three types of electron beam control devices: the microstigmator, microlens, and microdeflector. A ray of electron beam emitted from the field emission microsource system normally carries astigmatism. The astigmatism is an electron beam aberration in which a circular electron beam is distorted into an elliptical one. The astigmatism can be corrected by using the stigmator. Then, in order to obtain a nanometer scale probe size, the electron beam needs to be focused using the electron lens. Finally, the deflector scans the electron beam across the substrate wafer to implement the exposure or imaging function. Therefore, the stigmator, lens, and deflector that form the electron beam control unit are the critical and indispensable components of an electron beam microcolumn system and ultimately determine the performance of an EBMC. Many accomplishments have been achieved in fabricating an electron beam microcolumn system. Fully-functional 1 kev columns with an electron beam probe size of 10 nm and a beam current in the order of 1 na have been reported [43, 44]. Figure 1.5 shows the photographs of some functional microcolumns developed using MEMS technology. As described above, one of the most important applications of the electron beam microcolumn is to employ an arrayed microcolumn system in the electron beam nanolithography. Many progresses have been made in this area [37, 48-49, 51-54]. Figure 1.6 shows the photographs of two developed x arrayed microcolumn systems. 6

34 (a) (b) (c) (d) (e) Figure 1.5 Photographs of the electron beam microcolumns developed by: (a) H.S. Kim, et al. 005 [45]; (b) S.S. Park, et al. 004 [46] and H.S. Kim et al., 003 [47]; (c) L.P. Muray, et al., 000 [48]; (d) I. Honjo, et al., 1997 [49]; and (e) E. Kratshmer, et al., 1996 [50]. (a) (b) Figure 1.6 Photographs of the x arrayed electron beam microcolumn systems developed by (a) L.P.Muray, et al., 000 [48] and (b) J.W. Jeong, et al., 005 [51]. 7

35 Table 1.1 summarizes some of the previous work on the development of the electron beam microcolumns. It is noted that most electron beam microcolumns have a diameter smaller than cm and a length of several centimeters. Table 1.1 Electron beam microcolumns reported in the literature References MC Diameter (cm) MC Length (cm) R. Saini, et al., 005 [41] 1x1 1 J.W. Jeong, et al., 005 [51] x 4 H.S. Kim, et al., 003 [47] Φ 0.65 R.Y. Lutsch, et al., 00 [61] D. Winkler, et al., 1998 [6] Φ 5 10 T. Ambe, et al., 00 [60] Φ.7 7.4* J.M. Krans, et al., 001 [59] Φ L.P. Muray, et al., 000 [48] x 4 A. Zlatkin, et al., 1999 [58] 1x1 0.05* J.Y. Park, et al., 1998 [54] x 0. R.H. Roberts, et al., 1997 [63] 5 11 I. Honjo, et al., 1997 [50] Φ 1 5 D.A. Crewe, et al., 1996 [57] Φ G.M. Shedd, et al., 1993[56] Φ * T.H.P Chang, et al., 1990 [55] E. Kratschmer, et al., 1995 [43] x 4 * Length as cited in [41]. As is well-known, two mechanisms are normally used to control the electron beam, i.e., electrostatic and magnetic. In the electrostatic electron beam control mechanism, the electron in an electric field (E) will experience the electrostatic force (F e ), F qe e = (1.1) where, q (= C) is the electron charge. This electrostatic force manipulates the electron beam motion. In the magnetic electron beam control mechanism, an electron beam moving in a magnetic field (B) will experience the Lorentz force (F m ), 8

36 F m = q v B (1.) where, q (= C) is the electron charge and v is the electron velocity. The electron beam can be controlled by the produced Lorentz force. Presently, all of the developed microcolumns are electrostatic microcolumns. This means, as illustrated in Figure 1.7, the stigmator, deflector, and focusing lens in the electron beam microcolumns are all electrostatic devices. The electrostatic octupole electrodes are employed as the stigmator and deflector and an electrostatic Einzel lens usually works as an electron focusing lens. E-beam source Electrostatic Octupole stigmator/deflector Electrostatic Einzel lens E-beam control system Figure 1.7 Schematic diagram of an electrostatic microcolumn Electrostatic Octupole Stigmator/Deflector Astigmatism is a type of aberration that exists in almost any type of electron beam device. Astigmatism deteriorates the shape and size of the electron beam probe and degrades the resolution of the electron beam. Astigmatism is a phenomenon in which a ray of electron beam probe that starts from an ideal circular shape ends up as an elliptical cross section after it passes through an electron optical system such as a 9

37 lens. In an electron beam microcolumn, the microstigmator is used to correct the astigmatism of the electron beam emitted from the field emission (FE) microsource. There are several possible reasons that an electron beam may carry astigmatism in the electron beam microcolumn: (1) the misalignment among the FE tip, the source lens, and the limiting aperture in the FE microsource will cause an axial asymmetry; () the material property of the FE tip may not be perfectly homogeneous, and in turn leads to an axially asymmetrical emission current; (3) the manufacturing error in the round circular shape of the source lens and the limiting aperture will cause the axial asymmetry and produce the astigmatism in the emission current; and (4) the buildup of dirt on the side of the aperture and the source lens will result in an asymmetrical electrostatic field. The stigmator usually possesses a multi-pole structure. The multi-pole structure can introduce the same type of asymmetry (with the opposite sign) as the original axial astigmatism carried by the emitted electron beam [64]. Thus, the mechanical deficiencies of the axially symmetrical system can be compensated by changing the excitations of the different components of the multi-pole field. Electrostatic octupole is exclusively employed in the currently developed electrostatic electron beam microcolumn. The biggest advantage of the electrostatic octupole is that it can work as both a stigmator and a deflector [65], which, in turn, makes for a compact column structure. It consists of eight electrodes as shown in Figure

38 Deflector Stigmator V Y F e = qe V A Y -V A -V X y x V X V A -V A X -V A V A (a) -V Y Y -V A (b) V A V Y+V A V Y -V A Electrode Stigmatic E-beam Astigmatic E-beam V X+V A V X -V A V X -V A X V X+V A Magnetic flux V Y -V A V Y+V A Stigmator/Deflector (c) Figure 1.8 Operational principle of the electrostatic octupole working as: (a) deflector; (b) stigmator; and (c) stigmator/deflector. When the octupole works as a deflector (Figure 1.8(a)), the eight electrodes are divided into X and Y groups. Two potentials, ±V X and ±V Y, are applied to the two groups of the electrodes in the X and Y directions respectively. This produces an electrostatic field E within the central bore area where the electron beam passes through. The electron in the electrostatic field E will experience an electrostatic force as shown in Equation (1.1). The electrostatic forces control the deflection of the electron beam along the X and Y directions. When the octupole works as a stigmator 31

39 (Figure 1.8(b)), the potentials applied to the electrodes produce a quadrupole electric field within the central bore area. This quadrupole electrostatic field corrects the astigmatism of the electron beam. By superimposing these two sets of potentials, the electrostatic octupole can implement the functions of the stigmator as well as the deflector. In the present electron beam microcolumn, the electrostatic octupole is exclusively used for the astigmatism correction [51, 54, 66-71]. Figure 1.9 shows photographs of the electrostatic octupoles developed by different research groups. In the early stage, the electrodes of the electrostatic octupole were fabricated individually using precision machining technology, and, then, the eight fabricated electrodes were assembled manually to form an octupole [66-67]. Recently, with the development of the MEMS fabrication technology, most of the octupoles are made from the silicon substrate wafers using deep reactive ion etching (DRIE) [51, 54, 68-69]. The electrostatic octupole stigmator/deflector has the advantages of simplicity and compactness. However the fabrication of the electrostatic octupole needs expensive DRIE process to etch through a silicon substrate wafer with a thickness of around 300 µm [68-69]. Meanwhile, the fabrications of ideally vertical, round, and smooth electrode surfaces remain the challenging issues. Additionally, the possibility of the charged-particle accumulation on the electrode during the manipulation of the electron beam can easily deteriorate the performance of the stigmator/deflector. 3

40 (a) (b) (c) (d) (e) (f) Figure 1.9 Photographs of the electrostatic octupoles developed by different research groups: (a) M.M. Gomati, et al [66]; (b) E. Yin, et al. 000 [67]; (c) H.S. Gross, et al [68]; (d) H. Kim, et al. 003 [69]; (e) L.P. Murav, et al. 000 [54]; and (f) J.W. Jeong, et al. 005 [51]. 1.. Electrostatic Einzel Lens Lenses are used for focusing a ray of the electron beam in the electron beam microcolumn. Any axially symmetrical field distribution, either electrostatic field or magnetic field, can be called a lens [7]. The electrostatic Einzel lens is exclusively employed for the electron beam focusing in the present electron beam microcolumn because of it simplicity and compactness [73-83]. The Einzel lens usually consists of three electrodes as shown in Figure The two outside electrodes are typically set at ground potential. The electron beam focusing effect is realized by adjusting the potential of the middle electrode [73-74]. 33

41 Figure 1.11(a) shows the fabrication process of an individual electrode of the Einzel lens. Figure 1.11(b) shows a photograph of a fabricated electrode with a round lens aperture. To construct a three-electrode Einzel lens, the three fabricated electrodes separated with two Pyrex glass spacers are bonded together, as shown in Figure 1.1(a), using a multi-layer anodic bonding technique [75-78]. Figure 1.1(b) shows a photograph of a fabricated multilayer Einzel microlens. 0 V +V 0 V E-beam F e = qe Focus point 0 V +V 0 V Figure 1.10 Principle of the electrostatic Einzel lens. (a) (b) Figure 1.11(a) Fabrication process of the individual electrode of the Einzel lens [47] and (b) a fabricated electrode with round lens aperture [46]. 34

42 (a) (b) Fig.1.1 Fabrication of the electrostatic Einzel lens: (a) multi-layer anodic bonding process and (b) the photograph of a fabricated Einzel lens [78]. Since the Einzel lens has three electrodes separated from each other, its fabrication usually requires a multilayer anodic bonding process. The bonding process used for the three electrodes and two Pyrex glass spacers makes the alignment an extremely difficult task. Another concern about employing the electrostatic lens in an electron beam microcolumn is the electrical breakdown problem. The electrical breakdown voltage in a vacuum is about 10 kv/mm [84]. In the presently developed electron beam microcolumn, the focusing voltage set on the middle electrode is usually several hundred volts. This means the spacer thickness between the two electrodes cannot be smaller than 100 µm. With the size of the electron beam microcolumn further scaled down, the electrical breakdown problem of the electrostatic lens will become more serious. In summary, the advantages of the electrostatic electron beam control devices, including the electrostatic octupole stigmator/deflector and the electrostatic Einzel lens, are: (a) the structures are simple and compact and (b) the octupole can be used as 35

43 a stigmator and a deflector simultaneously. The disadvantages of the electrostatic microcolumn are also obvious, and they are: (1) The electrostatic octupole needs an expensive DRIE fabrication process to etch through a silicon wafer with a thickness around 300 µm, and the aspect ratio, smoothness, and roundness of the electrode surface remain the challenging fabrication issues; () The electrostatic Einzel lens needs a multi-layer anodic bonding process which makes the three-electrode alignment extremely difficult; (3) The electrical breakdown is a major concern for the electrostatic electron beam control devices, especially when the device size is further scaled down; (4) The possibility of particle accumulation on the electrode surface can greatly deteriorate the performance of the device. 1.3 Research Objectives In order to overcome the drawbacks of the present electrostatic microcolumn, as discussed above, this research explores a new magnetic microcolumn, as shown in Figure 1.13, in which the electron beam control system is composed of three micromachined magnetic devices: (1) a magnetic microdeflector for the electron beam deflection/scanning; () a magnetic microstigmator for the electron beam astigmatism correction; and (3) a magnetic microlens for the electron beam focusing. 36

44 Magnetic microstigmator Magnetic microlens Magnetic microdeflector Electrostatic Microcolumn Magnetic Microcolumn Figure 1.13 Magnetic microcolumn consisting of the magnetic microdeflector, magnetic mirostigmator, and magnetic microlens, in substitution of the present electrostatic microcolumn. The objective of this research is to develop new micromachined magnetic devices for the electron beam control in an electron beam microcolumn with applications in the electron beam nanolithography and portable electron microscope. These magnetic electron beam control devices include: (1) magnetic microdeflector for the electron beam deflection/scanning; () magnetic microstigmator for astigmatism correction; and (3) magnetic microlens for electron beam focusing. These magnetic electron beam control devices are fabricated using novel MEMS (Microelectromechanical System) technology, a low-cost mass fabrication technique. The advantages of employing the magnetic electron beam control devices, compared to their electrostatic counterparts, are the following: (1) No complicated multilayer anodic bonding is involved; () Low-cost electroplating process instead of the expensive DRIE process; (3) The magnetic pole shape can be easily designed and fabricated in favor of the magnetic control of the electron beam; 37

45 (4) There is no concern for the electrical breakdown when the devices size is further scaled down; (5) The magnetic electron beam control devices inherently have higher sensitivity and lower aberrations [85]. The trade-offs of using the magnetic electron beam control devices in the electron beam microcolumn are: (a) their structures are more complex than those of the electrostatic devices, but the fabrication process of the magnetic devices is more reliable and the fabrication cost is lower; and (b) the magnetic devices need to consume power, but the power consumption is very low because of the small scale of the device. The specific tasks associated with this research are presented in the following chapters. Chapter introduces the development of the magnetic microdeflector. The principle of the magnetic microdeflector will be explained. A detailed design of the magnetic microdeflector will be described. The electron motion modeling of the proposed microdeflector structure will be derived, and the detailed simulation results will be presented. Then, the fabrication procedure of the microdeflector will also be described. Finally, the fabricated microdeflector assembled into an electron beam microcolumn will be tested and characterized. The experimental results will be reported and analyzed in details. Chapter 3 introduces the development of the magnetic microstigmator. The operational principle of the magnetic microstigmator will be explained. A detailed design of the magnetic microstigmator will be described. The electron motion 38

46 modeling of the proposed microstigmator structure will be derived, and the simulation results will be presented. Then, the detailed fabrication procedure of the microstigmator will be described. Finally, the fabricated microstigmator assembled into a microcolumn will be tested and characterized. The experimental results will be reported and analyzed in details. Chapter 4 introduces the development of the magnetic microlens. The operational principle of the magnetic microlens will be explained. A detailed design of the magnetic microlens will be described. The electron motion modeling of the proposed microlens structure will be derived, and the simulation results will be presented. Then, the detailed fabrication procedure of the microlens will be described. Finally, the fabricated microlens assembled into the microcolumn will be tested. The experimental results will be reported and analyzed. Chapter 5 introduces the modeling and simulation of the miniaturized magnetic electron beam control system that consists of the three proposed magnetic electron beam control devices: the microdefelctor, microstigmator, and microlens. First, the span ranges of the magnetic field in the space generated by the microdeflector, microstigmator, and microlens will be investigated in details. Then, the magnetic electron beam control system consisting of the three magnetic devices is modeled and simulated as a whole. The magnetic interference among the three devices will be investigated and discussed. Finally, in Chapter 6, the conclusions of this research will be drawn and recommendations for future work will be discussed. 39

47 CHAPTER MAGNETIC MICRODEFLECTOR FOR ELECTRON BEAM DEFLECTION/SCANNING.1 Introduction The electron beam deflector, which is one of the most important components of an electron beam microcolumn system, controls the electron beam deflection/scanning across the substrate wafer to implement the electron beam lithography. So far, the electrostatic octupole deflectors are exclusively used in the electron beam microcolumn. However, as described in Chapter 1, the magnetic deflector, compared to its electrostatic counterpart, has the advantages of low-cost fabrication process, no need for the expensive and complex DRIE process, easy design of the magnetic pole shape, and inherently higher sensitivity and lower aberrations. In addition, the microfabricated magnetic deflectors can greatly improve the scanning linearity and speed, and reduce the power consumption and the size of the microcolumn system. The proposed magnetic microdeflector consists of four magnetic poles coupled with micromachined solenoid-type microinductors as shown in Figure.1(a). Each microinductor is composed of a micromachined solenoid coil and a permalloy (81%Ni/19%Fe) magnetic core. The four magnetic poles are divided into two pairs which control the deflections of the electron beam in the X and Y axes, respectively. 40

48 The X deflector and the Y-deflector are on the opposite sides of the substrate wafer as shown in Figure.1(b). The Lorentz force exerted on an electron passing through a magnetic field can be expressed as, F m = qv B, (.1) where F m is the Lorentz force, q is the charge of the electron ( C), v is the electron velocity, and B is the magnetic flux density. Micromachined Coil Y-deflector X-deflector Magnetic core X-deflector Z Y Electron beam X Y-deflector (a) X-deflector Substrate Electron beam Y-deflector (b) Figure.1 Schematic diagram of the designed magnetic microdeflector: (a) 3-D view and (b) cross sectional view. As noted in Equation (.1), the Lorentz force experienced by the moving electron in a magnetic field depends on both the electron velocity and the magnetic field strength. Compared to a conventional air core microinductor, a NiFe permalloy 41

49 core microinductor produces a more uniform and stronger magnetic field in the central bore area where the electron beam passes through. The operational principle of the magnetic microdeflector is illustrated in Figure.. When a DC current is applied to the micromachined solenoid coil, a magnetic field is generated within the coil, and the magnetic flux is guided by the permalloy magnetic core to the central bore area. This generates a strong and directional magnetic field between the two magnetic inductors (Figure.(a)), and the Lorentz force thus acts on the passing electron beam. As shown in Figure.(b), if the magnetic field directs into the paper surface and the electron beam enters the central bore area from the top, the electron beam will be deflected to the left after it passes through the deflector. By reversing the direction of the magnetic field, which can be easily realized by changing the direction of the DC driving current applied to the inductor coils, the electron beam will be deflected to the right. Therefore, the designed magnetic microdeflector is capable of controlling the electron beam deflection/scanning in the X and Y directions, respectively. Micromachined coil Electron beam Magnetic field B A-A Electron beam A N Magnetic flux z y x A S Magnetic core Deflected electron beam (a) (b) Figure. Operational principle: (a) magnetic field distribution and (b) cross sectional view of the electron beam deflection. 4

50 . Design and Simulation of the Magnetic Microdeflector The electron motion in an external magnetic field can be described by the Euler-Lagrange equation of motion, d L L = 0 dt r& r (.) where r(= xi+yj+zk) is the displacement vector of the electron, dr r & = = v (.3) dt is the derivative of the displacement vector with respect to time, i.e. velocity of the electron (v), and L is the Lagrangian of the electron. In a pure magnetic field, the Lagrangian L of the electron motion can be expressed as [85], L = m c ( 1 v / c 1/ + qa v (.4) 0 ) where m 0 is the rest mass of the electron ( kg), c is the light speed ( m/s), v is the electron speed, q is the electron charge ( C), and A is the magnetic vector potential defined through the magnetic flux density B, B B i + B j + B k = A (.5) = x y z By substituting Equations (.3) - (.5) into Equation (.), the equation of motion for the electron moving in an external magnetic field can be written in a scalar form, d v 1 dt c d v 1 dt c d v 1 dt c 1/ 1/ 1/ dx = dt dy = dt dz = dt q m 0 q m 0 q m 0 dy B dt dz B dt z x dx B dt y dz dt dx dt dy dt B B B y z x (.6) 43

51 44 By solving Equation (.6 ), one can obtain the time dependence of the electron motion, i.e. x(t), y(t), and z(t), in an external magnetic field. In this research, however, the trajectory of the electron beam deflection is of more interest. For this purpose, one can assume the electron beam is originally moving along the Z axis. The electron speed v is defined as dt ds v = (.7) where, [ ] 1/ ) ( ) ( ) ( dz dy dx ds + + = (.8) Substituting Equation (.8) into Equation (.7), we obtain [ ] dz dz dy dz dx v dz dy dx v ds v dt 1/ 1/ 1 1 ) ( ) ( ) ( = + + = = (.9) Substituting Equation (.9) into Equation (.6), we can eliminate dt and obtain = = z y x y z x B B dz dy dz dx B dz dy dz dy dz dx c v v m q dz y d B dz dx B B dz dx dz dy dz dy dz dx c v v m q dz x d 1/ 0 1/ (.10) By solving Equation (.10), one can obtain the trajectory of the electron moving along the Z axis: x(z) and y(z). To investigate the magnetic field distribution produced by the proposed magnetic microdeflector, a 3-D magnetic microdeflector model (Figure.3(a)) was built for finite element simulation using MagNet software

52 (INFOLYTICA Corporation). The magnetic flux density B produced by one pair of the microinductors with a driving current of 50 ma is shown in Figure.3(b). Because the central bore area is where the electron beam passes through, the magnetic field distribution between the two magnetic cores is of primary interest. The B field distribution between the two magnetic poles is shown in Figure.4. The distance between the two opposite magnetic poles is 500 µm. (a) (b) Figure.3 (a) 3-D model of the magnetic microdeflector and (b) B field distribution with a driving current of 50 ma. 45

53 Y X 500 µm 600 µm Y X Core tip Z (a) X 5 µm Z X 500 µm (b) Figure.4 Simulation results of the designed microdeflector: (a) B field distribution at XY plane (Z=0) and (b) B field distribution at XZ plane (Y=0). Based on the operational principle of the magnetic microdeflector, the component along the X direction of the magnetic flux density field, B x, is the main factor influencing the motion of a passing electron beam. Simulation results also show that the magnitudes of the other two components of the magnetic field, B y and B z, are at least two to three orders smaller than that of B x within the central bore area. A uniform B x field is critical to reduce the aberrations of the deflected electron beam. The B x field distribution within the central bore area (100 µm 100 µm) in the XY plane at Z=0 is plotted in Figure.5(a), which presents the desired field uniformity. Figure.5(b) shows the B x distribution along the Z axis with driving currents varying 46

54 from 10 ma to 50 ma. The designed magnetic microdeflector has a thickness of approximately 100 µm. Nevertheless, as shown in Figure.5(b), when the deflector is set at Z=0, the influential region of the magnetic field spans from Z= µm to Z= µm in the space. Therefore, the motion of the electron is affected by the stray magnetic field before the electron arrives at the location of the deflector, and the motion remains being affected by the field after the electron leaves the deflector. By decreasing the distance between the two opposite magnetic poles, the stray magnetic flux can be reduced, and the magnetic field can be more confined within the central bore area. (a) 10 ma 30 ma 50 ma 0 ma 40 ma (b) Figure.5 Simulation results: (a) B x field distribution in the central bore region (100 µm 100 µm) at XY plane (Z=0) and (b) B x field distribution along the Z axis at the center (X=0 and Y=0). 47

55 0.5 mm pole-distance 0.5 mm pole-distance 10 ma 0 ma 30 ma 40 ma 50 ma 10 ma 0 ma 30 ma 40 ma 50 ma (a) (b) Figure.6 Simulation results of the magnetic microdeflector with 0.5 mm poledistance: (a) Electron deflection and (b) deflection angle with driving current varying from 10 ma to 50 ma. The electron trajectory Equation (.10) was solved using the numerical computation software Mathematica (Wolfram Research, Inc). As described previously, the magnitude of B x is two or three orders larger than those of B y and B z, thus only the B x field effect was considered in the numerical calculation. The electron is assumed to move along the Z-axis direction. In such a case, as expressed in Equation (.1), the Lorentz force resulted from the B x field will deflect the electron to the Y-axis direction. Figure.6(a) shows the simulation results of the electron deflection along the Z axis with driving currents varying from 10 to 50 ma for a magnetic microdeflector with 0.5 mm distance between the two magnetic poles. Figure.6(b) shows the variation of the tangent angles of the electron trajectory with respect to the Z axis at different driving currents. 48

56 .3 Fabrication of the Magnetic Microdeflector Figure.7 illustrates the brief fabrication procedures of the designed magnetic microdeflector. Pleases see Appendix A for more detailed information. During the fabrication, a -inch <100> silicon wafer oxidized on both sides was used as the substrate (Figure.7(a)). First, the -inch silicon wafer was anisotropically etched on the backside using KOH solution. The wet etching continued until the remaining silicon membrane thickness reached about 0 µm (Figure.7(b)). The bottom conductor lines (Cu) of the inductor coil were electroplated on the front side of the substrate wafer (Figure.7(c)). Then a layer of AZ photoresist was spin-coated onto the bottom conductor lines and patterned (Figure.7(d)). The vias for connection between the bottom and top conductor lines were electroplated into the patterned windows (Figure.7(e)). After that, the NiFe permalloy core was electroplated with a layer of AZ photoresist working as an isolation layer (Figure.7(f)). The top conductor lines of the solenoid-type inductors were then fabricated by using electroplating method (Figure.7(g)). After that, the remaining silicon membrane together with the silicon oxide layer was dry-etched by using RIE (reactive ion etching) (Figure.7(h)). Finally, the silicon wafer was diced into chips and two microfabricated chips were bonded together using epoxy (Figure.7(i)). The fabrication process of the solenoid-type microinductors using MEMS technology was reported previously [44, 45]. 49

57 (a) (b) (c) (f) (g) (h) (d) (e) (i) Cu NiFe Si AZ SiO Figure.7 Schematic diagram of the fabrication steps for magnetic microdeflector. Front-side (X-deflector) Back-side (Y-deflector) Front-side (X-deflector) Back-side (Y-deflector) 1 cm 1 cm 1 cm 1 cm 300 µm Micromachined coil 500 µm Micromachined coil Magnetic core 0.5mm Magnetic core 1 mm Through-hole in the Si substrate Through-hole in the Si substrate (a) (b) Figure.8 Microphotographs of the two fabricated magnetic microdeflectors: (a) 0.5mm and (b) 1mm between the magnetic poles. 50

58 Microphotographs of the two fabricated magnetic microdeflectors with different magnetic pole-distance are shown in Figure.8. The size of the diced chip is 1 cm x 1 cm. The chip has one pair of micromachined inductors on each side. The distances between the magnetic poles are 0.5 mm (Figure.8(a)) and 1.0 mm (Figure.8(b)), respectively. In order to characterize the micromachined solenoid type microinductors, an HP LCR meter was used to measure the resistance and the inductance of the microinductor at different driving frequencies. The measured results are shown in Figure.9. The resistance of the micromachined coil remains at 1.4 Ω at DC and the driving frequencies lower than 10 khz. After that, the coil resistance increases rapidly to.6 Ω when the driving frequency reaches 1 MHz. The inductance of the fabricated microin ductor gradually decreases from µh to 0.5 µh when the driving frequency rises from DC to 1 MHz. Resistance (Ω) Inductance (µh) Frequency (Hz) (a) Frequency (Hz) (b) Figure.9 Measured electrical parameters of the fabricated magnetic microinductors with respect to the driving frequency: (a) resistance and (b) inductance. 51

59 The magnetic microdeflector is usually operated at a fast-scanning mode to control the electron beam, thus the dynamic property of the device is critical to its performance. If a step signal is applied to the microinductor which is mainly an LR circuit, the current in the inductor will increase exponentially to a steady state value. To investigate the dynamic property of the fabricated magnetic microdeflector, the transient response of the micromachined solenoid type microinductors was measured and the result is shown in Figure.10. The measured rise time of the microinductor is 5 ns with respect to a 50 ma step signal. Therefore, the hysteresis of the magnetic microdeflector is very small. The fabricated magnetic microdeflector possesses excellent static and dynamic properties. t r rise time t r = 5 ns Figure.10 Measured step response of the fabricated magnetic microinductor..4 Experimental Results and Discussion of the Magnetic Microdeflector The fabricated magnetic microdeflector was assembled in an electron beam microcolumn (EBMC) developed by the CEBT Company for testing. Figure.11(a) shows the structure of the electron beam microcolumn employed in the experiment and the major components of the microcolumn include the electron emission emitter, 5

60 the source lens (extractor, accelerator, and limiting aperture), the octupole stigmator, Einzel lens, and the fabricated magnetic microdeflector. Figure.11(b) shows the photograph of an EBMC assembled with the fabricated magnetic microdeflector. Field emission tip Source lens Electrostatic stigmator Einzel lens Magnetic microdeflector (a) (b) Figure.11 The electron beam microcolumn (EBMC) used for testing: (a) schematic diagram and (b) microphotograph of the EBMC assembled with the fabricated magnetic microdeflector. The electron beam energy used for testing was 80 ev and the emission current was na. The working distance between the microdeflector and a copper grid specimen (400 mesh) was 17 mm. The electron beam deflection was measured by a comparison of the current images of the copper grid specimen. These current images were provided by the CEBT Company. Figure.1(a) shows the current images of the copper grid sample at different driving currents applied to the magnetic microdeflector with a pole-distance of 1.0 mm. As shown in Figure.1(b), the measured electron beam deflection increases linearly to 100 µm when the driving current rises from 0 ma to 50 ma. Figure.13(a) shows the current images of the 53

61 copper grid sample at different driving currents applied to the magnetic microdeflector with a pole-distance of 0.5 mm. As shown in Figure.13(b), the measured electron beam deflection increases linearly to 10 µm when the driving current rises from 0 ma to 50 ma. The measured electron beam deflections for the two microdeflectors are summarized in Figure.14 as well as their simulation results. Considering the resistance of the micromachined coils of the microdeflector is around 1 Ω, the electrical power needed for an electron beam to be deflected at a distance of 10 µm is only about 3 mw for the microdeflector with a pole-distance of 0.5 mm. The developed magnetic microdeflector shows an excellent performance in controlling the electron beam deflection. 0 ma 10 ma 0 ma 30 ma 40 ma 17µm 50 ma (a) (b) Figure.1 Measurement results of the magnetic microdeflector (1.0 mm poledistance) with driving current varying from 0 ma to 50 ma: (a) Current images of the copper grid specimen and (b) electron beam deflection vs. driving current. 54

62 0 ma 10 ma 0 ma 30 ma 40 ma 17µm 50 ma (a) (b) Figure.13 Measurement results of the magnetic microdeflector (0.5 mm poledistance) with driving current varying from 0 ma to 50 ma: (a) Current images of the copper grid specimen and (b) electron beam deflection vs. driving current. Figure.14 Measurement and simulation results of the electron beam deflection of the two magnetic microdeflectors with 0.5 mm and 1.0 mm bore diameters. 55

63 .5 Conclusion A magnetic microdeflector has been designed, fabricated, tested, and characterized for the electron beam deflection/scanning in an electron beam microcolumn. The developed magnetic microdeflector demonstrates excellent performance in controlling the electron beam deflection/scanning in the electron beam microcolumn. Experimental results show that the two developed magnetic microdeflectors with pole distances of 1 mm and 0.5 mm successfully deflect electron beams (80 ev) distances of 100 µm and 10 µm, respectively, under the conditions of a driving current of 50 ma, an electrical power consumption of 3.5 mw, and a working distance of 17 mm. The fabricated magnetic microdeflector possesses excellent dynamic property, as shown by the rise time of 5ns with respect to a 50 ma step signal. In conclusion, the developed magnetic microdeflector has excellent capability of deflecting the electron beam in the electron beam microcolumn system with large scanning linearity and low power consumption. 56

64 CHAPTER 3 MAGNETIC MICROSTIGMATOR FOR ELECTRON BEAM ASTIGMATISM CORRECTION 3.1 Introduction Electron beam astigmatism is a form of aberration that exists in almost all types of electron beam devices, such as the electron microscopes and the electron beam lithography systems. Electron beam astigmatism deteriorates the shape of the electron beam probe and, in turn, degrades the resolution of the electron beam device and deforms the electron micrographs of the objects. As shown in Figure 3.1, when a ray of electron beam passes through an electron lens with different focal lengths at X and Y directions, it will be focused into two lines at right angles to one another, i.e., line image 1 and, at different planes. The separation between the two focus planes is a measure of the degree of astigmatism of the lens. The least confusion plane or infocus plane is located between the line image 1 and planes. A stigmatic circular electron beam, after passing through the lens, forms an astigmatic ellipse image at least confusion plane. The astigmatism of the electron beam emitted from the field emission (FE) microsource of the electron beam microcolumn, as shown in Figure 3., is resulting from several reasons. First, the misalignment among the FE tip, the source lens, and the limiting aperture in the FE microsource unit causes the tilts and shifts of the local 57

65 optical axes. Second, the ellipticity of the source lens and the limiting aperture because of the manufacturing error can cause electron beam astigmatism. Finally, the buildup of dirt on the central bore areas of the limiting aperture and the source lens can result in an asymmetrical electrostatic field and, in turn, caused the electron beam astigmatism. The astigmatism carried by the electron beam emitted from the FE microsource can be corrected by using a multi-pole stigmator [64]. The multi-pole structure can introduce the same type of asymmetry (with the opposite sign) as the axial astigmatism of the original source. By changing the excitations of the different components of the multi-pole fields, the mechanical deficiencies of the axially asymmetrical system can be compensated and the astigmatism can be corrected. Electron lens Circular object x z y Line image 1 Image of least confusion Line image (a) (b) Figure 3.1 Astigmatic electron beam resulting from passing through an electron lens with different focal lengths in X and Y direction: (a) circular beam and (b) elliptical image of least confusion. 58

66 Field emission (FE) tip Extractor, Accelerator, and limiting aperture Field emission source Stigmator Focusing lens Electron beam control X- and Y-deflector Wafer stage Figure 3. Schematic diagram of an electron beam microcolumn. The stigmator can be either electromagnetic or electrostatic in nature. The electrostatic octupole electrodes are exclusively employed as the stigmator in the currently developed microcolumn system. However, as described in Chapter 1, the magnetic stigmator, compared to its electrostatic counterpart, has the advantages of a low-cost fabrication process, the omission of the expensive and complex DRIE process, the simplicity of designing of the magnetic pole shape, and the inherently higher sensitivity and lower aberrations. In this research, an octupole magnetic microstigmator is proposed for astigmatism correction in an electron beam microcolumn system. The proposed magnetic microstigmator consists of eight magnetic poles coupled with solenoid type microinductors. The microinductors are divided into four pairs as shown in Figure 3.3. Each pair of the microinductors is composed of two micromachined solenoid coils and a permalloy (81%Ni/19%Fe) magnetic core. 59

67 Electron Beam Solenoid-type Microinductors (a) (b) Figure 3.3 Schematic diagram of the designed magnetic microstigmator: (a) 3-D view and (b) top view. NiFe magnetic cores The Lorentz force exerted on an electron passing through a magnetic field can be expressed as, F m = qv B, (3.1) where F m is the Lorentz force exerted on the moving electron, q is the charge of the electron ( C), v is the electron velocity, and B is the magnetic flux density. As noted in Equation (3.1), the Lorentz force experienced by the moving electron in a magnetic field depends on both the electron velocity and the magnetic field strength. Compared to a conventional air core microinductor, the NiFe permalloy core microinductor produces a stronger and more directional magnetic field in the central bore area where the electron beam passes through. As shown in Figure 3.4(a), the electron beam experiences a Lorentz force (Equation (3.1)) when it passes through the magnetic field produced by the two magnetic poles coupled with the microinductors. The direction of the force exerted on the passing electron beam can 60

68 be determined by using the right-hand-thumb rule. Assuming the electron beam is directed into the plane of the paper, and the produced magnetic field is from right to left (Figure 3.4(a)), then, the Lorentz force experienced by the electron beam points downward, and the electron beam will be pulled toward the two magnetic poles. Vise versa, if the generated magnetic fluxes point from left to right and the moving direction of the electron beam remains directed into the plane of the paper (Figure 3.4(b)), the Lorentz force exerted on the passing electron beam will push the electron beam away from the magnetic poles. The operational principle of the proposed magnetic microstigmator for correcting the electron beam astigmatism is illustrated in Figure 3.5. When a ray of an electron beam with an elliptical shape passes through the microstigmator with its direction of motion into the plane of the paper (Figure 3.5(a)), the magnetic field produced by the four pairs of the magnetic poles will exert Lorentz forces on the different portions of the electron beam. The direction and strength of the force are determined by the magnetic fields produced by the eight magnetic poles. Because of the Lorentz forces, the electron beam is either expanded or compressed at its different portions. By adjusting the amplitude and the direction of the driving current applied to the microinductors, the elliptical shape of the electron beam can then be corrected accordingly into a round shape as shown in Figure 3.5(b). Therefore, the astigmatism associated with the original electron beam is corrected. 61

69 Lorentz force Electron beam Magnetic flux S N Microinductors N S (a) (b) Figure 3.4 Electron beam passing by a pair of microinductors element: (a) the electron beam pulled toward the element and (b) the electron beam pushed away from the element due to action of the Lorentz force. 6

70 Lorentz force Magnetic flux N N S S Electron beam S N S N (a) N S N S S N S N (b) Figure 3.5 Operational principle of the proposed magnetic microstigmator: (a) uncorrected astigmatic electron beam and (b) corrected circular electron beam. 3. Design and Simulation of the Magnetic Microstigmator In this research, an octupole magnetic microstigmator is proposed for electron beam astigmatism correction in an electron beam microcolumn. The proposed magnetic microstigmator consists of eight magnetic poles coupled with the micromachined solenoid-type microinductors. The eight magnetic poles are divided into four pairs as shown in Figure 3.3. Each microinductor is composed of a 63

71 micromachined solenoid coil and a permalloy (81%Ni/19%Fe) magnetic core. To investigate the magnetic field distribution produced by the proposed magnetic microstigmator, a simulation based on a 3-D magnetic microstigmator model (Figure 3.6(a)) was performed using MagNet software (INFOLYTICA Corporation). In the simulation, the central bore area has a diameter of 1 mm, and the electron beam is moving along the Z direction. Figure 3.6(b) and (c) show the produced magnetic field distributions when driving currents of 50 ma and 400 ma were applied to the microinductors of the magnetic microstigmator. It is noted from the simulation results that the NiFe magnetic poles started reaching saturation when a driving current of 400 ma was applied to the coupled microinductors. During the astigmatism correction, it is usually demanded that the magnetic core is not saturated. Figure 3.7 presents the simulation results of the magnetic field distribution within the central bore area when a driving current of 50 ma is applied to the microinductors of the magnetic microstigmator. Figure 3.7(a) shows the vector plot of the B field distribution at the plane where the microstigmator is placed, i.e., the XY plane (Z=0). The vector plot clearly indicates that a quadrupole magnetic field is produced by the eight magnetic poles. Figure 3.7(b) is the contour plot of the B field distribution at the XY plane (Z=0) and it shows that a group of concentric contour circles of the B field distribution is produced by the eight magnetic poles. The group of concentric contour circles (Figure 3.7(b)) indicates that the magnetic field B has an axially symmetrical distribution within the central bore area of the magnetic microstigmator. The bore diameter of the magnetic microstigmator is 1 mm. 64

72 Micromachined coils NiFe permalloy core (a) (b) (c) Figure 3.6 (a) 3-D model of the proposed magnetic microstigmator with a bore diameter of 1 mm and B field distributions of the microstigmator with a driving current of (b) 50 ma and (c) 400 ma. 65

73 66 (a) (b) Figure 3.7 (a) Vector plot of the B field and (b) contour plot of the B field distribution at XY plane (Z=0) around the poles of the microstigmator (I=50mA). X Y N N N N S S S S X Y N N N N S S S S

74 300 ma 00 ma 100 ma 50 ma (a) 5 µm 10 µm 15 µm 0 µm (b) Figure 3.8 Simulation results: (a) B field distribution along the radial direction (Z=0) with driving currents varying from 50 ma to 300 ma, and (b) B field distribution along the Z axis at different radial locations with a driving current of 50 ma. 67

75 Based on the operational principle of the magnetic microstigmator, the magnetic field B is the main factor influencing the motion of a passing electron beam. Figure 3.8(a) shows the simulation results of the B field distribution along the radial direction (r) with the driving current varying from 50 ma to 300 ma. The simulation results of the B field distributions along the Z direction, i.e. the electron beam moving direction, at different radial locations with a driving current of 50 ma are shown in Figure 3.8(b). Although, the designed magnetic microstigmator has a thickness of approximately 100 µm, the influential region of the magnetic field, as shown in Figure 3.8(b), spans from Z= µm to Z= µm in the space when the microstigmator is set at Z=0. Therefore, the motion of the electron is affected by the stray magnetic field before the electron arrives at the location of the microstigmator, and the motion remains affected by the field after the electron leaves the microstigmator. By decreasing the bore diameter, the stray magnetic flux will be reduced and the magnetic field can be better confined within the central bore area. Based on the operational principle of the designed magnetic microstigmator, the eight magnetic poles produce a quadrupole magnetic field within the central bore area as shown in Figure 3.9. When an astigmatic electron beam passes through the stigmator, the magnetic field will exert Lorentz forces on the different portions of the electron beam. The directions and strengths of the Lorentz forces are determined by the produced magnetic fields. For example, as shown in Figure 3.9, when the electron beam moves along the Z direction that is directed into the plane of the paper, the electrons located on the X axis will experience Lorentz forces along the X direction, 68

76 and the electrons on the Y axis will experience Lorentz forces along the Y direction. The electrons on the two diagonals will experience Lorentz forces in the direction normal to the diagonals in the XY plane. With those Lorentz forces, the elliptically shaped electron beam will be tuned into a round shape as shown in Figure 3.9, and thus the astigmatism associated with the original electron beam is corrected. y x a b r Magnetic field Astigmatic elliptical Stigmatic round electron beam electron beam Lorentz force direction Figure 3.9 Schematic diagram of the astigmatism correction of an elliptical electron beam passing through the magnetic field produced by the microstigmator. 69

77 70 The electron trajectory equation (.10) derived in Chapter is rewritten here, = = z y x y z x B B dz dy dz dx B dz dy dz dy dz dx c v v m q dz y d B dz dx B B dz dx dz dy dz dy dz dx c v v m q dz x d 1/ 0 1/ (3.) By solving Equation (3.), one can obtain the trajectory of the electron moving along the z axis: x(z) and y(z). To investigate the electron trace in the quadrupole field generated by the magnetic microstigmator, Equation (3.) was solved using the numerical computation software Mathematica (Wolfram Research, Inc). The magnetic field distribution was extracted from the finite element simulation results obtained by the MagNet software (INFOLYTICA Corporation). Figure 3.10 presents the simulation results of the traces of the electrons at different locations within the central bore area of the magnetic microstigmator as indicated in Figure 3.9. Figure 3.10(a) depicts the traces of the electrons on the X axis with initial locations of X = µm, 4 µm, 6 µm, 8 µm, and 10 µm. Figure 3.10(b) plots the traces of the electrons on the Y axis with initial locations of Y = µm, 4 µm, 6 µm, 8 µm, and 10 µm. Figure 3.11 shows the simulation results of the astigmatism correction of an elliptical electron beam for the magnetic microstigmator with a bore diameter of 1 mm. The semimajor and semiminor axes of the original elliptical electron beam are set as 10 µm and 8 µm, respectively, and the driving current is 50 ma.

78 (a) (b) Figure 3.10 Simulation results of the traces of the electrons at different radial locations: (a) electrons on the X axis and (b) electrons on the Y axis. Initial Beam Corrected Beam (a) (b) Figure 3.11 Simulation results of the astigmatism correction of an elliptical electron beam with a semimajor axis of 10 µm and a semiminor axis of 8 µm: (a) the schematic and (b) top view. Suppose the magnetic microstigmator is set at Z=0, and the electron beam moves along the Z axis. Also assume the semimajor axis of the elliptical electron beam is located on the Y-axis and the semiminor axis is on the X axis as illustrated in Figure 3.9. When this electron beam passes through the microstigmator, the elliptical shape will be corrected into a round shape due to the Lorentz forces acting on it. The stigmatic point is defined as the position where the semimajor axis of the elliptical electron beam becomes equal to its semiminor axis. Figure 3.1(a) and (b) show the 71

79 simulation results of the variation of the stigmatic points corresponding to the different driving currents applied to the two magnetic microstigmators with bore diameters of 1 mm and 0.5 mm, respectively. The initial electron beam is assumed to have an elliptical shape with a semimajor axis of 10 µm and a semiminor axis of 8 µm. Figure 3.13 plots the relationship between the stigmatic point and the driving current applied to the magnetic microstigmators. It is noted that the stigmatic point decreases with the driving current applied to the microstigmator. This is because the magnetic field required for correcting the astigmatism within the central bore area becomes stronger with the increase of the applied driving current. Figure 3.13 also shows that the microstigmator with a smaller bore diameter is more efficient in the correction of the astigmatism. This is because, with a smaller bore diameter, more magnetic flux is confined within the central bore area with the same driving current applied. Therefore, a larger Lorentz force is generated to correct the astigmatism of the electron beam. 300 ma 00 ma 100 ma D=1mm 300 ma 00 ma 100 ma D=0.5mm 50 ma Semimajor axis Semiminor axis 50 ma Semimajor axis Semiminor axis (a) (b) Figure 3.1 Simulation results of the variation of the stigmatic points with driving current varying from 50 ma to 300 ma: magnetic microstigmators with bore diameters of (a) D=1 mm and (b) D=0.5mm. 7

80 Figure 3.13 Stigmatic point vs. driving current applied to the two microstigmators with bore diameters of 1 mm and 0.5 mm, respectively. 3.3 Fabrication of the Magnetic Microstigmator Figure 3.14 illustrates the brief fabrication procedures of the designed magnetic microstigmator. Pleases see Appendix A for more detailed information. During the fabrication, a -inch <100> silicon wafer oxidized on both sides was used as the substrate (Figure 3.14(a)). First, the -inch silicon wafer was anisotropically etched on the backside using a KOH solution. The wet etching continued until the remaining silicon membrane thickness reached about 0 µm (Figure 3.14(b)). The bottom conductor lines (Cu) of the inductor coil were electroplated on the front side of the substrate wafer (Figure 3.14(c)). The NiFe permalloy core was then fabricated using the electroplating method with a layer of AZ photoresist working as an isolation layer (Figure 3.14(d)). Then, the top conductor lines of the solenoid-type inductors were fabricated (Figure 3.14(e)). The remaining silicon membrane, together with the silicon oxide layer, was then dry-etched using RIE (reactive ion etching) (Figure 3.14(f)). 73

81 (a) (d) (b) (e) (c) (f) Figure 3.14 The fabrication steps for the magnetic microstigmator. 1 cm 1 cm 1 cm 1 cm 00 µm 00 µm Micromachined coil Magnetic pole Through-hole in the substrate (a) (b) Figure 3.15 Microphotographs of the fabricated magnetic microstigmators with bore diameters of (a) 1 mm and (b) 0.5 mm. Microphotographs of the fabricated magnetic microstigmators with bore diameters of 1.0 mm and 0.5 mm are shown in Figure 3.15 (a) and (b), respectively. The size of the diced chip is 1 cm x 1 cm. The measured resistance of one pair of the micromachined solenoid type coils is around 1 Ω. 74

82 3.4 Experimental Results and Discussion of the Magnetic Microstigmator The fabricated magnetic microstigmator was assembled in an electron beam microcolumn (EBMC) developed by CEBT Company for testing. Figure 3.16(a) shows the structure of the microcolumn used in the experiment. Major components of the EBMC include the electron emitter, the source lens (extractor, accelerator, and limiting aperture), the electrostatic octupole, the Einzel focusing lens, and the fabricated magnetic microstigmator. Figure 3.16(b) shows a photograph of the microcolumn assembled with the fabricated magnetic microstigmator. Field emission tip Source lens Electrostatic Octupole Einzel lens Magnetic microstigmator (a) (b) Figure 3.16 Electron beam microcolumn (EBMC): (a) schematic diagram and (b) microphotograph of EBMC assembled with the fabricated magnetic microstigmator. Microcolumn Magnetic microstigmator Copper grid (400 mesh) Phosphor screen 1.5 mm 36 mm Figure 3.17 Experimental setup for testing the fabricated magnetic microstigmator. 75

83 The major function of the stigmator is to adjust the shape of the electron beam probe and, in turn, to correct the astigmatism of the electron beam. To observe the shape variation of the electron beam probe which is controlled by the fabricated magnetic microstigmator when the electron beam passes through the EBMC, a copper grid specimen (400 mesh) and a Phosphor screen were assembled with the microcolumn as shown in Figure The working distance between the Phosphor screen and the magnetic microstigmator is ~37.5 mm. The electron beam energy used for testing was 00 ev and the magnitude of the emission current was around 400 na. The working distance between the magnetic microstigmator and the specimen (400 mesh copper grid) was ~1.5 mm. The Phosphor screen images of the electron beam probe obtained by the CEBT Company are shown in Figure Figure 3.18(a) shows the electron beam probe image when no driving current was applied to the magnetic microstigmator with a bore diameter of 1.0 mm. When a driving current of 50 ma was applied to the microinductor pairs 1 and 3, a compressive Lorentz force was produced and exerted on the passing electron beam probe. The original electron beam probe was thus compressed along the directions of the microinductor pairs 1 and 3, as shown in Figure 3.18(b). When the driving current was switched to the microinductor pairs and 4, the electron beam probe was then compressed along the directions of pairs and 4 as shown in Figure 3.18(c). When the driving current of 50 ma was applied to all the four pairs of the microinductors, the passing electron beam probe experienced compressive Lorentz 76

84 forces from all directions. Therefore, as shown in Figure 3.18(d), the electron beam probe maintained its original circular shape Lorentz force 1 (a) 4 3 (b) (c) (d) Figure 3.18 Phosphor screen image of the electron beam probe: (a) no driving current applied to the magnetic microstigmator; 50 ma driving current applied to (b) the pairs of 1 and 3; (c) the pairs of and 4; and (d) all four pairs of the microinductors. 77

85 0 ma Grid image Deviation Angle 100 ma D = 1 mm 00 ma 300 ma (a) (b) Figure 3.19 (a) Current images of the copper grid specimen and (b) variation of the deviation angle of the copper grid image for magnetic microstigmator with a bore diameter of D = 1 mm and the driving current varying from 0 to 300 ma. Figure 3.19(a) shows the current images of the copper grid sample with different driving currents applied to the magnetic microstigmator with a bore diameter of 1 mm. These current images were obtained by the CEBT Company. As shown in Figure 3.19(b), the deviation angle of the copper grid sample gradually decreases when the driving current increases from 0 ma to 300 ma. After the driving current reaches 300 ma, the copper grid current image was corrected into a quasi-square shape, which means that nearly all of the initial astigmatism of the electron beam has been corrected by using the developed magnetic microstigmator. Figure 3.0(a) shows 78

86 the current images of the copper grid sample with different driving currents applied to the magnetic microstigmator with a bore diameter of 0.5 mm. As shown in Figure 3.0(b), the deviation angle of the copper grid sample gradually decreases when the driving current increases from 0 ma to 300 ma. After the driving current reaches 300 ma, the copper grid current image was corrected into a square shape with right angles, which means that the initial astigmatism of the electron beam was corrected by using the developed magnetic microstigmator. 0 ma Grid image Deviation Angle 100 ma D=0.5 mm 00 ma 300 ma (a) (b) Figure 3.0 (a) Current images of the copper grid specimen and (b) variation of the deviation angle of the copper grid image for the magnetic microstigmator with a bore diameter of D = 0.5 mm and the driving current varying from 0 to 300 ma. 79

87 Figure 3.1 shows the variation of the measured deviation angle and the calculated stigmatic point with different driving currents applied to the magnetic microstigmators with bore diameters of 1.0 mm and 0.5 mm, respectively. The deviation angles of the square copper grid for the microstigmator with 1.0 mm bore diameter decreases from 9 o to 1 o with an increase of the driving current from 50 ma to 300 ma, while for the microstigmator with 0.5 mm bore diameter the deviation angles decrease from 8 o to 0. o with an increase of the driving current from 50 ma to 300 ma. Considering the total resistance of the eight microinductors is around 4 Ω, the electrical power needed to correct the electron beam of 00 ev is only ~0.4 W. As defined previously, the stigmatic point is the position where the astigmatism is corrected. The stigmatic points shown in Figure 3.1 were extracted from the simulation results presented in Figure As shown in Figure 3.1, both the measured deviation angle and the calculated stigmatic point decrease with the driving current, which means the larger the driving current, the better the astigmatism correction is. It is also noted that the trend of the decrease of the measured deviation angle with an increase of the driving current is similar to that of the calculated stigmatic point decreasing with the driving current. This is because the deviation angles of the copper grid image are resulting from the elliptical shape of the electron beam probe that produced the current images of the copper grid. When the astigmatism or the elliptical electron beam is corrected by the microstigmator, the deviation angle of the current images is accordingly reduced. 80

88 Measured Deviation Angle: D=1 mm D=0.5 mm Calculated Stigmatic Point: D=1 mm D=0.5 mm Figure 3.1 Measured deviation angles of the copper grid image and the simulation results of the stigmatic points varying with driving currents applied to the magnetic microstigmators with bore diameters of 1.0 mm and 0.5 mm. 3.5 Conclusion A novel magnetic microstigmator was designed, fabricated, tested, and characterized for the electron beam astigmatism correction in the electron beam microcolumn. Experimental results show that, with a driving current of ~ 300 ma and a low electrical power consumption of 0.4 W, the astigmatism of the electron beam (00 ev) can be effectively corrected by the two fabricated magnetic microstigmators with bore diameters of 1 mm and 0.5 mm, respectively. The experimental results demonstrate that the developed magnetic microstigmator has excellent capability of correcting the electron beam astigmatism with low power consumption in the electron beam microcolumn. 81

89 CHAPTER 4 MAGNETIC MICROLENS FOR ELECTRON BEAM FOCUSING 4.1 Introduction The function of the lens in the electron beam microcolumn is to focus a divergent ray of electron beam emitted from the electron cathode or field emission tip. The lens can be defined as a device, either electrostatic or magnetic, that produces an axially symmetrical field distribution in the space. Due to the simplicity and compactness, the electrostatic Einzel lens is exclusively employed for electron beam focusing in the current electron beam microcolumn [73-83]. However, the fabrication of the electrostatic Einzel lens needs a multi-layer anodic bonding process, which makes the three-electrode alignment extremely difficult. Electrical breakdown is another concern for the electrostatic electron beam control devices, especially when the device size is further scaled down. Finally, the possibility of particle accumulation on the electrode surface can greatly deteriorate the performance of the device. Therefore, in this research, a magnetic microlens is proposed for electron beam focusing in an electron beam microcolumn. The proposed magnetic microlens will be fabricated using low-cost MEMS technology. 8

90 Solenoid coil r Electron trajectory Z (a) H Axially symmetrical magnetic field H Z H r Z (b) Figure 4.1 (a) Trajectory of the electron in an axially symmetrical magnetic field and (b) magnetic field strength along the off-axis flux line. Figure 4.1 illustrates the working principle of a magnetic lens. An axially symmetrical magnetic field generated by a typical solenoid coil is shown in Figure 4.1(a). The off-axis magnetic flux lines, which are not on the central axis (Z-axis) of the solenoid coil, possess not only the axial magnetic field component (H z ) but also the radial component (H r ). The relative magnetic field strength of such off-axis flux lines is plotted in Figure 4.1(b). The axial component of the magnetic field (H z ) reaches its highest value in the middle of the solenoid coil. The variation of the radial 83

91 component of the magnetic field (H r ) is more complicated. First, the H r reaches a peak value close to the left end of the coil. Then, the H r gradually decreases and reaches zero in the middle of the coil. After that, the amplitude of H r increases again, but in an opposite direction and it reaches another peak value near the right end of the coil. Finally, the H r gradually vanishes at a very distant point. When an off-axis electron moves parallel to the Z-axis of the axially symmetrical field from the left, the axial field component (H z ) initially has no effect on the electron since the movement of the electron is parallel to the Z-axis. However, the electron will be subjected to the Lorentz force resulting from the radial field component (H r ). The Lorentz force exerted on an electron passing through the magnetic field can be expressed as Equation (.1). The Lorentz force will force the electron to move in the azimuthal direction of the axially symmetrical field. This azimuthal motion of the electron, combined with its axial motion, makes the electron move in a helical (spiral) path inside the lens field (Figure 4.1(a)). Once the electron obtains an azimuthal velocity, it is no longer moving parallel to the Z-axis and, in turn, H z will exert the Lorentz force on the electron. This Lorentz force will pull the electron toward the central Z-axis. When the electron passes through the middle line of the magnetic lens, the direction of H r is reversed. In turn, the electron will be accelerated in the opposite azimuthal direction, which counters the azimuthal motion of the electron imposed by the H r from the left part of the magnetic lens. As a result, the motion of the electron resumes its original direction parallel to the Z-axis when leaving the field of the magnetic lens as shown in Figure 4.1(a). 84

92 Electron beam Micromachined spiral coil NiFe shell Substrate (a) Electron Beam NiFe shell Substrate Spiral coil (b) Figure 4. Schematic diagram of the designed magnetic microlens: (a) 3D view and (b) cross sectional view. In this research, a magnetic microlens is proposed for the electron beam focusing in the electron beam microcolumn. The proposed magnetic microlens is composed of three micromachined spiral coils (Figure 4.). The three micromachined planar spiral coils are vertically stacked together. These coils are capsulated by the NiFe permalloy magnetic shell in order to reduce the magnetic flux leakage in the space and to confine the magnetic fluxes within the central bore area. 85

93 NiFe shell S S S N N Axially symmetrical field N (a) Spiral coil Electron beam Electron trace Axially symmetrical field Spiral coil (b) Figure 4.3 Operational principle of the proposed magnetic microlens: (a) axially symmetrical magnetic field produced within the central bore area; (b) electron beam focused by the lens field. 86

94 The operational principle of the proposed magnetic microlens is illustrated in Figure 4.3. A DC driving current is applied to the group of the three micromachined planar spiral coils wrapped by the top and bottom NiFe permalloy shells. An axially symmetrical magnetic field is then produced within the central bore area as shown in Figure 4.3(a). Because of the NiFe permalloy shells, most of the generated magnetic fluxes will be confined within the central bore area, and this strengthens the magnetic field at the center of the microlens. When a divergent ray of electron beam passes through the central bore area of the magnetic microlens, the electrons of the electron beam will have tapering helical trajectories due to the Lorentz force exerted on them and in turn the electron beam can be focused by the axially symmetrical magnetic field as shown in Figure 4.3(b). The proposed magnetic microlens, therefore, realizes the focusing of the passing electron beam. 4. Design and Simulation of the Magnetic Microlens In this research, a magnetic microlens is proposed for the electron beam focusing in an electron beam microcolumn. The proposed magnetic microlens is composed of three micromachined spiral coils (Figure 4.). The three micromachined planar spiral coils are vertically stacked together. These coils are capsulated by the NiFe permalloy magnetic shell in order to reduce the magnetic flux leakage and confine the magnetic fluxes within the central bore area. The electron trajectory equation (Equation (.10)) stated in Chapter in the Cartesian coordinate system is rewritten here for convenience, 87

95 = = z y x y z x B B dz dy dz dx B dz dy dz dy dz dx c v v m q dz y d B dz dx B B dz dx dz dy dz dy dz dx c v v m q dz x d 1/ 0 1/ (4.1) However, in the case of the magnetic microlens, we need to deal with an axially symmetrical magnetic field and a spiral shape electron trajectory. Therefore, an electron trajectory equation in the cylindrical coordinate system is more favorable here. In the cylindrical system, the coordinates r, θ, and z are defined through the Cartesian ones as: x=r cosθ, y=r sinθ, and z=z. Substituting x, y, and z into Equation (4.1), the electron trajectory equation in the cylindrical coordinate system can be written as = = z r z r B dz dr B dz d r dz d r dz dr c v m v q dz d dz dr dz d r B B dz dr dz d r dz d r dz dr c v m v q dz d r dz r d 1/ 0 1/ θ θ θ θ θ θ θ (4.) To investigate the magnetic field distribution produced by the magnetic microlens, a 3-D magnetic microlens model (Figure 4.4(a)) was built for finite element simulation using MagNet software (INFOLYTICA Corporation). The B field distribution produced by a driving current of 50mA applied to the spiral coils of a magnetic microlens with a bore diameter of 00 µm is shown in Figure 4.4(b). Each of the three spiral coils has 30 turns.

96 NiFe shell Planar spiral coil (a) Figure 4.4 (a) 3-D model of the proposed magnetic microlens and (b) magnetic field (B) distribution of the microlens with a driving current of 50 ma. (b) Figure 4.5 shows the simulation results of the B field distribution within the central bore area of the magnetic microlens. A driving current of 50 ma was applied to all the three planar spiral coils of the magnetic microlens and the length of the 89

97 microlens is L=00 µm. Figure 4.5(a) shows the vector plot of the B field distribution at the plane where the top NiFe shell is located (Z=L/). The vector plot clearly indicates that an axially symmetrical magnetic field is produced by the three planar spiral coils of the microlens. Figure 4.5(b) shows the contour plot of the B field distribution within the central bore area at the plane of Z=L/, and the concentric contour circles of the B field distribution illustrate an axially symmetrical magnetic field distribution produced by the planar spiral coils. Figure 4.5(c) shows the contour plot of the B field distribution within the central bore area of the microlens at the middle plane of the microlens, i.e., Z=0. Following the operational principle illustrated in Figure 4.3, the axially symmetrical magnetic field produced by the magnetic microlens can accomplish the focusing of a ray of divergent electron beam when it passes through the microlens. Figure 4.6 shows the simulation results of the B field distribution along the axial direction of the microlens at the sagittal plane of the microlens. A driving current of 50 ma was applied to the three planar spiral coils of the magnetic microlens in the simulation. Figure 4.6(a) is the vector plot of the B field distribution and it clearly shows that the magnetic fluxes off the central Z-axis, i.e., r>0, have the magnetic field components in both the axial direction (B z ) and radial direction (B r ). Figure 4.6(b) is the contour plot of the B field distribution along the axial direction of the magnetic microlens. 90

98 z=l/ z=0 z=-l/ Top shell z r Bottom shell (a) z=l/ z=0 z=-l/ Top shell z r Bottom shell (b) z=l/ z=0 z=-l/ Top shell z r Bottom shell (c) Figure 4.5 Simulation results of the magnetic microlens with a driving current of 50 ma: (a) vector plot of the magnetic field B; the contour plot of B field at planes of (b) Z=L/ =100 µm and (c) Z=0 within the aperture of the magnetic microlens. 91

99 Lens diameter Top shell z r Lens length (a) Bottom Shell Lens diameter Top shell E-Beam Lens length Bottom Shell (b) Figure 4.6 Simulation results of the magnetic field distribution along the axial direction of the magnetic microlens with a driving current of 50 ma: (a) vector plot and (b) contour plot. Figure 4.7 shows the simulation results of the magnetic field components, B z and B r, at r = 10 µm along the Z direction. As shown in Figure 4.7(a), the axial component of the magnetic field (B z ) reaches its highest value at the middle plane (Z=0) of the microlens. The variation of the radial component of the magnetic field (B r ) at r = 10 µm is plotted in Figure 4.7(b). It is noted that the amplitude of the B r field is approximately one to two orders smaller than that of the B z field. 9

100 r = 10 µm (a) r = 10 µm (b) Figure 4.7 Magnetic field (B) variation along the axial Z-direction of the magnetic microlens (r = 10 µm and I = 50 ma): (a) B z and (b) B r. To obtain a strong electron beam focusing effect, the magnetic field or the magnetic energy should be confined within a small range of area and the maximum magnitude of the B z field (B zmax =B z at z=0) should be made as large as possible. There are three main parameters affecting the amplitude of the B zmax : (1) the microlens length L, () the microlens diameter D (or aperture), and (3) the driving current I. 93

101 Figure 4.8 shows the relationship between the B zmax and the length of the microlens with different lens diameters of 00 µm, 300 µm, and 400 µm. The B zmax initially increases with the lens length. After reaching a peak value, the amplitude of B zmax drops off with increasing of the lens length. It is noted that the B zmax usually reaches its maximum value at the lens length that is equal to the lens bore diameter. This is a very important and useful result for designing the magnetic microlens. Thereafter, the simulation results are obtained from the microlenses having equal diameter (D) and length (L), i.e. D=L. Figure 4.8 B zmax vs. lens length with lens diameter of 00 µm, 300 µm, and 400 µm. (driving current I = 50 ma). In addition to the lens diameter and the lens length, another important parameter largely affecting the amplitude of B zmax is the driving current. The relationship between the driving current and the amplitude of B zmax at different lens diameters is shown in Figure 4.9. It is noted that B zmax increases linearly with the driving current. Moreover, the smaller the lens diameter, the larger the B zmax is. 94

102 Figure 4.9 B zmax vs. driving current with different lens diameters (D). To calculate the electron trajectory in the magnetic field generated by the magnetic microlens, the numerical simulation software MATHEMATICA was used to solve for the electron trajectory differential equation (4.). The magnetic field distributions were obtained from the previous 3D finite element simulation using MagNet software (INFOLYTICA Corporation). Figure 4.10 plots the electron trajectories, i.e., radial displacement (r) and the corresponding azimuthal angle (Θ) of the electrons at energy levels of 100 ev, 300 ev, and 500 ev. The original radial coordinate of the electrons is 10 µm. The plot shows that the higher the energy of the electron is, the longer the focal length (f) of the magnetic microlens will be. It is also noted that, although the higher energy electron beam has a longer focal length, its focused probe size is smaller than that of the lower energy electron beam. 95

103 r 0 = 10 µm 500 ev 300 ev 100 ev f r mi 500 ev 300 ev 100 ev Figure 4.10 Trajectories of the electrons at different energy levels (Lens diameter D= 00 µm and B zmax = 50 mt). 500 ev 300 ev 100 ev 500 ev 300 ev 100 ev Figure 4.11 Simulation results of the focal length and demagnification percentage ratio of the magnetic microlens with a lens diameter of 00 µm at different electron energy levels. 96

104 Figure 4.11 plots the simulation results of the focal length and the demagnification percentage ratio of the electron beam versus the magnetic field (B zmax ) at different energy levels. The demagnification percentage ratio is defined as follows, rmin DM = 100% (4.3) r 0 where, as shown in Figure 4.10, r 0 is the initial radial distance of the electron and r min is the minimum radial distance the electron obtains. The magnetic microlens used for simulation has a lens diameter of 00 µm. The simulation results show that the focal length decreases with the amplitude of the B zmax, while the demagnification percentage ratio increases with the B zmax. It is also noted that, similar to the results shown in Figure 4.10, the higher energy electron beam has a longer focal length but a smaller demagnification ratio. 4.3 Fabrication of the Magnetic Microlens The designed magnetic microlens was fabricated using MEMS technology. Figure 4.1 illustrates the brief fabrication procedures of the designed magnetic microlens. Pleases see Appendix B for more detailed information. During the fabrication, a -inch <100> silicon wafer oxidized on both sides was used as the substrate (Figure 4.1(a)). First, the -inch silicon wafer was anisotropically etched on the backside using KOH solution. The wet etching continued until the remaining silicon membrane thickness reached about 0 µm (Figure 4.1(b)). The bottom NiFe layer was electroplated on the front side of the substrate wafer (Figure 4.1(c)). The first spiral planar coil was then fabricated using the electroplating method with a layer 97

105 of AZ photoresist working as an isolation layer (Figure 4.1(d)). Then, the second and third spiral planar coils were fabricated in sequence (Figure 4.1(e) and Figure 4.1(f)). After that, the top NiFe shell was electroplated (Figure 4.1(g)). Finally, the remaining silicon membrane, together with the silicon oxide layer, was dry-etched by using RIE (reactive ion etching) (Figure 4.1(h)). (a) (e) (b) (f) (c) (g) (d) (h) SiO Si NiFe Cu Photoresist Figure 4.1 Schematic diagram of the fabrication steps for the magnetic microlens. Figure 4.13 shows a microphotograph of a fabricated spiral coil with 30 turns. After fabrication, the silicon wafer was diced into chips. Figure 4.14 shows the microphotographs of the diced microlens chip with a size of 1 cm x 1 cm. The fabricated magnetic microlens has a bore diameter of 00 µm and the measured coil resistance is ~50 Ω. 98

106 00 µm Figure 4.13 Microphotograph of a micromachined planar spiral coil. Spiral coil pad 50 µm NiFe Shell NiFe Shell 1 cm 00 µm Through hole 1 cm Figure 4.14 Microphotographs of the fabricated magnetic microlens. 4.4 Experimental Results and Discussion of the Magnetic Microlens The fabricated magnetic microlens was assembled in an electron beam microcolumn (EBMC) that was developed by CEBT Company for testing. Figure 4.15(a) shows the structure of the microcolumn used in the experiment. Major components of the EBMC include the electron emission emitter, the source lens (extractor, accelerator, and limiting aperture), the electrostatic octupole, the electrostatic Einzel lens, and the fabricated magnetic microlens. Figure 4.15(b) shows a photograph of the microcolumn assembled with the fabricated magnetic microlens. 99

107 Field emission tip Source lens Electrostatic Octupole Einzel lens Magnetic Microlens (a) (b) Figure 4.15 Electron beam microcolumn (EBMC): (a) schematic diagram and (b) microphotograph of EBMC assembled with the fabricated magnetic microlens. The microlens is used to focus the electron beam in the electron beam microcolumn. To observe the focusing effect of the developed magnetic microlens, a copper grid specimen (400 mesh) was assembled to the microcolumn as shown in Figure The working distance between the copper grid and the magnetic microlens is ~1.5 mm. Microcolumn Magnetic microlens Copper grid (400 mesh) 1.5 mm Figure 4.16 Experimental setup for testing the fabricated magnetic microlens. 100

108 I = 0 ma I = 50 ma (a) I = 100 ma (b) I = 150 ma (c) (d) Figure 4.17 Measured current images of the copper grid with different driving currents applied to the fabricated magnetic microlens. The electron beam energy used for testing was1 kev and the magnitude of the emission current was around 0 na. Figure 4.17 shows the current images of the copper grid samples with the lens driving current varying from 0 ma to 150 ma. These current images were measured by the CEBT Company. It is noted that, when no driving current is applied to the microlens (I = 0 ma), the copper grid image is severely out of focus, and the edge of the square grid is difficult to discern. This blur is caused by the divergent electron beam probe passing through the copper grid edge. With an increase of the lens driving current from 0 ma to 150 ma, the edges of the square grid become more and more discernible. It is noted that, when the driving current reaches 150 ma, the current image shows a much sharper contrast at the edge 101

109 of the square grid than that with no driving current applied to the magnetic microlens. This sharp contrast at the grid edge is resulting from the focusing of the electron beam probe passing through the copper grid. The experimental results clearly show that the developed magnetic microlens can effectively focus the electron beam of 1 kev with a driving current of 150 ma. 4.5 Conclusion A novel magnetic microlens has been designed, theoretically analyzed, fabricated, and tested for the electron beam focusing in an electron beam microcolumn system. First, the principle of the magnetic microlens was introduced. Then, the design criteria for the magnetic microlens were investigated and a detailed design of the magnetic microlens was described. After that, the detailed fabrication procedure of the microlens was described. Finally, the fabricated microlens assembled in a microcolumn was tested. The experimental results clearly show that, with a driving current of 150 ma, the developed magnetic microlens can effectively focus an electron beam of 1 kev. 10

110 CHAPTER 5 MINIATURIZED MAGNETIC ELECTRON BEAM CONTROL SYSTEM 5.1 Introduction All of the currently developed electron beam microcolumns employ an electrostatic electron beam control system that mainly includes the electrostatic octupole working as both stigmator and deflector, and an electrostatic Einzel lens for the electron beam focusing, as shown in Figure 5.1. Electron beam source Electrostatic octupole stigmator/deflector Electrostatic Einzel lens Electron beam control Figure 5.1 Schematic diagram of an electrostatic electron beam microcolumn. The advantages of the electrostatic electron beam control devices are the simplicity and compactness of the device structure. However, there are also obvious disadvantages of using these electrostatic e-beam control devices. First, the fabrication of an electrostatic octupole requires an expensive deep RIE process to etch through a silicon substrate wafer with a thickness of around 300 µm. Other challenges in the fabrication process include obtaining electrode surface with acceptable aspect 103

111 ratio, smoothness, and roundness of the electrode surface. Second, the multilayer anodic bonding process required for the Einzel lens fabrication makes the threeelectrode alignment an extremely difficult task. Third, the electrical breakdown is a major concern for all the electrostatic electron beam control devices. The electrical breakdown limit in the vacuum is about 10 kv/mm. At present, the Einzel lens focusing voltage is several hundreds volts. With the device size further scaled down, the electric breakdown problem will become more serious. Finally, the possible particle accumulation on the electrode surface can greatly deteriorate the performance of the device. Magnetic Microcolumn Magnetic microstigmator Magnetic microlens Magnetic microdeflector Figure 5. Schematic diagram of the electron beam microcolumn with magnetic electron beam control devices. To solve the problems associated with the electrostatic electron beam control system which is employed in the currently developed electron beam microcolumns, this research proposes a miniaturized magnetic electron beam control system to be used in the electron beam microcolumn. As shown in Figure 5., the proposed system 104

112 consists of the magnetic microdeflector, magnetic microstigmator, and magnetic microlens. The advantages of the proposed magnetic electron beam control devices are: (1) no complicated multilayer anodic bonding is needed; () low-cost electroplating method replaces the high-cost deep RIE process; (3) the magnetic pole shape can be easily designed and fabricated; (4) no expensive high-voltage source is needed as in the electrostatic microcolumn ; (5) there is no electrical breakdown concern when the device size is further scaled down; and (6) compared to their electrostatic counterparts, magnetic electron beam control devices inherently have higher sensitivity and smaller aberrations. B Electron beam Stigmator Lens (a) Deflector z B Electron beam Stigmator Lens Deflector z (b) Figure 5.3 (a) No magnetic field interference and (b) magnetic field interference among the three magnetic electron beam control devices. 105

113 The miniaturized magnetic electron beam control system is composed of three micromachined magnetic devices: the magnetic microstigmator to correct the electron beam astigmatism, the magnetic microlens to focus the electron beam, and the magnetic microdeflector to deflect/scan the electron beam across the substrate wafer. The three devices employ the magnetic field to control the electron beam motion by using the Lorentz force, which, when exerted on an electron passing through a magnetic field, can be expressed as Equation (.1). To construct the magnetic electron beam control system, the three developed magnetic devices are stacked together (Figure 5.) and assembled in the electron beam microcolumn. Because of the limited space of the electron beam microcolumn, the three magnetic devices are required to be assembled as close to each other as possible. However, as described in the previous chapters, the magnetic field generated by each of the three devices spans a certain range along the axial Z direction. As shown in Figure 5.3 (a), if the three devices are separated far enough, then the magnetic field produced by each individual device will not be able to interfere with one another. Nevertheless, when the three devices are set too close to each other, magnetic field interference will be produced among the three magnetic devices as shown in Figure 5.3(b). This magnetic field interference may cause a serious problem in controlling the electron beam motion and will largely deteriorate the performance of the electron beam microcolumn. 106

114 5. Modeling and Simulation of the Miniaturized Magnetic Electron Beam Control System Magnetic microstigmator Y Z X Magnetic microlens Magnetic microdeflector Figure 5.4 3D model of the three vertically stacked magnetic electron beam control devices. The miniaturized magnetic electron beam control system is composed of three micromachined magnetic devices which are the magnetic microstigmator, magnetic microlens, and magnetic microdeflector. These three magnetic devices are vertically stacked together and assembled in the electron beam microcolumn to control the electron beam motion. To investigate the magnetic interference among the three 107

115 magnetic electron beam control devices, a 3-D model of the three vertically-stacked devices (Figure 5.4) was built for simulation using the MagNet software (INFOLYTICA Corporation). As described above, the magnetic field produced by each of the three magnetic devices spans a certain range along the axial Z direction, or assembly direction. Before exploring the magnetic interference among the three magnetic devices, the span range of the magnetic field distribution produced by each of the magnetic devices in the space will be investigated individually Magnetic Field Distribution of the Magnetic Microdeflector To investigate the span of the magnetic field distribution generated by the magnetic microdeflector in the space, the magnetic microstigmator and magnetic microlens in the 3D system model (Figure 5.4) were disabled to prevent magnetic interference among the devices. In the finite element simulation, the distance between the two magnetic poles of the microdeflector varied from 50 µm to 1000 µm, and the driving current varied from 0 ma to 50 ma. These parameters were chosen for the simulation based on the design criteria of the magnetic microdeflector and its practical application in the electron beam microcolumn. Figure 5.5 shows the B field distribution of the magnetic microdeflector with a pole distance of 1.0 mm and a driving current of 50 ma. 108

116 The simulation focused on the span range of the magnetic field distribution along the electron beam moving direction, i.e., the axial Z direction. Figure 5.6 shows the magnetic field B distribution in the cross section plane XZ (Y=0) of the microdeflector. The designed magnetic microdeflector has a thickness of approximately 100 µm, and the thickness of the NiFe permalloy core is around 5 µm. Z Y X Figure 5.5 Simulation results of the magnetic field B distribution of the designed magnetic microdeflector with a pole distance of 1mm and a driving current of 50 ma. 109

117 Z x 5 µm 1 mm Figure 5.6 Simulation results of the magnetic field B distribution of the microdeflector at XZ plane (Y=0) with a pole distance of 1 mm and a driving current of 50 ma. The span range of the magnetic field distribution in the space generated by the microdeflector is mainly related to two important factors. One is the driving current applied to the micromachined inductors of the microdeflector. The other factor is the distance between the two magnetic poles of the microdeflector. A parametric study was employed in the simulation. In the finite element simulation, the pole distance of the magnetic microdeflector varied from 50 µm to 1000 µm, and the driving current varied from 0 ma to 50 ma. Given the small diameter of a ray of an electron beam, the investigation of the magnetic field distribution focused on the central region, i.e., the central axis and its vicinity, of the device. The magnetic field distribution in this area largely affects the motion of the passing electron beam. 110

118 0 ma 30 ma 40 ma 50 ma (a) (b) Figure 5.7 (a) Magnetic field B distributions along the Z axis (X=0 and Y=0) of the microdeflector with a pole distance of 1.0 mm and (b) the variation of the span range with different driving currents applied to the microdeflector. Figure 5.7 shows the magnetic field B distributions varying along the Z axis (X=0 and Y=0) of the microdeflector with different driving currents. The microdeflector was set at Z=0, the thickness of the microinductor coupled with the NiFe permalloy core is around 100 µm, and the distance between the two magnetic poles is 1.0 mm. As shown in Figure 5.7(a), the magnetic field B distribution along the Z axis spans a much larger range in the space than the physical dimension of the 111

119 microdeflector, i.e., 100 µm. Figure 5.7(b) depicts the span range of the magnetic field distribution with different driving currents applied to the microdeflector. Here the span range is defined as the distance between Z=0 and the location where the B drops below the value of 1x10-4 T. As shown in Figure 5.7(b), the span range almost increases linearly with the driving currents. This means that the magnetic interference issue may become more severe with larger driving currents. Pole distance: µm 750 µm µm 4 50 µm (a) (b) Figure 5.8 (a) Magnetic field B distributions along the Z axis (X=0 and Y=0) of the microdeflector with a driving current of 50 ma and (b) the variation of the span range with different pole distances of the microdeflectors. 11

120 In addition to the driving current, the other important factor influencing the span range of the magnetic field in the space is the distance between the two magnetic poles of the microdeflector. Figure 5.8 shows the variation of the magnetic field B distribution along the Z axis (X=0 and Y=0) of the microdeflector resulting from different pole distances. The driving current applied to the microdeflector was 50 ma. As shown in Figure 5.8(a), the maximum magnetic field B at the location of the microdeflector (Z=0) increases with the pole distance decreasing from 1000 µm to 50 µm. However, it is also noted that the magnetic field B with a larger peak value at Z=0 will drop more quickly along the Z axis than one with a smaller peak value at Z=0. This observation is verified by the curve plotted in Figure 5.8(b) which shows the span range increases rapidly with the pole distance of the microdeflector. This is because when the distance between the two magnetic poles becomes smaller, more magnetic fluxes will be confined within the central bore area and, in turn, the magnetic flux leakage is largely reduced. Therefore, the smaller the pole distance, the less the magnetic interference will be produced by the microdeflector on the neighboring devices. Additionally, the microdeflector with a smaller pole distance has higher power consumption efficiency due to its less magnetic flux leakage. 5.. Magnetic Field Distribution of the Magnetic Microstigmator To investigate the magnetic field distribution generated by the magnetic microstigmator in the space, the magnetic microlens and magnetic microdeflector in the 3D system model (Figure 5.4) were disabled in the simulation. In the finite 113

121 element simulation, the central bore diameter of the magnetic microstigmator varied from 500 µm to 1000 µm, and the driving current varied from 50 ma to 300 ma. These parameters were chosen for the simulation based on the design criteria of the magnetic microstigmator and its practical application in the electron beam microcolumn. Figure 5.9 shows the B field distribution of the magnetic microstigmator with a bore diameter of 1.0 mm and a driving current of 100 ma. Y Z X Figure 5.9 Simulation results of the magnetic field B distribution of the designed magnetic microstigmator with a bore diameter of 1mm and a driving current of 100 ma. The simulation focused on the span range of the magnetic field distribution along the axial Z direction. Figure 5.10 shows the magnetic field B distribution in the cross section plane XZ (Y=0) of the microstigmator. The designed microstigmator has a thickness of approximately 100 µm, and the thickness of the NiFe permalloy core is around 5 µm. The bore diameter of the microstigmator is 1.0 mm. 114

122 Z X 5 µm 1 mm Figure 5.10 Simulation results of the magnetic field B distribution of the microstigmator at XZ plane (Y=0) with a bore diameter of 1 mm and a driving current of 100 ma. 115

123 r = 10 µm 1 50 ma 100 ma ma 4 00 ma 5 50 ma ma (a) (b) Figure 5.11 (a) Magnetic field B distributions along the Z direction (r =10 µm) of the microstigmator with a bore diameter of 1 mm and (b) the variation of the span range with different driving currents applied to the microstigmator. The span range of the magnetic field distribution in the space generated by the microstigmator is mainly related to two important factors. One is the driving current applied to the micromachined inductors of the microstigmator. The other factor is the central bore diameter of the microstigmator. A parametric study was performed in the 116

124 finite element simulation of the magnetic microstigmator. In the simulation, the central bore diameters of the magnetic microstigmator varied from 500 µm to 1000 µm, and the driving current varied from 50 ma to 300 ma. Given the small diameter of a ray of an electron beam, the investigation of the magnetic field distribution focused on the central region, i.e., the central axis and its vicinity. The magnetic field variation in this area largely affects the motion of the passing electron beam. One thing that is worthwhile to mention here is that, as shown in Figure 3.7 in Chapter 3, the magnetic field B distribution within the central bore area of the magnetic microstigmator is axially symmetrical. Therefore, locations having the equal radial distance with respect to the central axis possess the same B field magnitudes. The magnetic field B distributions varying with the applied driving current and the bore diameter along the Z direction at a radial distance of r = 10 µm are summarized and plotted in Figure 5.11 and Figure 5.1, respectively. Figure 5.11 shows the magnetic field B distributions varying along the Z direction with different driving currents at a radial distance of r = 10 µm. The microstigmator is set at Z=0 and the bore diameter of the microstigmator is 1.0 mm. The designed microstigmator has a thickness of approximately 100 µm, and the thickness of the NiFe permalloy core is around 5 µm. As shown in Figure 5.11(a), the magnetic field B distribution along the Z direction spans a much larger range than the physical dimension of the microstigmator, i.e., 100 µm. Figure 5.11(b) depicts the span range of the magnetic field distribution with different driving currents applied to the microstigmator. Here the span range is defined as the distance between 117

125 Z=0 and the location where the B drops below the value of 1x10-4 T. As shown in Figure 5.11(b), the span range increases almost linearly with the driving currents. This means that the magnetic interference issue may become more severe with larger driving currents. Bore diameter: µm 750 µm µm 4 50 µm (a) (b) Figure 5.1 (a) Magnetic field B distributions along the Z direction (r = 10 µm) of the microstigmator with a driving current of 300 ma and (b) the variation of the span range with different bore diameters of the microstigmators. 118

126 In addition to the driving current, the other important factor largely influencing the span range of the magnetic field is the central bore diameter of the microstigmator. Figure 5.1 shows the variation of the magnetic field B distribution along the Z direction (r = 10 µm) with different bore diameters. The driving current applied to the microstigmator was 300 ma. As shown in Figure 5.8(a), the maximum magnetic field at the location of the microstigmator (Z=0) increases with the bore diameter decreasing from 1000 µm to 50 µm. It is noted that the magnetic field B with a larger peak value at Z=0 drops more rapidly than that with a smaller peak value at Z=0. This observation is verified by the curve plotted in Figure 5.1(b) which shows that the span range increases rapidly with the bore diameter of the microstigmator. This is because when the central bore diameter becomes smaller, more magnetic fluxes are confined within the central bore area and, in turn, the magnetic flux leakage is largely reduced. Therefore, the smaller the bore diameter is, the less the magnetic interference will be produced by the microstigmator. Additionally, the microstigmator with smaller bore diameter has higher power consumption efficiency due to the less magnetic flux leakage Magnetic Field Distribution of the Magnetic Microlens To investigate the magnetic field distribution generated by the magnetic microlens, the magnetic microdeflector and magnetic microstigmator in the 3D system model (Figure 5.4) were disabled in this simulation. In the finite element simulation, the central bore diameter of the magnetic microlens varied from 00 µm 119

127 to 500 µm, and the driving current varied from 50 ma to 00 ma. These parameters were chosen for the simulation based on the design criteria of the magnetic microlens and its practical application in the electron beam microcolumn. Figure 5.13 shows the B field distribution of the magnetic microlens with a bore diameter of 00 µm and a driving current of 50 ma. Y Z X Figure 5.13 Simulation results of the magnetic field B distribution of the designed magnetic microlens with a lens diameter of 00 µm and a driving current of 50 ma. The simulation focused on the span range of the magnetic field distribution along the axial Z direction. Figure 5.14 shows the magnetic field B distribution in the cross sectional plane of the magnetic microlens. Both the bore diameter and the length of the designed microlens are 00 µm, and the microlens consists of three planar coils stacked together and wrapped by the bottom and the top NiFe permalloy shells. 10

128 00 µm Z r 00 µm Figure 5.14 Simulation results of the magnetic field B distribution along the Z axis (X=0 and Y=0) of the magnetic microlens with a bore diameter of 00 µm and a driving current of 100 ma. 11

129 1 50 ma 100 ma ma 4 00 ma (a) (b) Figure 5.15 (a) Magnetic field B distributions along the Z axis (r =0) of the microlens with a bore diameter of 00 µm and (b) the variation of the span range with different driving currents applied to the microlens. The span range of the magnetic field distribution in the space produced by the microlens is mainly related to two important factors. One factor is the driving current applied to the micromachined planar spiral coils of the microlens. The other factor is the bore diameter of the microlens. A parametric study was performed in the finite 1

130 element simulation of the magnetic microlens. In the simulation, the central bore diameter of the magnetic microstigmator varied from 00 µm to 500 µm, and the driving current varied from 50 ma to 00 ma. Given the small diameter of a ray of an electron beam, the investigation of the magnetic field distribution focused on the central region, i.e., the Z-axis and its vicinity. The magnetic field variation in this area largely affects the motion of the passing electron beam. As described in Chapter 4, the magnetic field B distribution within the central bore area of the magnetic microlens is axially symmetrical. Therefore, locations having equal radial distances with respect to the central axis possess the same B field magnitudes. The B field distributions varying with the driving currents and the bore diameters along the Z axis (r = 0) are summarized and plotted in Figure 5.15 and Figure 5.16, respectively. Figure 5.15 shows the magnetic field B distributions varying along the Z axis (r = 0) of the microlens with different driving currents. The microlens was set at Z=0 and both the bore diameter and the length of the microlens are 00 µm. As shown in Figure 5.15(a), the magnetic field B distribution along the Z axis spans a much larger range in the space than the physical dimension of the microlens. Figure 5.15(b) depicts the span range of the magnetic field distribution with different driving currents applied to the microlens. Here the span range is defined as the distance between Z=0 and the location where the B drops below the value of 1x10-4 T. As shown in Figure 5.15(b), the span range increases with the driving currents. This means that with the larger driving currents, the magnetic interference becomes more severe. 13

131 Bore diameter: µm 400 µm µm 4 00 µm (a) (b) Figure 5.16 (a) Magnetic field B distributions along the Z axis (r = 0) of the microlens with a driving current of 50 ma and (b) the variation of the span range with different bore diameters of the microlens. 14

132 In addition to the driving current, the other important factor largely influencing the span range of the magnetic field in the space is the central bore diameter of the microlens. Figure 5.16 shows the variation of the magnetic field B distribution along the Z axis (r = 0) with different bore diameters. The driving current applied to the microlens was 50 ma. As shown in Figure 5.16(a), the maximum magnetic field at the location of the microlens (Z=0) decreases with a lens bore diameter increasing from 00 µm to 500 µm. It is also noted that the magnetic field B of the microlens with a smaller bore diameter has a larger peak value at Z=0 as well as a narrower FWHP (Full Width at Half Peak). Figure 5.16(b) shows that the span range deceases rapidly with the increasing of the bore diameter of the microlens. This is because when the central bore area becomes smaller, both the magnetic field and the magnetic flux leakage at the center of the lens become stronger. Therefore, with the same driving current, the larger the bore diameter is, the less the magnetic interference will be produced by the microlens. However, when the bore diameter becomes larger, the strength of the magnetic field produced within the central bore area becomes weaker with the same applied driving current, and, in turn, the electron beam focusing is less efficient. Therefore, in the design of the microlens, a compromise between the lens diameter and the span range of the magnetic field needs to be considered depending on the specific application. 15

133 5..4 The Miniaturized Magnetic Electron Beam Control System The miniaturized magnetic electron beam control system consists of three micromachined magnetic devices: magnetic microstigmator; magnetic microlens; and magnetic microdeflector. The three devices are stacked together and assembled in the electron beam microcolumn to realize the control of the electron beam motion. Since the electron beam microcolumn has limited chamber space, the assembled devices are close to each other. The magnetic interference among the three magnetic devices becomes a major concern when constructing the miniaturized magnetic electron beam control system. In the previous sections, the magnetic interference in terms of the span range of the magnetic field distribution for each individual device has been investigated. From the simulation results presented in Section , it is noted that: (1) among the magnetic microdeflectors with pole distances varying from 50 µm to 1000 µm and driving currents varying from 10 ma to 50 ma, the one with a pole distance of 1000 µm and a driving current of 50 ma has the largest magnetic field span range or the most severe magnetic interference; () among the magnetic microstigmators with bore diameters varying from 50 µm to 1000 µm and driving current varying from 50 ma to 300 ma, the one with a bore diameter of 1000 µm and a driving current of 300 ma has the largest magnetic field span range; and (3) among the magnetic microlens with lens diameters varying from 00 µm to 500 µm and driving currents varying from 50 ma to 00 ma, the one with a lens diameter of 00 µm and a driving current of 00 ma has the largest magnetic field span range. Table 16

134 5.1 summarizes the largest span ranges of the three devices based on the previous simulation results. Table 5.1 The three devices with largest calculated field span range. Devices Microstigmator (D=1mm, I=300mA) Microlens (D=00µm, I=00mA) Microdeflector (D=1mm, I=50mA) Span Range ± 1150 µm ± 1830 µm ± 180 µm As shown in Table 5.1, the microlens has the largest span range, ±1900 µm, while the microdeflector and the microstigmator have similar field span ranges of around ±100 µm. Microstigmator L 1 Y Z Microlens Z X X Microdeflector L (a) (b) Figure D models of the three vertically-stacked magnetic electron beam control devices: (a) schematic and (b) side view. 17

135 Figure 5.17 shows the 3D models built for finite element analysis (FEA). To investigate the magnetic interference within the miniaturized magnetic electron beam control system, the three devices with largest field span ranges (Table 5.1) were selected in the simulation: (1) the microstigmator model has a bore diameter of 1 mm and a driving current of 300 ma; () the microlens model has a lens diameter of 00 µm and a driving current of 00 ma; and (3) the microdeflector model has a pole distance of 1 mm and a driving current of 50 ma. Based on the simulation results summarized in Table 5.1, in order to avoid the interference among the three magnetic electron beam control devices, the distance between the microstigmator and microlens (L 1 ) and the distance between the microlens and microdeflector (L ) should be larger than 3 mm. Microstigmator Microlens Microdeflector Figure 5.18 FEA simulation results of the magnetic electron beam control system with magnetic interference among the three devices (L 1 =L =1.5 mm). 18

136 Stigmator Lens Deflector (a) (b) Figure 5.19 Magnetic field B distribution (a) at XZ plane (Y=0) and (b) along the Z direction (X=10 µm and Y=0) with L 1 = L = 1.5 mm. Figure 5.18 shows the FEA simulation results of the magnetic electron beam control system in which the two distances, L 1 and L, were set at 1.5 mm. As shown in Figure 5.18, with L 1 =L =1.5 mm, a severe magnetic interference is existed among the devices. The magnetic field distributions of the eight magnetic poles of the microstimator and the two magnetic poles of the microdeflector are heavily interfered with the magnetic field generated by the magnetic microlens as shown in Figure Figure 5.19(a) shows the magnetic field B distribution at the XZ plane (Y=0). It clearly indicates that the magnetic fluxes produced by the magnetic microlens interfere with the magnetic field generated by the microstigmator and the microdeflector. Figure 5.19(b) depicts the magnetic field B distribution along the Z 19

137 direction. The three peaks from high to low are in turn produced by the microstigmator, microlens, and microdeflector. Due to the proximity of the three magnetic devices, the two peaks generated by the microstigmator and microdeflector are almost buried into the strong magnetic field produced by the microlens. The magnetic interference largely affects the ability of the three magnetic devices to individually control the electron beam motion and ultimately deteriorates the performance of the whole electron beam microcolumn. Figure 5.0 FEA simulation results of the magnetic electron beam control system without magnetic interference among the three devices (L 1 =L =3.5 mm). 130

138 Stigmator Lens Deflector (a) (b) Figure 5.1 Magnetic field magnetic B distribution (a) at XZ plane (Y=0) and (b) along the Z axis (X=10 µm and Y=0) with L 1 = L =3.5 mm. Figure 5.0 shows the FEA simulation results of the magnetic electron beam control system in which both L 1 and L were set at 3.5 mm. Based on the data shown in Table 5.1, with a distance larger than 3 mm, the magnetic interference can be prevented among the three devices. This is verified by the results presented in Figure 5.0, which indicates that neither of the magnetic field distributions of the microstigmator and the microdeflector has been affected by the magnetic field produced by the microlens. Figure 5.1(a) shows the magnetic field B distribution at the XZ plane with L 1 = L =3.5 mm. Figure 5.1(b) depicts the magnetic field distribution along the Z direction. It is noted that, with L 1 = L =3.5 mm, the three peaks from high to low that are produced by the three individual devices are clearly separated out from each other. 131