The potential array is refined using overrelaxation methods allowing voltage contours and ion trajectories to be computed and plotted. The traditional approach to lens design has been either to confine the problem to situations where the approximate solutions of the paraxial ray equations could be used, or to find a good handbook where numerical. The electrostatic field to calculate the force exerted by some electric charges, q1, q2, q3. Charged particle dynamics inside electrostatic quadrupole. Design of the objective magnetic and electrostatic lenses. Electrostatic lenses are of great importance in the design of low energy electrostatic accelerators like cockcroftwalton and. Improved digital methods for the precise calculation of electric fields and trajectories. In general, electrostatic lenses have much larger aberrations than their optical counterparts. In this research, design electrostatic einzel lens threeelectrode accelerating and decelerating l2mm, 20mm operated under different.
The modification of an existing design or the generation of a completely new one is performed interactively with a graphics screen and mouse. Electrostatic lenses are of great importance in the design of low energy electrostatic. In order to obtain an optimum design, it is necessary to reduce the aberration of the focusing lenses. This paper describes the influence of the front electrode bore angle on the electron optical performance of the twoelectrode electrostatic immersion lens. Electrostatic force and electric charge electrostatic force charges at rest. This principle states that the interaction between any two charges is completely unaffected by the presence of other. Request pdf design of an electrostatic lens using the charge density method a computational investigation has been.
A solenoid lens is the magnetic equivalent of the electrostatic einzel lens. Electrostatic lenses are used for the extraction, preparation and rst acceleration of electron and ion beams. Pdf the effect of bore diameters in two electrodes. Design of the objective magnetic and electrostatic lenses for low. Even though all electrostatic lenses are thick you can go quite far with simple, thin lens, ideas though ultimately you will need accurate data to produce or analyse the final design. V ery often ion optics with electrostatic lenses is called electron optics. Electrode geometries for the three einzel lens models. The first device discussed is an electrostatic lens scanner with an optoelectronic feedback loop. It is shown that the focusspot size calculated from the classical formulas taking into account the coefficients found is in good agreement with the. This systems was predesigned for an ion beam modification and trajectory controlling.
The results obtained for the objective magnetic lens and the electrostatic lens for the preferable design were compared with the results of the recent published papers. An electrostatic lens field is determined by the pole piece and the electrostatic deflector, and the. Pdf theoretical design of electrostatic lens accelerating and. The book covers the basic theory of the motion of charged particles in electrostatic fields and describes several methods for the calculation of the potential and field distribution for various electrode geometries. The electrostatic immersion lens includes a top electrode configured with a first voltage applied thereto, an upper bottom electrode configured with a second voltage applied thereto, and a lower bottom electrode configured with a third voltage applied thereto. The spherical and chromatic aberration coefficients of this lens have been determined. Electrostatic lens article about electrostatic lens by. Kuoyung hung, chaochih fan, fangang tseng, and yiko chen, design and fabrication of a copolymer aspheric biconvex lens utilizing thermal energy and electrostatic force in a dynamic fluidic, opt. Different potential functions are used to describe a a threeaperture lens, b a threetube lens and c a twoaperture, centertube lens. Theoretical study of short electrostatic lens for the columbia ion microprobe alexander d.
Accepted 8 10 2012 abstract the paper handles a new method that is utilized in determining the best bore diameter of two. Optics elements for modeling electrostatic lenses and. The energetic electrons produce an enhanced copy of the light image when they strike a phosphor screen. The general properties of electrostatic lenses and the electrostatic immersion lens are also considered. Mems lens scanners for freespace optical interconnects. He has a very limited number of degrees of freedom. The lens design was optimized using the simulation data obtained with a performance characteristics of the electrostatic lens system. These fields bend charged particle orbits in a manner analogous to the bending of light rays by shaped glass lenses. Chapter 2 particle motion in electric and magnetic fields. Research of the national bureau of standards 76a 2735. Cn103688334a method and apparatus for controlling an. Second edition enables readers to design lens systems for focusing beams of charged particles that have useful characteristics.
Electrostatic lenses are of great importance in the design of low energy electrostatic accelerators like cockcroftwalton and vandegraaff accelerators. Practical conditions specify lens materials, safety considerations fix lens thickness, fashion dictates lens. Electron optics is a mathematical framework for the calculation of electron trajectories along electromagnetic fields. Three element cylindrical electrostatic lens systems for. It may be found in cathode ray tubes, ion beam and electron beam experiments, and ion propulsion systems. An electrostatic field with axial or plane symmetry which acts upon beams of charged particles of uniform velocity as glass lenses act on light beams. However, the four element lens systems can be operated with a constant magnification while keeping the image position also constant. In cgs electrostatic system, the unit of charge is called as statecoulumb or esu of charge. Tutorial model of an einzel lens comsol multiphysics. One difference concerns their respective aberrations. Simion is an electrostatic lens analysis and design program. This is different from a regular motor, which is based on magnetic. Electric and magnetic field lenses the subject of charged particle optics is introduced in this chapter.
Brenner, gary johnson, and gerhard randerspehrson raraf, columbia university, 6 south broadway, irvington, new york 10533. It is based on constrained nonlinear optimization techniques. Electrostatic lenses are used for the extraction and acceleration of electron and ion beams. An electrostatic lens system for the deceleration of high. An electrostatic lens is a device that assists in the transport of charged particles.
This book enables readers to design lens systems having useful characteristics. The design of the lens incorporates space for the scanning coils, the stigmator, and the beamlimiting aperture n all modern fe sems employ a semiimmersion lens design u sample sits in an electromagnetic or electrostatic field generated by the lens u significantly lowers spherical aberrations allowing better resolution. In this system electrostatic constant c1 for vacuum or air, one stat coulomb is defined that amount of charge which when placed at a distance of 1 cm in air from an equal. One embodiment relates to an objective lens utilizing magnetic and electrostatic fields which is configured to focus a primary electron beam onto a surface of a target substrate. The objective lens includes a magnetic pole piece and an electrostatic deflector configured within the pole piece. Here, the use of commercially available optical design programs is described as a tool to aid in solving charged particle optics problems. Electrostatic lens systems, 2nd edition 2nd edition d. Spectacle lens design the goal of the spectacle lens designer is to give the patient clear vision at all distances through any portion of the spectacle lens. This particular model consists of three axially aligned cylinders. Simple analytical method to design electrostatic einzel lens. Related content the design of threeelement electrostatic electron lenses d w o heddlethe magnification behaviour of a fiveelement electrostatic lens d w o heddle and n papadovassilakis. If the cylinder is very long or is terminated without distorting the field within, the trajectories of charged particles inside it. One embodiment relates to an electronicallyvariable electrostatic immersion lens in an electron beam apparatus. The potential and field are evaluated by the simple analytical method for a particular cylindrical einzel lens and optical properties are also evaluated approximately by the simple optical method following the section model.
A computeraided design of focused ion beam fib system consisting of three electrostatic lenses approximated by the spline lens model, has been investigated in the present work. Electric and magnetic field lenses 108 6 electric and magnetic field lenses the subject of charged particle optics is introduced in this chapter. The concern is the control of the transverse motion of particles by shaped electric and magnetic fields. The paper handles a new method that is utilized in determining the best bore diameter of two electrodes of the electrostatic lens design. We deal with eqds consisting of electrode pairs with rotational symmetry design. Even though all electrostatic lenses are thick you can go quite far with simple, thin lens, ideas though ultimately you will need accurate data. Electronicallyvariable immersion electrostatic lens. This type of motor is based on coulomb forces, and its energy output is related to the change in electrostatic energy that occurs when charges are moved between the terminals of a highvoltage hv supply.
For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an optical instrument. The development of the design of magnetic and electrostatic lenses to control beams of electrons or ions has proceeded largely independently in several different. Optimum design of electrostatic lenses 954 solving laplaces equation with the given boundary condi tions. Very often ion optics with electrostatic lenses is called electron optics. In terms of lens design, this means that the aperture, or f number, of an electrostatic lens is usually limited to keep these aberrations to a tolerable level. A method of design for electrostatic lenses with given source parameters, first. Alabdullah department of physics college of science university of mosul received 5 2012. The book covers the basic theory of the motion of charged particles in electrostatic fields and describes several methods for the calculation of. Theoretical study of short electrostatic lens for the. Electrostatic force can be attractive electrostatic force can be repulsive electrostatic force acts through empty space electrostatic force much stronger than gravity electrostatic forces are inverse square law forces proportional to 1r 2. Parameters of a single lens composed of two coaxial cylinders have been numerically calculated for the case of energy spread in a chargedparticle beam. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or.
In simion an electrostatic lens is defined as a twodimensional electrostatic potential array containing both electrode and nonelectrode points. The potential changes abruptly at the boundary, but. Exploring focal and aberration properties of electrostatic lenses. An einzel lens is an electrostatic device used for focusing charged particle beams. An improvement in the optical properties obtained by the proposed design was noticed to be improved compared to the published results. This work focuses on the design and implementation of an electrostatic lens system to produce highintensity, lowenergy ion beams, by means of numerical simulation of the beam trajectories simion 7. The electrode bore shape is the most important geometrical parameter in any electron optical. Spherochromatic aberration of a single electrostatic lens. The focusing characteristics of electron beam in twoelement cylindrical lens systems are investigated with two different nonlinear autoregressive.
A method of controlling deflection of a charged particle beam in an electrostatic lens includes establishing a symmetrical electrostatic lens configuration comprising a plurality of electrodes disposed at unadjusted positions that are symmetric with respect to the central ray trajectory with applied unadjusted voltages that create fields symmetric with respect to the central ray trajectory. Any really useful lens will consist of more than two elements and it can be very helpful to look at the system as a combination of lenses. Accurate calculations of properties of the twotube electrostatic lens. The term optics is used because magnetic and electrostatic lenses act upon a charged particle beam similarly to optical lenses upon a light beam electron optics calculations are crucial for the design of electron microscopes and particle accelerators. In the optimization process of a transfer optics consisting of five einzel lenses, a comparison with the results obtained by means of the charge density method has proven, that this rather simple potential model is sufficiently accurate to allow a reliable preselection of promising lens designs. A possible electrostatic lens consists of a cylindrical surface along which the potential varies as the square of the distance from some original plane. Then for an arbitrary set of the electrode potential. Electrostatic lens article about electrostatic lens by the free dictionary. The outer cylinders are grounded, while the cylinder in the middle is held at a fixed. Electron beams, lenses, and optics, volume i deals with the physics of electron beams, lenses, and optics and covers topics ranging from the paraxial ray in symmetrical electric fields to the analytical determination of electrostatic fields. As an example, we can consider the treatment of cylindrical electrostatic lenses. Mems lens scanners for freespace optical interconnects by jeffrey brian chou. The text covers the basic theory of the motion of charged particles in electrostatic fields and describes several methods for the calculation of the potential and field distribution for various electrode geometries.
However, the bore diameter is considered the most important geometrical parameter in any electron optical. Accurate calculations of electrostatic potentials for cylindrically symmetric lenses. Prediction of twoelement cylindrical electrostatic lens parameters. Osa design and fabrication of a copolymer aspheric bi.
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