Coulomb Interactions in a Focused Ion Beam System with a Dynamic Corrected Deflection Field

Transcription

1 3rd Internatonal Conference on Mechatroncs and Industral Informatcs (ICMII 205) Coulomb Interactons n a Focused Ion Beam System wth a Dynamc Corrected Deflecton Feld Wenpng L, a *, Qan L,b and Junbao Lu2,c School of Physcs and Nuclear Energy Engneerng, Behang Unversty Bejng, Chna 2 Insttute of Electrcal Engneerng, Chnese Academy of Scences, Bejng, Chna a lwp@buaa.edu, blqan34@buaa.edu, clujb@mal.ee.ac.cn Keywords: Coulomb nteractons; dynamc correcton; three-dmenson on trajectory Abstract. Focused on beam systems complement conventonal processng methods and can be used to prototype and modfy a dverse range of nano-devces and sensors. Controllable ncdent focused on beam s dffcult to obtan due to Coulomb nteractons among ons. In ths paper, Coulomb nteractons of a practcal FIB system wth a dynamc corrected deflecton feld are obtaned through solvng Newton-Lorentz equatons n three-dmenson (3D). Frstly, the prncple of the dynamc correcton s analyzed and ts 3D realzaton s gven. Secondly, the prncple of N-body Monte Carlo method s researched n detal before the source parameter, the 3D feld, and the number of N are determned. In the end, the equatons are solved by ffth-order Runge-Kutta algorthm and 3D on trajectory s gven for a 30kV FIB through the Mebs software. Smulaton results concde to the expermental those from our Canon 3+ system. Introducton Focused on beam and ts relatve systems are versatle tools for nanoengneerng and nanoscence applcatons. These systems complement conventonal processng methods and can be used to prototype and modfy a dverse range of nano-devces and sensors [-3]. The qualty and precson of FIB fabrcaton manly depend on parameters of ncdent focused on beam such as velocty, the spot, and the beam current densty dstrbuton. As on s much heaver than electron, Coulomb on-on nteractons play an mportant role n the spot and beam current densty [-2]. Much attenton was pad to Coulomb nteractons n the Ga LMIS of FIB systems [-3], as the current densty at the tp reaches above 02Am-2. P. Krut pad more attenton to Coulomb nteractons of two-lens FIB column under dfferent magng modes [4-5]. However, error s ntroduced as they have gnored the deflectng feld whch s essental to a real FIB system. In ths paper, Coulomb nteractons of a practcal FIB system wth a dynamc corrected deflecton feld are obtaned through solvng 3D Newton-Lorentz equatons. 3D on trajectory s gven and the smulaton results are analyzed wth some experments on our FIB-SEM dual-beam system. Three-dmenson Dynamc Correcton Feld Accordng to the dynamc correcton theory [6], the deflecton feld curvature can be corrected by a dynamc focus lens and the deflecton astgmatsm by an octupole stgmator Prncple of Dynamc Correcton The dynamc focus lens has the same feld dstrbuton as the focusng lens to produce a negatve behavor, whose polar coordnates form can be expressed as φ ( z, r ) = φ ( z ) φ " ( z )r 2 + φ ( 4) ( z )r 4 + L. () 4 64 The feld dstrbuton of an octupole stgmator can be decomposed nto two quadrupole felds as gven n Eq. (2) along the XOY and POQ planes as shown n Fg.. φ a (r, θ, z ) = Vaφ 2 (r, z ) cos 2θ Vaφ 6 (r, z ) cos 6θ + L (2.) 205. The authors - Publshed by Atlants Press 340

2 φb ( r, θ, = Vbφ2 ( r, sn 2θ Vbφ6 ( r, sn 6θ +L (2.2) where ( r, θ, s the polar coordnates, φ2( r, and φ6( r, are the second and sxth harmonc components on the ( r, plane. Consderng the superposton of electrc sgnals, the objectve lens can also work as a dynamc focus lens f we apply the sutable exctaton as shown n Fg.2 and the two pre-lens deflectors can as two stgmators n Fg.3. Deflecton feld curvature, deflecton dstorton and astgmatsm wll be corrected by applyng sutable potentals on the objectve lens and the deflectors [7]. Fg. Schematc dagram of the stgmator Fg.2 Equvalent dynamc focus lens Fg.3 Three-dmenson dynamc corrected deflecton fled Realzaton of Three-dmenson Dynamc Correcton Feld The spatal fled of dynamc focus lens at arbtrary pont can be obtaned by nterpolatng the felds at mesh ponts. The felds at mesh ponts are obtaned through the second-order Fnte Element Method (FEM) wth the relatve accuracy of 0-5. Hermte nterpolaton s appled to get the feld at arbtrary pont as t can easly get dervatves wth arbtrary order. The spatal fled of dynamc stgmators at arbtrary pont wll be calculated by the fnte dfference method through the Mebs software EO-3D. Based on the superposton of electrc sgnals, both the deflecton feld and the correcton one are obtaned at the same tme as shown n Fg.3. 34

3 Three-dmenson Ion Trajectory Ion trajectory n three dmensons can be calculated by Newton-Lorentz equatons of ons emttng from the source durng the samplng tme, whch s called N-body Monte Carlo method. Prncple of N-body Monte Carlo Method The prncple of N-body Monte Carlo method s llustrated n Fg.5. Bunches of ons are created near the object plane wth random ntal postons, drectons, knetc energes and dstrbutons correspondng to the FIB source. The paths of each partcle n the bunch of N partcles are computed by solvng the Newton-Lorentz equaton of moton: ( E + v B ) ma = q for =,, N. (3) where m s the mass of on consderng relatvty theory, q s the charge, E s the electrc feld, B s the magnetc flux densty, v s the velocty, a s the acceleraton and the footnote represents the -th partcle. The electrc feld E can be rewrtten nto E = E + E wth Coulomb nteracton among ons. Where E L s the external electrc feld and E C s the Coulomb nteracton feld. Usng Coulomb s nverse square law, the dscrete Coulomb repulson felds E C can be expressed as: N q r rj EC = 3. (4) 4πε 0 = r r ( j) j Ion source parameters, the 3D feld, and N should be determned n order to get the on trajectory. Realzaton of N-body Monte Carlo Method The parameter of the FIB source s lsted n Table. Smlar to the dynamc correcton feld, spatal feld dstrbuton of lens can be got. As regard to the deflectng feld, t has been obtaned by calculatng the dynamc correcton feld. N represents the number of ons emttng from the source durng the samplng tme and t determnes the axal length of the bunch L. L = Nvq / I. (4) Where I s the beam current, v s the speed of ons (Ga + 5 s m / s under 30kV). N can be determned to keep L large enough compared to the physcal dmensons of FIB and long enough to elmnate the endng effects. When L s chosen as 0μm, N closed to the source wll be Table Orgnal parameters of 0.μA Ga LMIS Class Ga LMIS Dameter of the vrtual source Energy spread Angular current densty L C 50nm wth Gaussan ntensty dstrbuton 5ev, Gaussan dstrbutons 30μA/sr, unform dstrbuton The parameters of lenses, deflectors, and dynamc correcton unts are lsted n Tables 2 and 3. 3D trajectory s traced by ffth-order Runge-Kutta algorthm wth Coulomb nteractons. Ion trajectory from 0mm and the beam current densty dstrbuton at the sample are shown n Fg.4-5 respectvely. The measured resoluton of our FIB system s shown n Fg.6 under 500pA. Table 2 Optcal parameters of the pre-lens deflectors (Dynamc lens voltage s V) Class Deflecton voltage [v] Stgmator voltage [v] Deflector Deflector 2 Deflector Deflector 2 0.3mmX0.3mm feld

4 Table 3 Optcal poston of the FIB system Class Source Lens Lens 2 Deflector Deflector 2 Sample z[mm] Fg.4 Three-dmenson on trajectory of the FIB system Fg.5 Beam current densty dstrbuton at 500pA Fg.6 Expermental resoluton of our system Summary Controllable ncdent focused on beam s realzed by smulatng Coulomb nteractons of a real FIB system wth the dynamc corrected deflecton feld. The beam current densty dstrbuton at the sample concdes to the expermental resoluton from our Canon 3 + system. 3D on trajectory from the on source to the specmen can also lay foundaton for the FIB mechancal desgn. Ths work s supported by the Natonal Natural Scence Foundaton of Chna (Grant No ) and the Fundamental Research Funds for the Central Unverstes (Grant No. YWF-5-WLXY-022). References [] Jon Orloff, Mark Utlant and Lynwood Swanson, Hgh resoluton focused on beams: FIB and ts applcatons, Kluwer Academc/Plenum Publshers, New York, [2]Tomáš Radlčka, Bohumla Lencová, Ultramcroscopy. 08 (2008) [3] K. Maranowsk, T. Ohnweler, E. Ples, Coulomb nteractons n a low-voltage focused on beam system, Nucl. Instru. and Meth. A 645 (20) 6-9. [4]P. Krut, L.J. Vjgen, Jang Xnrong, Coulomb nteractons n mcrofocussed electron and on beams, Nucl. Instru. and Meth. A 363 (998) [5] J.B, P.W.H.de Jager, J.E.Barth and P.Krut, Influence of Coulomb nteractons on current densty dstrbuton n a two-lens focused on beam, Mcroelectronc Engneerng. 4/42 (998)

5 [6] Xeqng Zhu, Haonng Lu and Erc Munro, Dynamc correcton of aberratons n focusng and deflecton system wth shaped beams, SPIE 2522: [7]Wenq Gu, Xangguo Ma and Wenpng L, Nano-Mcro fabrcaton by focused on beam, Bejng Unversty of Technology Press, Bejng,