Supporting routines for the SRIM code

NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 257 (2007) 601–604 www.elsevier.com/locate/nimb

Supporting routines for the SRIM code Ma´rius Pavlovicˇ *, Ivan Strasˇ´ık Slovak University of Technology, Faculty of Electrical Engineering and Information Technology, Ilkovicˇova 3, SK-812 19 Bratislava, Slovak Republic Available online 12 January 2007

Abstract The SRIM code is used for calculating physical quantities related to ion-beam modification of materials. This paper presents supporting routines for the SRIM code, that improve its validity, precision, and ease of use of, make a link to the formalisms used in ion-optics and generally broaden its application potential. Several routines have been merged into a single software package S3M – SRIM Supporting Software Modules. S3M enables the user to calculate beams traversing thin targets, to run SRIM with finite-emittance beams and to simulate beam-transport with scattering and collimation. It has been successfully tested and used for the simulation of beam-transport channels and ion-implantation. Ó 2007 Elsevier B.V. All rights reserved. PACS: 41.85.p; 41.75.Ak, Cn; 34.50.s; 02.50.r Keywords: Beam-transport; Ion scattering; Ion-implantation; SRIM; Monte Carlo; Statistics

1. Introduction The SRIM code is often used for calculating physical quantities related to ion-beam modification of materials [1]. The present paper enlarges the scope of SRIM by the addition of routines that: (1) process SRIM output data; (2) prepare SRIM input data; (3) convert SRIM output data into SRIM input data and (4) perform special transformations of SRIM output data. These routines are presented in an integrated package S3M – SRIM Supporting Software Modules that contains beam-generation, statistical evaluation and beam-transport modules. S3M overcomes some limitations of the standard SRIM code and links SRIM to conventional ion-optics formalisms. As a result, SRIM calculations can be performed with realistic input beam data (beam-size, emittance, energy-spread

*

Corresponding author. Tel.: +421 2 602 91 106, fax: +421 2 654 27 207. E-mail address: [email protected] (M. Pavlovicˇ). 0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.01.047

and dispersion effects). In addition, beam-transport lines containing scattering and collimating elements can be simulated. Thus S3M combines the SRIM Monte Carlo simulation of a beam passing through matter with conventional beam-transport through optical elements. In this paper, the S3M modules are presented with an emphasis on features relevant to ion-implantation and beam preparation. 2. Theoretical background To provide a link between conventional ion-optics and the SRIM Monte Carlo formalisms, it is necessary to define two basic concepts: (1) the transfer-matrix and (2) the socalled ‘‘sigma-matrix’’. SRIM (Monte Carlo) simulates the beam as a sequence of individual particles, whereas ion-optics uses a matrix representation of the envelope of the whole beam. In an ion-optical element without acceleration, the transverse co-ordinates of individual particles are transformed from the entrance to the exit of the element by a so-called transfer-matrix T:

M. Pavlovicˇ, I. Strasˇı´k / Nucl. Instr. and Meth. in Phys. Res. B 257 (2007) 601–604

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0

y

1

0

B y0 C B C B C @zA z0

EXIT

10

y

1

T 11

T 12

T 13

T 14

BT B 21 ¼B @ T 31

T 22 T 32

T 23 T 33

B 0C T 24 C CB y C CB C T 34 A@ z A

T 41 T 42 0 1 y B y0 C B C ¼ TB C @zA

T 43

T 44

z0

;

z0

ENTRANCE

ð1Þ

of the individual particles, thus converting an ensemble of particles to the envelope representation used in ionoptics codes based on matrix formalism. It also contains its own transfer-matrix module that performs the transformation according to Eq. (1). The module is typically used to simulate the beam passage through several foils separated by optical elements [3]. 3.3. Beam-generation module

ENTRANCE

where x, y, z are particle position co-ordinates longitudinally, horizontally and vertically, y 0 = dy/dx and z 0 = dz/ dx. The transfer-matrix is an attribute of the beam-transport system. The region occupied by the beam in the phase-space is characterized by the ‘‘sigma-matrix’’ of the beam Mr and its volume is called the beam emittance. The ‘‘sigmamatrix’’ is an attribute of the beam and can be constructed from data produced by a Monte Carlo simulation using its statistical definition: 0 1 hyyi hyy 0 i hyzi hyz0 i B hy 0 yi hy 0 y 0 i hy 0 zi hy 0 z0 i C B C Mr ¼ B ð2Þ C: @ hzyi hzy 0 i hzzi hzz0 i A hz0 yi hz0 y 0 i hz0 zi hz0 z0 i 3. S3M Modules 3.1. Statistical module The statistical module evaluates the beam parameters after passage through a thin target [2]. ‘‘Thin’’ means less than the particle range. A thin target may be a stripping foil, a part of a beam-diagnostic element, a vacuum window or an element traversed by the beam. It can also be a slice of an implantation target. In this case, the particles are transmitted and SRIM records their parameters in the TRANSMIT.TXT file. S3M reads the TRANSMIT.TXT file and makes a statistical analysis of energies, momenta, positions and angles. A special routine is provided to convert the TRANSMIT.TXT file into a TRIM.DAT input file. In this way, a beam exiting a thin target can be used as input for a subsequent SRIM simulation and complex multi-layer structures can be analysed with the possibility of investigating processes of interest in individual layers. Another option allows the filtering of particles exceeding a certain threshold of a chosen parameter like energy, position or angle. The threshold is specified with respect to the standard deviation of the statistical distribution of that parameter. As an example, a collimator can be represented using this tool by filtering particles exceeding its aperture. 3.2. Beam-transport module The beam-transport module displays and calculates the beam emittance and ‘‘sigma-matrix’’ from the coordinates

The beam-generation module is important for exact ionimplantation simulations. By default, SRIM Monte Carlo starts with a point-like, zero-emittance, mono-energetic beam with no dispersion at the target surface. In some case, this may not be a sufficiently accurate model. The beamgeneration module overcomes this approximation by generating a TRIM.DAT input file according to the optical parameters of the incoming beam. The user specifies beam-dimensions in the phase-space, energy-spread, beam-emittance, dispersion and the statistical distribution. The beam parameters, including the emittance, may differ in the horizontal and vertical planes so that asymmetric beams can be handled. This is of interest for medical beams [4–6]. The module calculates the beam-contour in phase-space according to the Courant-Snyder invariant. The beam-contour is filled-in randomly by particles following a specified statistical distribution that can be Gaussian or uniform. In addition, each particle is given an energy following a specified energy-distribution that is characterized by the mean energy and the energy-spread. Finally, the particle’s energy is translated into its relative deviation with respect to the reference momentum p0 and the particle position in the phase-space is modified according to the dispersion function D. The reference momentum corresponds to the mean energy. The shift DðDp =p0 Þ is added to the particle’s initial position and the angle ðdD=dx ÞðDp =p0 Þ is added to the particle’s initial divergence. The modified particle co-ordinates are recorded in the TRIM.DAT file. The inclusion of the dispersion effects into the beammodel is not usually available in codes like SRIM. Dispersion causes a correlation between the particle position (angle) and its momentum. If the beam-line is not achromatic, it may cause a correlation between the particle range and its position, which may deform the shape of the implanted region. 4. Results The results presented demonstrate the software applied to 50 MeV protons being implanted in iron. Proton implantation in metals may be used to investigate radiation damage induced by high-energy particles [7,8]. Fig. 1 shows an emittance diagram of the beam as generated by the beam-generation module. The beam-diameter has been set to 3 mm, beam-divergence is 3 mrad, beamemittance is 4.5p mm mrad and energy-spread is 4%. The

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3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Horizontal position, Y [mm]

Fig. 1. Emittance diagram of the incoming beam as produced by the beam-generation module. Maximum beam-size (diameter) = 3 mm, RMS (1r) beam-radius = 0.5 mm, maximum beam-divergence = 3 mrad, RMS (1r) beam-divergence = 1 mrad, energy-spread = 4%, beam-emittance (total) = 4.5p mm mrad, 50E3 ions, dispersion D = 0 m.

same beam-parameters are assumed in the horizontal and the vertical planes. The beam-diameter and beam-divergence always represent the maximum values that can be given to a beam particle, i.e. they correspond to the cutoff values of the respective distributions (beam-profile and angular distribution). In addition, the RMS (1r) values of the distributions must be specified. Thus the shape of the distribution can be controlled by the user. The energy represents the mean-value of the energy-distribution and the energy-spread corresponds to a certain number of standard deviations that is also specified by the user. In the case presented, the maximum values of the beam-diameter and the beam-divergence represent three standard deviations of the distribution. The energy-spread corresponds to one standard deviation. There is no dispersion. Fig. 2 shows the horizontal (XY) view of the corresponding SRIM simulation. Fig. 3 shows the same SRIM simulation including dispersion of 0.05 m.

Fig. 3. Illustration of the dispersion effects. SRIM simulation of a real 50 MeV proton beam implanted in iron with finite dispersion at the target surface. Horizontal (XY) plane. Maximum beam-size (diameter) = 3 mm, RMS (1r) beam-radius = 0.5 mm, maximum beam-divergence = 3 mrad, RMS (1r) beam-divergence = 1 mrad, mean energy = 50 MeV, energyspread = 4%, beam-emittance (total) = 4.5p mm mrad, 50E3 protons, dispersion D = 0.05 m.

10000

1000

Number of ions

Horizontal divergence, dY/dX [mrad]

M. Pavlovicˇ, I. Strasˇı´k / Nucl. Instr. and Meth. in Phys. Res. B 257 (2007) 601–604

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0.1 5

10

15

20

25

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35

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Kinetic energy [MeV]

Fig. 4. Energy statistics in 3 mm depth as produced by the statistical module. A standard SRIM simulation using the point-like, monoenergetic incoming beam, 50 MeV protons implanted in iron, 50E3 particles.

Fig. 4 illustrates the energy-distribution of the beam after passing a 3 mm slice of the target as produced by the statistical module. 5. Discussion

Fig. 2. SRIM simulation of a real 50 MeV proton beam implanted in iron. Horizontal (XY) plane. Maximum beam-size (diameter) = 3 mm, RMS (1r) beam-radius = 0.5 mm, maximum beam-divergence = 3 mrad, RMS (1r) beam-divergence = 1 mrad, mean energy = 50 MeV, energyspread = 4%, beam-emittance (total) = 4.5p mm mrad, 50E3 protons, dispersion D = 0 m.

Results presented in Figs. 1–4 are compared quantitatively to results of standard SRIM simulations without S3M support (Table 1). The longitudinal range is not affected by the type of simulation. Longitudinal range straggling increases because of the contribution from the energy-spread of the incoming beam, which is not affected by dispersion effects. The lateral and radial ranges and straggling are largely influenced by the size of the incoming beam. Dispersion introduces a correlation between the particle range and its position (Fig. 3). It also affects the lateral

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M. Pavlovicˇ, I. Strasˇı´k / Nucl. Instr. and Meth. in Phys. Res. B 257 (2007) 601–604

Table 1 Ion statistics for different types of SRIM simulations

Longitudinal range Longitudinal range straggling Lateral projected range Lateral projected range straggling Radial range Radial range straggling

Point-like mono-energetic beam (standard SRIM)

Real-beam, dispersion = 0 m

Real-beam, dispersion = 0.05 m

4.25 mm 88.2 lm 143 lm 199 lm 226 lm 169 lm

4.25 mm 183 lm 423 lm 530 lm 665 lm 348 lm

4.25 mm 184 lm 626 lm 773 lm 965 lm 508 lm

50 MeV protons implanted in iron, beam-diameter = 3 mm, beam-divergence = 3 mrad, beam-emittance = 4.5p mm mrad, mean energy = 50 MeV, energy-spread = 4%, 50E3 incident protons.

ion statistics because it modifies the effective size of the incoming beam. A rather high-energy-spread of 4% has been chosen to make the effect visible on the scale set automatically by SRIM. The energy-spread of practical beams is typically lower and depends on the type of accelerator and beam preparation. However, the dispersion function can be significantly larger than 0.05 m, if the beam-line is designed without proper control of the dispersion function. It can reach several metres depending on the beam-line configuration. Fig. 4 is an example of the energy statistics performed by the statistical module. This SRIM simulation has been run with 50 MeV mono-energetic proton beam passing through a 3 mm iron layer that can be a slice of the full target. The distribution is presented on a semi-logarithmic scale to see particles with energies much lower than the mean energy. The mean energy of the distribution is 24.84 MeV and the standard deviation is 0.71 MeV. However, the minimum energy in the spectrum is 5.95 MeV. The low-energy particles underwent an elastic nuclear scattering that is accompanied by larger energy loss compared to particles that have been loosing energy by electronic stopping. The elastic nuclear scattering also leads to large angular kicks and these particles are likely to be lost in the following beam-transport elements. The filtering option is provided to limit the distributions above a certain number of standard deviations to exclude those particles from the beam. 6. Conclusions S3M has been successfully run and tested for many different applications including ion-implantation, beamtransport, ion-scattering and the delivery of medical

beams. It has been developed for the ion-implantation and beam-transport communities to improve SRIM simulations of experiments, especially as far as the realism of the input beam model is concerned. It is particularly suitable for investigation of the influence of beam parameters on the ion statistics and ion distributions in the target. Acknowledgements This work was carried out in the framework of VEGA 1/3188/06 supported by the Scientific Grant Agency of the Ministry of Education of Slovak Republic and MedAustron Interreg IIIA Project funded by European Union, Republic of Austria and Country of Lower Austria. The authors are indebted to Philip Bryant for his language-revision of the manuscript. References [1] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. [2] M. Pavlovicˇ, I. Strasˇ´ık, M. Rajcˇan, in: D. Pudisˇ, P. Bury, I. Jamnicky´, I. Martincˇek (Eds.), Proceedings of the 11th International Workshop on Applied Physics of Condensed Matter, 15–17 June 2005, Mala´ Lucˇivna´, Slovak Republic, p. 235. [3] I. Strasˇ´ık, M. Pavlovicˇ, M. Mozolı´k, in: M. Weis, J. Vajda (Eds.), Proceedings of the 12th International Conference on Applied Physics of Condensed Matter, 21–23 June 2006, Mala´ Lucˇivna´, Slovak Republic, p. 79. [4] M. Pavlovicˇ, Nucl. Instr. and Meth. A 438 (1999) 548. [5] M. Pavlovicˇ, E. Griesmayer, R. Seemann, Nucl. Instr. and Meth. A 545 (2005) 412. [6] M. Rajcˇan, M. Pavlovicˇ, Rep. Pract. Oncol. Radiother. 9 (6) (2004) 235. [7] V. Slugenˇ, J. Kuriplach, P. Ballo, P. Domonkosˇ, Nucl. Fusion 44 (2004) 93. [8] V. Slugenˇ et al., Fus. Eng. Des. 70 (2004) 141.