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The mean projected range and range straggling of Xe ions implanted in Si and Si1N1.375H0.603
MATERIALS SCIENCE & EWINEERING ELSEVIER
B
Materials Scienceand EngineeringB39 (1996) 133-137
The mean projected range and range straggling of Xe ions implanted in Si and SilN1.375H0.603 Ke-Ming
Wang”, Bo-Rong Shi”, Hai-Yan aDepartmmt bAcademy
&ob,
Wei-Wang”,
hi-Jun
Ding”
of Physics, Shandong University, Jinan 250100, Shandong, Peoples’ Republic of China of Sciences of Environment and Protection, Beijing 100012, Peoples’ Republic of China CDeparbnent of Physics, University at Albany, Albany, NY 12222, USA
Received20September 1995;in revisedform 6 December 1995
Abstract Xe ions at energiesfrom 50 to 400 keV as well as from 600, 800 and 1000keV were implanted into Si and Si,N,,,,,H,,,,,, respectively.The meanprojected rangesand range stragglingsare measuredby Rutherford backscatteringof MeV He ions. The values obtained are compared with different calculation procedures.The resultsshow that the maximum differencesbetween experimental and calculated values are ll%, 14% and 7% by transport of ions in matter (TRIM), projected range algorithm (PRAL) and Wang and Shi (WS) calculation procedure based on Biersack’smodel, respectively. The experimental range stragglingsare higher than the calculatedonesfor the caseof 50-400 keV Xe ions implantedinto amorphousSi. As for the case of 600, 800and 1000keV Xe implantedinto Si,N1,375H0,603, the maximum differencesbetweenexperimentaland calculatedvalues of the meanprojected range are 25%, 26% and 15%by TRIM, PRAL and WS, respectively.Also it is observedthat there are significant deviations of the experimentalvalues from the calculatedvaluesfor the range straggling.
Keywords:
Silicon;Ion implantation;Siliconnitride
1. Introduction
low-velocity ion ranges in solids [6]. In 1980-1982 Biersack proposed a simpler approach to calculate the
Since the early 1960’s a great deal of work has appeared in the literature with the aim of improving
mean projected range and range straggling based on the
interatomic potential, nuclear stopping cross section and electronic stopping cross section. A number of papers have been published on the range profiles of ions in solids [l-5]. However the experimental data to this point have been mainly concerned with lower energy regions (several hundred keV) and elemental target. More measurements of the range profile in the higher energy region and for polyatomic targets are needed in order to improve the present understanding of atomic collision processes and to test the validity of the interatomic potentials, nuclear stopping cross sections, electronic stopping cross sections and theoretical framework for calculating the range profile parameters. In range theory, the final range profiles have been calculated using either analytic transport theory or Monte-Carlo calculations. The theory of LindhardScharff-Sch@tt (LSS) is widely used for calculation of 0921-51071961315.00 0 1996- ElsevierScienceS.A. All rightsreserved
analysis of the directional angular spread of ion motion as a function of energy, and established projected range algorithm (PRAL) calculation procedure [7,8]. Usually, implantation profiles are described by Pearson-IV distributions with four moments: mean projected range, range straggling, skewness and kurtosis [9]. The mean projected ranges and range stragglings related to them are especially important. The projected range is used to predict the average penetration depth in design of ion bombardment experiments. The range straggling is even more important because it controls the density of ions in the implanted layer. The main purposes of this work are first, to measure the mean projected range and range straggling of Xe ions at energies from 50 to 400 keV as well as from 600, 800 and 1000 keV in Si and Si,N,,,,,H,,,,, by Rutherford backscattering of MeV He ions, respectively; second, to compare results obtained with’TRIM code [lo],
134
Ke-Ming
Wang et al. / Materials Science and Engineering B39 (1996) 133-137
PRAL and Wang and Shi’s calculation procedure based on Biersack’s angular spread model OyS).
2. Experimental Polished n-type single crystal silicon wafers of (100) orientation with 5 R cm resistivity were used as samples. The samples were amorphized by means of Ar+ irradiation with different energies to a total dose of 2 x 10” ions per cm2 at room temperature to obtain an amorphous layer thicker than the predicted Xe range. The implantation energy of Xe ion was varied between 50 and 400 keV with increments of 50 keV. The current density was less than 1 PA cm - 2 to avoid excessive heating of the sample. To minimize sputtering effects on the range profiles and to have enough sensitivity of the backscattering measurement, the doses of 4 x lOI ions per cm* and 2 x 1015 ions per cm2 were chosen at lower and higher energies, respectively. Implantations above 200 keV were carried out using double-charged Xe2 + . All implantations were performed at room temperature. In order to ensure uniformity over the implanted area, a two-directional electrostatic system for parallel scanning was used. A neutral beam trap was also used. The hydrated silicon nitride (SilN1,375H,,,6,,3) film has a thickness of 1 p by chemical vapour deposition (CVD). The quality of the film was checked by Rutherford backscattering (RBS) to ensure that it was not contaminated before implantation, 600, 800 and 1000 keV Xe ions were implanted into the SilN1,375H0,6,,3 film at room temperature with the dose of 1 x 1016 ions per cm2. To our knowledge, there is no experimental data on the sputtering yield of SilN1,375H,,6,,3 by 800-1000 keV Xe ions. We used the TRIM code to simulate it. The sputtering yields are 0.5714 atoms per ion, 0.5000 atoms per ion and 0.3571 atoms per ion for Si, N, and H for the case of SilN1,375H0,6,,3 implanted by 1000 keV Xe ions. The sputtering thickness estimated is less than 16 A which causes an error of 1% in the range measurement. Therefore the effect of sputtering on the range measurement can be neglected. The mean projected range and range straggling were measured by Rutherford backscattering of MeV He ion beams. Some samples were measured twice with the beam impinging perpendicularly onto the sample surface and under an angle of 50” with the sample’s normal, Tilted geometry improves the depth resolution of the measurements. Backscattered He ions were registered by a silicon barrier detector placed at 165” with respect to the beam direction. The beam size is about 2 x 2 mm2. When the implant distribution in depth is Gaussian, the depth profile can be described by the projected range and range straggling which is the standard deviation of the Gaussian distribution in depth.
The range straggling has been obtained from the measured full width at half maximum (FWHM) after performing the deconvolution process under the assumption that the estimated energy straggling of He ions in Si and SilN,,375H0.6,,3 and the system resolution are both Gaussian [ 111. Calculated values of the He ion energy straggling normalized to Bohr’s theory were used [12]. The error assignment was estimated from the stability of the Si energy edge of the spectrum. The error assignment was determined by + 2 channels. Each channel was equal to 42 8, for the case of Si. The lower and higher energy implantations were performed on an ion implanter made at the Shandong University and 4.3 MV Dynamitron accelerator of University at Albany, USA, respectively. The RBS measurements were carried out at 1.7 MV tandem accelerator of the Shandong University and 4.3 MV Dynamitron accelerator of University at Albany, respectively.
3. Results and discussion All backscattering energy spectra show a nearly Gaussian distribution for Xe ion implanted in Si. These spectra were fitted via a computer program to obtain the values of the peak position and FWHM of depth distribution of implanted Xe ions. These were related to the projected range and range straggling of Xe ions, respectively. Fig. 1 depicts a typical energy spectrum of 2.1 MeV He ions backscattered from 150 keV Xe ions implanted in amorphous Si. In order to improve the depth resolution, we have used the glancing angle Rutherford backscattering to measure the range profile of Xe ions at lower energy region,
/ 3
i
Xe * ‘.
800
400 Channels
Fig. 1. Typical Rutherford backscattering spectrum of 2.1 MeV He ions for 150 keV Xe ions implanted in amorphous Si.
Ke-Ming
Wang et al. 1 Materials
Science
and Engineering
839 (1996)
135
133-137
--- Xe-Si St
Fig. 2. Calculated nuclear cross section &, electronic stopping cross section S, and total stopping cross section S, as a function of energy for Xe ion incident on amorphous Si.
Gibbons et al. [13] used the LSS procedure to calculate the mean projected range and range straggling for various ions in solids. Based on Biersack’s angular spread model, Wang and Shi have established an efficient method for calculating range and range straggling of heavy ions in solids. The detail of the WS calculation has been described elsewhere [14]. The important input quantities in the present calculation are reliable nuclear and total stopping cross section as functions of energy. During the calculation, the nuclear stopping cross section S,,, proposed by Wilson, Haggmark and Biersack (WHB) [15] and implemented by Littmark and Ziegler [16] has been used. To obtain the total stopping cross section, we required the electronic stopping cross section S,. Vargas-Aburto et al. [17] and Montenegro et al. [18] have derived an equation for S, of ions moving at non-relativistic velocities in solid target. Although this equation was obtained through a semiphenomenological analysis of the different mechanisms, its final form does not depend, in principle, on any adjustable parameter: Fig. 2 shows the calculated nuclear stopping cross section S,,, electronic stopping cross section S, and total stopping cross section S, as a function of energy E for Xe ions incident on amorphous Si. One of the purposes of this work is to compare the experimental mean projected range and range straggling of Xe ions in Si with the WS code. In order to improve the prediction of projected range and range straggling, it is necessary to consider higher energy loss moments in nuclear stopping, such as the second moment of nuclear energy loss in Biersack’s model. Fig. 3 compares the experimental data with calculated values on the mean projected range and
10
10 ENERGY(ke$ z ’
10 4
Fig. 3. Comparison of experimental with calculated values of the mean projected range and range straggling for Xe ions implanted at energies from 50 to 4OOkeV in amorphous Si. The lines represent calculated values by WS based on Biersack’s model. The solid line for ARp is obtained after including the second order energy loss. Square and triangle represent experimental data for R/, and AR,,, respectively.
range straggling. The calculated values are obtained by WS. The result indicates that there is a good agreement between the measured projected ranges and calculated values. The maximum difference between them is less than 7%. As for the range straggling, the maximum difference between experimental and calculated values of range straggling is less than 32%. For comparison, calculated value by TRIM’89 and PRAL are included also. Table 1 lists the comparison of experimental data with calculated values by TRIM’89, PRAL and WS on mean projected range and range straggling for Xe ions implanted in amorphous Si at energies from 50 to 400 keV. The results show that the maximum differences Table 1 Comparison of experimental and calculated values of mean projected range Rp and range straggling ARp for 50-400 keV Xe ions implanted into amorphous Si
E(keV)
Exp. TRIM
PRAL
WS
EXP.
TRIM
PRAL
WS
50 100 150 200 250 300 350 400
332 299 498 483 664 651 831 804 997 965 1246 1120 1412 1255 1578 1421
292 470 632 788
315 514 702 880 1061 1237 1449 1588
108 163 186 253 294 373 412 506
79 123 168 214 238 289 319 337
75 111 142, 170
86 132 172 209 245 280 319 345
1068 1376
222 269
136
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Wang et al. / Materials
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B39 (1996)
133-137
Table 2 Comparison of experimental and calculated values of mean projected range R,, and range straggling AR,, for 200-1000 keV Xe ions implanted into amorphous Si. 200-600 keV Xe data came from Ref. [19]. 850-1000 keV data came from Ref. [20] E(keV)
200 300 400 500 600 850 1000
RpO% EXP.
TRIM
PRAL
WS
AR,&) EXP.
TRIM
PRAL
WS
891 1220 1559 1869 2154 3100 3700
785(1.14) 1220(1.09) 1421(1.10) 1699(1.10) 1980(1.09) 2654( 1.17) 3055(1.21)
790(1.13) 1089(1.12) 1379(1.13) 1664(1.12) 1944(1.11) 2631(1.18) 3034( 1.22)
880(1.01) 1237(0.99) 1588(0.98) 1955(0.96) 2309(0.93) 3138(0.99) 3647(1.01)
278 362 474 547 655 810 934
230 289 337 401 463 613 655
170 222 269 313 354 464 497
209 280 345 411 470 594 666
between experimental and calculated values are ll%, 14% and 7% by TRIM, PRAL, WS, respectively. In order to compare the other published data [19,20] with different calculation procedures, Table 2 lists the data for 200 to 1000 keV Xe ions implanted in amorphous Si. The results show that the maximum differences between the calculated and experimental data of mean projected range are 21%, 22% and 7%, by TRIM’89, PRAL and WS, respectively. However, the experimental range stragglings are larger than the calculated values by different calculation procedure. Fig. 4 shows the depth distributions of 600 and 800 keV Xe ions implanted into SilN1,375H0,603 film obtained by normal incidence Rutherford backscattering of 2.4 MeV He ions. It is observed that the depth distributions are still nearly Gaussian. Table 3 lists the comparison of experimental values with TRIM code, PRAL and WS calculation procedure for 600, 800 and 1000 keV Xe ions implanted into SilN,,375H0,603. In the calculation, the density of SilN1,375H0,6,,3 is estimated to be 2.9 g cm-3. It is important to mention that the Energy 1.7 400 /
1.8 I
(MeV)
1.9 I
2.0 I
l
/
5 200 t
0
I
:. , .
..
-.
n
8.:. t
% ‘_o
4. Summary The mean projected range and range straggling of Xe ions implanted at energies from 50 to 400 keV in amorphous Si as well as from 600, 800 and 1000 keV in have been measured by Rutherford SiK3dLo3 backscattering with MeV He ions. The measured values are compared with TRIM code, PRAL and WS calculation procedure. For the case of 50-400 keV Xe ions implanted into amorphous Si, the maximum differences
2.1 I
0 GOOkeV Xe-SiNH 800keV Xe-SiNH
d
relative difference between the experimental and theoretical values is independent of the assumed density [21]. The results show that the maximum differences between experimental and calculated values of mean projected range are 25%, 26% and 15% by TRIM, PRAL and WS, respectively. The experimental range straggling is higher than that calculated by different codes. This phenomenon is somewhat similar to the result reported by Behar et al. [22]. According to Ref. [22], the mean projected ranges are systematically lower than experimental ones, being on average around 30% and the experimental values of range straggling always exceed the predicted ones with the difference being almost 100% for Pb, Bi and Au ions implanted into boron films by the TRIM code. They found that good agreement between experimental and calculated values of the mean projected range was improved after considering the correlation between the nuclear and electronic stopping power in the ZBL calculation.
I
00
Table 3 Comparison of experimental and calculated values of mean projected range Rp and range straggling ARpfor 600 keV, 800 keV and 1000 keV Xe ions implanted into Si,N,,,,,Ho,ao3 E&W
0
860
Channel Fig. 4. Depth distribution of 600 and 800 keV Xe ions implanted in WJl.375%603 films. The open and full circles represent the data of 600 and 800 keV Xe ions, respectively.
600 800 1000
$,(A) EXP. TRIM
PRAL
WS
AR,,& EXP.
1763 1447 2269 1855 2979 2245
1410 1812 2207
1611 447 2058 558 2518 647
TRIM
PRAL WS
306
190 231 268
351 418
272 326 376
Ke-Ming
Wang
et al. ] Materials
Science
between the experimental and calculated values of mean projected range are 1 l%, 14% and 7% by TRIM, PRAL and WS, respectively. For the published data of 2001000 keV Xe ions implanted into amorphous Si, the maximum differences between the experimental and calculated values of mean projected range are 21%, 22% and 7% by TRIM, PRAL and WS, respectively. However, the experimental range stragglings are higher than calculated values by different calculation procedures. As for the data of 600, 800 and 1000 keV Xe ions implanted into W1.375H0.603, the maximum differences between experimental and calculated values of the mean projected range are 25%, 26% and 1594, by TRIM code, PRAL and WS calculations, respectively. It is found that there are significant deviations of the experimental data of range straggling from calculated values. More measurements of range profile of implanted ions in a higher energy region and for polyatomic target are needed to test the prediction by different calculation procedures.
Acknowledgements The authors would like thank Professor W.A. Lanford of University at Albany and Ji-Tian Liu, Ju-Xin Lu and Xiang-Dong Liu of Shandong University for their help in this work.
References [I] P.L. Grande, P.F.P. Fichtner, M. Behar and F.C. Zawislak, ~Vucl. Instr. and Methods, B35 (1988) 17.
and Engineering
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133-137
137
[21 P.L. Grande, P.F.P. Fichtner, M. Behar, R.P. Livi, F.C. Zawis-
lak, J.P. Biersack, D. Fink and P. Mettens, Nucl. Znstr.and Methods,
B19/20
(1987)
25.
[31 K.-M. Wang, X.-J. Liu, Y.-H. Wang, J.-T. Liu, H.-Y. Guo and B.-R. Shi, Phys. Lett. A, 125 (1987) 399. F. [41 Besenbacher, J. Bmttiger, T. Laursen, P. Loftager and W. Miiller, Nucl. Instr. and Methods, B170 (1980) 183. J. Berthold and S. Kalbitzer, Phys. Lett. A, 92 (1982) 37. :; J. Lindhard, M. Scharff and H.E. SchiBtt, K. Dan Vidensk Selsk Mat. Fys. Medd., 33 (14) (1963) 1. [71 J.P. Biersack, iVzx/. lnstr. and Methods, 182/183 (1981) 199. PI J.P. Biersack, Z. Phys. A, 305(1982) 95. [91 H. Ryssel, K. Haberger, K. Haffman, G. Prinke, R. Dumcke and A. Sachs, IEEE Trans. Electron Devices, ED-27 (8) (1980) 1484. [lOI J.P. Biersack and L.G. Haggmark, iV&. Instr. and Methods, 174 (1980) 257. [Ill W.K. Chu, J.W. Mayer and M.A. Nicolet, Backscattering Spectrometry, Academic Press, New York, 1978. El21W.K.Chu, Phys. Rev. B, 13 (1976) 2057. u31 J.F. Gibbons, W.S. Johnson and S.W. Mylroie, Projected Range Statistics, Pennsylvania, Stroudsburg, 1975. [I41 K.-M. Wang and B.-R. Shi, J. Phys. D, 23 (1990) 1282. [151 W.D. Wilson, L.G. Haggmark and J.P. Biersack, Phys. Rev. B, 15 (1977) 2458. of U61U. Littmark and J.F. Ziegler, Handbook of Range Distribution Energetic Ions iu All Elements, Vo1.6, Pergamon, New York, 1978. C. Vargas-Aburto, S.A. Cruz and E.C. Montenegro, Rad. [I71 Effects, 80 (1984) 23. [I81 E.C. Montenegro, S.A. Cruz and C. Vargas-Aburto, Phys. Lett. A, 92 (1982) 195. El91C. Tan, Y. Xia, H. Yang, X. Sun, J. Liu, Z. Zheng and P. Zhu, Nucl. Instr. and Methods, B42 (1989) 1. PO1R.J. Schreuteikamp, J.R. Liefting, P.M. Zagwign, W.X. Liu and F.W. Saris, Nucl. Instr. and Methods, B48 (1990) 448. F. 1211 Abel, M. Behar and C. Cohen, h’ucl. Instr. and Methods, B30 (1988) 13. [221 M. Behar, P.L. Grande, R. Wanger de Oliveira and J.P. Biersack, ~Vzlcl. Instr. and Methods, B59/60 (1991) 1.
B
Materials Scienceand EngineeringB39 (1996) 133-137
The mean projected range and range straggling of Xe ions implanted in Si and SilN1.375H0.603 Ke-Ming
Wang”, Bo-Rong Shi”, Hai-Yan aDepartmmt bAcademy
&ob,
Wei-Wang”,
hi-Jun
Ding”
of Physics, Shandong University, Jinan 250100, Shandong, Peoples’ Republic of China of Sciences of Environment and Protection, Beijing 100012, Peoples’ Republic of China CDeparbnent of Physics, University at Albany, Albany, NY 12222, USA
Received20September 1995;in revisedform 6 December 1995
Abstract Xe ions at energiesfrom 50 to 400 keV as well as from 600, 800 and 1000keV were implanted into Si and Si,N,,,,,H,,,,,, respectively.The meanprojected rangesand range stragglingsare measuredby Rutherford backscatteringof MeV He ions. The values obtained are compared with different calculation procedures.The resultsshow that the maximum differencesbetween experimental and calculated values are ll%, 14% and 7% by transport of ions in matter (TRIM), projected range algorithm (PRAL) and Wang and Shi (WS) calculation procedure based on Biersack’smodel, respectively. The experimental range stragglingsare higher than the calculatedonesfor the caseof 50-400 keV Xe ions implantedinto amorphousSi. As for the case of 600, 800and 1000keV Xe implantedinto Si,N1,375H0,603, the maximum differencesbetweenexperimentaland calculatedvalues of the meanprojected range are 25%, 26% and 15%by TRIM, PRAL and WS, respectively.Also it is observedthat there are significant deviations of the experimentalvalues from the calculatedvaluesfor the range straggling.
Keywords:
Silicon;Ion implantation;Siliconnitride
1. Introduction
low-velocity ion ranges in solids [6]. In 1980-1982 Biersack proposed a simpler approach to calculate the
Since the early 1960’s a great deal of work has appeared in the literature with the aim of improving
mean projected range and range straggling based on the
interatomic potential, nuclear stopping cross section and electronic stopping cross section. A number of papers have been published on the range profiles of ions in solids [l-5]. However the experimental data to this point have been mainly concerned with lower energy regions (several hundred keV) and elemental target. More measurements of the range profile in the higher energy region and for polyatomic targets are needed in order to improve the present understanding of atomic collision processes and to test the validity of the interatomic potentials, nuclear stopping cross sections, electronic stopping cross sections and theoretical framework for calculating the range profile parameters. In range theory, the final range profiles have been calculated using either analytic transport theory or Monte-Carlo calculations. The theory of LindhardScharff-Sch@tt (LSS) is widely used for calculation of 0921-51071961315.00 0 1996- ElsevierScienceS.A. All rightsreserved
analysis of the directional angular spread of ion motion as a function of energy, and established projected range algorithm (PRAL) calculation procedure [7,8]. Usually, implantation profiles are described by Pearson-IV distributions with four moments: mean projected range, range straggling, skewness and kurtosis [9]. The mean projected ranges and range stragglings related to them are especially important. The projected range is used to predict the average penetration depth in design of ion bombardment experiments. The range straggling is even more important because it controls the density of ions in the implanted layer. The main purposes of this work are first, to measure the mean projected range and range straggling of Xe ions at energies from 50 to 400 keV as well as from 600, 800 and 1000 keV in Si and Si,N,,,,,H,,,,, by Rutherford backscattering of MeV He ions, respectively; second, to compare results obtained with’TRIM code [lo],
134
Ke-Ming
Wang et al. / Materials Science and Engineering B39 (1996) 133-137
PRAL and Wang and Shi’s calculation procedure based on Biersack’s angular spread model OyS).
2. Experimental Polished n-type single crystal silicon wafers of (100) orientation with 5 R cm resistivity were used as samples. The samples were amorphized by means of Ar+ irradiation with different energies to a total dose of 2 x 10” ions per cm2 at room temperature to obtain an amorphous layer thicker than the predicted Xe range. The implantation energy of Xe ion was varied between 50 and 400 keV with increments of 50 keV. The current density was less than 1 PA cm - 2 to avoid excessive heating of the sample. To minimize sputtering effects on the range profiles and to have enough sensitivity of the backscattering measurement, the doses of 4 x lOI ions per cm* and 2 x 1015 ions per cm2 were chosen at lower and higher energies, respectively. Implantations above 200 keV were carried out using double-charged Xe2 + . All implantations were performed at room temperature. In order to ensure uniformity over the implanted area, a two-directional electrostatic system for parallel scanning was used. A neutral beam trap was also used. The hydrated silicon nitride (SilN1,375H,,,6,,3) film has a thickness of 1 p by chemical vapour deposition (CVD). The quality of the film was checked by Rutherford backscattering (RBS) to ensure that it was not contaminated before implantation, 600, 800 and 1000 keV Xe ions were implanted into the SilN1,375H0,6,,3 film at room temperature with the dose of 1 x 1016 ions per cm2. To our knowledge, there is no experimental data on the sputtering yield of SilN1,375H,,6,,3 by 800-1000 keV Xe ions. We used the TRIM code to simulate it. The sputtering yields are 0.5714 atoms per ion, 0.5000 atoms per ion and 0.3571 atoms per ion for Si, N, and H for the case of SilN1,375H0,6,,3 implanted by 1000 keV Xe ions. The sputtering thickness estimated is less than 16 A which causes an error of 1% in the range measurement. Therefore the effect of sputtering on the range measurement can be neglected. The mean projected range and range straggling were measured by Rutherford backscattering of MeV He ion beams. Some samples were measured twice with the beam impinging perpendicularly onto the sample surface and under an angle of 50” with the sample’s normal, Tilted geometry improves the depth resolution of the measurements. Backscattered He ions were registered by a silicon barrier detector placed at 165” with respect to the beam direction. The beam size is about 2 x 2 mm2. When the implant distribution in depth is Gaussian, the depth profile can be described by the projected range and range straggling which is the standard deviation of the Gaussian distribution in depth.
The range straggling has been obtained from the measured full width at half maximum (FWHM) after performing the deconvolution process under the assumption that the estimated energy straggling of He ions in Si and SilN,,375H0.6,,3 and the system resolution are both Gaussian [ 111. Calculated values of the He ion energy straggling normalized to Bohr’s theory were used [12]. The error assignment was estimated from the stability of the Si energy edge of the spectrum. The error assignment was determined by + 2 channels. Each channel was equal to 42 8, for the case of Si. The lower and higher energy implantations were performed on an ion implanter made at the Shandong University and 4.3 MV Dynamitron accelerator of University at Albany, USA, respectively. The RBS measurements were carried out at 1.7 MV tandem accelerator of the Shandong University and 4.3 MV Dynamitron accelerator of University at Albany, respectively.
3. Results and discussion All backscattering energy spectra show a nearly Gaussian distribution for Xe ion implanted in Si. These spectra were fitted via a computer program to obtain the values of the peak position and FWHM of depth distribution of implanted Xe ions. These were related to the projected range and range straggling of Xe ions, respectively. Fig. 1 depicts a typical energy spectrum of 2.1 MeV He ions backscattered from 150 keV Xe ions implanted in amorphous Si. In order to improve the depth resolution, we have used the glancing angle Rutherford backscattering to measure the range profile of Xe ions at lower energy region,
/ 3
i
Xe * ‘.
800
400 Channels
Fig. 1. Typical Rutherford backscattering spectrum of 2.1 MeV He ions for 150 keV Xe ions implanted in amorphous Si.
Ke-Ming
Wang et al. 1 Materials
Science
and Engineering
839 (1996)
135
133-137
--- Xe-Si St
Fig. 2. Calculated nuclear cross section &, electronic stopping cross section S, and total stopping cross section S, as a function of energy for Xe ion incident on amorphous Si.
Gibbons et al. [13] used the LSS procedure to calculate the mean projected range and range straggling for various ions in solids. Based on Biersack’s angular spread model, Wang and Shi have established an efficient method for calculating range and range straggling of heavy ions in solids. The detail of the WS calculation has been described elsewhere [14]. The important input quantities in the present calculation are reliable nuclear and total stopping cross section as functions of energy. During the calculation, the nuclear stopping cross section S,,, proposed by Wilson, Haggmark and Biersack (WHB) [15] and implemented by Littmark and Ziegler [16] has been used. To obtain the total stopping cross section, we required the electronic stopping cross section S,. Vargas-Aburto et al. [17] and Montenegro et al. [18] have derived an equation for S, of ions moving at non-relativistic velocities in solid target. Although this equation was obtained through a semiphenomenological analysis of the different mechanisms, its final form does not depend, in principle, on any adjustable parameter: Fig. 2 shows the calculated nuclear stopping cross section S,,, electronic stopping cross section S, and total stopping cross section S, as a function of energy E for Xe ions incident on amorphous Si. One of the purposes of this work is to compare the experimental mean projected range and range straggling of Xe ions in Si with the WS code. In order to improve the prediction of projected range and range straggling, it is necessary to consider higher energy loss moments in nuclear stopping, such as the second moment of nuclear energy loss in Biersack’s model. Fig. 3 compares the experimental data with calculated values on the mean projected range and
10
10 ENERGY(ke$ z ’
10 4
Fig. 3. Comparison of experimental with calculated values of the mean projected range and range straggling for Xe ions implanted at energies from 50 to 4OOkeV in amorphous Si. The lines represent calculated values by WS based on Biersack’s model. The solid line for ARp is obtained after including the second order energy loss. Square and triangle represent experimental data for R/, and AR,,, respectively.
range straggling. The calculated values are obtained by WS. The result indicates that there is a good agreement between the measured projected ranges and calculated values. The maximum difference between them is less than 7%. As for the range straggling, the maximum difference between experimental and calculated values of range straggling is less than 32%. For comparison, calculated value by TRIM’89 and PRAL are included also. Table 1 lists the comparison of experimental data with calculated values by TRIM’89, PRAL and WS on mean projected range and range straggling for Xe ions implanted in amorphous Si at energies from 50 to 400 keV. The results show that the maximum differences Table 1 Comparison of experimental and calculated values of mean projected range Rp and range straggling ARp for 50-400 keV Xe ions implanted into amorphous Si
E(keV)
Exp. TRIM
PRAL
WS
EXP.
TRIM
PRAL
WS
50 100 150 200 250 300 350 400
332 299 498 483 664 651 831 804 997 965 1246 1120 1412 1255 1578 1421
292 470 632 788
315 514 702 880 1061 1237 1449 1588
108 163 186 253 294 373 412 506
79 123 168 214 238 289 319 337
75 111 142, 170
86 132 172 209 245 280 319 345
1068 1376
222 269
136
Ke-Ming
Wang et al. / Materials
Science
and Engineering
B39 (1996)
133-137
Table 2 Comparison of experimental and calculated values of mean projected range R,, and range straggling AR,, for 200-1000 keV Xe ions implanted into amorphous Si. 200-600 keV Xe data came from Ref. [19]. 850-1000 keV data came from Ref. [20] E(keV)
200 300 400 500 600 850 1000
RpO% EXP.
TRIM
PRAL
WS
AR,&) EXP.
TRIM
PRAL
WS
891 1220 1559 1869 2154 3100 3700
785(1.14) 1220(1.09) 1421(1.10) 1699(1.10) 1980(1.09) 2654( 1.17) 3055(1.21)
790(1.13) 1089(1.12) 1379(1.13) 1664(1.12) 1944(1.11) 2631(1.18) 3034( 1.22)
880(1.01) 1237(0.99) 1588(0.98) 1955(0.96) 2309(0.93) 3138(0.99) 3647(1.01)
278 362 474 547 655 810 934
230 289 337 401 463 613 655
170 222 269 313 354 464 497
209 280 345 411 470 594 666
between experimental and calculated values are ll%, 14% and 7% by TRIM, PRAL, WS, respectively. In order to compare the other published data [19,20] with different calculation procedures, Table 2 lists the data for 200 to 1000 keV Xe ions implanted in amorphous Si. The results show that the maximum differences between the calculated and experimental data of mean projected range are 21%, 22% and 7%, by TRIM’89, PRAL and WS, respectively. However, the experimental range stragglings are larger than the calculated values by different calculation procedure. Fig. 4 shows the depth distributions of 600 and 800 keV Xe ions implanted into SilN1,375H0,603 film obtained by normal incidence Rutherford backscattering of 2.4 MeV He ions. It is observed that the depth distributions are still nearly Gaussian. Table 3 lists the comparison of experimental values with TRIM code, PRAL and WS calculation procedure for 600, 800 and 1000 keV Xe ions implanted into SilN,,375H0,603. In the calculation, the density of SilN1,375H0,6,,3 is estimated to be 2.9 g cm-3. It is important to mention that the Energy 1.7 400 /
1.8 I
(MeV)
1.9 I
2.0 I
l
/
5 200 t
0
I
:. , .
..
-.
n
8.:. t
% ‘_o
4. Summary The mean projected range and range straggling of Xe ions implanted at energies from 50 to 400 keV in amorphous Si as well as from 600, 800 and 1000 keV in have been measured by Rutherford SiK3dLo3 backscattering with MeV He ions. The measured values are compared with TRIM code, PRAL and WS calculation procedure. For the case of 50-400 keV Xe ions implanted into amorphous Si, the maximum differences
2.1 I
0 GOOkeV Xe-SiNH 800keV Xe-SiNH
d
relative difference between the experimental and theoretical values is independent of the assumed density [21]. The results show that the maximum differences between experimental and calculated values of mean projected range are 25%, 26% and 15% by TRIM, PRAL and WS, respectively. The experimental range straggling is higher than that calculated by different codes. This phenomenon is somewhat similar to the result reported by Behar et al. [22]. According to Ref. [22], the mean projected ranges are systematically lower than experimental ones, being on average around 30% and the experimental values of range straggling always exceed the predicted ones with the difference being almost 100% for Pb, Bi and Au ions implanted into boron films by the TRIM code. They found that good agreement between experimental and calculated values of the mean projected range was improved after considering the correlation between the nuclear and electronic stopping power in the ZBL calculation.
I
00
Table 3 Comparison of experimental and calculated values of mean projected range Rp and range straggling ARpfor 600 keV, 800 keV and 1000 keV Xe ions implanted into Si,N,,,,,Ho,ao3 E&W
0
860
Channel Fig. 4. Depth distribution of 600 and 800 keV Xe ions implanted in WJl.375%603 films. The open and full circles represent the data of 600 and 800 keV Xe ions, respectively.
600 800 1000
$,(A) EXP. TRIM
PRAL
WS
AR,,& EXP.
1763 1447 2269 1855 2979 2245
1410 1812 2207
1611 447 2058 558 2518 647
TRIM
PRAL WS
306
190 231 268
351 418
272 326 376
Ke-Ming
Wang
et al. ] Materials
Science
between the experimental and calculated values of mean projected range are 1 l%, 14% and 7% by TRIM, PRAL and WS, respectively. For the published data of 2001000 keV Xe ions implanted into amorphous Si, the maximum differences between the experimental and calculated values of mean projected range are 21%, 22% and 7% by TRIM, PRAL and WS, respectively. However, the experimental range stragglings are higher than calculated values by different calculation procedures. As for the data of 600, 800 and 1000 keV Xe ions implanted into W1.375H0.603, the maximum differences between experimental and calculated values of the mean projected range are 25%, 26% and 1594, by TRIM code, PRAL and WS calculations, respectively. It is found that there are significant deviations of the experimental data of range straggling from calculated values. More measurements of range profile of implanted ions in a higher energy region and for polyatomic target are needed to test the prediction by different calculation procedures.
Acknowledgements The authors would like thank Professor W.A. Lanford of University at Albany and Ji-Tian Liu, Ju-Xin Lu and Xiang-Dong Liu of Shandong University for their help in this work.
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[21 P.L. Grande, P.F.P. Fichtner, M. Behar, R.P. Livi, F.C. Zawis-
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