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Low energy ion implantation simulation using a modified binary collision approximation code
cw .__
Nuclear Instruments
and Methods in Physics Research B 102 (1995) 228-231
NOMB
El E8
Beam Interactions with Materials 8 Atoms
!s
ELSEVIER
Low energy ion implantation simulation using a modified binary collision approximation code J. Arias
*, M.
Jaraiz, L. Pelaz, L.A. Bail&, J. Barbolla
Dept. de E. y Electrhzica, Facultad de Ciencias, Uniuersidad de Valladolid, 47011 Valladolid, Spain
Abstract We have developed a modified version of the binary collision approximation code MARLOWE with the aim of accurately predict the implanted dopant profiles, even in the low energy case. In our simulations, instead of using the asymptotic path of the projectile, the path of the colliding particles is carefully evaluated for each collision. In order to avoid the computation time penalty of such calculation, the data of the outgoing particles is tabulated previously for a large set of collision events, and an interpolation is done during the main Monte Carlo simulation. The simulated profiles show a better agreement with the experimental data for low energy implants, while the accuracy for the high energy implants is maintained.
2. Computer simulation
1. Introduction The ever smaller feature size of the new silicon electronic devices demand, as a routine step in their fabrication, the use of low energy ion implantation in order to obtain shallow junctions. For the simulation of the implantation process in this low energy regime, in the range of hundreds to a few thousands eV, two different kinds of simulation codes can be used. The molecular dynamics (MD) calculation method is very accurate but also very computer time consuming because all the interatomic forces are taken into account in the computation of the projectile path, and many timesteps are required for each collision. The other approach is the binary collision approximation (BCA). Here only the forces between the projectile and the closest target are evaluated, and this leads to a classical central force two body scattering. The path of each moving particle is approximated by a series of straight line segments, each one over a collision asymptote. This last simulation model is much less time consuming than the MD, and gives good simulation profiles for medium and high implantation energies. However in the low energy range it yields poor results. In this work we have developed a binary collision code with a projectile path calculation more accurate than the asymptotic one in order to fit the low energy experimental profiles, while maintaining a reduced computer time in the simulations.
Corresponding 423013. l
author.
Tel.
+34
83 423225,
fax
+34
83
We have chosen the binary collision approximation code MARLOWE [l] as the starting point of our study because it has proved to be a successful tool to analyze and predict the results of ion implantation on crystalline targets. In our simulations we have used a highly modified version of MARLOWE. Some of its many features are described in Ref. [2]. We have used the Universal ZBL [3] interatomic potential with a cutoff distance of 0.3 nm. We have also tested a specific boron-silicon interatomic potential [4], but no substantial differences with the results of the universal potential were found. The default OenRobinson [I] model for electronic stopping is not used in our version of MARLOWE. The electronic energy loss of incoming ions is calculated through the Local Electron Density approximation. A spherically symmetric electronic distribution is placed at the target atom location, and the electronic energy loss is computed along the path of the ion, assuming a constant electronic density at each point of the path [5]. We use the proton electronic stopping model developed by Echenique et al. [6] and the heavy ion scaling rules of Brandt and Kitagawa [7]. Some approximations to the mentioned models were used in order to improve the computational efficiency. In the simulations the impact point of each ion is randomly chosen on the surface of the target. The amorphous silicon is simulated by the random rotation of the crystal lattice in each collision [ 11. It is usually assumed in the binary collision approximation that at the start of the collision the projectile and the target are far enough so that they do not interact with each
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(94)00809-4
J. Arias et al. /Nucl.
229
Instr. and Meth. in Phys. Res. B 102 (1995) 228-231
described above were used. This process involves the exact calculation of the projectile and target trajectories, subtracting the inelastic losses along the path. In the calculation of the scattering tables the initial value of the potential energy in the collision is subtracted from the kinetic energy of the projectile in order to maintain constant the total energy, that would otherwise be incorrectly increased.
3. Results
0 0
2
.4
.5
.B
1.0
Probability
Fig. 1. Potential energy-kinetic energy ratio vs. probability at the beginning of each collision event for 80 keV and 0.5 keV boron implant into amorphous silicon.
other. That means that the interatomic potential at the start of a collision must be negligible compared to the kinetic energy. If this is not the case, the asymptotic path approximation might yield poor results. In order to test the accuracy of the asymptotic path approximation we have carried out some simulations of boron implantation into silicon at room temperature. Fig. 1 shows the results for 0.5 keV and 80 keV simulations. The probability of the initial potential energy-kinetic energy ratio of each collision events differs clearly for the two implants. As can be seen in the graph, the number of collisions with an initial energy ratio greater than 0.1 is about 13% in the 0.5 keV implant, while it is negligible in the 80 keV implant. As a result, we expect that the low energy implant yields a simulated profile with a larger error than the high energy implant, because the asymptotic path approximation is not accurate enough. In an attempt to correct the trajectories of the colliding particles we have developed a modified version of MARLOWE. The aim was also to reduce the computation time needed in the evaluation of the two body scattering parameters and the electronic inelastic energy losses. In this version the scattering angles, the deflection points of the particles and the inelastic energy losses were tabulated before the simulation. During the simulation an interpolation procedure is used to speed up the computation. The tables are stored on a disk file and they have to be calculated only once for each set of atoms. The entries in the tables for each possible collision are the projectile kinetic energy, the impact parameter and the distance from the projectile position to its uncorrected collision point 5 [l]. The data in the tables were calculated following a scheme similar to the one used in the molecular dynamics method, but it is much simpler, because only two particles are involved. The repulsive only Universal ZBL interatomic potential, and the electronic energy loss model
We have tested the new code with some published experimental data [5] of channelled boron implants into silicon in the energy range of 10 to 100 keV. The agreement between the simulated and the experimental profiles in this energy range is good, as can be seen, for example in Fig. 2 for an 80 keV implant. As expected, in the high energy regime the asymptotic path approximation works well, and no major differences with the new model were found, except for a slightly increased channeling as can be seen on the trailing edge and on the raising of the profile at about 500 nm (the leading edge, at 500 nm, is fixed by the electronic stopping in the (100) channel a that energy). In the low energy range the results of the two models differ clearly. In Figs. 3 and 4 the simulated profiles obtained using the asymptotic path approximation and the corrected model, respectively, are presented together with the experimental profiles [8] for a 500 eV boron implant into amorphous and crystalline silicon. Except for the scattering calculation, the remaining parameters, such as the interatomic potential and the inelastic energy loss model, are the same in the two simulations. Regarding the experimental profiles, and as it was mentioned by the authors in a previous paper [9], the low temperature annealing, following the sample implantation, has only a little effect on the boron profile, and they expect that the
Fig. 2. 80 keV boron implantation into crystalline silicon (0” off the (100) axis). The experimental data [7] and the simulated profiles for the hvo models discussed in the text are shown.
III. SEMICONDUCTOR
RADIATION
EFFECTS
230
J. Arias et al. /Nucl.
Instr. and Meth. in Phys. Res. B IO2 (1995) 228-231
Fig. 3. Experimental [8] and simulated profiles for a 500 eV boron implant into amorphous and crystalline silicon (0” off (100) axis). The simulated profiles were obtained with the asymptotic path model.
SIMS measurement could be the responsible of the small differences between the annealed and the as-implanted boron profiles. The experimental profiles for the amorphous and the crystalline targets are very similar in this low implantation energy range. This can be explained considering the large scattering cross sections of the target atoms which leads to rapid de-channeling [S]. In consequence the crystalline and amorphous target will have similar scattering probabilities. On the other hand, in this low energy range the critical angles for channeling are large, and this leads to the conclusion that the ion motion is channelled during most of its path. The result for this large angle scattering and channelled motion is a polygonal-like path with very short segments (= 1 nm) which do not differ much from the random trajectories in the amorphous target [4]. lo=j..‘.x,,
..I.”
,“...’
““1
The simulated profiles obtained with the asymptotic path approximation model (Fig. 3) show a shallower profile for the amorphous target case, as it would be expected for a high energy implant. However, the results obtained with the new model (Fig. 4) show very similar profiles for the amorphous and crystalline target, and the agreement with the experimental data is better than those for the asymptotic model. This capability of the new model of reproducing the characteristic aspects of low energy implantation can be explained in terms of a more accurate scattering angle calculation, that takes into account the potential energy at the beginning of the collision. The remaining discrepancies (now probably within the SIMS accuracy) between the simulated profiles and the experimental data might be due to the fact that in our simulations no multiple target interactions are allowed. The simple momentum average model for simultaneous collisions included in the MARLOWE code [l], seems to introduce a substantial error in energy transfer, leading to deeper profiles. A more sophisticated model for multiple interactions, as the mentioned by GIrtner et al. [4], which uses the momentum average procedure only if the projectile is outside an interaction sphere centred in the target atoms, might yield even more accurate profiles.
4. Conclusions As a result of the above discussion we can conclude that the binary collision models based on asymptotic trajectories are not accurate enough to reproduce the experimental low energy implantation profiles. The peculiarities of the low energy implants are not well reproduced by this kind of models, which continue to exhibit the high energy characteristics even in low energy implants, as is for example the fact that the simulated profiles for the amorphous and crystalline targets are very different, while the experimental data show similar profiles. The more accurate binary collision approximation model described here is based on the detailed precalculation of the path of the particles for a set of collision events, using a numeric method similar to the MD calculations, together with the use of an interpolation procedure in order to reduce the computation time. This new model yields simulated profiles that reproduce the experimental data behavior. It also proves that the binary collision codes continue to yield good results where one would expect it to be essential to use a molecular dynamics code, while the computational time needed for the BCA code is orders of magnitude lower than the time needed for the equivalent MD run.
References Fig. 4. Experimental [8] and simulated profiles for a 500 eV boron implant into amorphous and crystalline silicon (0” off (100) axis). The simulated profiles were obtained with the detailed trajectory model.
[l] M.T. Robinson, I.M. Torrens, Phys. Rev. B (1974) 5008. [2] M. Jaraiz, J. Arias, L.A. Bailon and J.J. Barbolla, Vacuum 44 (1993) 321.
231
.I. Arias et al. / Nucl. Instr. and Meth. in Phys. Res. B 102 (1995) 228-231 [3] J.F. Ziegler, J.P. Biersack, U. Littmark, in: The Stopping and Range of Ions in Solids (Pergamon, 1985) p. 41. [4] K. G’artner, M. Nitschke, W. Eckstein, Nucl. Instr. and Meth. B 83 (1993) 87. [5] K.M. Klein, C. Park, A.F. Tasch, IEEE IEDM 90 (1990) 745. [6] P.M. Echenique, R.M. Nieminen, J.C. Ashley and R.H. Ritchie, Phys. Rev. A 33 (1986) 897.
[7] W. Brandt and M. Kitagawa, Phys. Rev. B 25 (1982) 5631. [S] A. Bousetta, J.A. Van den Berg, R. Valizadeh, D.G. Armour, P.C. Zalm, Nucl. Instr. and Meth. B 55 (1991) 565. [9] A. Bousetta, J.A. Van den Berg, R. Valizadeh, D.G. Armour, P.C. Zalm, Appl. Phys. Rev. Lett. 58 (1991) 1626.
III. SEMICONDUCTOR
RADIATION
EFFECTS
Nuclear Instruments
and Methods in Physics Research B 102 (1995) 228-231
NOMB
El E8
Beam Interactions with Materials 8 Atoms
!s
ELSEVIER
Low energy ion implantation simulation using a modified binary collision approximation code J. Arias
*, M.
Jaraiz, L. Pelaz, L.A. Bail&, J. Barbolla
Dept. de E. y Electrhzica, Facultad de Ciencias, Uniuersidad de Valladolid, 47011 Valladolid, Spain
Abstract We have developed a modified version of the binary collision approximation code MARLOWE with the aim of accurately predict the implanted dopant profiles, even in the low energy case. In our simulations, instead of using the asymptotic path of the projectile, the path of the colliding particles is carefully evaluated for each collision. In order to avoid the computation time penalty of such calculation, the data of the outgoing particles is tabulated previously for a large set of collision events, and an interpolation is done during the main Monte Carlo simulation. The simulated profiles show a better agreement with the experimental data for low energy implants, while the accuracy for the high energy implants is maintained.
2. Computer simulation
1. Introduction The ever smaller feature size of the new silicon electronic devices demand, as a routine step in their fabrication, the use of low energy ion implantation in order to obtain shallow junctions. For the simulation of the implantation process in this low energy regime, in the range of hundreds to a few thousands eV, two different kinds of simulation codes can be used. The molecular dynamics (MD) calculation method is very accurate but also very computer time consuming because all the interatomic forces are taken into account in the computation of the projectile path, and many timesteps are required for each collision. The other approach is the binary collision approximation (BCA). Here only the forces between the projectile and the closest target are evaluated, and this leads to a classical central force two body scattering. The path of each moving particle is approximated by a series of straight line segments, each one over a collision asymptote. This last simulation model is much less time consuming than the MD, and gives good simulation profiles for medium and high implantation energies. However in the low energy range it yields poor results. In this work we have developed a binary collision code with a projectile path calculation more accurate than the asymptotic one in order to fit the low energy experimental profiles, while maintaining a reduced computer time in the simulations.
Corresponding 423013. l
author.
Tel.
+34
83 423225,
fax
+34
83
We have chosen the binary collision approximation code MARLOWE [l] as the starting point of our study because it has proved to be a successful tool to analyze and predict the results of ion implantation on crystalline targets. In our simulations we have used a highly modified version of MARLOWE. Some of its many features are described in Ref. [2]. We have used the Universal ZBL [3] interatomic potential with a cutoff distance of 0.3 nm. We have also tested a specific boron-silicon interatomic potential [4], but no substantial differences with the results of the universal potential were found. The default OenRobinson [I] model for electronic stopping is not used in our version of MARLOWE. The electronic energy loss of incoming ions is calculated through the Local Electron Density approximation. A spherically symmetric electronic distribution is placed at the target atom location, and the electronic energy loss is computed along the path of the ion, assuming a constant electronic density at each point of the path [5]. We use the proton electronic stopping model developed by Echenique et al. [6] and the heavy ion scaling rules of Brandt and Kitagawa [7]. Some approximations to the mentioned models were used in order to improve the computational efficiency. In the simulations the impact point of each ion is randomly chosen on the surface of the target. The amorphous silicon is simulated by the random rotation of the crystal lattice in each collision [ 11. It is usually assumed in the binary collision approximation that at the start of the collision the projectile and the target are far enough so that they do not interact with each
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(94)00809-4
J. Arias et al. /Nucl.
229
Instr. and Meth. in Phys. Res. B 102 (1995) 228-231
described above were used. This process involves the exact calculation of the projectile and target trajectories, subtracting the inelastic losses along the path. In the calculation of the scattering tables the initial value of the potential energy in the collision is subtracted from the kinetic energy of the projectile in order to maintain constant the total energy, that would otherwise be incorrectly increased.
3. Results
0 0
2
.4
.5
.B
1.0
Probability
Fig. 1. Potential energy-kinetic energy ratio vs. probability at the beginning of each collision event for 80 keV and 0.5 keV boron implant into amorphous silicon.
other. That means that the interatomic potential at the start of a collision must be negligible compared to the kinetic energy. If this is not the case, the asymptotic path approximation might yield poor results. In order to test the accuracy of the asymptotic path approximation we have carried out some simulations of boron implantation into silicon at room temperature. Fig. 1 shows the results for 0.5 keV and 80 keV simulations. The probability of the initial potential energy-kinetic energy ratio of each collision events differs clearly for the two implants. As can be seen in the graph, the number of collisions with an initial energy ratio greater than 0.1 is about 13% in the 0.5 keV implant, while it is negligible in the 80 keV implant. As a result, we expect that the low energy implant yields a simulated profile with a larger error than the high energy implant, because the asymptotic path approximation is not accurate enough. In an attempt to correct the trajectories of the colliding particles we have developed a modified version of MARLOWE. The aim was also to reduce the computation time needed in the evaluation of the two body scattering parameters and the electronic inelastic energy losses. In this version the scattering angles, the deflection points of the particles and the inelastic energy losses were tabulated before the simulation. During the simulation an interpolation procedure is used to speed up the computation. The tables are stored on a disk file and they have to be calculated only once for each set of atoms. The entries in the tables for each possible collision are the projectile kinetic energy, the impact parameter and the distance from the projectile position to its uncorrected collision point 5 [l]. The data in the tables were calculated following a scheme similar to the one used in the molecular dynamics method, but it is much simpler, because only two particles are involved. The repulsive only Universal ZBL interatomic potential, and the electronic energy loss model
We have tested the new code with some published experimental data [5] of channelled boron implants into silicon in the energy range of 10 to 100 keV. The agreement between the simulated and the experimental profiles in this energy range is good, as can be seen, for example in Fig. 2 for an 80 keV implant. As expected, in the high energy regime the asymptotic path approximation works well, and no major differences with the new model were found, except for a slightly increased channeling as can be seen on the trailing edge and on the raising of the profile at about 500 nm (the leading edge, at 500 nm, is fixed by the electronic stopping in the (100) channel a that energy). In the low energy range the results of the two models differ clearly. In Figs. 3 and 4 the simulated profiles obtained using the asymptotic path approximation and the corrected model, respectively, are presented together with the experimental profiles [8] for a 500 eV boron implant into amorphous and crystalline silicon. Except for the scattering calculation, the remaining parameters, such as the interatomic potential and the inelastic energy loss model, are the same in the two simulations. Regarding the experimental profiles, and as it was mentioned by the authors in a previous paper [9], the low temperature annealing, following the sample implantation, has only a little effect on the boron profile, and they expect that the
Fig. 2. 80 keV boron implantation into crystalline silicon (0” off the (100) axis). The experimental data [7] and the simulated profiles for the hvo models discussed in the text are shown.
III. SEMICONDUCTOR
RADIATION
EFFECTS
230
J. Arias et al. /Nucl.
Instr. and Meth. in Phys. Res. B IO2 (1995) 228-231
Fig. 3. Experimental [8] and simulated profiles for a 500 eV boron implant into amorphous and crystalline silicon (0” off (100) axis). The simulated profiles were obtained with the asymptotic path model.
SIMS measurement could be the responsible of the small differences between the annealed and the as-implanted boron profiles. The experimental profiles for the amorphous and the crystalline targets are very similar in this low implantation energy range. This can be explained considering the large scattering cross sections of the target atoms which leads to rapid de-channeling [S]. In consequence the crystalline and amorphous target will have similar scattering probabilities. On the other hand, in this low energy range the critical angles for channeling are large, and this leads to the conclusion that the ion motion is channelled during most of its path. The result for this large angle scattering and channelled motion is a polygonal-like path with very short segments (= 1 nm) which do not differ much from the random trajectories in the amorphous target [4]. lo=j..‘.x,,
..I.”
,“...’
““1
The simulated profiles obtained with the asymptotic path approximation model (Fig. 3) show a shallower profile for the amorphous target case, as it would be expected for a high energy implant. However, the results obtained with the new model (Fig. 4) show very similar profiles for the amorphous and crystalline target, and the agreement with the experimental data is better than those for the asymptotic model. This capability of the new model of reproducing the characteristic aspects of low energy implantation can be explained in terms of a more accurate scattering angle calculation, that takes into account the potential energy at the beginning of the collision. The remaining discrepancies (now probably within the SIMS accuracy) between the simulated profiles and the experimental data might be due to the fact that in our simulations no multiple target interactions are allowed. The simple momentum average model for simultaneous collisions included in the MARLOWE code [l], seems to introduce a substantial error in energy transfer, leading to deeper profiles. A more sophisticated model for multiple interactions, as the mentioned by GIrtner et al. [4], which uses the momentum average procedure only if the projectile is outside an interaction sphere centred in the target atoms, might yield even more accurate profiles.
4. Conclusions As a result of the above discussion we can conclude that the binary collision models based on asymptotic trajectories are not accurate enough to reproduce the experimental low energy implantation profiles. The peculiarities of the low energy implants are not well reproduced by this kind of models, which continue to exhibit the high energy characteristics even in low energy implants, as is for example the fact that the simulated profiles for the amorphous and crystalline targets are very different, while the experimental data show similar profiles. The more accurate binary collision approximation model described here is based on the detailed precalculation of the path of the particles for a set of collision events, using a numeric method similar to the MD calculations, together with the use of an interpolation procedure in order to reduce the computation time. This new model yields simulated profiles that reproduce the experimental data behavior. It also proves that the binary collision codes continue to yield good results where one would expect it to be essential to use a molecular dynamics code, while the computational time needed for the BCA code is orders of magnitude lower than the time needed for the equivalent MD run.
References Fig. 4. Experimental [8] and simulated profiles for a 500 eV boron implant into amorphous and crystalline silicon (0” off (100) axis). The simulated profiles were obtained with the detailed trajectory model.
[l] M.T. Robinson, I.M. Torrens, Phys. Rev. B (1974) 5008. [2] M. Jaraiz, J. Arias, L.A. Bailon and J.J. Barbolla, Vacuum 44 (1993) 321.
231
.I. Arias et al. / Nucl. Instr. and Meth. in Phys. Res. B 102 (1995) 228-231 [3] J.F. Ziegler, J.P. Biersack, U. Littmark, in: The Stopping and Range of Ions in Solids (Pergamon, 1985) p. 41. [4] K. G’artner, M. Nitschke, W. Eckstein, Nucl. Instr. and Meth. B 83 (1993) 87. [5] K.M. Klein, C. Park, A.F. Tasch, IEEE IEDM 90 (1990) 745. [6] P.M. Echenique, R.M. Nieminen, J.C. Ashley and R.H. Ritchie, Phys. Rev. A 33 (1986) 897.
[7] W. Brandt and M. Kitagawa, Phys. Rev. B 25 (1982) 5631. [S] A. Bousetta, J.A. Van den Berg, R. Valizadeh, D.G. Armour, P.C. Zalm, Nucl. Instr. and Meth. B 55 (1991) 565. [9] A. Bousetta, J.A. Van den Berg, R. Valizadeh, D.G. Armour, P.C. Zalm, Appl. Phys. Rev. Lett. 58 (1991) 1626.
III. SEMICONDUCTOR
RADIATION
EFFECTS