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Influence of initial charge and charge state fluctuations on high-energy ion ranges and track formation
Nuclear Instruments and Methods in Physics Research B 148 (1999) 159±163
In¯uence of initial charge and charge state ¯uctuations on highenergy ion ranges and track formation F.F. Komarov *, A.F. Komarov, A.M. Mironov Institute of Applied Physics Problems, Belarussian State University, 7 Kurchatova Street, 220064 Minsk, Belarus
Abstract A model used for calculating the depth distribution of implanted atoms and the energy deposited into the electron and nuclear subsystems of solids is studied. The model is based on the transport equations and takes into account the initial charge and the ¯uctuations of charge states of high-energy ions (E > 1 MeV/amu). The critical dose of 250 MeV Xe ions necessary for the formation of deep amorphous layers in Si, GaAs and InP have been estimated. The process of the formation of continuous track regions in InP by 250 MeV Xe ions is studied. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 02.60.Cb; 34.50.Bw; 61.80.Az; 61.82.Fk Keywords: Ion Implantation; High Energy; Ion Charge; Track
1. Introduction The penetration of ions in solids and the major processes accompanying such penetration of medium-energy ions (E < 10 MeV) are described well by the Monte Carlo method or by solving the Boltzmann kinetic equation. However, experimental results [1±3] obtained for high-energy ion implantation (E P 1 MeV/amu) dier considerably from theoretical predictions, both for the distributions of implanted atoms and for the radiationinduced defects. For a number of ion-target combinations the experimental values of the mean
* Corresponding author. Tel.: +375 172 774833; fax: +375 172 780417; e-mail: k@rfe.bsu.unibel.by
straggling of ion projected range DRp exceed the theoretical values by a factor of 1.5±5, and the experimentally measured values of asymmetry of the depth distribution pro®les are strongly shifted in the positive direction in comparison to the calculated pro®les. These discrepancies between theory and experiment cannot be explained by the channeling eect, since the dierence in the shapes of the ion-range distribution functions is observed near the mean projected range Rp . We suppose that the observed eects can be explained by the charge state ¯uctuations of high-energy ions. The present paper is a development of an approach suggested in Refs. [4±6]. Here we allow for the eect of ¯uctuations in the charge state of ions not only on the ion-range characteristics but also on the depth distributions
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 8 2 8 - 3
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F.F. Komarov et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 159±163
of the energy deposited into the electron and nuclear subsystems of the solid. 2. Theoretical model In our case the distribution function of the ion ¯ux in the target U E; g; q; x must depend not only on the initial ion energy, the depth x in the target, the angle h between the direction normal to the surface and the direction of ion propagation (g cos h) but also on the ion charge q. The direct kinetic equation for the distribution function of the ion ¯ux is oU E; g; q; x ox Z Z 0 0 0 N drn U E ; g ; q; x ÿ drn U E; g; q; x
g
o U E; g; q; xSe E; q oE X N rq0 !q U E; g; q0 ; x ÿ rq!q0 U E; g; q; x;
N
q0
1 where drn is the dierential scattering cross section for an ion corresponding to the transition of the ion from a state with energy E, direction of motion g, and charge q to a state with parameters E0 ; g0 , and q, respectively; dr0n is the dierential cross section of the inverse transition; Se is the electron stopping cross section; and N is the concentration of atoms in the target. In Eq. (1) the last (collision) term directly describes ¯uctuations of the ion charge states and the summation over q0 is done over all possible charge states. In contrast to the standard approaches [7± 9], to allow for ¯uctuations in electron stopping we must take into account the dependence of electron stopping on the ion charge, given by 2 E; qSp E; Se E; q Zeff
2
where Zeff (E, q) is the eective charge which depends on the degree q of ionization of the ions; and Sp (E) is the cross section of electron stopping for protons. Assuming that the equipartition rule is valid in the Lindhard energy loss from close and
distant collisions, we used the following formula to calculate the eective charge " 2 # 1 2 q 2 Zeff E; q Zeff E 1 ; 3 2 Zeff E where Zeff (E) is the mean eective charge of the ions at a given energy E, calculated in the Brandt± Kitagawa model [9]. The electron capture and stripping cross section were calculated on the assumption that the charge distributions are Gaussian, which is in good agreement with the experimental data [10]. The mean values q0 of the ion charge were calculated on the basis of the model of Ziegler et al [7] while the variance of the ion distribution over the charges was represented by the simple Bohr formula [11] 1=2 q0 5=3 ; 4 d 0:5 q0 1 ÿ Z where Z is the nuclear charge of the ion. With the Gaussian distribution of the charge states and the dominance of single-particle processes in the variation of the charge states of ions, the cross section of variation of the charges of the ions moving in the target is described by the following expression [10] rq!q1 r0 exp a q ÿ q0 ;
5
where rq!q1 is the cross section of loss (+) or capture ()) of a single electron by a moving ion, and a 0.5dÿ2 . For ion energies E < Ec 1=3 1=2 50ZT q0 keV/amu we use the Bohr formula [11] v 3 0 1=3 ; 6 r0 pa20 ZT q20 v while for E > Ec we use the formula proposed by Nikolaev et al. [10] v 5 0 : 7 r0 2pa20 ZT2=3 q5=2 0 v In (6) and (7), a0 and v0 are the atomic units of length and velocity, v is the ion velocity, and ZT is the nuclear charge of the target atoms. The cross section rq!q1 can be obtained as a function of the ion velocity and the target's atomic number if we equate the model cross section (5)
F.F. Komarov et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 159±163
and the actual electron-loss cross section calculated by (6) and (7) at q q0 . In other words, the fact that r0 rq!qÿ1 at q q0 is used to determine r0 . 3. Results and discussion The distribution moments for aluminum implanted into silicon are listed in Table 1 as functions of the initial charge state of the ions. As expected, the mean projected ion range Rp increases as the initial charge of the ions decreases. This occurs because of the decrease in electron stopping at small depths, where the equilibrium distribution of atoms over the charge states has not enough time to set in. More important, however, is the eect of the initial charge state on the higher-order moments of the distributions (DRp and Sk). For instance, the discrepancy in the values of DRp reaches 23% and 12% for the implantation of boron and aluminum ions, respectively. For the asymmetry Sk, the discrepancy reaches 48% and 27% for the implantation of boron and aluminum, respectively. As the ion energy rises, the eect of the initial charge state of the ion on the parameters of the implantation pro®les gets stronger. The results of these calculations make it possible to conclude that the strong discrepancy between the distribution moments of the implanted atoms obtained in the given model and those obtained on the basis of standard calculations [7,8] takes place due to the eect of ion charge ¯uctuations rather than to the choice of the initial ion charge state.
161
The calculations of the parameters of the distribution of atoms over the target depth as functions of the ion energy for silicon bombarded by aluminum ions were done with and without account of ¯uctuations of the ion charge distributions. Allowing for the charge state ¯uctuations modi®es the value of Rp very slightly. At the same time, such ¯uctuations have a strong eect on DRp and especially on Sk. For instance, at the ion energy of 100 MeV, the value of DRp nearly doubles. The variation of Sk may be considerably greater. Numerical solution of the direct kinetic equation (1) makes it possible to extract information about the total depth distributions of the implanted atoms (Fig. 1) and the distribution pro®les of the energy deposited in inelastic (track formation) and other (defect formation) processes (Fig. 2 (a)). Fig. 1 shows that the results of calculations with our model correspond better to the experimental data than those of standard calculations for the distribution pro®le of aluminum atoms implanted in silicon at E 100 MeV. The experimental pro®les exhibit a greater dispersion of ions over the ranges than the one yielded by our model, which is an indication of the highly approximate nature of the ion charge-exchange cross section
Table 1 Spatial moments of the distribution of aluminum with energy 100 MeV implanted in silicon (with allowance for ¯uctuations in ion charge) for various initial charge states of the incident ions q
Rp (lm)
1 2 6 8 12
40.40 40.37 40.16 39.98 39.50
DRp (lm) 0.97 0.96 0.95 0.93 0.86
Sk )3.59 )3.60 )3.73 )3.94 )4.70
Fig. 1. Distribution of aluminum with energy 100 MeV implanted in silicon. The solid curve depicts the calculated pro®le obtained with allowance for ¯uctuations in charge state of the ions, the dashed curve represents the results of standard modeling [7], and the circles indicate the experimental data of La Ferla et al. [2].
162
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value ecr . For dierent semiconductors ecr varies over a broad range. For instance, for silicon ecr 6 ´ 1020 keV/cm3 at lower temperatures and increases up to 5 ´ 1021 keV/cm3 at room temperature. For GaAs crystals, the value of ecr is (2.5±3) ´ 1020 keV/cm3 at low temperatures and (8.3±3) ´ 1021 keV/cm3 at room temperature [12,13] while for InP this value is smaller by a factor of 5±10. Since ecr NSnmax D;
Fig. 2. (a) Distribution pro®les for the energy deposited in inelastic (1, 2) and elastic (3, 4) processes as the result of 250 MeV Xe implantation in InP. Curves 1 and 3 represent the results of standard modeling [7], 2 and 4 are the results obtained on the basis of the present model. (b) Distribution pro®les for xenon with energy 250 MeV implanted in InP calculated on the basis of the present model (2) and the standard model [7] (1).
used in the present paper. The considerably higher dispersion of ions over the range in our model (compared to that obtained by standard calculations) is also characteristic of depth distributions of radiation-induced defects created as a result of elastic collisions with target atoms (curve 4 in Fig. 2 (a)). Fig. 2 (b) depicts the calculated distribution pro®les for 250 MeV xenon ions implanted in indium phosphide obtained in our model (curve 2) and in standard calculations [7] (curve 7). Using the dE/dx pro®le, one can calculate the dose of high-energy ions at which an amorphous layer is formed deep inside semiconductors and insulators near the maximum in the elastically deposited energy. For instance, in view of the energy criterion, amorphization of a local volume of a crystal occurs when the energy elastically deposited within a unit volume reaches a critical
8
where N is the concentration of atoms in the crystal, Sn (1/N)(dE/dx)n , and D is the ion dose, we can easily calculate the ion dose needed for the formation of a buried amorphous layer. For example, for 250 MeV Xe ions implantation in InP (Fig. 2), the amorphization ion dose Damo is approximately (1±2) ´ 1012 ion/cm2 at low temperatures and (8±20) ´ 1012 ion/cm2 at room temperature. These data are in good agreement with the experimental results obtained recently [14]. The depth in crystal at which track formation is possible can also easily be found. If we base our calculations on the mechanism of thermal peak formation due to strong electron excitation, as a result of which local cylindrical domains melt [15] and are then rapidly quenched, the critical ion energy losses per unit range for track formation in the InP crystal are approximately 1.7±1.9 keV/nm (the upper and lower values of (dE/dx)thr are given for the case where the process is described with and without allowance for the latent heat of melting). The information drawn from Fig. 2(a) (curve 2) suggests that in the case being discussed, tracks can be formed starting at the crystal's surface to 10±15 lm deep. The experiment of Gaiduk et al. [14] showed that there are continuous track regions at depths up to 10±12 lm. The broken tracks at x P 10 lm observed in the experiment may have taken place due to statistical ¯uctuations in the charge-exchange processes involving the loss of one or several electrons by the ion, when in a certain segment of the range dE/dx becomes larger than the value (dE/dx)thr for track formation. Hence when III-V semiconductors are irradiated by high-energy ions, an extremely complicated pattern of structural transformations over the depth of the crystal can be observed, including
F.F. Komarov et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 159±163
continuous track regions, discontinuous tracks, fairly weakly damaged regions, and amorphous regions at the end of ion ranges in the crystal.
4. Conclusions Numerical modeling suggests that ¯uctuations in the charge states of ions have a strong eect on the formation of implantation pro®les in high-energy ion implantation. As the atomic number of the ion increases, the in¯uence of this eect diminishes. Numerical calculations of the distributions of the energy released by ions in inelastic and elastic processes make it possible to describe such important phenomena as the formation of continuous and broken tracks and latent amorphous layers inside the crystal.
References [1] A. La Ferla, A. Difranko, E. Rimini, G. Ciavola, G. Ferla, Mater. Sci. Eng. B 2 (1989) 69.
163
[2] A. La Ferla, L. Torrisi, G. Galvagno, E. Rimini, G. Ciavola, A. Carnera, A. Gasparotto, Nucl. Instr. and Meth. B 73 (1993) 9. [3] A.M. Zaitsev, S.A. Fedotov, A.A. Melnikov, F.F. Komarov, W.R. Fahrner, V.S. Varichenko, E.H. te Kaat, Nucl. Instr. and Meth. B 82 (1993) 421. [4] A.F. Burenkov, F.F. Komarov, S.A. Fedotov, Phys. Status Solidi. B 169 (1992) 93. [5] A.F. Burenkov, F.F. Komarov, S.A. Fedotov, Nucl. Iustr. and Meth. B 67 (1992) 30. [6] A.F. Burenkov, F.F. Komarov, S.A. Fedotov, Nucl. Instr. and Meth. B 67 (1992) 35. [7] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985. [8] A.F. Burenkov, F.F. Komarov, M.A. Kumakhov, M.M. Temkin, Tables of Ion Implantation Spatial Distribution, Gordon and Breach, New York, 1986. [9] W. Brandt, M. Kitagawa, Phys. Rev. B 25 (1982) 5631. [10] H.-D. Betz, Rev. Mod. Phys. 44 (1972) 465. [11] N. Bohr, Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd. 18(8) (1948). [12] W. Wesch, E. Wendler, G. Gotz, J. Appl. Phys. 65 (1989) 519. [13] W. Wesch, Nucl. Instr. and Meth. B 68 (1992) 340. [14] P.I. Gaiduk, O. Herre, P. Meier, F.F. Komarov, E. Wendler, W. Wesch, S. Klaumunzer, Phys. Rev. Lett. (in press). [15] F.F. Komarov, Langmuir 12 (1996) 199.
In¯uence of initial charge and charge state ¯uctuations on highenergy ion ranges and track formation F.F. Komarov *, A.F. Komarov, A.M. Mironov Institute of Applied Physics Problems, Belarussian State University, 7 Kurchatova Street, 220064 Minsk, Belarus
Abstract A model used for calculating the depth distribution of implanted atoms and the energy deposited into the electron and nuclear subsystems of solids is studied. The model is based on the transport equations and takes into account the initial charge and the ¯uctuations of charge states of high-energy ions (E > 1 MeV/amu). The critical dose of 250 MeV Xe ions necessary for the formation of deep amorphous layers in Si, GaAs and InP have been estimated. The process of the formation of continuous track regions in InP by 250 MeV Xe ions is studied. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 02.60.Cb; 34.50.Bw; 61.80.Az; 61.82.Fk Keywords: Ion Implantation; High Energy; Ion Charge; Track
1. Introduction The penetration of ions in solids and the major processes accompanying such penetration of medium-energy ions (E < 10 MeV) are described well by the Monte Carlo method or by solving the Boltzmann kinetic equation. However, experimental results [1±3] obtained for high-energy ion implantation (E P 1 MeV/amu) dier considerably from theoretical predictions, both for the distributions of implanted atoms and for the radiationinduced defects. For a number of ion-target combinations the experimental values of the mean
* Corresponding author. Tel.: +375 172 774833; fax: +375 172 780417; e-mail: k@rfe.bsu.unibel.by
straggling of ion projected range DRp exceed the theoretical values by a factor of 1.5±5, and the experimentally measured values of asymmetry of the depth distribution pro®les are strongly shifted in the positive direction in comparison to the calculated pro®les. These discrepancies between theory and experiment cannot be explained by the channeling eect, since the dierence in the shapes of the ion-range distribution functions is observed near the mean projected range Rp . We suppose that the observed eects can be explained by the charge state ¯uctuations of high-energy ions. The present paper is a development of an approach suggested in Refs. [4±6]. Here we allow for the eect of ¯uctuations in the charge state of ions not only on the ion-range characteristics but also on the depth distributions
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 8 2 8 - 3
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of the energy deposited into the electron and nuclear subsystems of the solid. 2. Theoretical model In our case the distribution function of the ion ¯ux in the target U E; g; q; x must depend not only on the initial ion energy, the depth x in the target, the angle h between the direction normal to the surface and the direction of ion propagation (g cos h) but also on the ion charge q. The direct kinetic equation for the distribution function of the ion ¯ux is oU E; g; q; x ox Z Z 0 0 0 N drn U E ; g ; q; x ÿ drn U E; g; q; x
g
o U E; g; q; xSe E; q oE X N rq0 !q U E; g; q0 ; x ÿ rq!q0 U E; g; q; x;
N
q0
1 where drn is the dierential scattering cross section for an ion corresponding to the transition of the ion from a state with energy E, direction of motion g, and charge q to a state with parameters E0 ; g0 , and q, respectively; dr0n is the dierential cross section of the inverse transition; Se is the electron stopping cross section; and N is the concentration of atoms in the target. In Eq. (1) the last (collision) term directly describes ¯uctuations of the ion charge states and the summation over q0 is done over all possible charge states. In contrast to the standard approaches [7± 9], to allow for ¯uctuations in electron stopping we must take into account the dependence of electron stopping on the ion charge, given by 2 E; qSp E; Se E; q Zeff
2
where Zeff (E, q) is the eective charge which depends on the degree q of ionization of the ions; and Sp (E) is the cross section of electron stopping for protons. Assuming that the equipartition rule is valid in the Lindhard energy loss from close and
distant collisions, we used the following formula to calculate the eective charge " 2 # 1 2 q 2 Zeff E; q Zeff E 1 ; 3 2 Zeff E where Zeff (E) is the mean eective charge of the ions at a given energy E, calculated in the Brandt± Kitagawa model [9]. The electron capture and stripping cross section were calculated on the assumption that the charge distributions are Gaussian, which is in good agreement with the experimental data [10]. The mean values q0 of the ion charge were calculated on the basis of the model of Ziegler et al [7] while the variance of the ion distribution over the charges was represented by the simple Bohr formula [11] 1=2 q0 5=3 ; 4 d 0:5 q0 1 ÿ Z where Z is the nuclear charge of the ion. With the Gaussian distribution of the charge states and the dominance of single-particle processes in the variation of the charge states of ions, the cross section of variation of the charges of the ions moving in the target is described by the following expression [10] rq!q1 r0 exp a q ÿ q0 ;
5
where rq!q1 is the cross section of loss (+) or capture ()) of a single electron by a moving ion, and a 0.5dÿ2 . For ion energies E < Ec 1=3 1=2 50ZT q0 keV/amu we use the Bohr formula [11] v 3 0 1=3 ; 6 r0 pa20 ZT q20 v while for E > Ec we use the formula proposed by Nikolaev et al. [10] v 5 0 : 7 r0 2pa20 ZT2=3 q5=2 0 v In (6) and (7), a0 and v0 are the atomic units of length and velocity, v is the ion velocity, and ZT is the nuclear charge of the target atoms. The cross section rq!q1 can be obtained as a function of the ion velocity and the target's atomic number if we equate the model cross section (5)
F.F. Komarov et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 159±163
and the actual electron-loss cross section calculated by (6) and (7) at q q0 . In other words, the fact that r0 rq!qÿ1 at q q0 is used to determine r0 . 3. Results and discussion The distribution moments for aluminum implanted into silicon are listed in Table 1 as functions of the initial charge state of the ions. As expected, the mean projected ion range Rp increases as the initial charge of the ions decreases. This occurs because of the decrease in electron stopping at small depths, where the equilibrium distribution of atoms over the charge states has not enough time to set in. More important, however, is the eect of the initial charge state on the higher-order moments of the distributions (DRp and Sk). For instance, the discrepancy in the values of DRp reaches 23% and 12% for the implantation of boron and aluminum ions, respectively. For the asymmetry Sk, the discrepancy reaches 48% and 27% for the implantation of boron and aluminum, respectively. As the ion energy rises, the eect of the initial charge state of the ion on the parameters of the implantation pro®les gets stronger. The results of these calculations make it possible to conclude that the strong discrepancy between the distribution moments of the implanted atoms obtained in the given model and those obtained on the basis of standard calculations [7,8] takes place due to the eect of ion charge ¯uctuations rather than to the choice of the initial ion charge state.
161
The calculations of the parameters of the distribution of atoms over the target depth as functions of the ion energy for silicon bombarded by aluminum ions were done with and without account of ¯uctuations of the ion charge distributions. Allowing for the charge state ¯uctuations modi®es the value of Rp very slightly. At the same time, such ¯uctuations have a strong eect on DRp and especially on Sk. For instance, at the ion energy of 100 MeV, the value of DRp nearly doubles. The variation of Sk may be considerably greater. Numerical solution of the direct kinetic equation (1) makes it possible to extract information about the total depth distributions of the implanted atoms (Fig. 1) and the distribution pro®les of the energy deposited in inelastic (track formation) and other (defect formation) processes (Fig. 2 (a)). Fig. 1 shows that the results of calculations with our model correspond better to the experimental data than those of standard calculations for the distribution pro®le of aluminum atoms implanted in silicon at E 100 MeV. The experimental pro®les exhibit a greater dispersion of ions over the ranges than the one yielded by our model, which is an indication of the highly approximate nature of the ion charge-exchange cross section
Table 1 Spatial moments of the distribution of aluminum with energy 100 MeV implanted in silicon (with allowance for ¯uctuations in ion charge) for various initial charge states of the incident ions q
Rp (lm)
1 2 6 8 12
40.40 40.37 40.16 39.98 39.50
DRp (lm) 0.97 0.96 0.95 0.93 0.86
Sk )3.59 )3.60 )3.73 )3.94 )4.70
Fig. 1. Distribution of aluminum with energy 100 MeV implanted in silicon. The solid curve depicts the calculated pro®le obtained with allowance for ¯uctuations in charge state of the ions, the dashed curve represents the results of standard modeling [7], and the circles indicate the experimental data of La Ferla et al. [2].
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value ecr . For dierent semiconductors ecr varies over a broad range. For instance, for silicon ecr 6 ´ 1020 keV/cm3 at lower temperatures and increases up to 5 ´ 1021 keV/cm3 at room temperature. For GaAs crystals, the value of ecr is (2.5±3) ´ 1020 keV/cm3 at low temperatures and (8.3±3) ´ 1021 keV/cm3 at room temperature [12,13] while for InP this value is smaller by a factor of 5±10. Since ecr NSnmax D;
Fig. 2. (a) Distribution pro®les for the energy deposited in inelastic (1, 2) and elastic (3, 4) processes as the result of 250 MeV Xe implantation in InP. Curves 1 and 3 represent the results of standard modeling [7], 2 and 4 are the results obtained on the basis of the present model. (b) Distribution pro®les for xenon with energy 250 MeV implanted in InP calculated on the basis of the present model (2) and the standard model [7] (1).
used in the present paper. The considerably higher dispersion of ions over the range in our model (compared to that obtained by standard calculations) is also characteristic of depth distributions of radiation-induced defects created as a result of elastic collisions with target atoms (curve 4 in Fig. 2 (a)). Fig. 2 (b) depicts the calculated distribution pro®les for 250 MeV xenon ions implanted in indium phosphide obtained in our model (curve 2) and in standard calculations [7] (curve 7). Using the dE/dx pro®le, one can calculate the dose of high-energy ions at which an amorphous layer is formed deep inside semiconductors and insulators near the maximum in the elastically deposited energy. For instance, in view of the energy criterion, amorphization of a local volume of a crystal occurs when the energy elastically deposited within a unit volume reaches a critical
8
where N is the concentration of atoms in the crystal, Sn (1/N)(dE/dx)n , and D is the ion dose, we can easily calculate the ion dose needed for the formation of a buried amorphous layer. For example, for 250 MeV Xe ions implantation in InP (Fig. 2), the amorphization ion dose Damo is approximately (1±2) ´ 1012 ion/cm2 at low temperatures and (8±20) ´ 1012 ion/cm2 at room temperature. These data are in good agreement with the experimental results obtained recently [14]. The depth in crystal at which track formation is possible can also easily be found. If we base our calculations on the mechanism of thermal peak formation due to strong electron excitation, as a result of which local cylindrical domains melt [15] and are then rapidly quenched, the critical ion energy losses per unit range for track formation in the InP crystal are approximately 1.7±1.9 keV/nm (the upper and lower values of (dE/dx)thr are given for the case where the process is described with and without allowance for the latent heat of melting). The information drawn from Fig. 2(a) (curve 2) suggests that in the case being discussed, tracks can be formed starting at the crystal's surface to 10±15 lm deep. The experiment of Gaiduk et al. [14] showed that there are continuous track regions at depths up to 10±12 lm. The broken tracks at x P 10 lm observed in the experiment may have taken place due to statistical ¯uctuations in the charge-exchange processes involving the loss of one or several electrons by the ion, when in a certain segment of the range dE/dx becomes larger than the value (dE/dx)thr for track formation. Hence when III-V semiconductors are irradiated by high-energy ions, an extremely complicated pattern of structural transformations over the depth of the crystal can be observed, including
F.F. Komarov et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 159±163
continuous track regions, discontinuous tracks, fairly weakly damaged regions, and amorphous regions at the end of ion ranges in the crystal.
4. Conclusions Numerical modeling suggests that ¯uctuations in the charge states of ions have a strong eect on the formation of implantation pro®les in high-energy ion implantation. As the atomic number of the ion increases, the in¯uence of this eect diminishes. Numerical calculations of the distributions of the energy released by ions in inelastic and elastic processes make it possible to describe such important phenomena as the formation of continuous and broken tracks and latent amorphous layers inside the crystal.
References [1] A. La Ferla, A. Difranko, E. Rimini, G. Ciavola, G. Ferla, Mater. Sci. Eng. B 2 (1989) 69.
163
[2] A. La Ferla, L. Torrisi, G. Galvagno, E. Rimini, G. Ciavola, A. Carnera, A. Gasparotto, Nucl. Instr. and Meth. B 73 (1993) 9. [3] A.M. Zaitsev, S.A. Fedotov, A.A. Melnikov, F.F. Komarov, W.R. Fahrner, V.S. Varichenko, E.H. te Kaat, Nucl. Instr. and Meth. B 82 (1993) 421. [4] A.F. Burenkov, F.F. Komarov, S.A. Fedotov, Phys. Status Solidi. B 169 (1992) 93. [5] A.F. Burenkov, F.F. Komarov, S.A. Fedotov, Nucl. Iustr. and Meth. B 67 (1992) 30. [6] A.F. Burenkov, F.F. Komarov, S.A. Fedotov, Nucl. Instr. and Meth. B 67 (1992) 35. [7] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985. [8] A.F. Burenkov, F.F. Komarov, M.A. Kumakhov, M.M. Temkin, Tables of Ion Implantation Spatial Distribution, Gordon and Breach, New York, 1986. [9] W. Brandt, M. Kitagawa, Phys. Rev. B 25 (1982) 5631. [10] H.-D. Betz, Rev. Mod. Phys. 44 (1972) 465. [11] N. Bohr, Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd. 18(8) (1948). [12] W. Wesch, E. Wendler, G. Gotz, J. Appl. Phys. 65 (1989) 519. [13] W. Wesch, Nucl. Instr. and Meth. B 68 (1992) 340. [14] P.I. Gaiduk, O. Herre, P. Meier, F.F. Komarov, E. Wendler, W. Wesch, S. Klaumunzer, Phys. Rev. Lett. (in press). [15] F.F. Komarov, Langmuir 12 (1996) 199.