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Self-trapped exciton model of heavy-ion track registration
cm
Nuclear lnsuuments
and Methods in Physics Research B 116 (1996) 33-36
__
. . __
KlOLi!4l
B
Beam Interactions with Materials&Atoms
!!i!z
ELSEVIER
Self-trapped exciton model of heavy-ion track registration Noriaki Itoh Deparhnenr of Physics, Osaka Institute of Technology, 16 Omiya 5, Asahi-Ku, Osaka 535, Japan
Abstract Relaxation of densely generated self-trapped excitons along heavy-ion tracks is discussed. It is pointed out that track registration can be caused by lattice misfit resulting from densely generated self-trapped excitons. The stopping power dependence of the radius of the region in which the average density of the self-trapped excitons coincides with the molecular concentration has been evaluated for CI quartz, using the formulae by Katz et al. [Radiat. Eff. Def. Solids 114 (1990) 151 of radial density of excitation. The result agrees with the stopping power dependence of the track radius obtained by Meftah et al. [Phys. Rev. B 48 (1993) 9201. The heavy-ion damage cross sections of several materials are discussed in terms of the presence and absence of self-trapping of excitons.
1. Introduction Irradiation of some insulators with energetic heavy ions in an energy range higher than 1 MeV/amu per nucleon induces heavily damaged zone along their paths [l-3]. The damage formation by heavy ions of this energy range is significant above a certain threshold electronic stopping power, and therefore it is genetally accepted that damage is not due to elastic collisions but due to electronic encounters. Since electronic excitation itself does not create lattice disorder directly, the mechanism by which the electronic excitation energy is converted to the energy of forming lattice disorder has been disputed. The mechanisms of track registration which have been suggested may be divided into three categories: due to inhomogeneous charge distribution, due to thermal spike and due to direct electron-lattice coupling to induce local lattice disorder. The mechanism of the first category was initially suggested by Fleisher and coworkers [ 1,6,7] and called the ion-explosion model. The thermal spike model has been treated by several authors [S and references therein] and used to explain the major experimental results, such as the threshold stopping power and the size of damaged zone. Self-trapping of an exciton, which occurs when the exciton-lattice coupling overcomes the freedom of the translational motion of an exciton, localizes the electronic excitation energy by introducing local lattice distortion [4,5] and can be the cause of track registration. We call the model of the third category self-trapped exciton (SIB) model. The overlap of the materials, in which excitons are self-trapped and those in which tracks are registered, has been pointed out [9]. Although the thermal spike or local temperature. rise along ion paths is induced also by electron-lattice coupling, all phonon modes should be activated according to the equipartition rule in a thermal 0168-583X/96/$15.00 Copyright PII SOl68-583X(96)00006-7
spike. On the other hand, self-trapping activates specific phonon modes and consequently induces local lattice distortion without raising overall temperature. Track registration is strongly material dependent [lo]. Tracks are registered in some insulators, SiO,, mica and some minerals, in a range, in which tracks are not registered in MgO, alumina, semiconductors and metals. The STE model suggests that the criterion for self-trapping of an exciton [4,5] can be the material criterion for track registration: self-trapping of excitons occurs neither in MgO nor in semiconductors. Metals should be treated differently, since no exciton exists in metals. In the present paper, we examine the primary lattice relaxation in heavy ion tracks and try to find whether the STE model is indeed realistic. Recent experimental observation has provided detailed information on the track structures particularly for OLquartz: it is most likely that amorphization is induced in tracks [ 111 and furthermore the radius of the tracks has been determined as a function of stopping power [12]. Thus, it is of interest to examine whether the STB model can explain this experimental observation.
2. Description of the model Primary electronic encounters of solids with heavy ions induce free carriers, electrons, holes and excitons. When the density of excitation is sufficiently high, the number of the former two are approximately the same, since the excitation of electrons and holes localized on the defect sites can be disregarded. In insulators, in which the binding energy of excitons is much higher than thermal energy, the ionization of excitons to electron-hole pairs can be
0 19% Elsevier Science B.V. All rights reserved
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34
Instr. and Meth. in Phys. Res. B 116 (1996) 33-36
disregarded. Furthermore, electron-hole pairs are converted to excitons by a time constant rc [13]: To =
K/&‘Te~n,
(1)
where k is the dielectric constant, p the mobility of electrons or holes, whichever is higher, and n the concentration of electron-hole pairs. The value of re can be shorter than 0.1 ps when n exceeds 10” cme3. Thus excitons are the major products of electronic excitation of insulating solids 0.1 ps after penetration of a heavy ion, before no appreciable atomic motion is induced. The excitons couple more strongly with the lattice than electrons and holes [14]. In fact it has been shown that excitons are self-trapped in 01 quartz [15], but neither electrons nor holes are self-trapped [ 161. ‘Ihe number of electron-hole pairs, and consequently, excitons created by electronic excitation is given by E/W, where E is absorbed energy and W is a constant about three times larger than the band-gap energy [17]. Thus, two thirds of absorbed energy is converted to phonons in a short time due to electron-phonon and hole-phonon interactions, while one third goes to formation of self-trapped excitons. The stopping power of the ions that can cause track registration is often higher than 1 keV/nm and the concentration of the electron-hole pairs can be as high as that of the SiO, unit in the lattice. Petite et al. [18] have shown that electron-hole pairs generated by a subpicosecond laser pulse are converted to self-trapped excitons in 150 fs. Assuming that the hole mobility is 1 cm2/V s [19], we evaluated the diffusion length of electron-hole pairs to be 0.6 nm. Evidently, self-trapped excitons are created at a high concentration along heavy-ion paths. Self-trapping of excitons is known to lead to catastrophic local lattice disorder [20]. In o( quartz, a self-trapped exciton is considered to exhibit a structure shown in Fig. 1 [21,22]: a Si-0 bond is broken, with the hole occupying an oxygen p orbital and the electron localized by the Coulomb field of the hole. It can emit a 2.8 eV photon upon recombination. Since an unrelaxed exciton possesses about 8.5 eV, 5.7 eV is spent to lattice distortion, shown in Fig. 1. It has been shown that formation of a self-trapped
exciton induces an expansion by a molecular volume [23]. Although the self-trapped excitons created by conventional ionizing radiation in cx quartz recombine to restore perfect lattice, creation of such a catastrophic disorder at all lattice sites is considered to induce permanent damage. We presume that if the self-trapped excitons are generated at a high density, the recombination does not necessarily lead to restoration of the perfect lattice. This presumption is obvious in view of the bond scission in the self-trapped configuration. At a high density, the configuration of the self-trapped excitons will be altered because of their mutual interaction and results in local disorder: bond switch will cause ring formation and further bond scission under strained condition will convert crystalline structure to amorphous structure. The process of amorphization by formation of defects has been discussed by several. authors [24]. It is also plausible that oxygen atoms are displaced into interstitial position, forming oxygen molecules [25] under dense electronic excitation. All of these processes will occur within a picosecond, approximately the inverse of the lattice characteristic frequency. We suggest that ion tracks are registered along their path, if self-trapped excitons are produced at such a high density that all SiO, units are excited. Suppose that D(r) is the dose deposited per unit area in a coaxial cylindrical shell of a thickness a of a molecular layer, at a distance r from the path of an ion. D(r) is mainly governed by the secondary ionization by delta rays. The number p(r) of self-trapped excitons per unit area produced at a distance r from the ion path is given by p(r) = D(r)/W. (2) We presume that a track is registered if the average concentration of self-trapped excitons within a radius is larger than the concentration of SiO, molecules: namely track radius R is given by $-kRrp(r)
dr=$.
Since the second excitation of a single molecular unit requires an energy higher than the first excitation, the path lengths of delta rays will be enhanced if all SiO, molecules along the path of delta rays are excited. Thus, taking an average over R appears to be appropriate. In the calculation we disregarded the diffusion of electron-hole pairs. 3. Track radius in LYquartz We use the formulae for the energy density deposition obtained by Katz et al. [26,27]. According to these authors, D(r) is given by
Fig. 1. A schematic model of a self-trapped exciton in cy quartz.
N. Itoh / Nucl. Instr. and Meth. in Phys. Res. B 116 (1996) 33-36
Q
Fig. 2. The stopping power dependence of the calculated (open circles) and experimental (full circles) heavy-ion track radius in OL quartz. The experimental results are taken from Ref. [ 121.
where N is the density of SiO, molecular units, ER is the Rydberg energy, m is the electron mass, c is the light velocity, uB is the Bohr radius, (Y is a constant relating the energy and range of delta rays, p is ion velocity divided by light velocity, Z* is the effective charge of ions and 6 and T are the ranges of delta rays having the band-gap energy and kinematically limited maximum energy, respectively. The model is similar to that of Tombrello [28], although he took into account only the energy density, rather than the integrated energy density. We carried out numerical calculation of R for several incident ions using Eqs. (3) and (4). The results of calculation are compared with experimental results by Meftah et al. [12] in Fig. 2, which plots R as a function of stopping power. In the figure, R calculated with W = 38 eV is plotted. This value is about four times the band-gap energy and slightly larger than the expected value of W. Because of the semi-qualitative nature of the model, we consider that the agreement between experimental results and calculated values is excellent for stopping powers below 21 keV/nm. The disagreement above this value of stopping power is probably due to secondary effects. According to Katz’s formula, the increase in the stopping power does not necessarily increase the excitation density near the ion path, but increases the energy of delta rays and consequently the radial range of energy deposition. Thus, it appears that an increase in excitation density outside the calculated R reduces the diffusion rate of electron-hole pairs and increases the track radius.
4. Track registration in other materials The critical issues on track registration in other materials are: (1) to explain why the tracks of heavy ions having stopping power of about 10 keV/nm is registered in CL
35
quartz, mica and some other materials such as magnetic insulators, but not in MgO, alumina and semiconductors, (2) why registration in polymer occurs at lower stopping power and that in metals occurs in higher stopping power. The material constants invblved in Eqs. (3) and (4) are only N, W and a. Density of the material is also involved through the range of delta rays. D increases as the density of the material increases and as W decreases, but the differences of D and W among insulators is not extensive. Therefore tracks should be registered in this energy range for many insulators, in which self-trapping of excitons is induced. Tracks are known to be registered in fused silica, in which excitons are self-trapped. The absence of track registration in MgO can be ascribed to the absence of self-trapping. Similarly, semiconductors have smaller W values, but because of the absence of self-trapping, no track registration is expected. Tracks have been observed for alumina, but with much smaller track radius comparing with SiO, [3,29]. Although the self-trapping of excitons in alumina is controversial, even if it occurs, it should occur at limited conditions, accompanied with themml activation [30]. Thus, the density of the self-trapped excitons in alumina is considered much lower than the value evaluated using Eqs. (3) and (4). Self-trapping of excitons in magnetic materials is not yet known. However, excitons are self-trapped in some oxides with relatively low ionicity, such as Y,O, [31]. Thus, track registration of magnetic oxides may be caused by self-trapping. Polymers can be heavily damaged by conventional ionizing radiation. Thus the track registration in polymers is expected to be different from that of inorganic insulators, in which the damage by conventional ionizing irradiation is less extensive. In fact tracks are registered in polymers at much lower stopping power [1,2]. On the other hand, neither damage by ionizing radiation nor self-trapping df excitons occurs in metals. However, as it is the case for the STE mechanism, if bonds of atoms along heavy-ion paths are weakened simultaneously, track registration may be induced. This may happen when substantial fraction of electrons is depleted from ion paths. This could occur at higher stopping power as usually observed [32]. In conclusion, the STE model of track registration appears to be successful for stopping power range of lo-60 keV/nm. It explains the track radius for SiO, and the material dependence of track registration in this stopping power range.
References [ll R.L. Fleisher, P.B. Price and R.M. Walker, Nuclear Tracks in Solids (Univ. of California Press, Berkeley, 1975). 121 B.E. Fisher and R. Spohr, Rev. Mod. Phys. 55 (1983) 907. 131 M. Toulemonde, S. Bouffard and E. Studer, Nucl. Ins&. and Meth. B 91 (1994) 108. 141 E.I. Rashba, Excitons, eds. E.I. Rashba and M.D. Sturge (North-Holland, Amsterdam, 1982) p. 543.
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[5] Y. Toyozawa, Physica B+C 117/l 18 (1983) 23. [6] R.L. Fleisher, P.B. Price and R.M. Walker, J. Appl. Phys. 36 (1965) 3465. [7] R.L. Fleisher, Prog. Mater. Sci. 10 (1981) 97. [S] M. Toulemonde, C. Dufour and E. Paumier, Phys. Rev. B 46 (1992) 14362. [9] N. Itoh, Radiat. Eff. Def. Solids 110 (1989) 19. [lo] L.T. Chadderton, D. Fink, Y. Gamaly, H. Moeckel, L. Wang, H. Gmichi and F. Hosoi, Nucl. Instr. and Meth. B 91 (1994) 71. [ 1l] J.P. Duraud, F. Jollet, Y. Langevin and E. Dooryhee, Nucl. Instr. and Meth. B 32 (1988) 248. [12] A. Meftah, F. Brisard, J.M. Constantini, E. Dooryhee, M. Hage-Ali, M. Hervieu, J.P. Stoquert, F. Studer and M. Toulemonde, Phys. Rev. B 48 (1993) 920. [13] R.E. Howard and R. Smoluchowski, Phys. Rev. 116 (1959) 314. 1141N. Itoh, K. Tanimura, A.M. Stoneham and A.H. Harker, J. Phys. Condens. Matter 1 (1989) 3911. [15] W. Hayes, M.J. Kaane, 0. Salminen, R.L. Wood and S.P. Doherty, J. Phys. C 17 (1984) 2943. [16] W. Hayes and T.J.L. Jenkins, J. Phys. C 19 (1986) 6211. [17] R.C. Alig and S. Bloom, Phys. Rev. Lett. 35 (197.5) 1522. [IS] G. Petite, P. Daguzan, S. Guizard and P. Martin, Suppl. Rev. Le Vide, Sci. Techn. Appl. 275 (1995) 223. [19] R.C. Hughes, Solid State Electron. 21 (1978) 251. 1201D.L. Griscom, Proc. 3rd Int. Frequency Control Symp. (Electronic Industries Association, 1979) p. 98.
[21] A.J. Fisher, W. Hayes and A.M. Stoneham, J. Phys. Condens. Matter 2 (1990) 6707. [22] A. Shluger and E. Stefanovich, Phys. Rev. B 42 (19%) %64. [23] K. Tanimura, T. Tanaka and N. Itoh, Phys. Rev. Lett. 51 ( 1983) 423. [24] V.J.B. Torres, P.M. Masti and A.M. Stoneham, J. Phys. C 20 (1987) L143. [25] D.L. Griscom, J. Ceram. Sot. Jpn. 99 (1991) 923. [26] R. Katz, K.S. Loh, L. Daling and G.-R. Huang, Radiat. Eff. Def. Solids 114 (19%) 15. [27] M.P.R. Waligorski, R.N. Hamm and R. Katz, Nucl. Tracks Radiat. Meas. 11 (1986) 309. [28] T.A. Tombrello, Nucl. Instr. and Meth. B, to be published. [29] B. Canut, A. Benyagoub, G. Marest, A. Meftah, N. Moncoffre, S.M.M. Ramos, F. Studer, P. Thevenard and M, Toulemonde, Phys. Rev. B 51 (1995) 12194. [30] P.A. Kulis, M.J. Springis, I.A. Tale and J.A. Valbis, Phys. Status Solidi A 58 (1980) 225; J. Valbis and N. Itoh, Radiat. Eff. Def. Solids 116 (1991) 171. [31] W. Hayes, M.J. Kane, 0. Salminen and A.I. Kuznetsov, J. Phys. C 17 (1984) L383. [32] A. Iwase, S. Sasaki, T. Iwata and T. Nihira, Phys. Rev. Lett. 58 (1987) 2450; L. Civale, A.D. Marwick, T.K. Worthington, M.A. Kirk, J.R. Thompson, L. Krusin-Elbaum, Y. Sun, J.R. Clem and F. Holtzberg, Phys. Rev. Lett. 67 (1991) 648.
Nuclear lnsuuments
and Methods in Physics Research B 116 (1996) 33-36
__
. . __
KlOLi!4l
B
Beam Interactions with Materials&Atoms
!!i!z
ELSEVIER
Self-trapped exciton model of heavy-ion track registration Noriaki Itoh Deparhnenr of Physics, Osaka Institute of Technology, 16 Omiya 5, Asahi-Ku, Osaka 535, Japan
Abstract Relaxation of densely generated self-trapped excitons along heavy-ion tracks is discussed. It is pointed out that track registration can be caused by lattice misfit resulting from densely generated self-trapped excitons. The stopping power dependence of the radius of the region in which the average density of the self-trapped excitons coincides with the molecular concentration has been evaluated for CI quartz, using the formulae by Katz et al. [Radiat. Eff. Def. Solids 114 (1990) 151 of radial density of excitation. The result agrees with the stopping power dependence of the track radius obtained by Meftah et al. [Phys. Rev. B 48 (1993) 9201. The heavy-ion damage cross sections of several materials are discussed in terms of the presence and absence of self-trapping of excitons.
1. Introduction Irradiation of some insulators with energetic heavy ions in an energy range higher than 1 MeV/amu per nucleon induces heavily damaged zone along their paths [l-3]. The damage formation by heavy ions of this energy range is significant above a certain threshold electronic stopping power, and therefore it is genetally accepted that damage is not due to elastic collisions but due to electronic encounters. Since electronic excitation itself does not create lattice disorder directly, the mechanism by which the electronic excitation energy is converted to the energy of forming lattice disorder has been disputed. The mechanisms of track registration which have been suggested may be divided into three categories: due to inhomogeneous charge distribution, due to thermal spike and due to direct electron-lattice coupling to induce local lattice disorder. The mechanism of the first category was initially suggested by Fleisher and coworkers [ 1,6,7] and called the ion-explosion model. The thermal spike model has been treated by several authors [S and references therein] and used to explain the major experimental results, such as the threshold stopping power and the size of damaged zone. Self-trapping of an exciton, which occurs when the exciton-lattice coupling overcomes the freedom of the translational motion of an exciton, localizes the electronic excitation energy by introducing local lattice distortion [4,5] and can be the cause of track registration. We call the model of the third category self-trapped exciton (SIB) model. The overlap of the materials, in which excitons are self-trapped and those in which tracks are registered, has been pointed out [9]. Although the thermal spike or local temperature. rise along ion paths is induced also by electron-lattice coupling, all phonon modes should be activated according to the equipartition rule in a thermal 0168-583X/96/$15.00 Copyright PII SOl68-583X(96)00006-7
spike. On the other hand, self-trapping activates specific phonon modes and consequently induces local lattice distortion without raising overall temperature. Track registration is strongly material dependent [lo]. Tracks are registered in some insulators, SiO,, mica and some minerals, in a range, in which tracks are not registered in MgO, alumina, semiconductors and metals. The STE model suggests that the criterion for self-trapping of an exciton [4,5] can be the material criterion for track registration: self-trapping of excitons occurs neither in MgO nor in semiconductors. Metals should be treated differently, since no exciton exists in metals. In the present paper, we examine the primary lattice relaxation in heavy ion tracks and try to find whether the STE model is indeed realistic. Recent experimental observation has provided detailed information on the track structures particularly for OLquartz: it is most likely that amorphization is induced in tracks [ 111 and furthermore the radius of the tracks has been determined as a function of stopping power [12]. Thus, it is of interest to examine whether the STB model can explain this experimental observation.
2. Description of the model Primary electronic encounters of solids with heavy ions induce free carriers, electrons, holes and excitons. When the density of excitation is sufficiently high, the number of the former two are approximately the same, since the excitation of electrons and holes localized on the defect sites can be disregarded. In insulators, in which the binding energy of excitons is much higher than thermal energy, the ionization of excitons to electron-hole pairs can be
0 19% Elsevier Science B.V. All rights reserved
N. Itoh/Nucl.
34
Instr. and Meth. in Phys. Res. B 116 (1996) 33-36
disregarded. Furthermore, electron-hole pairs are converted to excitons by a time constant rc [13]: To =
K/&‘Te~n,
(1)
where k is the dielectric constant, p the mobility of electrons or holes, whichever is higher, and n the concentration of electron-hole pairs. The value of re can be shorter than 0.1 ps when n exceeds 10” cme3. Thus excitons are the major products of electronic excitation of insulating solids 0.1 ps after penetration of a heavy ion, before no appreciable atomic motion is induced. The excitons couple more strongly with the lattice than electrons and holes [14]. In fact it has been shown that excitons are self-trapped in 01 quartz [15], but neither electrons nor holes are self-trapped [ 161. ‘Ihe number of electron-hole pairs, and consequently, excitons created by electronic excitation is given by E/W, where E is absorbed energy and W is a constant about three times larger than the band-gap energy [17]. Thus, two thirds of absorbed energy is converted to phonons in a short time due to electron-phonon and hole-phonon interactions, while one third goes to formation of self-trapped excitons. The stopping power of the ions that can cause track registration is often higher than 1 keV/nm and the concentration of the electron-hole pairs can be as high as that of the SiO, unit in the lattice. Petite et al. [18] have shown that electron-hole pairs generated by a subpicosecond laser pulse are converted to self-trapped excitons in 150 fs. Assuming that the hole mobility is 1 cm2/V s [19], we evaluated the diffusion length of electron-hole pairs to be 0.6 nm. Evidently, self-trapped excitons are created at a high concentration along heavy-ion paths. Self-trapping of excitons is known to lead to catastrophic local lattice disorder [20]. In o( quartz, a self-trapped exciton is considered to exhibit a structure shown in Fig. 1 [21,22]: a Si-0 bond is broken, with the hole occupying an oxygen p orbital and the electron localized by the Coulomb field of the hole. It can emit a 2.8 eV photon upon recombination. Since an unrelaxed exciton possesses about 8.5 eV, 5.7 eV is spent to lattice distortion, shown in Fig. 1. It has been shown that formation of a self-trapped
exciton induces an expansion by a molecular volume [23]. Although the self-trapped excitons created by conventional ionizing radiation in cx quartz recombine to restore perfect lattice, creation of such a catastrophic disorder at all lattice sites is considered to induce permanent damage. We presume that if the self-trapped excitons are generated at a high density, the recombination does not necessarily lead to restoration of the perfect lattice. This presumption is obvious in view of the bond scission in the self-trapped configuration. At a high density, the configuration of the self-trapped excitons will be altered because of their mutual interaction and results in local disorder: bond switch will cause ring formation and further bond scission under strained condition will convert crystalline structure to amorphous structure. The process of amorphization by formation of defects has been discussed by several. authors [24]. It is also plausible that oxygen atoms are displaced into interstitial position, forming oxygen molecules [25] under dense electronic excitation. All of these processes will occur within a picosecond, approximately the inverse of the lattice characteristic frequency. We suggest that ion tracks are registered along their path, if self-trapped excitons are produced at such a high density that all SiO, units are excited. Suppose that D(r) is the dose deposited per unit area in a coaxial cylindrical shell of a thickness a of a molecular layer, at a distance r from the path of an ion. D(r) is mainly governed by the secondary ionization by delta rays. The number p(r) of self-trapped excitons per unit area produced at a distance r from the ion path is given by p(r) = D(r)/W. (2) We presume that a track is registered if the average concentration of self-trapped excitons within a radius is larger than the concentration of SiO, molecules: namely track radius R is given by $-kRrp(r)
dr=$.
Since the second excitation of a single molecular unit requires an energy higher than the first excitation, the path lengths of delta rays will be enhanced if all SiO, molecules along the path of delta rays are excited. Thus, taking an average over R appears to be appropriate. In the calculation we disregarded the diffusion of electron-hole pairs. 3. Track radius in LYquartz We use the formulae for the energy density deposition obtained by Katz et al. [26,27]. According to these authors, D(r) is given by
Fig. 1. A schematic model of a self-trapped exciton in cy quartz.
N. Itoh / Nucl. Instr. and Meth. in Phys. Res. B 116 (1996) 33-36
Q
Fig. 2. The stopping power dependence of the calculated (open circles) and experimental (full circles) heavy-ion track radius in OL quartz. The experimental results are taken from Ref. [ 121.
where N is the density of SiO, molecular units, ER is the Rydberg energy, m is the electron mass, c is the light velocity, uB is the Bohr radius, (Y is a constant relating the energy and range of delta rays, p is ion velocity divided by light velocity, Z* is the effective charge of ions and 6 and T are the ranges of delta rays having the band-gap energy and kinematically limited maximum energy, respectively. The model is similar to that of Tombrello [28], although he took into account only the energy density, rather than the integrated energy density. We carried out numerical calculation of R for several incident ions using Eqs. (3) and (4). The results of calculation are compared with experimental results by Meftah et al. [12] in Fig. 2, which plots R as a function of stopping power. In the figure, R calculated with W = 38 eV is plotted. This value is about four times the band-gap energy and slightly larger than the expected value of W. Because of the semi-qualitative nature of the model, we consider that the agreement between experimental results and calculated values is excellent for stopping powers below 21 keV/nm. The disagreement above this value of stopping power is probably due to secondary effects. According to Katz’s formula, the increase in the stopping power does not necessarily increase the excitation density near the ion path, but increases the energy of delta rays and consequently the radial range of energy deposition. Thus, it appears that an increase in excitation density outside the calculated R reduces the diffusion rate of electron-hole pairs and increases the track radius.
4. Track registration in other materials The critical issues on track registration in other materials are: (1) to explain why the tracks of heavy ions having stopping power of about 10 keV/nm is registered in CL
35
quartz, mica and some other materials such as magnetic insulators, but not in MgO, alumina and semiconductors, (2) why registration in polymer occurs at lower stopping power and that in metals occurs in higher stopping power. The material constants invblved in Eqs. (3) and (4) are only N, W and a. Density of the material is also involved through the range of delta rays. D increases as the density of the material increases and as W decreases, but the differences of D and W among insulators is not extensive. Therefore tracks should be registered in this energy range for many insulators, in which self-trapping of excitons is induced. Tracks are known to be registered in fused silica, in which excitons are self-trapped. The absence of track registration in MgO can be ascribed to the absence of self-trapping. Similarly, semiconductors have smaller W values, but because of the absence of self-trapping, no track registration is expected. Tracks have been observed for alumina, but with much smaller track radius comparing with SiO, [3,29]. Although the self-trapping of excitons in alumina is controversial, even if it occurs, it should occur at limited conditions, accompanied with themml activation [30]. Thus, the density of the self-trapped excitons in alumina is considered much lower than the value evaluated using Eqs. (3) and (4). Self-trapping of excitons in magnetic materials is not yet known. However, excitons are self-trapped in some oxides with relatively low ionicity, such as Y,O, [31]. Thus, track registration of magnetic oxides may be caused by self-trapping. Polymers can be heavily damaged by conventional ionizing radiation. Thus the track registration in polymers is expected to be different from that of inorganic insulators, in which the damage by conventional ionizing irradiation is less extensive. In fact tracks are registered in polymers at much lower stopping power [1,2]. On the other hand, neither damage by ionizing radiation nor self-trapping df excitons occurs in metals. However, as it is the case for the STE mechanism, if bonds of atoms along heavy-ion paths are weakened simultaneously, track registration may be induced. This may happen when substantial fraction of electrons is depleted from ion paths. This could occur at higher stopping power as usually observed [32]. In conclusion, the STE model of track registration appears to be successful for stopping power range of lo-60 keV/nm. It explains the track radius for SiO, and the material dependence of track registration in this stopping power range.
References [ll R.L. Fleisher, P.B. Price and R.M. Walker, Nuclear Tracks in Solids (Univ. of California Press, Berkeley, 1975). 121 B.E. Fisher and R. Spohr, Rev. Mod. Phys. 55 (1983) 907. 131 M. Toulemonde, S. Bouffard and E. Studer, Nucl. Ins&. and Meth. B 91 (1994) 108. 141 E.I. Rashba, Excitons, eds. E.I. Rashba and M.D. Sturge (North-Holland, Amsterdam, 1982) p. 543.
36
N. Itoh/Nucl.
Instr. and Meth. in Phys. Res. B 116 (1996) 33-36
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