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Deuteron induced secondary electron emission from titanium deuteride surface
Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Deuteron induced secondary electron emission from titanium deuteride surface Ke Jianlin ⇑, Liu Meng, Zhou Changgeng Institute of Nuclear Physics and Chemistry, CAEP, Mianyang 621900, China
a r t i c l e
i n f o
Article history: Received 23 October 2011 Received in revised form 25 February 2012 Available online 6 March 2012 Keywords: Secondary electron emission Secondary electron yield Deuteron beam Titanium deuteride
a b s t r a c t The secondary electron yield from titanium deuteride surface induced by deuterons was measured in the 80–254 keV energy range using a quotient method. The clean surface was produced by removing the oxide layers and absorbed gases on the titanium deuteride target by self-sputtering with deuterons. The maximum value of the secondary electron yield is about 1.37 at 143 keV. The secondary electron yield of deuterons in titanium deuteride was compared with the yield of deuterons in Ti, measured in the current study, and with the yield of protons in Ti, measured by Hasselkamp et al. in 1990: values were found to be similar when comparing ions with the same velocity. This suggests the weak influence of the deuteriding process on secondary electron emission. The relation between secondary electron yield and electronic stopping power of deuterons in titanium deuteride was also discussed, with an expansion of the theory of Sternglass. From the results the partition factor B is a little larger than 0.5, which may be related to the derivation from the equipartition rule near the stopping power maximum or to the cascade process which is neglected in the theory of Sternglass. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
c ¼ K b ðdE=dxÞe ;
In accelerator-driven D–D or D–T neutron sources, the secondary electrons from the target and the walls can seriously influence the load capacity and breakdown characteristics of an accelerating tube. In the past decades, much experimental and theoretical work has been directed toward proton-induced emission of secondary electron from metal surfaces, but the situation is less satisfactory in the case of deuteron [1–3], especially for that from metal deuterides/tritides, where only results for ErD2 and ScD2 under deuteron bombardment have been reported by Wurtz and Tapp [1]. Ion-induced secondary electron emission is assumed to be a result of two distinguishable processes: potential emission and kinetic emission. The potential emission is related to the neutralization of the bombarding ion and can be neglected in the ion energy range of the current work. The kinetic emission is basically understood as a combination of three processes [4,5]: (1) energy loss of incident ion to the electrons of the medium, which mainly refer to electronic energy loss, because the contribution of the recoiling target atoms can be neglected under bombardment with high-energy light ions, (2) transport of electrons to the surface with a series of collisions, and (3) escape from the surface. Although none of these three processes have been understood clearly, the secondary electron yield c can be obtained through the equation shown below:
where (dE/dx)e is the electronic stopping power of the solid, b is a parameter related to energy deposition in the target, and K is a parameter related only to the target material. In the present research, quotient method [6] was used to measure the secondary electron yields of the accelerator-used target. Titanium deuteride target, which is often used in accelerator-driven D–D neutron source, was selected to perform the experiment because it is not radioactive or contaminated by incident deuteron. Based on the results of the current study, the influence of deuteriding process on secondary electron emission was discussed. The relationship between secondary electron yield and the electronic stopping power of deuterons in TiD2 was also investigated.
⇑ Corresponding author. Tel.: +86 0816 249 3591. E-mail address: [email protected] (K. Jianlin). 0168-583X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2012.02.033
ð1Þ
2. Experimental 2.1. Experimental set-up The experiment was performed at a cock-croft accelerator in Institute of Nuclear Physics and Chemistry by deuterons with a selected energy in the 80–254 keV range. A schematic diagram of the measuring arrangement is shown in Fig. 1. When the electrode is biased by 200–300 V negative potential, electrons are prohibited to leave the target and the measured current ID is equal to the incoming deuteron current. In the case of 250–350 V positive potential, electrons are repelled from the target and the measured current Itotal is equal to the sum of the deuteron current and of
2
K. Jianlin et al. / Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
Fig. 2. Variation of secondary electron yields as a function of deuteron fluence for TiD2 target bombarded with 122 keV deuterons.
Fig. 1. Schematic diagram of the experimental setup. The DC electrical source is adjustable from 500 to +500 V. The value of the current was measured by I = V/R.
the outgoing electron current. The secondary electron yield per incident deuteron is then given by the equation
c¼
ðItotal ID Þ : ID
ð2Þ
electron yield from the Ti target as a function of the deuteron fluence which was accumulated firstly at 122 keV, then at 188 keV and finally at 250 keV: this was performed to show the influence of the incident deuteron energy on the cleaning process. The result shows that the yield reaches the same plateau value even by considering different deuteron energies.
3. Results and discussion
2.2. Surface treatment
3.1. Secondary electron yields from titanium deuteride surface
The targets were exposed to air before insertion into the vacuum, so it is necessary to clean the surface of the targets before performing the experiment. When performing the experiment, self-sputtering with deuterons was used in the TiD2 surface cleaning to remove the oxide layers and absorbed gases and to compensate for the preferentially sputtered deuterium. In secondary electron emission studies, surface cleaning was mostly achieved by heating or sputtering. It has been shown by Baragiola et al. [7] that the yield in aluminum obtained by sputtering with argon ions is the same to that of in situ evaporation. In the present study, heating and evaporation of the TiD2 target would accelerate the release of deuterium, so cleaning the TiD2 surface by these methods was not feasible. Furthermore, sputtering with Ar+ sputter-gun at low energies, which has been often used in the cleaning of pure metal surfaces [1,8], was not used because of its preferential sputtering. Accordingly to the theory of preferential sputtering [9], the sputtering yield of deuterium is much larger than titanium, which might change the deuterium titanium ratio of the target surface and finally influence the accuracy of the measured yields. Fortunately, the preferentially sputtered deuterium could be partially compensated if the surface cleaning is achieved by self-sputtering with deuterons. Fig. 2 shows the variation of the secondary electron yield from the TiD2 target bombarded with 122 keV deuterons as a function of the deuteron fluence. At the outset, the yield decreased significantly reaching a plateau indicating that the oxide layers and the absorbed gases were removed: the experiment was then performed. Also the cleaning of the Ti surface was achieved by deuteron sputtering. However, the results for Ti metal may not be very accurate because the deuterons used for cleaning may contaminate the surface of the Ti metal. Fig. 3 shows the variation of the secondary
Fig. 4 shows the secondary electron yield of deuterons in TiD2 as a function of the incident deuteron energy. In the 80–254 keV deuteron energy range, the secondary electron yield increases at first and then decreases as the deuteron energy increases. This finding is in agreement with the trend of electronic stopping power. The maximum value of the secondary electron yield is about 1.37 at 143 keV. Secondary electron emission mainly occurs by electronic effects at medium- and high-projectile velocities; no mass dependence is expected in the aforementioned energy range [10]: in other words,
Fig. 3. Variation of the secondary electron yield from the Ti target as a function of the deuteron fluence accumulated firstly by 122 keV, then by 188 keV, and finally by 250 keV deuterons.
K. Jianlin et al. / Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
Fig. 4. Secondary electron yields of deuterons in TiD2 (square) and Ti (circles). The solid line is the fit of the experimental data for deuterons in TiD2 by Eq. (5). Diamonds are data from [11]. The proton energy was normalized to the deuteron energy with the same velocity: i.e., the plotted energy values have to be divided by factor 2 to obtain the real proton energy.
the secondary electron yields for protons and deuterons with the same velocity in the same material should be the same. Based on this hypothesis, an opportunity to compare the secondary electron yield in Ti induced by deuterons and protons is possible. The secondary electron yield in Ti induced by deuterons, from the current study, and by protons, in [11], are reported in Fig. 4 and compared with the yield in TiD2 induced by deuterons. The proton energy has been normalized to the deuteron energy with the same velocity (i.e., the plotted energy values have to be divided by a factor 2 to obtain the real proton energy). The measured yield of deuterons in TiD2 is slightly lower than the measured yield of deuterons in Ti, but higher than the yield of protons in Ti from [11] when the same velocity is considered. The surface of the Ti metal in [11] was cleaned by an Ar+ sputter-gun, which does not modify the pure metal target [12], so that a clean Ti surface is obtained. The higher yield for deuterons in Ti in the current study compared with that of protons in Ti [11] can be due to the modification of the target induced by the deuteron surface cleaning process considered in this study. The higher yield of deuterons from TiD2 compared with that of protons in Ti [11] may be the result of its higher electronic stopping power, lower density, and lower work function: nevertheless the discrepancy is low and indicates the weak influence of the deuteriding process on secondary electron emission. The detailed analyses are given below. (A) According to Eq. (1), the secondary electron yield is approximately proportional to the electronic stopping power (dE/ dx)e: the electronic stopping powers of deuteron in TiD2 and Ti metal have been calculated by using the SRIM program [13] and are shown in Fig. 5: the former is about 10% larger than the latter. (B) Secondary electron yield is also related to the transport process of electrons to the surface. In the theory of Sternglass [4], the probability that an electron is transported to the surface is proportional to the inelastic mean free path (IMFP), without considering the cascade of electrons. Lesiak et al. [14] showed that the IMFP can be influenced by density changes, whereas the influence accounting for hydrogen is negligible. The density of TiD2 is about 13% lower than Ti, so the distinction of IMFPs between TiD2 and Ti is not significant.
3
Fig. 5. Electronic stopping power of deuterons in TiD2 and Ti calculated by SRIM [13].
(C) The probability to escape from the surface is related to the work function of the surface. Based on the energy spectrum of the secondary electrons, Cazques calculated the escape probability from the metal surface [15]. The escape probability is proportional to u3, where u is the work function of the surface. The work function of TiH2 is from 0.1 to 0.2 V lower than Ti, according to Kandasamy et al. [16]. Considering the similar properties of TiH2 and TiD2, the work function of TiD2 is also a little lower than that of Ti. This finding indicates an increase of escape probability in TiD2. However, the increase is very weak compared with the total probability. 3.2. Variation of cexp/(dE/dx)e with deuteron energy The ratio of secondary electron yield in TiD2 with respect to the electronic stopping power cexp/(dE/dx)e is shown in Fig. 6, as a function of the deuteron energy. The mean value of cexp/(dE/dx)e is 0.071Å/eV in TiD2, which is a little higher than 0.069Å/eV in Ti reported by Hasselkamp et al. [11], but lower than the mean value 0.1 ± 0.05 Å/eV for various metals and semiconductors [11]. This is probably due to their relatively higher work function.
Fig. 6. Variation of c/(dE/dx)e with deuteron energy in TiD2 and Ti. The electronic stopping power was calculated by SRIM [13]. The solid line is the fitted results by Eq. (5).
4
K. Jianlin et al. / Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
4. Conclusions
Table 1 Parameters for the least-square fit of secondary electron yield in TiD2. Target
TiD2
K (Å/eV) b
0.176 ± 0.004 0.65 ± 0.06
The decrease of cexp/(dE/dx)e, i.e., Kb, is about 18.5% by increasing the deuteron energy from 80 to 254 keV: this decrease is mostly due to the b parameter because K is a parameter approximately independent from the bombarded ions. Schou calculated b by using a transport theory [5,17]: in his calculation, b remains at 0.3 as Be, Mg, and Al are bombarded by protons in the 100– 1000 keV energy range [17]. However, Schou’s theory is so complicated that b has been calculated only for these three metals. Sternglass has given a semi-empirical formula for the ion-induced secondary electron yields of metals [4]. In his theory, b is not a mentioned parameter, but it is similar to the concept of d-electrons: the electronic energy loss of the incident ion is divided into distant and close collisions [18]. The former leads to the direct generation of low energetic electrons with isotropic angular distribution. The latter leads to the forward generation of few high energetic d-electrons. Based on the equipartition rule [18], the secondary electron yields under light ion bombardment is given by [4]
c ¼ 0:5K ðdE=dxÞe ½1 þ Fðv i Þ;
ð3Þ
where F(vi) represents the transport of d-electrons generated in close collision and is given by the relation
Fðv i Þ ¼ ð1 þ me v 2i =200Þ1 ;
ð4Þ
where me is the mass of the electron and vi is the velocity of the incident ions. Some conclusions in this theory agree with various experimental results in the high-velocity regime [19]. However, when close to the stopping power maximum, the equipartition rule is not yet valid [20,21]. Koschar checked the pre-equilibrium stopping power by using secondary electron yield as a probe [21]. The partition factor B = 0.59 ± 0.05 is larger than 0.5 (the equipartition rule works at B = 0.5). Considering the deviation from the equipartition rule, Eq. (3) is expanded to
c ¼ 0:5K ðdE=dxÞe ½1 B þ B Fðv i Þ;
ð5Þ
where B describes the contribution of close collision to the electronic energy loss. The analyzed yield of the deuterons in TiD2 with least-square fit by Eq. (5) is shown in Figs. 4 and 6 for comparison with the experimental data. The fitting parameters are shown in Table 1. An increase of B = 0.65 ± 0.06 is also observed in the present study. However the increase of B in [21] may be due to the additional screening of tightly bound projectile electrons inside the target, while this effect could be negligible for deuteron bombardment [22] in the current study. On the other hand, the increase of B may be due to the cascade process which has been proven important in electron generation [5,23] but is absent in the theory of Sternglass. Thus, the fact that B is larger than 0.5 indicates that more cascade electrons may be generated by d-electron due to its higher energy.
The secondary electron yield from the TiD2 surface under deuteron bombardment in the 80–254 kV energy range was measured via quotient method. In the experiment, self-sputtering with deuterons was used in surface cleaning to remove the oxide layers and absorbed gases and to compensate for the preferentially sputtered deuterium in the meanwhile. The measured yield of deuterons in TiD2 is slightly lower than the measured yield of deuterons in Ti in the current study, but higher than the yield of protons in Ti from [11] when the same velocity is considered. The higher yield for deuterons in Ti in the current study compared with that of protons in Ti [11] can be due to the modification of the target induced by the deuteron surface cleaning process considered in this study. The higher yield of deuterons from TiD2 compared with that of protons in Ti [11] may be the result of its higher electronic stopping power, lower density, and lower work function. However, the discrepancy is low and indicates the weak influence of the deuteriding process on secondary electron emission. An expansion of the theory of Sternglass was used to study the relationship between the secondary electron yield and the electronic stopping power of deuterons in TiD2. The partition factor B is larger than 0.5, which may be related to the derivation from the equipartition rule near the stopping power maximum or to the cascade process neglected in the theory of Sternglass. Acknowledgments The authors gratefully acknowledge the members of the accelerator operation and maintenance group in INPC for their help on this experiment. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
J.L. Wurtz, C.M. Tapp, J. Appl. Phys. 43 (1972) 3318. T.A. Thornton, J.N. Anno, J. Appl. Phys. 48 (1977) 1718. R.A. Baragiola, E.V. Alonso, A. Oliva-Folrio, Phys. Rev. B 19 (1979) 121. E.J. Sternglass, Phys. Rev. 198 (1957) 1. J. Schou, Phys. Rev. B 22 (1980) 2141. D. Hasselkamp, Particle induced electron emission II, Springer Tracts in Modern Physics, 123, Springer, Berlin, 1992 (p. 8). R.A. Baragiola, E.V. Alonso, J. Ferron, A. Oliva-Folrio, Surf. Sci. 90 (1979) 240. G. Lakits, F. Aumayr, H. Winter, Rev. Sci. Instrum. 60 (1989) 3151. E. Taglauer, Appl. Phys. A 51 (1990) 238. D. Hasselkamp, Particle induced electron emission II, Springer Tracts in Modern Physics, 123, Springer, Berlin, 1992 (p. 44). D. Hasselkamp, S. Hippler, A. Scharmann, T. Schmehl, Ann. Physik Leipzig 47 (1990) 555. D. Hasselkamp, Particle induced electron emission II, Springer Tracts in Modern Physics, 123, Springer, Berlin, 1992 (p. 7). J.F. Ziegler, M.D. Ziegler, J.P. Biersack, Nucl. Instr. and Meth. B 26 (8) (2010) 1818. B. Lesiak, J. Zemek, P. Jiricek, Appl. Surf. Sci. 252 (2006) 2741. J. Cazaux, Appl. Surf. Sci. 257 (2010) 1002. K. Kandasamy, N.A. Surplice, J. Phys. D Appl. Phys. 17 (1984) 387. J. Schou, Scanning Microsc. 2 (1988) 607. H.A. Bethe, Ann. Physik 5 (1930) 325. P. Sigmund, S. Tougaard, Inelastic Particle-Surface Collisions, Springer Series in Chemical Physics, 17, Springer, Berlin, 1981 (p. 2). W. Brabdt, M. Kitagawa, Phys. Rev. B 25 (1982) 5631. P. Koschar, K. Kroneberger, A. Clouvas, M. Burkhard, W. Meckbach, O. Heil, Phys. Rev. A 40 (1989) 3632. A. Mann, W. Brandt, Phys. Rev. B 24 (1981) 4999. P.A. Wolff, Phys. Rev. 95 (1954) 56.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Deuteron induced secondary electron emission from titanium deuteride surface Ke Jianlin ⇑, Liu Meng, Zhou Changgeng Institute of Nuclear Physics and Chemistry, CAEP, Mianyang 621900, China
a r t i c l e
i n f o
Article history: Received 23 October 2011 Received in revised form 25 February 2012 Available online 6 March 2012 Keywords: Secondary electron emission Secondary electron yield Deuteron beam Titanium deuteride
a b s t r a c t The secondary electron yield from titanium deuteride surface induced by deuterons was measured in the 80–254 keV energy range using a quotient method. The clean surface was produced by removing the oxide layers and absorbed gases on the titanium deuteride target by self-sputtering with deuterons. The maximum value of the secondary electron yield is about 1.37 at 143 keV. The secondary electron yield of deuterons in titanium deuteride was compared with the yield of deuterons in Ti, measured in the current study, and with the yield of protons in Ti, measured by Hasselkamp et al. in 1990: values were found to be similar when comparing ions with the same velocity. This suggests the weak influence of the deuteriding process on secondary electron emission. The relation between secondary electron yield and electronic stopping power of deuterons in titanium deuteride was also discussed, with an expansion of the theory of Sternglass. From the results the partition factor B is a little larger than 0.5, which may be related to the derivation from the equipartition rule near the stopping power maximum or to the cascade process which is neglected in the theory of Sternglass. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
c ¼ K b ðdE=dxÞe ;
In accelerator-driven D–D or D–T neutron sources, the secondary electrons from the target and the walls can seriously influence the load capacity and breakdown characteristics of an accelerating tube. In the past decades, much experimental and theoretical work has been directed toward proton-induced emission of secondary electron from metal surfaces, but the situation is less satisfactory in the case of deuteron [1–3], especially for that from metal deuterides/tritides, where only results for ErD2 and ScD2 under deuteron bombardment have been reported by Wurtz and Tapp [1]. Ion-induced secondary electron emission is assumed to be a result of two distinguishable processes: potential emission and kinetic emission. The potential emission is related to the neutralization of the bombarding ion and can be neglected in the ion energy range of the current work. The kinetic emission is basically understood as a combination of three processes [4,5]: (1) energy loss of incident ion to the electrons of the medium, which mainly refer to electronic energy loss, because the contribution of the recoiling target atoms can be neglected under bombardment with high-energy light ions, (2) transport of electrons to the surface with a series of collisions, and (3) escape from the surface. Although none of these three processes have been understood clearly, the secondary electron yield c can be obtained through the equation shown below:
where (dE/dx)e is the electronic stopping power of the solid, b is a parameter related to energy deposition in the target, and K is a parameter related only to the target material. In the present research, quotient method [6] was used to measure the secondary electron yields of the accelerator-used target. Titanium deuteride target, which is often used in accelerator-driven D–D neutron source, was selected to perform the experiment because it is not radioactive or contaminated by incident deuteron. Based on the results of the current study, the influence of deuteriding process on secondary electron emission was discussed. The relationship between secondary electron yield and the electronic stopping power of deuterons in TiD2 was also investigated.
⇑ Corresponding author. Tel.: +86 0816 249 3591. E-mail address: [email protected] (K. Jianlin). 0168-583X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2012.02.033
ð1Þ
2. Experimental 2.1. Experimental set-up The experiment was performed at a cock-croft accelerator in Institute of Nuclear Physics and Chemistry by deuterons with a selected energy in the 80–254 keV range. A schematic diagram of the measuring arrangement is shown in Fig. 1. When the electrode is biased by 200–300 V negative potential, electrons are prohibited to leave the target and the measured current ID is equal to the incoming deuteron current. In the case of 250–350 V positive potential, electrons are repelled from the target and the measured current Itotal is equal to the sum of the deuteron current and of
2
K. Jianlin et al. / Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
Fig. 2. Variation of secondary electron yields as a function of deuteron fluence for TiD2 target bombarded with 122 keV deuterons.
Fig. 1. Schematic diagram of the experimental setup. The DC electrical source is adjustable from 500 to +500 V. The value of the current was measured by I = V/R.
the outgoing electron current. The secondary electron yield per incident deuteron is then given by the equation
c¼
ðItotal ID Þ : ID
ð2Þ
electron yield from the Ti target as a function of the deuteron fluence which was accumulated firstly at 122 keV, then at 188 keV and finally at 250 keV: this was performed to show the influence of the incident deuteron energy on the cleaning process. The result shows that the yield reaches the same plateau value even by considering different deuteron energies.
3. Results and discussion
2.2. Surface treatment
3.1. Secondary electron yields from titanium deuteride surface
The targets were exposed to air before insertion into the vacuum, so it is necessary to clean the surface of the targets before performing the experiment. When performing the experiment, self-sputtering with deuterons was used in the TiD2 surface cleaning to remove the oxide layers and absorbed gases and to compensate for the preferentially sputtered deuterium. In secondary electron emission studies, surface cleaning was mostly achieved by heating or sputtering. It has been shown by Baragiola et al. [7] that the yield in aluminum obtained by sputtering with argon ions is the same to that of in situ evaporation. In the present study, heating and evaporation of the TiD2 target would accelerate the release of deuterium, so cleaning the TiD2 surface by these methods was not feasible. Furthermore, sputtering with Ar+ sputter-gun at low energies, which has been often used in the cleaning of pure metal surfaces [1,8], was not used because of its preferential sputtering. Accordingly to the theory of preferential sputtering [9], the sputtering yield of deuterium is much larger than titanium, which might change the deuterium titanium ratio of the target surface and finally influence the accuracy of the measured yields. Fortunately, the preferentially sputtered deuterium could be partially compensated if the surface cleaning is achieved by self-sputtering with deuterons. Fig. 2 shows the variation of the secondary electron yield from the TiD2 target bombarded with 122 keV deuterons as a function of the deuteron fluence. At the outset, the yield decreased significantly reaching a plateau indicating that the oxide layers and the absorbed gases were removed: the experiment was then performed. Also the cleaning of the Ti surface was achieved by deuteron sputtering. However, the results for Ti metal may not be very accurate because the deuterons used for cleaning may contaminate the surface of the Ti metal. Fig. 3 shows the variation of the secondary
Fig. 4 shows the secondary electron yield of deuterons in TiD2 as a function of the incident deuteron energy. In the 80–254 keV deuteron energy range, the secondary electron yield increases at first and then decreases as the deuteron energy increases. This finding is in agreement with the trend of electronic stopping power. The maximum value of the secondary electron yield is about 1.37 at 143 keV. Secondary electron emission mainly occurs by electronic effects at medium- and high-projectile velocities; no mass dependence is expected in the aforementioned energy range [10]: in other words,
Fig. 3. Variation of the secondary electron yield from the Ti target as a function of the deuteron fluence accumulated firstly by 122 keV, then by 188 keV, and finally by 250 keV deuterons.
K. Jianlin et al. / Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
Fig. 4. Secondary electron yields of deuterons in TiD2 (square) and Ti (circles). The solid line is the fit of the experimental data for deuterons in TiD2 by Eq. (5). Diamonds are data from [11]. The proton energy was normalized to the deuteron energy with the same velocity: i.e., the plotted energy values have to be divided by factor 2 to obtain the real proton energy.
the secondary electron yields for protons and deuterons with the same velocity in the same material should be the same. Based on this hypothesis, an opportunity to compare the secondary electron yield in Ti induced by deuterons and protons is possible. The secondary electron yield in Ti induced by deuterons, from the current study, and by protons, in [11], are reported in Fig. 4 and compared with the yield in TiD2 induced by deuterons. The proton energy has been normalized to the deuteron energy with the same velocity (i.e., the plotted energy values have to be divided by a factor 2 to obtain the real proton energy). The measured yield of deuterons in TiD2 is slightly lower than the measured yield of deuterons in Ti, but higher than the yield of protons in Ti from [11] when the same velocity is considered. The surface of the Ti metal in [11] was cleaned by an Ar+ sputter-gun, which does not modify the pure metal target [12], so that a clean Ti surface is obtained. The higher yield for deuterons in Ti in the current study compared with that of protons in Ti [11] can be due to the modification of the target induced by the deuteron surface cleaning process considered in this study. The higher yield of deuterons from TiD2 compared with that of protons in Ti [11] may be the result of its higher electronic stopping power, lower density, and lower work function: nevertheless the discrepancy is low and indicates the weak influence of the deuteriding process on secondary electron emission. The detailed analyses are given below. (A) According to Eq. (1), the secondary electron yield is approximately proportional to the electronic stopping power (dE/ dx)e: the electronic stopping powers of deuteron in TiD2 and Ti metal have been calculated by using the SRIM program [13] and are shown in Fig. 5: the former is about 10% larger than the latter. (B) Secondary electron yield is also related to the transport process of electrons to the surface. In the theory of Sternglass [4], the probability that an electron is transported to the surface is proportional to the inelastic mean free path (IMFP), without considering the cascade of electrons. Lesiak et al. [14] showed that the IMFP can be influenced by density changes, whereas the influence accounting for hydrogen is negligible. The density of TiD2 is about 13% lower than Ti, so the distinction of IMFPs between TiD2 and Ti is not significant.
3
Fig. 5. Electronic stopping power of deuterons in TiD2 and Ti calculated by SRIM [13].
(C) The probability to escape from the surface is related to the work function of the surface. Based on the energy spectrum of the secondary electrons, Cazques calculated the escape probability from the metal surface [15]. The escape probability is proportional to u3, where u is the work function of the surface. The work function of TiH2 is from 0.1 to 0.2 V lower than Ti, according to Kandasamy et al. [16]. Considering the similar properties of TiH2 and TiD2, the work function of TiD2 is also a little lower than that of Ti. This finding indicates an increase of escape probability in TiD2. However, the increase is very weak compared with the total probability. 3.2. Variation of cexp/(dE/dx)e with deuteron energy The ratio of secondary electron yield in TiD2 with respect to the electronic stopping power cexp/(dE/dx)e is shown in Fig. 6, as a function of the deuteron energy. The mean value of cexp/(dE/dx)e is 0.071Å/eV in TiD2, which is a little higher than 0.069Å/eV in Ti reported by Hasselkamp et al. [11], but lower than the mean value 0.1 ± 0.05 Å/eV for various metals and semiconductors [11]. This is probably due to their relatively higher work function.
Fig. 6. Variation of c/(dE/dx)e with deuteron energy in TiD2 and Ti. The electronic stopping power was calculated by SRIM [13]. The solid line is the fitted results by Eq. (5).
4
K. Jianlin et al. / Nuclear Instruments and Methods in Physics Research B 280 (2012) 1–4
4. Conclusions
Table 1 Parameters for the least-square fit of secondary electron yield in TiD2. Target
TiD2
K (Å/eV) b
0.176 ± 0.004 0.65 ± 0.06
The decrease of cexp/(dE/dx)e, i.e., Kb, is about 18.5% by increasing the deuteron energy from 80 to 254 keV: this decrease is mostly due to the b parameter because K is a parameter approximately independent from the bombarded ions. Schou calculated b by using a transport theory [5,17]: in his calculation, b remains at 0.3 as Be, Mg, and Al are bombarded by protons in the 100– 1000 keV energy range [17]. However, Schou’s theory is so complicated that b has been calculated only for these three metals. Sternglass has given a semi-empirical formula for the ion-induced secondary electron yields of metals [4]. In his theory, b is not a mentioned parameter, but it is similar to the concept of d-electrons: the electronic energy loss of the incident ion is divided into distant and close collisions [18]. The former leads to the direct generation of low energetic electrons with isotropic angular distribution. The latter leads to the forward generation of few high energetic d-electrons. Based on the equipartition rule [18], the secondary electron yields under light ion bombardment is given by [4]
c ¼ 0:5K ðdE=dxÞe ½1 þ Fðv i Þ;
ð3Þ
where F(vi) represents the transport of d-electrons generated in close collision and is given by the relation
Fðv i Þ ¼ ð1 þ me v 2i =200Þ1 ;
ð4Þ
where me is the mass of the electron and vi is the velocity of the incident ions. Some conclusions in this theory agree with various experimental results in the high-velocity regime [19]. However, when close to the stopping power maximum, the equipartition rule is not yet valid [20,21]. Koschar checked the pre-equilibrium stopping power by using secondary electron yield as a probe [21]. The partition factor B = 0.59 ± 0.05 is larger than 0.5 (the equipartition rule works at B = 0.5). Considering the deviation from the equipartition rule, Eq. (3) is expanded to
c ¼ 0:5K ðdE=dxÞe ½1 B þ B Fðv i Þ;
ð5Þ
where B describes the contribution of close collision to the electronic energy loss. The analyzed yield of the deuterons in TiD2 with least-square fit by Eq. (5) is shown in Figs. 4 and 6 for comparison with the experimental data. The fitting parameters are shown in Table 1. An increase of B = 0.65 ± 0.06 is also observed in the present study. However the increase of B in [21] may be due to the additional screening of tightly bound projectile electrons inside the target, while this effect could be negligible for deuteron bombardment [22] in the current study. On the other hand, the increase of B may be due to the cascade process which has been proven important in electron generation [5,23] but is absent in the theory of Sternglass. Thus, the fact that B is larger than 0.5 indicates that more cascade electrons may be generated by d-electron due to its higher energy.
The secondary electron yield from the TiD2 surface under deuteron bombardment in the 80–254 kV energy range was measured via quotient method. In the experiment, self-sputtering with deuterons was used in surface cleaning to remove the oxide layers and absorbed gases and to compensate for the preferentially sputtered deuterium in the meanwhile. The measured yield of deuterons in TiD2 is slightly lower than the measured yield of deuterons in Ti in the current study, but higher than the yield of protons in Ti from [11] when the same velocity is considered. The higher yield for deuterons in Ti in the current study compared with that of protons in Ti [11] can be due to the modification of the target induced by the deuteron surface cleaning process considered in this study. The higher yield of deuterons from TiD2 compared with that of protons in Ti [11] may be the result of its higher electronic stopping power, lower density, and lower work function. However, the discrepancy is low and indicates the weak influence of the deuteriding process on secondary electron emission. An expansion of the theory of Sternglass was used to study the relationship between the secondary electron yield and the electronic stopping power of deuterons in TiD2. The partition factor B is larger than 0.5, which may be related to the derivation from the equipartition rule near the stopping power maximum or to the cascade process neglected in the theory of Sternglass. Acknowledgments The authors gratefully acknowledge the members of the accelerator operation and maintenance group in INPC for their help on this experiment. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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