- Email: [email protected]
Computer simulation of chemical erosion of graphite due to hydrogen ion bombardment
Nuclear Instruments and Methods in Physics Research B 202 (2003) 195–200 www.elsevier.com/locate/nimb
Computer simulation of chemical erosion of graphite due to hydrogen ion bombardment J.H. Liang a
a,*
, M. Mayer b, J. Roth b, W. Eckstein
b
Department of Engineering and System Science, National Tsing Hua University, 101, Section 2, Kuang Fu Road, Hsinchu 30043, Taiwan, ROC b Max-Planck-Institute fuer Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching, Germany
Abstract Chemical erosion of graphite due to hydrogen ion bombardment has been investigated theoretically by applying a model of chemical erosion to the TRIDYN code. The model involves the formation of methane at the end of the ion track as well as the kinetic emission of hydrocarbons from the target surface. Model calculations were performed for ion energies ranging from 10 to 1000 eV and at target temperatures ranging from 300 to 900 K. Good agreement between calculated and measured erosion yields is obtained. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 79.20.Rf; 81.40.Wx; 61.80.Jh Keywords: Plasma–material interaction; Chemical erosion; Hydrocarbon; Graphite; Hydrogen retention; Thermonuclear fusion
1. Introduction With such advantages as a low atomic number, excellent thermomechanical properties and high thermal conductivity, graphite is a widely used material for plasma facing components in thermonuclear fusion devices [1]. One major disadvantage of graphite, however, is its high erosion yield due to chemical erosion by hydrogen ion bombardment, especially at elevated temperatures [1]. Since the chemical erosion of graphite substantially reduces the lifetime of plasma facing components, causes undesired plasma contamina-
tion problems and contributes to a high tritium inventory in redeposited hydrogen containing layers due to codeposition [2], it has been the subject of numerous studies in recent decades [3,4]. Chemical erosion of graphite under hydrogen exposure arises from the release of volatile hydrocarbons (e.g. methane molecules) that are formed by chemical reactions of carbon atoms with energetic hydrogen ions [1] and/or thermal hydrogen atoms [5]. The formation and release of hydrocarbons is a complex process depending on target temperature, ion fluence, ion energy, ion flux, surface state of the target material, etc. Chemical erosion of carbon by hydrogen ion bombardment is caused by two different processes [3]:
*
Corresponding author. Tel.: +886-3-5714-661; fax: +886-35720-724. E-mail address: [email protected] (J.H. Liang).
(1) After slowing down, the thermalized hydrogen ions hydrogenate carbon atoms to CH3 –C
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)01857-8
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J.H. Liang et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 195–200
complexes. The CH3 -radicals can be released at target temperatures above 400 K. This is called the thermally activated (or thermal) process, which is further enhanced by radiation damage. (2) At low surface temperatures all available carbon atoms are hydrated, but no thermal release of hydrocarbons occurs. Instead, hydrocarbon radicals, which are bound to the surface with considerably lower binding energy than carbon atoms, are released due to ion induced desorption. In the present paper, this is referred to as the surface process.
emission (i.e. emitted from the target surface) and is herein referred to as the ‘‘surface erosion yield’’. Ytherm represents the chemical erosion yield of graphite due to thermally activated hydrocarbon emission (i.e. emitted from the bulk of the target material) and is herein referred to as the ‘‘thermal erosion yield’’. Ychem ¼ ðYsurf þ Ytherm Þ, Yphys and Ytotal ¼ ðYchem þ Yphys Þ denote the chemical, physical and total erosion yields, respectively. The development of the present model in simulating chemical erosion of graphite under hydrogen ion irradiation is based on the following observations:
When doped graphites are bombarded with hydrogen ions, complex modifications of the surface layer can be observed, like enrichment of the doping element (such as Si or Ti) due to preferential erosion of carbon. Simultaneous bombardment with hydrogen and carbon ions results in an interplay between the deposition of carbon layers and re-erosion. If only physical sputtering plays a role, these dynamic surface changes can be simulated with a dynamic TRIM code like TRIDYN [6], which takes into account changes in surface composition. However, the original TRIDYN code is not able to calculate chemical erosion, thus severely limiting its applicability for simulating the impact of hydrogen ions on carbon containing materials. Molecular dynamics codes are able to calculate chemical erosion in principle, but are much too slow to include dynamic surface changes at high bombardment fluences. In this study, we have applied a chemical erosion model to the well-known TRIDYN (dynamic composition TRIM, version 4.01) Monte-Carlo simulation code [6]. The chemical erosion model is based on the model proposed by Roth [3,7]. Various ion-target conditions such as target temperature, ion fluence and ion energy were investigated in determining both chemical and physical erosion yields.
(1) the production of hydrocarbons is dependent on the atomic fraction of hydrogen retained in graphite, i.e. the ratio H/C [3,5,8]; (2) hydrogen retention in graphite saturates at a maximum atomic fraction ðH=CÞmax , which decreases from 0.42 at 300 K to 0.003 at 873 K [9–11]; (3) surface damage due to energetic hydrogen-ion bombardment increases the production of hydrocarbons [3,12,13] and (4) the production of hydrocarbons is proportional to the range distribution function of hydrogen ions implanted in graphite [13].
2. Simulation model In this study, Ysurf denotes the chemical erosion yield of graphite due to surface hydrocarbon
It is proposed that the ith implanted hydrogen ion will chemically erode Ysurf;i and Ytherm;i carbon atoms from the target material according to the following equations: Ysurf;i ¼ a
ðH=CÞxi fd;i ; ðH=CÞmax
Ytherm;i ¼ b
if 0 6 xi 6 xsurf ;
ðH=CÞxi Roth Y ; ðH=CÞmax therm
if 0 6 xi :
ð1Þ
ð2Þ
Following M€ oller [13], Ysurf;i is assumed to be proportional to surface damage or nuclear energy loss in the region near the target surface. In Eq. (1), fd;i denotes the average nuclear-energy deposition function produced by the ith implanted hydrogen ion between the target surface (x ¼ 0) and xsurf ; xsurf denotes the cutoff depth for Ysurf and is represented by 1 nm [14]; and a is a fitting parameter for the surface process. In Eq. (2), b is a fitting parameter for the thermal process and the
J.H. Liang et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 195–200
where the superscript ‘‘calc’’ denotes the calculated value of the erosion yield Y yielded from this study. Further, an iteration procedure using the least-squares fitting technique was employed in this study to obtain the best-fitting parameters a and b such that the following condition is satisfied: calc Roth Ysurf;therm ¼ Ysurf;therm :
ð4Þ
The above equations were implemented into the TRIDYN simulation code to perform the associated computations. TRIDYN was developed on the basis of the TRIM.SP simulation code [15,16], which is valid only for low fluence ion implantation (i.e. static mode). TRIDYN allows for dynamic composition changes in the target material, thus making it especially applicable for high fluence ion implantation (i.e. dynamic mode). A detailed description of TRIDYN can be found in [6,16,17]. It should also be emphasized that the proposed model does not incorporate any additional model into TRIDYN in order to obtain calc Yphys . Neither diffusion nor segregation effects are taken into account. Furthermore, a number of 106 simulation particles have been adopted in all of the TRIDYN computations based on an optimization between statistical variation and computation time. The incident ions are hydrogen and the target material is graphite (q ¼ 2:266 g/cm3 ). The ion fluence (U) and ion flux (/) are 1:25 1019 ions/ cm2 and 1016 ions/cm2 s [7], respectively. Notably, these ion fluence and ion flux represent typical values used in laboratory experiments for measuring erosion yield. The target temperatures (T ) under investigation in the present study range
from 300 to 900 K, while the ion energies (E) are between 10 and 1000 eV.
3. Results and discussion Fig. 1 depicts the relative importance of Ysurf , Ytherm and Yphys in relation to ion energy and target temperature. The values of Y Roth are adopted herein for illustration. At low ion energies (<100 eV) and low target temperatures (300–660 K), erosion is dominated by Ysurf . Conversely, Yphys is dominant when ion energies are high (>100 eV) and target temperatures are either low (300–660 K) or high (>1000 K). Ytherm is of prime importance at target temperatures between 700 and 1000 K. Notably, Ysurf , Ytherm and Yphys coincide at the point where E ¼ 100:4 eV and T ¼ 660:7 K. Table 1 lists the best-fitting parameters a and b yielded in this study for hydrogen ions impinged into graphite at elevated temperatures. Both a and b shows a slight dependence on target temperature in order to achieve close approximation to RothÕs fitting formulas, but are independent of ion energy. In addition, b is larger than unity because a fraction of incident hydrogen ions are reflected from the target surface and a fraction of incident hydrogen ions end up at a target depth that is not yet saturated with hydrogen. Fig. 2 compares Y calc and Y Roth with target temperatures at an ion energy of 100 eV. As can be seen, our model agrees well with Y Roth . Recalled that RothÕs fitting 1200 Yphys H+ into C 900
φ = 1016 ions/cm 2-sec
Ytherm
T (K)
superscript ‘‘Roth’’ denotes the erosion yield Y by using RothÕs fitting formulas [3], which fit to a variety of experimental data. Also, xi represents the position (i.e. the range) in graphite where the ith implanted hydrogen ion ceases. Ysurf;i and Ytherm;i are both in proportion to the hydrogen to carbon ratio (H/C) already present in the depth xi . In order to compare the experimental data contained in RothÕs fitting formulas, we have used the fluence-averaged surface and thermal erosion yields of graphite: 1 X calc Ysurf;therm ¼ Ysurf;therm;i ; ð3Þ U i
197
600 Yphys
Ysurf 300 1E+1
1E+2
1E+3
1E+4
E ( eV ) Fig. 1. Ysurf , Ytherm and Yphys as functions of ion energy and target temperature for graphite bombarded by hydrogen ions.
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Table 1 Best-fitting parameters a and b for graphite bombarded by hydrogen ions at various target temperatures aa
b
300 473 573 673 773 873
0.00769 0.00901 0.0105 0.0135 0.0153 0.0142
1.28 1.31 1.34 1.39 1.43 1.45
Y ( C/H+ )
T (K)
1E+0 1E- 1 1E-2 Yphys
Ysurf
1E-3 1E-4 1E+0
H+ into C (773 K)
Y ( C/H+ )
a
Calculated according to the number of hydrocarbons pro. duced per eV/A
H+ into C (30 K) φ = 1016 ions/cm2-sec = 1.25 x 1019 ions/cm2
Ytherm
1E-1 1E-2 1E-3 1E-4 1E+1
Yphys
Ysurf
1E+2
1E+3
E ( eV ) Fig. 3. Ysurf , Ytherm and Yphys as a function of ion energy for graphite bombarded by hydrogen ions at target temperatures of 300 and 773 K.
Fig. 2. Comparison of Ysurf , Ytherm , Yphys and Ytotal with target temperature for graphite bombarded by 100 eV hydrogen ions.
formulas were obtained by a best fit to experimental data, our model is thus in good agreement with the underlying experimental data as well. Fig. 3 compares Y calc and Y Roth as a function of ion energy at target temperatures of 300 and 773 K. Notably, Y calc and Y Roth shown in the figure are indicated by symbols and solid curves, respec-
tively. Again, our model shows good agreement calc dewith Y Roth . It should be pointed out that Ysurf Roth viates from Ysurf at high ion energies (E > 100 calc calc eV), but since Ysurf is much smaller than Yphys and calc Ytherm , this discrepancy can be disregarded. It Roth should also be kept in mind that Ysurf was obtained by fitting it to the experimental data and the error may be substantial for small values. Fig. 4 shows Y calc versus ion fluence at an ion energy of 100 eV and at target temperatures of 300 calc and 773 K. As shown, Ysurf emerges when ion fluence reaches a threshold value Ucrit surf , increases as ion fluence increases and then gradually saturates calc at a saturation fluence Usat surf . Ytherm follows a similar sat curve but possesses smaller Ucrit therm and Utherm . The crit crit existence of Usurf and Utherm is in qualitative agreement with the finding in other studies [10,11] that a threshold ion fluence is required for the desorption of hydrocarbons. Furthermore, Ucrit surf , crit sat Usat , U and U decrease as target tempersurf therm therm sat crit ature increases. Also notice that Ucrit surf , Usurf , Utherm sat and Utherm increase as ion energy increases. Concalc versely, Yphys for carbon shows a slow decrease with ion fluence and then saturates. The decrease calc of Yphys is approximately 30% and 7% for graphite
J.H. Liang et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 195–200
Fig. 5 shows the calculated fluence evolution of hydrogen depth profiles in graphite during implantation of 100 eV hydrogen ions at target temperatures of 300 and 773 K. As can be seen, the hydrogen depth profile builds up linearly with time as long as ion fluence remains low. As ion fluence increases, the effects of chemical and physical erosion tend to shift the hydrogen depth profile towards the target surface. At high ion fluences, most of the layers near the target surface are saturated with hydrogen at the ratio ðH=CÞmax .
1E+0 300 K
1E-1
100 eV H+ into C
Ycalc phys
773 K 1E-2 1E-3 1E-4 1E-1
Ycalc therm
1E-2 1E-3 1E-4 1E-1
Ycalc surf
199
1E-2
4. Conclusions
1E-3 1E-4 1E+14
1E+15
1E+16
1E+17
(
1E+18
ions/cm2
1E+19
1E+20
)
calc calc calc Fig. 4. Ysurf , Ytherm and Yphys as a function of ion fluence for graphite bombarded by 100 eV hydrogen ions at target temperatures of 300 and 773 K.
bombarded by 1:25 1019 cm2 100 eV hydrogen ions at target temperatures of 300 and 773 K, respectively. This is due to the implantation of hydrogen ions into the surface layer, which reduces carbon concentration and hence the partial sputtering yield of carbon. The fact that ðH=CÞmax increases at lower target temperatures explains why calc the steady-state value of Yphys for carbon decreases as target temperature decreases.
1E+1 100 eV H+ into C 1E+0
=
1017
ions/cm2
300 K
1016
773 K
H/C
1E-1 1015 1E-2 1014 1E-3 1E-4 0
2
4
6
8
10
x ( nm ) Fig. 5. Dynamic depth profiles of implanted 100 eV hydrogen ions in graphite at target temperatures of 300 and 773 K.
Inclusion of a kinetic model together with two fitting parameters (a and b) has successfully extended the applicability and feasibility of the TRIDYN code to simulate the chemical erosion of graphite under hydrogen ion bombardment. This model includes chemical erosion due to the formation and thermal release of CH4 at the end of the ion track (thermal process) and the release of CH3 from the target surface due to kinetic emission (surface process). The latter is assumed to be proportional to nuclear energy loss within the topmost nm. This model agrees well with RothÕs fitting formulas, which are a fit to various experimental data [3] at different ion energies and target temperatures. The fitting parameters a and b are independent of ion energy, but shows a small dependency on target temperature in order to achieve close approximation to RothÕs fitting formulas. However, the variations of both a and b with target temperature are smaller than the general accuracy of RothÕs fitting formulas and, keeping in mind the large scatter of the underlying experimental data, it is thus sufficient to use constant values of a ¼ 0:01 and b ¼ 1:35 without a significant loss of accuracy. The modified TRIDYN code allows one to calculate fluence dependence of the chemical erosion yield of graphite, dynamic changes in the surface layers of doped graphites under hydrogen ion bombardment and the effects of simultaneous bombardment of target materials with carbon and hydrogen ions. Such calculations will be the subject of future research studies.
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Acknowledgements The authors would like to acknowledge the Max-Planck-Institute for Plasmaphysik (Federal Republic of Germany) and the National Science Council (Republic of China) for their financial support for this research project.
References [1] J. Roth, E. Vietzke, A.A. Haasz, Nucl. Fusion Suppl. 1 (1991) 63. [2] M. Mayer, V. Philipps, P. Wienhold, H.G. Esser, J. von Seggern, M. Rubel, J. Nucl. Mater. 290–293 (2001) 381. [3] J. Roth, J. Nucl. Mater. 266–269 (1999) 51. [4] O. Auciello, A.A. Haasz, P.C. Stangeby, Radiat. Eff. 89 (1985) 63. [5] M. Balooch, D.R. Olander, J. Chem. Phys. 63 (1975) 4772.
[6] W. M€ oller, W. Eckstein, J.P. Biersack, Comput. Phys. Commun. 51 (1988) 355. [7] J. Roth, C. Garcia-Rosales, Nucl. Fusion 36 (1996) 1647; corrigendum Nucl. Fusion 37 (1997) 897. [8] S.K. Erents, C.M. Braganza, G.M. McCracken, J. Nucl. Mater. 63 (1976) 399. [9] D.K. Brice, B.L. Doyle, W.R. Wampler, J. Nucl. Mater. 111–112 (1982) 598. [10] W. M€ oller, B.M.U. Scherzer, J. Appl. Phys. 64 (1988) 4860. [11] W. M€ oller, J. Nucl. Mater. 162–164 (1989) 138. [12] J. Roth, J. Bohdansky, N. Poschenrieder, M.K. Sinha, J. Nucl. Mater. 63 (1976) 222. [13] W. M€ oller, B.M.U. Scherzer, Appl. Phys. Lett. 50 (1987) 1870. [14] C. Garcia-Rosales, J. Roth, J. Nucl. Mater. 196–198 (1992) 573. [15] J.P. Biersack, W. Eckstein, Appl. Phys. A 34 (1984) 73. [16] W. Eckstein, Computer Simulation of Ion–Solid Interactions, Springer, Berlin, 1991. [17] W. M€ oller, D. Bouchier, D. Burat, V. Stambouli, Surf. Coat. Technol. 51 (1992) 190.
Computer simulation of chemical erosion of graphite due to hydrogen ion bombardment J.H. Liang a
a,*
, M. Mayer b, J. Roth b, W. Eckstein
b
Department of Engineering and System Science, National Tsing Hua University, 101, Section 2, Kuang Fu Road, Hsinchu 30043, Taiwan, ROC b Max-Planck-Institute fuer Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching, Germany
Abstract Chemical erosion of graphite due to hydrogen ion bombardment has been investigated theoretically by applying a model of chemical erosion to the TRIDYN code. The model involves the formation of methane at the end of the ion track as well as the kinetic emission of hydrocarbons from the target surface. Model calculations were performed for ion energies ranging from 10 to 1000 eV and at target temperatures ranging from 300 to 900 K. Good agreement between calculated and measured erosion yields is obtained. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 79.20.Rf; 81.40.Wx; 61.80.Jh Keywords: Plasma–material interaction; Chemical erosion; Hydrocarbon; Graphite; Hydrogen retention; Thermonuclear fusion
1. Introduction With such advantages as a low atomic number, excellent thermomechanical properties and high thermal conductivity, graphite is a widely used material for plasma facing components in thermonuclear fusion devices [1]. One major disadvantage of graphite, however, is its high erosion yield due to chemical erosion by hydrogen ion bombardment, especially at elevated temperatures [1]. Since the chemical erosion of graphite substantially reduces the lifetime of plasma facing components, causes undesired plasma contamina-
tion problems and contributes to a high tritium inventory in redeposited hydrogen containing layers due to codeposition [2], it has been the subject of numerous studies in recent decades [3,4]. Chemical erosion of graphite under hydrogen exposure arises from the release of volatile hydrocarbons (e.g. methane molecules) that are formed by chemical reactions of carbon atoms with energetic hydrogen ions [1] and/or thermal hydrogen atoms [5]. The formation and release of hydrocarbons is a complex process depending on target temperature, ion fluence, ion energy, ion flux, surface state of the target material, etc. Chemical erosion of carbon by hydrogen ion bombardment is caused by two different processes [3]:
*
Corresponding author. Tel.: +886-3-5714-661; fax: +886-35720-724. E-mail address: [email protected] (J.H. Liang).
(1) After slowing down, the thermalized hydrogen ions hydrogenate carbon atoms to CH3 –C
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)01857-8
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complexes. The CH3 -radicals can be released at target temperatures above 400 K. This is called the thermally activated (or thermal) process, which is further enhanced by radiation damage. (2) At low surface temperatures all available carbon atoms are hydrated, but no thermal release of hydrocarbons occurs. Instead, hydrocarbon radicals, which are bound to the surface with considerably lower binding energy than carbon atoms, are released due to ion induced desorption. In the present paper, this is referred to as the surface process.
emission (i.e. emitted from the target surface) and is herein referred to as the ‘‘surface erosion yield’’. Ytherm represents the chemical erosion yield of graphite due to thermally activated hydrocarbon emission (i.e. emitted from the bulk of the target material) and is herein referred to as the ‘‘thermal erosion yield’’. Ychem ¼ ðYsurf þ Ytherm Þ, Yphys and Ytotal ¼ ðYchem þ Yphys Þ denote the chemical, physical and total erosion yields, respectively. The development of the present model in simulating chemical erosion of graphite under hydrogen ion irradiation is based on the following observations:
When doped graphites are bombarded with hydrogen ions, complex modifications of the surface layer can be observed, like enrichment of the doping element (such as Si or Ti) due to preferential erosion of carbon. Simultaneous bombardment with hydrogen and carbon ions results in an interplay between the deposition of carbon layers and re-erosion. If only physical sputtering plays a role, these dynamic surface changes can be simulated with a dynamic TRIM code like TRIDYN [6], which takes into account changes in surface composition. However, the original TRIDYN code is not able to calculate chemical erosion, thus severely limiting its applicability for simulating the impact of hydrogen ions on carbon containing materials. Molecular dynamics codes are able to calculate chemical erosion in principle, but are much too slow to include dynamic surface changes at high bombardment fluences. In this study, we have applied a chemical erosion model to the well-known TRIDYN (dynamic composition TRIM, version 4.01) Monte-Carlo simulation code [6]. The chemical erosion model is based on the model proposed by Roth [3,7]. Various ion-target conditions such as target temperature, ion fluence and ion energy were investigated in determining both chemical and physical erosion yields.
(1) the production of hydrocarbons is dependent on the atomic fraction of hydrogen retained in graphite, i.e. the ratio H/C [3,5,8]; (2) hydrogen retention in graphite saturates at a maximum atomic fraction ðH=CÞmax , which decreases from 0.42 at 300 K to 0.003 at 873 K [9–11]; (3) surface damage due to energetic hydrogen-ion bombardment increases the production of hydrocarbons [3,12,13] and (4) the production of hydrocarbons is proportional to the range distribution function of hydrogen ions implanted in graphite [13].
2. Simulation model In this study, Ysurf denotes the chemical erosion yield of graphite due to surface hydrocarbon
It is proposed that the ith implanted hydrogen ion will chemically erode Ysurf;i and Ytherm;i carbon atoms from the target material according to the following equations: Ysurf;i ¼ a
ðH=CÞxi fd;i ; ðH=CÞmax
Ytherm;i ¼ b
if 0 6 xi 6 xsurf ;
ðH=CÞxi Roth Y ; ðH=CÞmax therm
if 0 6 xi :
ð1Þ
ð2Þ
Following M€ oller [13], Ysurf;i is assumed to be proportional to surface damage or nuclear energy loss in the region near the target surface. In Eq. (1), fd;i denotes the average nuclear-energy deposition function produced by the ith implanted hydrogen ion between the target surface (x ¼ 0) and xsurf ; xsurf denotes the cutoff depth for Ysurf and is represented by 1 nm [14]; and a is a fitting parameter for the surface process. In Eq. (2), b is a fitting parameter for the thermal process and the
J.H. Liang et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 195–200
where the superscript ‘‘calc’’ denotes the calculated value of the erosion yield Y yielded from this study. Further, an iteration procedure using the least-squares fitting technique was employed in this study to obtain the best-fitting parameters a and b such that the following condition is satisfied: calc Roth Ysurf;therm ¼ Ysurf;therm :
ð4Þ
The above equations were implemented into the TRIDYN simulation code to perform the associated computations. TRIDYN was developed on the basis of the TRIM.SP simulation code [15,16], which is valid only for low fluence ion implantation (i.e. static mode). TRIDYN allows for dynamic composition changes in the target material, thus making it especially applicable for high fluence ion implantation (i.e. dynamic mode). A detailed description of TRIDYN can be found in [6,16,17]. It should also be emphasized that the proposed model does not incorporate any additional model into TRIDYN in order to obtain calc Yphys . Neither diffusion nor segregation effects are taken into account. Furthermore, a number of 106 simulation particles have been adopted in all of the TRIDYN computations based on an optimization between statistical variation and computation time. The incident ions are hydrogen and the target material is graphite (q ¼ 2:266 g/cm3 ). The ion fluence (U) and ion flux (/) are 1:25 1019 ions/ cm2 and 1016 ions/cm2 s [7], respectively. Notably, these ion fluence and ion flux represent typical values used in laboratory experiments for measuring erosion yield. The target temperatures (T ) under investigation in the present study range
from 300 to 900 K, while the ion energies (E) are between 10 and 1000 eV.
3. Results and discussion Fig. 1 depicts the relative importance of Ysurf , Ytherm and Yphys in relation to ion energy and target temperature. The values of Y Roth are adopted herein for illustration. At low ion energies (<100 eV) and low target temperatures (300–660 K), erosion is dominated by Ysurf . Conversely, Yphys is dominant when ion energies are high (>100 eV) and target temperatures are either low (300–660 K) or high (>1000 K). Ytherm is of prime importance at target temperatures between 700 and 1000 K. Notably, Ysurf , Ytherm and Yphys coincide at the point where E ¼ 100:4 eV and T ¼ 660:7 K. Table 1 lists the best-fitting parameters a and b yielded in this study for hydrogen ions impinged into graphite at elevated temperatures. Both a and b shows a slight dependence on target temperature in order to achieve close approximation to RothÕs fitting formulas, but are independent of ion energy. In addition, b is larger than unity because a fraction of incident hydrogen ions are reflected from the target surface and a fraction of incident hydrogen ions end up at a target depth that is not yet saturated with hydrogen. Fig. 2 compares Y calc and Y Roth with target temperatures at an ion energy of 100 eV. As can be seen, our model agrees well with Y Roth . Recalled that RothÕs fitting 1200 Yphys H+ into C 900
φ = 1016 ions/cm 2-sec
Ytherm
T (K)
superscript ‘‘Roth’’ denotes the erosion yield Y by using RothÕs fitting formulas [3], which fit to a variety of experimental data. Also, xi represents the position (i.e. the range) in graphite where the ith implanted hydrogen ion ceases. Ysurf;i and Ytherm;i are both in proportion to the hydrogen to carbon ratio (H/C) already present in the depth xi . In order to compare the experimental data contained in RothÕs fitting formulas, we have used the fluence-averaged surface and thermal erosion yields of graphite: 1 X calc Ysurf;therm ¼ Ysurf;therm;i ; ð3Þ U i
197
600 Yphys
Ysurf 300 1E+1
1E+2
1E+3
1E+4
E ( eV ) Fig. 1. Ysurf , Ytherm and Yphys as functions of ion energy and target temperature for graphite bombarded by hydrogen ions.
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Table 1 Best-fitting parameters a and b for graphite bombarded by hydrogen ions at various target temperatures aa
b
300 473 573 673 773 873
0.00769 0.00901 0.0105 0.0135 0.0153 0.0142
1.28 1.31 1.34 1.39 1.43 1.45
Y ( C/H+ )
T (K)
1E+0 1E- 1 1E-2 Yphys
Ysurf
1E-3 1E-4 1E+0
H+ into C (773 K)
Y ( C/H+ )
a
Calculated according to the number of hydrocarbons pro. duced per eV/A
H+ into C (30 K) φ = 1016 ions/cm2-sec = 1.25 x 1019 ions/cm2
Ytherm
1E-1 1E-2 1E-3 1E-4 1E+1
Yphys
Ysurf
1E+2
1E+3
E ( eV ) Fig. 3. Ysurf , Ytherm and Yphys as a function of ion energy for graphite bombarded by hydrogen ions at target temperatures of 300 and 773 K.
Fig. 2. Comparison of Ysurf , Ytherm , Yphys and Ytotal with target temperature for graphite bombarded by 100 eV hydrogen ions.
formulas were obtained by a best fit to experimental data, our model is thus in good agreement with the underlying experimental data as well. Fig. 3 compares Y calc and Y Roth as a function of ion energy at target temperatures of 300 and 773 K. Notably, Y calc and Y Roth shown in the figure are indicated by symbols and solid curves, respec-
tively. Again, our model shows good agreement calc dewith Y Roth . It should be pointed out that Ysurf Roth viates from Ysurf at high ion energies (E > 100 calc calc eV), but since Ysurf is much smaller than Yphys and calc Ytherm , this discrepancy can be disregarded. It Roth should also be kept in mind that Ysurf was obtained by fitting it to the experimental data and the error may be substantial for small values. Fig. 4 shows Y calc versus ion fluence at an ion energy of 100 eV and at target temperatures of 300 calc and 773 K. As shown, Ysurf emerges when ion fluence reaches a threshold value Ucrit surf , increases as ion fluence increases and then gradually saturates calc at a saturation fluence Usat surf . Ytherm follows a similar sat curve but possesses smaller Ucrit therm and Utherm . The crit crit existence of Usurf and Utherm is in qualitative agreement with the finding in other studies [10,11] that a threshold ion fluence is required for the desorption of hydrocarbons. Furthermore, Ucrit surf , crit sat Usat , U and U decrease as target tempersurf therm therm sat crit ature increases. Also notice that Ucrit surf , Usurf , Utherm sat and Utherm increase as ion energy increases. Concalc versely, Yphys for carbon shows a slow decrease with ion fluence and then saturates. The decrease calc of Yphys is approximately 30% and 7% for graphite
J.H. Liang et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 195–200
Fig. 5 shows the calculated fluence evolution of hydrogen depth profiles in graphite during implantation of 100 eV hydrogen ions at target temperatures of 300 and 773 K. As can be seen, the hydrogen depth profile builds up linearly with time as long as ion fluence remains low. As ion fluence increases, the effects of chemical and physical erosion tend to shift the hydrogen depth profile towards the target surface. At high ion fluences, most of the layers near the target surface are saturated with hydrogen at the ratio ðH=CÞmax .
1E+0 300 K
1E-1
100 eV H+ into C
Ycalc phys
773 K 1E-2 1E-3 1E-4 1E-1
Ycalc therm
1E-2 1E-3 1E-4 1E-1
Ycalc surf
199
1E-2
4. Conclusions
1E-3 1E-4 1E+14
1E+15
1E+16
1E+17
(
1E+18
ions/cm2
1E+19
1E+20
)
calc calc calc Fig. 4. Ysurf , Ytherm and Yphys as a function of ion fluence for graphite bombarded by 100 eV hydrogen ions at target temperatures of 300 and 773 K.
bombarded by 1:25 1019 cm2 100 eV hydrogen ions at target temperatures of 300 and 773 K, respectively. This is due to the implantation of hydrogen ions into the surface layer, which reduces carbon concentration and hence the partial sputtering yield of carbon. The fact that ðH=CÞmax increases at lower target temperatures explains why calc the steady-state value of Yphys for carbon decreases as target temperature decreases.
1E+1 100 eV H+ into C 1E+0
=
1017
ions/cm2
300 K
1016
773 K
H/C
1E-1 1015 1E-2 1014 1E-3 1E-4 0
2
4
6
8
10
x ( nm ) Fig. 5. Dynamic depth profiles of implanted 100 eV hydrogen ions in graphite at target temperatures of 300 and 773 K.
Inclusion of a kinetic model together with two fitting parameters (a and b) has successfully extended the applicability and feasibility of the TRIDYN code to simulate the chemical erosion of graphite under hydrogen ion bombardment. This model includes chemical erosion due to the formation and thermal release of CH4 at the end of the ion track (thermal process) and the release of CH3 from the target surface due to kinetic emission (surface process). The latter is assumed to be proportional to nuclear energy loss within the topmost nm. This model agrees well with RothÕs fitting formulas, which are a fit to various experimental data [3] at different ion energies and target temperatures. The fitting parameters a and b are independent of ion energy, but shows a small dependency on target temperature in order to achieve close approximation to RothÕs fitting formulas. However, the variations of both a and b with target temperature are smaller than the general accuracy of RothÕs fitting formulas and, keeping in mind the large scatter of the underlying experimental data, it is thus sufficient to use constant values of a ¼ 0:01 and b ¼ 1:35 without a significant loss of accuracy. The modified TRIDYN code allows one to calculate fluence dependence of the chemical erosion yield of graphite, dynamic changes in the surface layers of doped graphites under hydrogen ion bombardment and the effects of simultaneous bombardment of target materials with carbon and hydrogen ions. Such calculations will be the subject of future research studies.
200
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Acknowledgements The authors would like to acknowledge the Max-Planck-Institute for Plasmaphysik (Federal Republic of Germany) and the National Science Council (Republic of China) for their financial support for this research project.
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[6] W. M€ oller, W. Eckstein, J.P. Biersack, Comput. Phys. Commun. 51 (1988) 355. [7] J. Roth, C. Garcia-Rosales, Nucl. Fusion 36 (1996) 1647; corrigendum Nucl. Fusion 37 (1997) 897. [8] S.K. Erents, C.M. Braganza, G.M. McCracken, J. Nucl. Mater. 63 (1976) 399. [9] D.K. Brice, B.L. Doyle, W.R. Wampler, J. Nucl. Mater. 111–112 (1982) 598. [10] W. M€ oller, B.M.U. Scherzer, J. Appl. Phys. 64 (1988) 4860. [11] W. M€ oller, J. Nucl. Mater. 162–164 (1989) 138. [12] J. Roth, J. Bohdansky, N. Poschenrieder, M.K. Sinha, J. Nucl. Mater. 63 (1976) 222. [13] W. M€ oller, B.M.U. Scherzer, Appl. Phys. Lett. 50 (1987) 1870. [14] C. Garcia-Rosales, J. Roth, J. Nucl. Mater. 196–198 (1992) 573. [15] J.P. Biersack, W. Eckstein, Appl. Phys. A 34 (1984) 73. [16] W. Eckstein, Computer Simulation of Ion–Solid Interactions, Springer, Berlin, 1991. [17] W. M€ oller, D. Bouchier, D. Burat, V. Stambouli, Surf. Coat. Technol. 51 (1992) 190.