- Email: [email protected]
Dynamic Monte Carlo simulation for SIMS depth profiling of delta-doped layer
Nuclear Instruments and Methods in Physics Research B 153 (1999) 429±435
www.elsevier.nl/locate/nimb
Dynamic Monte Carlo simulation for SIMS depth pro®ling of delta-doped layer H.J. Kang b
a,*
, W.S. Kim a, D.W. Moon b, H.Y. Lee c, S.T. Kang c, R. Shimizu
d
a Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea Surface Analysis Group, Korea Research Institute of Standard and Science, Yusong, P.O. Box 102, Taejon 305-600, South Korea c Department of Physics, Yonsei University, Wonju 222-701, South Korea d Department of Applied Physics, Osaka University, Suita, Osaka 565-0871, Japan
Abstract Depth pro®ling of a multilayered thin ®lm (Ta2 O5 (18 nm)/SiO2 (0.5 nm)) on Si and a 1 nm ultra-thin single layer (Ta2 O5 (1 nm)/SiO2 (20 nm)) sample was studied by Secondary Ion Mass Spectrometry (SIMS) and Dynamic Monte Carlo simulation approach. This approach is based on the binary encounter model, taking into account (1) generation of both the interstitial atoms and vacancies and (2) annihilation of the vacancies. The observed 1±3 nm shift of the delta layer peak to the surface direction in SIMS depth pro®ling could be explained with Dynamic Monte Carlo simulation approach, which describes atomic mixing phenomena in depth pro®ling of multilayer systems. In the case of a 1 nm Ta2 O5 single layer on SiO2 , the primary ion energy dependence of the decay length was measured. It could be reproduced with the Monte Carlo simulation results. We observed that the depth resolution improved at higher energy rather than at lower energy in contrast to other generally observed cases. It showed that the deeper collision cascade minimized the ion beam mixing at the ultra-thin surface layer and improved the decay length at higher primary ion energy. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Depth pro®ling of doping elements has been widely applied to the semiconductor industry in the last decade. Recently, as the device size scaled down to below sub-micron, ultra-shallow implantation became popular [1]. Therefore, the depth resolution with nm accuracy has become increasingly important in process design [1]. However, it
* Corresponding author. Fax: +82-431-274-7811; e-mail: [email protected].
is dicult to extract the true depth pro®le directly from conventional SIMS analysis because of various problems such as collisional cascade mixing, knock on mixing, radiation enhanced diusion, preferential sputtering, segregation, matrix eect, surface roughness, etc. [2±6]. Even though these eects induced by ion sputtering are inevitable, many studies have been carried out to obtain an accurate pro®le by using the response function of these physical eects, but it has not been so successful yet. Hofmann [7] developed a simple analytical model, which is called the MRI model based on atomic mixing, surface roughness and signal
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 1 0 2 1 - 0
430
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
information depth for the estimation of depth resolution in the depth pro®ling. It was applied to AlAs/GaAs multilayer depth pro®ling successfully. In a computer simulation of depth pro®ling, the simulation codes based on binary collision approximation such as TRIDYN [8] or ACATDIFFUSE [9] have been used, which is quite successful in obtaining detailed information about sputtering and atomic mixing. Recently, we proposed the Monte Carlo simulation by incorporating annihilation processes into the model [10]. It described the Auger depth pro®les of the AlAs/ GaAs superlattice structure with very good accuracy. In the present study, we applied it to the SIMS depth pro®les of delta SiO2 multilayer. The SIMS pro®le shape of the delta layer was entirely determined by the physical processes occurring in the sample during analysis. The delta layer pro®le provides direct measurement of the broadening eects. This pro®le is, in fact, a response function. From the viewpoint of computer simulation, this response function can be applied to the estimation and improvement of the simulation model. The main purpose of this work is to understand the physical process occurring in SIMS depth pro®ling. In this work we used a delta oxide multilayer composed of seven thick Ta2 O5 layers separated by delta SiO2 layers, which was suggested as a new reference material for SIMS depth pro®ling [11]. Amorphous Ta2 O5 was chosen as the thick layer material because the surface topography is not signi®cantly developed by ion beam sputtering. In order to avoid the SIMS matrix eect at the interface of metal/oxide multilayer system, very thin SiO2 layers were chosen as delta layers so that the change in the chemical state of the thin-®lm materials is minimized at the oxide/oxide interfaces. 2. Experiment The Ta2 O5 /SiO2 multilayered thin ®lm composed of six SiO2 layers of 0.5 nm thickness between seven 18-nm Ta2 O5 layers were grown on an n-type Si (1 0 0) wafer by reactive sputter deposition of Ta and Si targets under oxygen gas ¯ow. Details of the thin ®lm deposition method and in
situ analysis of the stoichiometric compositions of the two oxide layers can be seen elsewhere [11]. Ta2 O5 layer 1 nm thick on SiO2 layer was also obtained by the SIMS depth pro®le. The pro®ling was performed on Cameca IMS-4f using various ion energies (7.5, 10 and 12.5 keV) and ion species (Ar , O 2 and Cs ) with 4.5 keV sample bias. Under these conditions, the kinetic energy and the incidence angle of the primary Ar ions are 3.0, 5.5, 8.0 keV and 52 , 42 , 39 from the surface normal, respectively. 3. Models of Monte Carlo simulation The Monte Carlo simulation model for the interactions of energetic ions with solid is based on the elastic collision by binary encounter with randomly distributed target atoms and inelastic collision with electron gas using Ziegler±Biersack± Littmark (ZBL) potential and Lindhard's equation, respectively [12]. Details of this program are seen elsewhere [10,12,13]. Therefore, for the depth pro®ling, newly introduced terms are described brie¯y. The eects of surface roughness and implanted primary ions are disregarded in these calculations. The interstitial atoms and vacancies generated by collisional cascade are distributed in pairs if the sputtered atoms are regarded as being sputtered only from the topmost atomic layer. These pairs migrate during collisional cascade and the vacancies are eventually annihilated by recombination with interstitial atoms or absorption into the sinks, e.g. surface, grain boundary, etc. Since the behavior of these interstitial atoms and vacancies is directly related to diusion in sputtering and range of atomic mixing in a complicated manner, it is very dicult to describe the migration processes of these pairs accurately. In the present simulation, therefore, all the interstitial±vacancy pairs are assumed to be completely recombined in the mixing zone. The total number of atoms of each layer, therefore, remains constant so that the atomic density in each atomic layer keeps invariant during sputtering. Otherwise, the atomic density tends to increase by a knock-in eect as sputtering proceeds.
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
The basic model used to treat the interstitial± vacancy pairs is as follows: First, it is assumed that each atomic layer is composed of N pseudo-atoms, where a pseudo-atom represents 109 ±1010 atoms, depending on the number of trajectories of primary ions in the Monte Carlo simulation. The Monte Carlo calculation is performed until the total number of sputtered atoms attains the number necessary to sputter N pseudo-atoms. The atomic mixing is generated by the collision cascade or both the incident ions and recoiled atoms, and the atom displaced from original layer to another layer is counted as an interstitial atom, leaving a vacancy at its original site. The numbers of both the vacancies and interstitial atoms are easily counted for each atomic layer. When the total number of pseudo-atoms in an atomic layer, N 0 , is larger than N , (N 0 > N ), we regard the excess atoms, (N 0 ÿ N ) as interstitial atoms while the difference, (N ÿ N 0 ), is regarded as vacancies for (N > N 0 ). Second, redistribution of atoms in an ith atomic layer is calculated as follows: (1) Vacancies are assumed to be annihilated with interstitial atoms in the previous (i ÿ 1)th layer and the composition of those atoms that ®ll the vacancies is proportional to atomic concentration in the relevant layer. (2) Interstitial atoms in the ith layer are to be added to the previous (i ÿ 1)th layer. The process described above is performed from the bottom layer to the top atomic layer. As a result, the total number of atoms of the top atomic layer becomes zero and the second atomic layer becomes the new top layer when N pseudoatoms are sputtered. In this simulation, 10 000 pseudo-atoms are considered to be in each atomic layer. For the SIMS depth pro®ling, the partial sputtering yield of each element was used. The Auger depth pro®ling can also be obtained considering the escape depth of Auger electrons and the atomic concentration of surface layer [10]. 4. Results and discussion Fig. 1 shows the SIMS depth pro®le of SiO for Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayer with a Cameca IMS-4f by various ion energies of O 2 ion
431
Fig. 1. The SIMS depth pro®les of SiO for a Ta2 O5 (18 nm)/ SiO2 (0.5 nm) multilayered system, sputtered with 3, 5.5 and 8 keV O 2 ion beam.
beams. It is of interest to note that the depth resolution is not signi®cantly deteriorated with the sputter depth for all the analysis conditions. This indicates that the surface topographic development is negligible under the sputtering conditions, which is con®rmed by measuring the average surface roughness of sample surfaces before and after ion beam sputtering [11]. Therefore, in this multilayered system, the physical process is expected to mainly contribute to the depth resolution of delta SiO2 layer. In this simulation, we calculate the depth pro®les of two delta SiO2 layers to compare with these experimental SIMS results. In Fig. 2, the in-depth composition pro®les of each element, until the ®rst delta layer is removed as sputtering proceeds, are shown. One can see how the sputter depth pro®le proceeds accompanied with altered layer due to preferential sputtering. As can be seen in Fig. 2, the delta-doped layer becomes broad and then is removed as the sputtering proceeds. An altered layer due to the preferential sputtering eect is formed at surface region, which remains during sputtering. Here, the sputtering yield at the initial stage was higher than that of steady state. It could be one of the causes for the peak shift of delta-doped layer to the surface direction. This is shown in Fig. 5 in more detail.
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Fig. 3. Calculated (a) and experimental (b) results of SIMS depth pro®les of Si for a Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayered system, sputtered with 3, 5.5 and 8 keV O 2 ions at incidence angle of 52 ; 42 ; and 39 from the surface normal, respectively.
Fig. 2. In depth composition pro®les of Ta, O, Si for a Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayered system during 5.5 keV O 2 sputtering.
The SIMS depth pro®les of the ®rst two delta layers, sputtered with O 2 ion beam in Fig. 1 were replotted (Fig. 3(b)) in linear scale to be compared with the calculated results. Here, the square bar indicates the SiO2 delta layer in the multilayered
sample. To convert the sputtering time to the sputter depth, the average sputtering time between delta layers was used. The calculation results were obtained with partial sputtering yield of Si in delta-doped SiO2 layer as the sputter etching proceeds. In simulation results (Fig. 3(a)), the peaks of delta layers shift to the surface direction, as the primary ion energy increases, which is in good agreement with experimental results (Fig. 3(b)). Similar peak shifts to the surface direction have been also obtained with Ar primary ion. The peak shifts to surface direction may be attributed to the incident angle dependence of primary ion, penetration depth dependence of primary ion energy or preferential sputtering eects in the initial state of sputtering. Actually, in SIMS measurement, the incidence angle depends on the primary
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
ion energy because of the sample bias voltage. Primary ion beam energies from 3 to 8 keV were used, and angles of incidence varied between 52 and 39 with respect to the surface normal. In simulation results, if the incidence angle changes from 42 to 52 with 3 keV Ar ion beam, the peak shifts did not change so much. But when we changed the primary Ar ion beam energy by ®xing up the incidence angle of 42 , the delta layer peaks shifted to the surface direction. Therefore the eect of the primary ion energy is the more dominant factor than that of the ion incidence angle in this case. The primary ion species was changed to investigate the mass dependence of peak shift of delta layer as shown in Fig. 4. In calculation results (Fig. 4(a)), the peak of delta layer did not
Fig. 4. Calculated (a) and experimental (b) results of SIMS depth pro®les of Si for a Ta2 O5 (18 nm)/SiO2 (0.5 nm) multi layered system, sputtered with 5.5 keV O 2 , Ar and Cs ion at the incidence angle of 42 .
433
shift signi®cantly, but there are peak shifts in experiments (Fig. 4(b)). Since the mass dierence of primary ion beam does not aect the peak shift as shown in the calculation, the peak shift in the experiment could be attributed to the dierence of sputtering yield between the initial stage and the steady state of sputtering. Actually,the sputtering rate in the initial stage is larger than that in the steady state due to the preferential sputtering especially with oxygen primary ions compared with argon primary ions as shown in Fig. 5. But it was not considered in converting sputtering time to sputter depth, which will shift the peak to the surface direction. The sputtering yield was 0.77 atoms/ion at the surface but it decreased continuously to the steady state value of 0.55 atoms/ion at the depth of 7 nm as shown in Fig. 5. Rough estimation gives a 1.3 nm peak shift to the surface direction, which is close to the experimentally observed additional shift for oxygen primary ions. However, in the experimental condition, primary oxygen ion implantation will compensate the preferential sputtering of oxygen, as reported elsewhere [14]. As mentioned in Section 3, the implantation eect of the primary ions was not considered in the calculations. For Ar and Cs primary ions, the primary ion implantation eect will not be signi®cant. But for O 2 ions, the implanted primary oxygen ions will aect the preferential sputtering process to decrease the preferential sputtering of oxygen atoms from Ta2 O5 layers. In practical SIMS depth pro®ling, the implantation eect of the primary ions should be considered. For this, the simulation model is under development. We can conclude that the peak shifts of delta layers in SIMS depth pro®ling are attributed mainly to the penetration depth of primary ion energy and the preferential sputtering eects at the initial state of sputtering for the oxide delta multilayers used in this analysis. To compare the simulation results with experimental results in more detail, the growth and decay length of delta-doped layer were obtained with exponential function and the width of delta layer with Gaussian function as commonly done in SIMS depth pro®ling [15]. The results are tabulated in Table 1. The depth resolutions become worse as the primary ion energies increase, which
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H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
Fig. 5. Sputtering yields of Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayers, sputtered with 5.5 keV Ar and O 2 ions as a function of depth.
describes the experimental results well. It is of interest to note that the growth lengths are in quite good agreement with experimental results, but the decay lengths are relatively larger than that of experiment. It means that the atomic mixing of the simulation is still a little bit overestimated, but generally the simulation is in quite good agreement with the experiment.
Fig. 6 shows the SIMS depth pro®le of Ta2 O5 (1 nm)/SiO2 (20 nm)/Si(substrate) using O 2 ion beam with various ion energies. Here the square bar indicates the ultra-thin Ta2 O5 layer at the surface. It is worthwhile to note that the depth resolution of the Ta2 O5 delta layer at the surface become better as the primary ion energy increases, which is in contrast to other generally observed cases. Actually, the high primary ion energy can improve the depth resolution of ultra-shallow layers at surface. The simulation results (Fig. 6(a)) describe the experimental results qualitatively. The decay length of Ta in this system at 16 keV O 2 primary ion beam is better than that at 3 keV O 2 primary ion beam. This phenomenon can be explained in terms of recoiled sputtering. In the case of low primary ion energy, the atomic mixing takes place in the delta layer at the surface, while in the case of high primary ion energy, the atomic mixing occurs at the deeper layer below the surface. Therefore, the back-scattered recoil atoms contribute to the depth pro®le with less atomic mixing at the surface delta layer. It showed that the deeper collision cascade minimize the ion beam mixing at the surface ultra-thin layer and improve the decay length at higher primary ion energy.
5. Conclusions The depth pro®ling of a multi-layered thin ®lm (Ta2 O5 (18 nm)/SiO2 (0.5 nm)) on Si and a 1 nm ultra-thin single layer (Ta2 O5 (1 nm)/SiO2 (20 nm)) sample were studied using SIMS technique and Dynamic Monte Carlo Simulation approach. This approach is based on the binary encounter model,
Table 1 Experimental and simulation results of depth resolution parameters of SiO2 delta layer in Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayer Primary ion
Primary ion energy peak position (keV)
Experiment
Simulation
Growth length (nm)
Decay length (nm)
Width (nm)
Growth length (nm)
Decay length (nm)
Width (nm)
O 2
2 3 5.5 8
ÿ 0.7 0.3 0.6
ÿ 1.3 2.6 2.8
ÿ 0.7 1.2 1.9
0.2 0.3 0.5 0.8
2.1 3.1 4.1 5.6
0.8 1.1 1.9 2.3
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435
observed cases, which could be con®rmed with Monte Carlo simulation. It showed that the deeper collision cascades minimize the ion beam mixing at the surface ultra-thin layer and improve the decay length at higher primary ion energy.
Acknowledgements The authors are very grateful to Dr. Y. Kimura and Dr. T. Asahata of Osaka University for stimulating discussions on simulation model. This research was ®nancially supported by the AtomicScale Surface Science Research Center at Yonsei University and by the Basic Science Research Institute Program, Ministry of Education, Project No. BSRI-98-2426. One of the authors (D.W. Moon) appreciates the support from Center for Molecular Science, Korea. One of the authors (H.J. Kang) gratefully acknowledges the support by the Japan Society for the Promotion of Science (JSPS-RFTF 96R 14101) for the cooperative research in Osaka University for one month.
References
Fig. 6. Calculated (a) and experimental (b) results of SIMS depth pro®le of Ta for a Ta2 O5 (1 nm)/SiO2 (20 nm)/Si(substrate) system, sputtered with various O 2 ion energies.
taking into account (1) generation of both the interstitial atoms and vacancy, and (2) annihilation of the vacancies in the atomic mixing zone. In the case of multi-layers, the observed 1±3 nm shift of the delta layer peak to the surface direction is in quite good agreement with Monte Carlo simulation approach, which can attributed to atomic mixing phenomena and the sputtering rate change during depth pro®ling of multi-layer systems. The peak broadening of the delta SiO2 layer could be explained only by atomic mixing. In the case of the 1 nm Ta2 O5 single layer, we observed the depth resolution was improved at high energy rather than at low energy in contrast to other generally
[1] Proc. Fourth Int. Workshop on the Measurement and Characterization of Ultra-Shallow Doping Pro®les in Semiconductors, J. Vac. Sci. Technol. B 16 (1998) 259. [2] K. Wittmaack, Vacuum 34 (1984) 119. [3] M. Moens, F.C. Adams, D.S. Simons, Anal. Chem. 59 (1987) 1518. [4] K.J. Kim, D.W. Moon, Appl. Phys. Lett. 60 (1992) 1178. [5] H.H. Andersen, Appl. Phys. 18 (1979) 131. [6] K. Wittmaack, in: D. Briggs, M.P. Seah (Eds.), Practical Surface Analysis, vol. II: Ion and Neutral Spectroscopy, ch. 3, Wiley, New York, 1992. [7] S. Hofmann, Surf. Interface Anal. 21 (1994) 673. [8] W. Moeller, W. Eckstein, Nucl. Instr. and Meth. B 2 (1984) 814. [9] Y. Yamamura, Nucl. Instr. and Meth. B 28 (1987) 17. [10] H.I. Lee, R. Shimizu, J. Vac. Sci. Technol. B 16 (1998) 2528. [11] K.J. Kim, D.W. Moon, Surf. Interface Anal. 26 (1998) 9. [12] H.J. Kang, E. Kawatoh, R. Shimizu, Jpn. J. Appl. Phys. 24 (1985) 1409. [13] H.J. Kang, J.H. Kim, Y.S. Kim, D.W. Moon, R. Shimizu, Surf. Sci. 226 (1990) 93. [14] D.W. Moon, K.J. Kim, Appl. Phys. Lett. 62 (1993) 3094. [15] M.G. Dowsett, J. Vac. Sci. Technol. B 12 (1994) 86.
www.elsevier.nl/locate/nimb
Dynamic Monte Carlo simulation for SIMS depth pro®ling of delta-doped layer H.J. Kang b
a,*
, W.S. Kim a, D.W. Moon b, H.Y. Lee c, S.T. Kang c, R. Shimizu
d
a Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea Surface Analysis Group, Korea Research Institute of Standard and Science, Yusong, P.O. Box 102, Taejon 305-600, South Korea c Department of Physics, Yonsei University, Wonju 222-701, South Korea d Department of Applied Physics, Osaka University, Suita, Osaka 565-0871, Japan
Abstract Depth pro®ling of a multilayered thin ®lm (Ta2 O5 (18 nm)/SiO2 (0.5 nm)) on Si and a 1 nm ultra-thin single layer (Ta2 O5 (1 nm)/SiO2 (20 nm)) sample was studied by Secondary Ion Mass Spectrometry (SIMS) and Dynamic Monte Carlo simulation approach. This approach is based on the binary encounter model, taking into account (1) generation of both the interstitial atoms and vacancies and (2) annihilation of the vacancies. The observed 1±3 nm shift of the delta layer peak to the surface direction in SIMS depth pro®ling could be explained with Dynamic Monte Carlo simulation approach, which describes atomic mixing phenomena in depth pro®ling of multilayer systems. In the case of a 1 nm Ta2 O5 single layer on SiO2 , the primary ion energy dependence of the decay length was measured. It could be reproduced with the Monte Carlo simulation results. We observed that the depth resolution improved at higher energy rather than at lower energy in contrast to other generally observed cases. It showed that the deeper collision cascade minimized the ion beam mixing at the ultra-thin surface layer and improved the decay length at higher primary ion energy. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Depth pro®ling of doping elements has been widely applied to the semiconductor industry in the last decade. Recently, as the device size scaled down to below sub-micron, ultra-shallow implantation became popular [1]. Therefore, the depth resolution with nm accuracy has become increasingly important in process design [1]. However, it
* Corresponding author. Fax: +82-431-274-7811; e-mail: [email protected].
is dicult to extract the true depth pro®le directly from conventional SIMS analysis because of various problems such as collisional cascade mixing, knock on mixing, radiation enhanced diusion, preferential sputtering, segregation, matrix eect, surface roughness, etc. [2±6]. Even though these eects induced by ion sputtering are inevitable, many studies have been carried out to obtain an accurate pro®le by using the response function of these physical eects, but it has not been so successful yet. Hofmann [7] developed a simple analytical model, which is called the MRI model based on atomic mixing, surface roughness and signal
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 1 0 2 1 - 0
430
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
information depth for the estimation of depth resolution in the depth pro®ling. It was applied to AlAs/GaAs multilayer depth pro®ling successfully. In a computer simulation of depth pro®ling, the simulation codes based on binary collision approximation such as TRIDYN [8] or ACATDIFFUSE [9] have been used, which is quite successful in obtaining detailed information about sputtering and atomic mixing. Recently, we proposed the Monte Carlo simulation by incorporating annihilation processes into the model [10]. It described the Auger depth pro®les of the AlAs/ GaAs superlattice structure with very good accuracy. In the present study, we applied it to the SIMS depth pro®les of delta SiO2 multilayer. The SIMS pro®le shape of the delta layer was entirely determined by the physical processes occurring in the sample during analysis. The delta layer pro®le provides direct measurement of the broadening eects. This pro®le is, in fact, a response function. From the viewpoint of computer simulation, this response function can be applied to the estimation and improvement of the simulation model. The main purpose of this work is to understand the physical process occurring in SIMS depth pro®ling. In this work we used a delta oxide multilayer composed of seven thick Ta2 O5 layers separated by delta SiO2 layers, which was suggested as a new reference material for SIMS depth pro®ling [11]. Amorphous Ta2 O5 was chosen as the thick layer material because the surface topography is not signi®cantly developed by ion beam sputtering. In order to avoid the SIMS matrix eect at the interface of metal/oxide multilayer system, very thin SiO2 layers were chosen as delta layers so that the change in the chemical state of the thin-®lm materials is minimized at the oxide/oxide interfaces. 2. Experiment The Ta2 O5 /SiO2 multilayered thin ®lm composed of six SiO2 layers of 0.5 nm thickness between seven 18-nm Ta2 O5 layers were grown on an n-type Si (1 0 0) wafer by reactive sputter deposition of Ta and Si targets under oxygen gas ¯ow. Details of the thin ®lm deposition method and in
situ analysis of the stoichiometric compositions of the two oxide layers can be seen elsewhere [11]. Ta2 O5 layer 1 nm thick on SiO2 layer was also obtained by the SIMS depth pro®le. The pro®ling was performed on Cameca IMS-4f using various ion energies (7.5, 10 and 12.5 keV) and ion species (Ar , O 2 and Cs ) with 4.5 keV sample bias. Under these conditions, the kinetic energy and the incidence angle of the primary Ar ions are 3.0, 5.5, 8.0 keV and 52 , 42 , 39 from the surface normal, respectively. 3. Models of Monte Carlo simulation The Monte Carlo simulation model for the interactions of energetic ions with solid is based on the elastic collision by binary encounter with randomly distributed target atoms and inelastic collision with electron gas using Ziegler±Biersack± Littmark (ZBL) potential and Lindhard's equation, respectively [12]. Details of this program are seen elsewhere [10,12,13]. Therefore, for the depth pro®ling, newly introduced terms are described brie¯y. The eects of surface roughness and implanted primary ions are disregarded in these calculations. The interstitial atoms and vacancies generated by collisional cascade are distributed in pairs if the sputtered atoms are regarded as being sputtered only from the topmost atomic layer. These pairs migrate during collisional cascade and the vacancies are eventually annihilated by recombination with interstitial atoms or absorption into the sinks, e.g. surface, grain boundary, etc. Since the behavior of these interstitial atoms and vacancies is directly related to diusion in sputtering and range of atomic mixing in a complicated manner, it is very dicult to describe the migration processes of these pairs accurately. In the present simulation, therefore, all the interstitial±vacancy pairs are assumed to be completely recombined in the mixing zone. The total number of atoms of each layer, therefore, remains constant so that the atomic density in each atomic layer keeps invariant during sputtering. Otherwise, the atomic density tends to increase by a knock-in eect as sputtering proceeds.
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
The basic model used to treat the interstitial± vacancy pairs is as follows: First, it is assumed that each atomic layer is composed of N pseudo-atoms, where a pseudo-atom represents 109 ±1010 atoms, depending on the number of trajectories of primary ions in the Monte Carlo simulation. The Monte Carlo calculation is performed until the total number of sputtered atoms attains the number necessary to sputter N pseudo-atoms. The atomic mixing is generated by the collision cascade or both the incident ions and recoiled atoms, and the atom displaced from original layer to another layer is counted as an interstitial atom, leaving a vacancy at its original site. The numbers of both the vacancies and interstitial atoms are easily counted for each atomic layer. When the total number of pseudo-atoms in an atomic layer, N 0 , is larger than N , (N 0 > N ), we regard the excess atoms, (N 0 ÿ N ) as interstitial atoms while the difference, (N ÿ N 0 ), is regarded as vacancies for (N > N 0 ). Second, redistribution of atoms in an ith atomic layer is calculated as follows: (1) Vacancies are assumed to be annihilated with interstitial atoms in the previous (i ÿ 1)th layer and the composition of those atoms that ®ll the vacancies is proportional to atomic concentration in the relevant layer. (2) Interstitial atoms in the ith layer are to be added to the previous (i ÿ 1)th layer. The process described above is performed from the bottom layer to the top atomic layer. As a result, the total number of atoms of the top atomic layer becomes zero and the second atomic layer becomes the new top layer when N pseudoatoms are sputtered. In this simulation, 10 000 pseudo-atoms are considered to be in each atomic layer. For the SIMS depth pro®ling, the partial sputtering yield of each element was used. The Auger depth pro®ling can also be obtained considering the escape depth of Auger electrons and the atomic concentration of surface layer [10]. 4. Results and discussion Fig. 1 shows the SIMS depth pro®le of SiO for Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayer with a Cameca IMS-4f by various ion energies of O 2 ion
431
Fig. 1. The SIMS depth pro®les of SiO for a Ta2 O5 (18 nm)/ SiO2 (0.5 nm) multilayered system, sputtered with 3, 5.5 and 8 keV O 2 ion beam.
beams. It is of interest to note that the depth resolution is not signi®cantly deteriorated with the sputter depth for all the analysis conditions. This indicates that the surface topographic development is negligible under the sputtering conditions, which is con®rmed by measuring the average surface roughness of sample surfaces before and after ion beam sputtering [11]. Therefore, in this multilayered system, the physical process is expected to mainly contribute to the depth resolution of delta SiO2 layer. In this simulation, we calculate the depth pro®les of two delta SiO2 layers to compare with these experimental SIMS results. In Fig. 2, the in-depth composition pro®les of each element, until the ®rst delta layer is removed as sputtering proceeds, are shown. One can see how the sputter depth pro®le proceeds accompanied with altered layer due to preferential sputtering. As can be seen in Fig. 2, the delta-doped layer becomes broad and then is removed as the sputtering proceeds. An altered layer due to the preferential sputtering eect is formed at surface region, which remains during sputtering. Here, the sputtering yield at the initial stage was higher than that of steady state. It could be one of the causes for the peak shift of delta-doped layer to the surface direction. This is shown in Fig. 5 in more detail.
432
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
Fig. 3. Calculated (a) and experimental (b) results of SIMS depth pro®les of Si for a Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayered system, sputtered with 3, 5.5 and 8 keV O 2 ions at incidence angle of 52 ; 42 ; and 39 from the surface normal, respectively.
Fig. 2. In depth composition pro®les of Ta, O, Si for a Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayered system during 5.5 keV O 2 sputtering.
The SIMS depth pro®les of the ®rst two delta layers, sputtered with O 2 ion beam in Fig. 1 were replotted (Fig. 3(b)) in linear scale to be compared with the calculated results. Here, the square bar indicates the SiO2 delta layer in the multilayered
sample. To convert the sputtering time to the sputter depth, the average sputtering time between delta layers was used. The calculation results were obtained with partial sputtering yield of Si in delta-doped SiO2 layer as the sputter etching proceeds. In simulation results (Fig. 3(a)), the peaks of delta layers shift to the surface direction, as the primary ion energy increases, which is in good agreement with experimental results (Fig. 3(b)). Similar peak shifts to the surface direction have been also obtained with Ar primary ion. The peak shifts to surface direction may be attributed to the incident angle dependence of primary ion, penetration depth dependence of primary ion energy or preferential sputtering eects in the initial state of sputtering. Actually, in SIMS measurement, the incidence angle depends on the primary
H.J. Kang et al. / Nucl. Instr. and Meth. in Phys. Res. B 153 (1999) 429±435
ion energy because of the sample bias voltage. Primary ion beam energies from 3 to 8 keV were used, and angles of incidence varied between 52 and 39 with respect to the surface normal. In simulation results, if the incidence angle changes from 42 to 52 with 3 keV Ar ion beam, the peak shifts did not change so much. But when we changed the primary Ar ion beam energy by ®xing up the incidence angle of 42 , the delta layer peaks shifted to the surface direction. Therefore the eect of the primary ion energy is the more dominant factor than that of the ion incidence angle in this case. The primary ion species was changed to investigate the mass dependence of peak shift of delta layer as shown in Fig. 4. In calculation results (Fig. 4(a)), the peak of delta layer did not
Fig. 4. Calculated (a) and experimental (b) results of SIMS depth pro®les of Si for a Ta2 O5 (18 nm)/SiO2 (0.5 nm) multi layered system, sputtered with 5.5 keV O 2 , Ar and Cs ion at the incidence angle of 42 .
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shift signi®cantly, but there are peak shifts in experiments (Fig. 4(b)). Since the mass dierence of primary ion beam does not aect the peak shift as shown in the calculation, the peak shift in the experiment could be attributed to the dierence of sputtering yield between the initial stage and the steady state of sputtering. Actually,the sputtering rate in the initial stage is larger than that in the steady state due to the preferential sputtering especially with oxygen primary ions compared with argon primary ions as shown in Fig. 5. But it was not considered in converting sputtering time to sputter depth, which will shift the peak to the surface direction. The sputtering yield was 0.77 atoms/ion at the surface but it decreased continuously to the steady state value of 0.55 atoms/ion at the depth of 7 nm as shown in Fig. 5. Rough estimation gives a 1.3 nm peak shift to the surface direction, which is close to the experimentally observed additional shift for oxygen primary ions. However, in the experimental condition, primary oxygen ion implantation will compensate the preferential sputtering of oxygen, as reported elsewhere [14]. As mentioned in Section 3, the implantation eect of the primary ions was not considered in the calculations. For Ar and Cs primary ions, the primary ion implantation eect will not be signi®cant. But for O 2 ions, the implanted primary oxygen ions will aect the preferential sputtering process to decrease the preferential sputtering of oxygen atoms from Ta2 O5 layers. In practical SIMS depth pro®ling, the implantation eect of the primary ions should be considered. For this, the simulation model is under development. We can conclude that the peak shifts of delta layers in SIMS depth pro®ling are attributed mainly to the penetration depth of primary ion energy and the preferential sputtering eects at the initial state of sputtering for the oxide delta multilayers used in this analysis. To compare the simulation results with experimental results in more detail, the growth and decay length of delta-doped layer were obtained with exponential function and the width of delta layer with Gaussian function as commonly done in SIMS depth pro®ling [15]. The results are tabulated in Table 1. The depth resolutions become worse as the primary ion energies increase, which
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Fig. 5. Sputtering yields of Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayers, sputtered with 5.5 keV Ar and O 2 ions as a function of depth.
describes the experimental results well. It is of interest to note that the growth lengths are in quite good agreement with experimental results, but the decay lengths are relatively larger than that of experiment. It means that the atomic mixing of the simulation is still a little bit overestimated, but generally the simulation is in quite good agreement with the experiment.
Fig. 6 shows the SIMS depth pro®le of Ta2 O5 (1 nm)/SiO2 (20 nm)/Si(substrate) using O 2 ion beam with various ion energies. Here the square bar indicates the ultra-thin Ta2 O5 layer at the surface. It is worthwhile to note that the depth resolution of the Ta2 O5 delta layer at the surface become better as the primary ion energy increases, which is in contrast to other generally observed cases. Actually, the high primary ion energy can improve the depth resolution of ultra-shallow layers at surface. The simulation results (Fig. 6(a)) describe the experimental results qualitatively. The decay length of Ta in this system at 16 keV O 2 primary ion beam is better than that at 3 keV O 2 primary ion beam. This phenomenon can be explained in terms of recoiled sputtering. In the case of low primary ion energy, the atomic mixing takes place in the delta layer at the surface, while in the case of high primary ion energy, the atomic mixing occurs at the deeper layer below the surface. Therefore, the back-scattered recoil atoms contribute to the depth pro®le with less atomic mixing at the surface delta layer. It showed that the deeper collision cascade minimize the ion beam mixing at the surface ultra-thin layer and improve the decay length at higher primary ion energy.
5. Conclusions The depth pro®ling of a multi-layered thin ®lm (Ta2 O5 (18 nm)/SiO2 (0.5 nm)) on Si and a 1 nm ultra-thin single layer (Ta2 O5 (1 nm)/SiO2 (20 nm)) sample were studied using SIMS technique and Dynamic Monte Carlo Simulation approach. This approach is based on the binary encounter model,
Table 1 Experimental and simulation results of depth resolution parameters of SiO2 delta layer in Ta2 O5 (18 nm)/SiO2 (0.5 nm) multilayer Primary ion
Primary ion energy peak position (keV)
Experiment
Simulation
Growth length (nm)
Decay length (nm)
Width (nm)
Growth length (nm)
Decay length (nm)
Width (nm)
O 2
2 3 5.5 8
ÿ 0.7 0.3 0.6
ÿ 1.3 2.6 2.8
ÿ 0.7 1.2 1.9
0.2 0.3 0.5 0.8
2.1 3.1 4.1 5.6
0.8 1.1 1.9 2.3
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observed cases, which could be con®rmed with Monte Carlo simulation. It showed that the deeper collision cascades minimize the ion beam mixing at the surface ultra-thin layer and improve the decay length at higher primary ion energy.
Acknowledgements The authors are very grateful to Dr. Y. Kimura and Dr. T. Asahata of Osaka University for stimulating discussions on simulation model. This research was ®nancially supported by the AtomicScale Surface Science Research Center at Yonsei University and by the Basic Science Research Institute Program, Ministry of Education, Project No. BSRI-98-2426. One of the authors (D.W. Moon) appreciates the support from Center for Molecular Science, Korea. One of the authors (H.J. Kang) gratefully acknowledges the support by the Japan Society for the Promotion of Science (JSPS-RFTF 96R 14101) for the cooperative research in Osaka University for one month.
References
Fig. 6. Calculated (a) and experimental (b) results of SIMS depth pro®le of Ta for a Ta2 O5 (1 nm)/SiO2 (20 nm)/Si(substrate) system, sputtered with various O 2 ion energies.
taking into account (1) generation of both the interstitial atoms and vacancy, and (2) annihilation of the vacancies in the atomic mixing zone. In the case of multi-layers, the observed 1±3 nm shift of the delta layer peak to the surface direction is in quite good agreement with Monte Carlo simulation approach, which can attributed to atomic mixing phenomena and the sputtering rate change during depth pro®ling of multi-layer systems. The peak broadening of the delta SiO2 layer could be explained only by atomic mixing. In the case of the 1 nm Ta2 O5 single layer, we observed the depth resolution was improved at high energy rather than at low energy in contrast to other generally
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