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Theoretical study of vacancy supersaturation during silicon crystal growth and nitrogen-doping effects
ARTICLE IN PRESS
Physica B 376–377 (2006) 130–132 www.elsevier.com/locate/physb
Theoretical study of vacancy supersaturation during silicon crystal growth and nitrogen-doping effects A. Taguchia, H. Kageshimaa,, K. Wadab a
NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan b Graduate School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan
Abstract We performed thermodynamical simulations of the vacancy supersaturation during silicon crystal growth and investigated nitrogendoping effects on the suppression of void formation and the enhancement of oxygen precipitates. Although the mechanism with the N2V complex has been proposed to explain the suppression, we found that it cannot reproduce the suppression even with nitrogen density as high as 1020 cm–3. On the other hand, the mechanism with the N2V2 complex can reproduce the suppression with about 1015 cm–3 of nitrogen, which is consistent with the experiments. It also explains the enhancement of oxygen precipitates. Therefore, the N2V2 complex plays the dominant role in the vacancy aggregation process. r 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Bb; 61.72.Yx; 81.10.Aj Keywords: Si crystal growth; Theory; Doping effect; Nitrogen
1. Introduction Nitrogen (N) doping is known to effectively suppress void formation during silicon crystal growth in both floatzone (FZ) Si and Czochralski (CZ) Si [1]. Since the void is an aggregate of vacancies (V’s), the doped nitrogen must disturb the aggregation. First-principles calculations have revealed that doped nitrogen atoms form stable complexes with vacancies [2–5]. In CZ–Si, the complexes with oxygen (O) are also important, since CZ–Si inevitably includes O as much as 1018 cm–3. First-principles calculations also have shown that N forms stable complexes with O [5]. Based on these results, mainly two mechanisms have been proposed to explain the N-doping effect [3–6]. One is that strongly combined N2V2 complexes suppress the V supersaturation [3–5]. The other is that rather weakly combined N2V complexes play the suppression role [6]. According to the latter mechanism, NO complex formation in CZ–Si somewhat weakens the suppression role of N in V aggregation. Although simulations assuming the latter Corresponding author. Tel.: +81 46 240 2925; fax: +81 46 240 4317.
E-mail address: [email protected] (H. Kageshima). 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.034
mechanism seem to reproduce the experimental results [6], the N2V2 formation was neglected. Therefore, it is not clear which mechanism best explains the experimental results. Here, we performed thermodynamical simulations on the V supersaturation during silicon crystal growth assuming the above two mechanisms to clarify which complex, N2V or N2V2, plays the dominant role in V aggregation. In this paper, we focus on CZ–Si, which is much more important in the Si technology than FZ–Si. We also simulated the experimentally observed enhancement of O precipitates due to N doping. 2. Method In the simulation, the densities of the various complexes were evaluated as a function of temperature by assuming thermal equilibrium for all complexes in the fixed total number densities of V, N, and O. These fixed total densities make it possible to simulate the V aggregation, because lowering the temperature causes a dramatic increase in the chemical potential of V. Since the V aggregation is a result of the large space variations of the V density created by the finite diffusion constants, our method is very simple but
ARTICLE IN PRESS A. Taguchi et al. / Physica B 376–377 (2006) 130–132
good enough for studying the aggregation. The total density of V was determined so that the void formation temperature is around 1060 1C for undoped Si. The thermal equilibrium for all related complexes is achieved by assuming the detailed balance condition for all reactions between the complexes. When the complexes show the reaction A þ B Ð C, the densities are thus assumed to obey the relation ½A½B ¼ ½C expfðDS þ kB ln N 0 Þ=kB þ DH=kB Tg. Here, N0 is the number density of Si lattice sites, DS is the configurational entropy, DH the reaction energy, kB the Boltzmann’s constant, and T temperature. The term DS+kB ln N0 expresses the reaction entropy. In the present simulations, DS was assumed to be zero for simplicity. To estimate DH, the results of the previous first-principles calculations of the complexes formed by N, V, and O were used [3–5]. Although large clusters of complexes are required in the simulation in order to clarify the V aggregation processes, the cluster size is limited in the first-principles calculations. Hence, we estimated the formation energies for such larger clusters by extrapolating from those of the small clusters calculated by the first-principles calculations. The simulations thus included clusters Vx and VxO up to x ¼ 100. We also similarly considered the N2V2Ox complexes upto x ¼ 12, since a N2V2 complex has 12 sites that can capture O [5]. The details of the simulation method will be presented elsewhere.
3. Results and discussion Before investigating the N-doping effect, we simulated the V aggregation in undoped CZ–Si. The results are shown in Fig. 1. Without N doping, the V100O cluster, which represents the voids in our simulation, grows at around 1060 1C by decreasing temperature from the melting point, 1018
1016
Density [cm-3]
1014
VO
1012
V
1010
V100O
108
106 400
600
800
1000
1200
1400
Temperature [°C] Fig. 1. Simulated densities of complexes as a function of temperature in undoped CZ–Si (without N doping).
131
which is in good agreement with experimental results [7]. It should be noted here that we neglected the formation of VxOy complexes (y41). Taking the formation of these complexes into account would have made it impossible to reproduce void formation, because quite stable VO2 complexes are formed even around the melting point. They capture almost all isolated V’s below 1100 1C; therefore, no void formation occurs. We think that the dynamical effect prevents the formation of such VO2 complexes in experiments. The diffusion of V is known to be more than five orders of magnitude faster than that of O [8,9]. Therefore, after VO complexes are formed, V can attack the VO much more often than O can. As a result, VxO complexes (x4 1) should be much more preferably formed than VOy complexes (y41). In addition, we have found that some VxOy defect formation processes are endothermic, indicating that such complexes are unstable and will rarely be formed [5]. Therefore, we only considered VxO complexes. Next, we doped N and attempted the simulation. When we neglect the formation of N2V2 and the related complexes, N2V complexes show a large density but cannot reduce the void formation temperature at all even if N is doped as high as 8 1020 cm–3 [Fig. 2(a)]. Since it has been reported that the NO complex reduces the N2V effect on V aggregation [6], we also attempted to neglect the formation of this NO complex. The simulated result [Fig. 2(b)], however, does not change at all from that with the NO complex. On the other hand, when we consider the formations of N2V2 and the related complexes, the void formation temperature decreases by about 50 1C with 8 1014 cm–3 of N, as shown in Fig. 3. The N2V2 mechanism well reproduces the experimental results. The present simulation results clearly show that the mechanism with the N2V2 complexes is preferable for explaining the experimentally observed N-doping effects. The difference between the N2V2 and the N2V complexes appears as a change in the density at the melting and the aggregation temperatures. The change in the N2V complexes is much smaller than that in the N2V2 complexes. This causes the difference in the efficiency of trapping V. The reason for the different change in the density is the difference in the binding energies of these complexes. At rather high temperatures near the melting point, the entropy effect plays a significant role and isolated defects are preferably formed. However, as temperature decreases, the binding energy becomes more important and larger complexes are preferably formed. Our first-principles calculations indicate that the energy gain in the reaction N2+V-N2V is only 0.82 eV, while that in the reaction N2V+V-N2V2 is 4.07 eV [3]. Since the binding energy of the N2V complexes is much smaller than that of the N2V2 complexes, the density of N2V cannot increase so quickly when the temperature decreases and cannot efficiently reduce the density of V. As a result, the V density is not reduced enough to suppress the void aggregation. Our result with N2V2 complexes (Fig. 3) also shows that a large density of N2V2O12 complexes is formed below
ARTICLE IN PRESS A. Taguchi et al. / Physica B 376–377 (2006) 130–132
132
1018
1018 N2V
1016
1016
NO 1014 Density [cm-3]
Density [cm-3]
1014 VO NV
1012
V
1010
V
N2V2O12
1012
VO
N2 NO NV
N2V2
1010 V100O N2V
108
108 V100O (a)
106 400
600
800
1000
1200
1400
106 400
600
1018
1000
1200
1400
Fig. 3. Simulated ensities of complexes as a function of temperature in N-doped CZ–Si, assuming the N2V2 mechanism. The N density is 8 1014 cm–3.
1016 N2V
only with N2V and NO complexes cannot explain the experimental suppression of void formation, but that taking into account N2V2 and related complexes can well reproduce the suppression of void formation and the enhanced O precipitation. The analysis of our results indicates that the difference between N2V and N2V2 comes from the difference in the binding energies.
1014 Density [cm-3]
800
Temperature [°C]
VO 1012
NV
1010
V
Acknowledgements
108 V100O 106 400 (b)
600
800
1000
1200
1400
The authors thank Hiroshi Inokawa and Yoshiro Hirayama for their helpful suggestions.
Temperature [°C]
Fig. 2. Simulated densities of complexes as a function of temperature in N-doped CZ–Si, assuming the N2V mechanism. The N and the O densities are 8 1020 and 8 1017 cm3, respectively. The formation of N2V2 and related complexes is neglected: (a) Simulation result taking into account NO formation and (b) neglecting NO formation.
600 1C from N2V2 complexes. Since N2V2O12 are representatives of O precipitates in our simulation, this indicates that N2V2 can be heterogeneous nucleation sites of O precipitates as we pointed out before [5]. Although our results do not reject the possibility of O precipitates forming from small vacancy clusters by the aggregation of a large amount of O, we think the O precipitates observed in the N-doped CZ–Si experiments are closely related with the N2V2 complexes. 4. Conclusions We have theoretically studied N-doping effects on void aggregation in CZ–Si. The results show that the mechanism
References [1] T. Abe, et al., MRS Proc. 59 (1986) 537; F. Shimura, et al., Appl. Phys. Lett. 48 (1986) 224; K. Nakai, et al., J. Appl. Phys. 89 (2001) 4301; X. Yu, et al., J. Appl. Phys. 92 (2002) 188; S. Binetti, et al., J. Phys.: Condens. Matter 14 (2002) 13247; Y. Yamanaka, et al., Solid Stat. Phen. 82–84 (2002) 63; J. Takahashi, et al., Jpn. J. Appl. Phys. 42 (2003) 363. [2] H. Sawada, K. Kawakami, Phys. Rev. B 62 (2000) 1851. [3] H. Kageshima, et al., Appl. Phys. Lett. 76 (2000) 3718. [4] H. Kageshima, et al., Mater. Res. Soc. Symp. Proc. 719 (2002) 79; H. Kageshima, et al., Proc. ICPS 26 (2002) H57; H. Kageshima, et al., Proc. ICPS 27 (2004) J5.093. [5] H. Kageshima, et al., Physica B 340–342 (2003) 626; A. Taguchi, et al., J. Appl. Phys. 97 (2005) 053514. [6] W.v. Ammon, et al., J. Crystal Growth 226 (2001) 19; W.v. Ammon, et al., Proceedings of the Fourth International Symposium on Advanced Science and Technology of Silicon Materials, 2004, Kona, HI, USA. [7] V.V. Voronkov, et al., J. Cryst. Growth 194 (1998) 76. [8] G.D. Watikins, J.W. Corbett, Phys. Rev. 121 (1961) 1001. [9] K. Wada, et al., J. Cryst. Growth 57 (1982) 535.
Physica B 376–377 (2006) 130–132 www.elsevier.com/locate/physb
Theoretical study of vacancy supersaturation during silicon crystal growth and nitrogen-doping effects A. Taguchia, H. Kageshimaa,, K. Wadab a
NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan b Graduate School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan
Abstract We performed thermodynamical simulations of the vacancy supersaturation during silicon crystal growth and investigated nitrogendoping effects on the suppression of void formation and the enhancement of oxygen precipitates. Although the mechanism with the N2V complex has been proposed to explain the suppression, we found that it cannot reproduce the suppression even with nitrogen density as high as 1020 cm–3. On the other hand, the mechanism with the N2V2 complex can reproduce the suppression with about 1015 cm–3 of nitrogen, which is consistent with the experiments. It also explains the enhancement of oxygen precipitates. Therefore, the N2V2 complex plays the dominant role in the vacancy aggregation process. r 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Bb; 61.72.Yx; 81.10.Aj Keywords: Si crystal growth; Theory; Doping effect; Nitrogen
1. Introduction Nitrogen (N) doping is known to effectively suppress void formation during silicon crystal growth in both floatzone (FZ) Si and Czochralski (CZ) Si [1]. Since the void is an aggregate of vacancies (V’s), the doped nitrogen must disturb the aggregation. First-principles calculations have revealed that doped nitrogen atoms form stable complexes with vacancies [2–5]. In CZ–Si, the complexes with oxygen (O) are also important, since CZ–Si inevitably includes O as much as 1018 cm–3. First-principles calculations also have shown that N forms stable complexes with O [5]. Based on these results, mainly two mechanisms have been proposed to explain the N-doping effect [3–6]. One is that strongly combined N2V2 complexes suppress the V supersaturation [3–5]. The other is that rather weakly combined N2V complexes play the suppression role [6]. According to the latter mechanism, NO complex formation in CZ–Si somewhat weakens the suppression role of N in V aggregation. Although simulations assuming the latter Corresponding author. Tel.: +81 46 240 2925; fax: +81 46 240 4317.
E-mail address: [email protected] (H. Kageshima). 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.034
mechanism seem to reproduce the experimental results [6], the N2V2 formation was neglected. Therefore, it is not clear which mechanism best explains the experimental results. Here, we performed thermodynamical simulations on the V supersaturation during silicon crystal growth assuming the above two mechanisms to clarify which complex, N2V or N2V2, plays the dominant role in V aggregation. In this paper, we focus on CZ–Si, which is much more important in the Si technology than FZ–Si. We also simulated the experimentally observed enhancement of O precipitates due to N doping. 2. Method In the simulation, the densities of the various complexes were evaluated as a function of temperature by assuming thermal equilibrium for all complexes in the fixed total number densities of V, N, and O. These fixed total densities make it possible to simulate the V aggregation, because lowering the temperature causes a dramatic increase in the chemical potential of V. Since the V aggregation is a result of the large space variations of the V density created by the finite diffusion constants, our method is very simple but
ARTICLE IN PRESS A. Taguchi et al. / Physica B 376–377 (2006) 130–132
good enough for studying the aggregation. The total density of V was determined so that the void formation temperature is around 1060 1C for undoped Si. The thermal equilibrium for all related complexes is achieved by assuming the detailed balance condition for all reactions between the complexes. When the complexes show the reaction A þ B Ð C, the densities are thus assumed to obey the relation ½A½B ¼ ½C expfðDS þ kB ln N 0 Þ=kB þ DH=kB Tg. Here, N0 is the number density of Si lattice sites, DS is the configurational entropy, DH the reaction energy, kB the Boltzmann’s constant, and T temperature. The term DS+kB ln N0 expresses the reaction entropy. In the present simulations, DS was assumed to be zero for simplicity. To estimate DH, the results of the previous first-principles calculations of the complexes formed by N, V, and O were used [3–5]. Although large clusters of complexes are required in the simulation in order to clarify the V aggregation processes, the cluster size is limited in the first-principles calculations. Hence, we estimated the formation energies for such larger clusters by extrapolating from those of the small clusters calculated by the first-principles calculations. The simulations thus included clusters Vx and VxO up to x ¼ 100. We also similarly considered the N2V2Ox complexes upto x ¼ 12, since a N2V2 complex has 12 sites that can capture O [5]. The details of the simulation method will be presented elsewhere.
3. Results and discussion Before investigating the N-doping effect, we simulated the V aggregation in undoped CZ–Si. The results are shown in Fig. 1. Without N doping, the V100O cluster, which represents the voids in our simulation, grows at around 1060 1C by decreasing temperature from the melting point, 1018
1016
Density [cm-3]
1014
VO
1012
V
1010
V100O
108
106 400
600
800
1000
1200
1400
Temperature [°C] Fig. 1. Simulated densities of complexes as a function of temperature in undoped CZ–Si (without N doping).
131
which is in good agreement with experimental results [7]. It should be noted here that we neglected the formation of VxOy complexes (y41). Taking the formation of these complexes into account would have made it impossible to reproduce void formation, because quite stable VO2 complexes are formed even around the melting point. They capture almost all isolated V’s below 1100 1C; therefore, no void formation occurs. We think that the dynamical effect prevents the formation of such VO2 complexes in experiments. The diffusion of V is known to be more than five orders of magnitude faster than that of O [8,9]. Therefore, after VO complexes are formed, V can attack the VO much more often than O can. As a result, VxO complexes (x4 1) should be much more preferably formed than VOy complexes (y41). In addition, we have found that some VxOy defect formation processes are endothermic, indicating that such complexes are unstable and will rarely be formed [5]. Therefore, we only considered VxO complexes. Next, we doped N and attempted the simulation. When we neglect the formation of N2V2 and the related complexes, N2V complexes show a large density but cannot reduce the void formation temperature at all even if N is doped as high as 8 1020 cm–3 [Fig. 2(a)]. Since it has been reported that the NO complex reduces the N2V effect on V aggregation [6], we also attempted to neglect the formation of this NO complex. The simulated result [Fig. 2(b)], however, does not change at all from that with the NO complex. On the other hand, when we consider the formations of N2V2 and the related complexes, the void formation temperature decreases by about 50 1C with 8 1014 cm–3 of N, as shown in Fig. 3. The N2V2 mechanism well reproduces the experimental results. The present simulation results clearly show that the mechanism with the N2V2 complexes is preferable for explaining the experimentally observed N-doping effects. The difference between the N2V2 and the N2V complexes appears as a change in the density at the melting and the aggregation temperatures. The change in the N2V complexes is much smaller than that in the N2V2 complexes. This causes the difference in the efficiency of trapping V. The reason for the different change in the density is the difference in the binding energies of these complexes. At rather high temperatures near the melting point, the entropy effect plays a significant role and isolated defects are preferably formed. However, as temperature decreases, the binding energy becomes more important and larger complexes are preferably formed. Our first-principles calculations indicate that the energy gain in the reaction N2+V-N2V is only 0.82 eV, while that in the reaction N2V+V-N2V2 is 4.07 eV [3]. Since the binding energy of the N2V complexes is much smaller than that of the N2V2 complexes, the density of N2V cannot increase so quickly when the temperature decreases and cannot efficiently reduce the density of V. As a result, the V density is not reduced enough to suppress the void aggregation. Our result with N2V2 complexes (Fig. 3) also shows that a large density of N2V2O12 complexes is formed below
ARTICLE IN PRESS A. Taguchi et al. / Physica B 376–377 (2006) 130–132
132
1018
1018 N2V
1016
1016
NO 1014 Density [cm-3]
Density [cm-3]
1014 VO NV
1012
V
1010
V
N2V2O12
1012
VO
N2 NO NV
N2V2
1010 V100O N2V
108
108 V100O (a)
106 400
600
800
1000
1200
1400
106 400
600
1018
1000
1200
1400
Fig. 3. Simulated ensities of complexes as a function of temperature in N-doped CZ–Si, assuming the N2V2 mechanism. The N density is 8 1014 cm–3.
1016 N2V
only with N2V and NO complexes cannot explain the experimental suppression of void formation, but that taking into account N2V2 and related complexes can well reproduce the suppression of void formation and the enhanced O precipitation. The analysis of our results indicates that the difference between N2V and N2V2 comes from the difference in the binding energies.
1014 Density [cm-3]
800
Temperature [°C]
VO 1012
NV
1010
V
Acknowledgements
108 V100O 106 400 (b)
600
800
1000
1200
1400
The authors thank Hiroshi Inokawa and Yoshiro Hirayama for their helpful suggestions.
Temperature [°C]
Fig. 2. Simulated densities of complexes as a function of temperature in N-doped CZ–Si, assuming the N2V mechanism. The N and the O densities are 8 1020 and 8 1017 cm3, respectively. The formation of N2V2 and related complexes is neglected: (a) Simulation result taking into account NO formation and (b) neglecting NO formation.
600 1C from N2V2 complexes. Since N2V2O12 are representatives of O precipitates in our simulation, this indicates that N2V2 can be heterogeneous nucleation sites of O precipitates as we pointed out before [5]. Although our results do not reject the possibility of O precipitates forming from small vacancy clusters by the aggregation of a large amount of O, we think the O precipitates observed in the N-doped CZ–Si experiments are closely related with the N2V2 complexes. 4. Conclusions We have theoretically studied N-doping effects on void aggregation in CZ–Si. The results show that the mechanism
References [1] T. Abe, et al., MRS Proc. 59 (1986) 537; F. Shimura, et al., Appl. Phys. Lett. 48 (1986) 224; K. Nakai, et al., J. Appl. Phys. 89 (2001) 4301; X. Yu, et al., J. Appl. Phys. 92 (2002) 188; S. Binetti, et al., J. Phys.: Condens. Matter 14 (2002) 13247; Y. Yamanaka, et al., Solid Stat. Phen. 82–84 (2002) 63; J. Takahashi, et al., Jpn. J. Appl. Phys. 42 (2003) 363. [2] H. Sawada, K. Kawakami, Phys. Rev. B 62 (2000) 1851. [3] H. Kageshima, et al., Appl. Phys. Lett. 76 (2000) 3718. [4] H. Kageshima, et al., Mater. Res. Soc. Symp. Proc. 719 (2002) 79; H. Kageshima, et al., Proc. ICPS 26 (2002) H57; H. Kageshima, et al., Proc. ICPS 27 (2004) J5.093. [5] H. Kageshima, et al., Physica B 340–342 (2003) 626; A. Taguchi, et al., J. Appl. Phys. 97 (2005) 053514. [6] W.v. Ammon, et al., J. Crystal Growth 226 (2001) 19; W.v. Ammon, et al., Proceedings of the Fourth International Symposium on Advanced Science and Technology of Silicon Materials, 2004, Kona, HI, USA. [7] V.V. Voronkov, et al., J. Cryst. Growth 194 (1998) 76. [8] G.D. Watikins, J.W. Corbett, Phys. Rev. 121 (1961) 1001. [9] K. Wada, et al., J. Cryst. Growth 57 (1982) 535.