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Dislocation–impurity interaction in Si
Materials Science and Engineering B 124–125 (2005) 293–296
Dislocation–impurity interaction in Si I. Yonenaga ∗ Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
Abstract Dynamic dislocation–impurity interactions in CZ–Si doped with light impurity (N), acceptor (B), donor (P, As, Sb) and neutral (Ge) impurities were investigated in comparison with those in undoped CZ–Si. Dislocation generation was effectively suppressed in B-, P- and As-doped Si when the concentration was higher than 1019 cm−3 , while Ge impurity did not strongly suppress dislocation generation. Dislocations were immobilized by the stable complexes formed through the impurity segregation and reaction. It was found that B and N impurities promptly form strong locking agents, while P and As impurities form highly dense locking agents along dislocations. Dislocation velocity in Si doped with electrically active impurities increased with increasing concentrations of not only the donor (P, As, Sb) but also the acceptor (B) impurities in the temperature range of 650–950 ◦ C. N and Ge impurities had no or little effect on the velocity of dislocations in motion. Co-doping of Si with Ge and B was effective for suppression of dislocation generation and retardation of dislocation velocity at low temperatures. © 2005 Elsevier B.V. All rights reserved. Keywords: Dislocation–impurity interaction; Generation; Immobilization; Velocity; Impurity segregation; Si
1. Introduction Understanding of dislocation–impurity interaction in crystals and wafers with large diameters is important for advanced silicon technology. This interaction has two aspects: (1) the effect of dislocations on the spatial distribution of impurities, as in gettering, defect reaction and complex formation, which is essential for dislocation-engineering; (2) the effect of impurities on the dynamic properties of dislocations, which is essential in the growth of dislocation-free crystals and the suppression of slippage and warpage during wafer processing. However, far less is known about the interaction of dislocations and impurities, except for those of oxygen impurity in Si crystals. The dislocation–oxygen interaction in Si is well known in terms of dislocation immobilization due to preferential segregation [1,2] and, indeed, basic knowledge of this is widely applied in the growth of bulk crystals and thin films and in device fabrication processing. The present author’s group succeeded in growing dislocation-free Si crystals by the Czochralski (CZ) method without the conventional Dash-necking process with heavy doping of boron (B) impurity at a concentration higher than 1018 cm−3 [3] for the growth of heavy Si crystals with large diameter. The present author has previously reported the
∗
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suppression of dislocation generation and the enhancement of dislocation velocities by certain kinds of impurities in Si [4–6]. The present paper details the dynamic interactions between dislocations and impurities in CZ–Si doped with light impurity (N) and acceptor (B), donor (P, As, Sb) and neutral (Ge) impurities at various concentrations up to 2.5 × 1020 cm−3 , as well as those in CZ–Si co-doped with Ge and B, hereafter termed (Ge + B) co-doped. 2. Experimental Specimens were prepared from dislocation-free CZ–Si crystals doped with various concentrations of B, P, As, Sb, N and Ge and co-doped with Ge and B at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively. All the CZ–Si crystals contained oxygen (O) impurity at a concentration of ≈1 × 1018 cm−3 . High purity float-zone-grown (FZ)-Si and undoped CZ–Si were also employed for purposes of comparison. Specimens were sectioned into rectangular shapes 2 mm × 3 mm × 15 mm with the long axis in the [1 1¯ 0] direction and the side surfaces parallel to ¯ planes. Scratches were drawn on the chemthe (1 1 1) and (1 1 2) ¯ surfaces in the [1 1¯ 0] direction at ically polished (1 1 1)/(1¯ 1¯ 1) room temperature with a diamond stylus to introduce preferential dislocation nucleation sites. The specimen was stressed at an elevated temperature by means of three-point bending in a vacuum. The motion of dislocations from the scratch was investigated by observing etch pits detected by a modified
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Sirtl etchant [7]. Details of the experimental procedures and the crystal growth have been described in previous reports [3–5]. 3. Results and discussion 3.1. Critical stress for dislocation generation A certain critical stress exists for generation of dislocations from a scratch in CZ–Si doped with certain impurities. No appreciable critical stress, however, has been measured for dislocation generation in high purity FZ–Si. Fig. 1 shows the dependence of the critical stress for dislocation generation at 900 ◦ C on the concentration of doped impurities in CZ–Si crystals. Data for various concentrations of oxygen (O) impurity are also included in the figure. The critical stress increases with increasing O concentration and becomes 8 MPa at about 1018 cm−3 , the standard level of O concentration in CZ–Si. The critical stress starts to increase remarkably when B, P and As concentrations exceed 1 × 1019 cm−3 . This means that B, P and As impurities at concentrations higher than ≈1 × 1019 cm−3 effectively suppress the generation of dislocations. Thus, the critical stress for dislocation generation observed within crystals doped with concentrations of B, P and As impurities less than 1 × 1019 cm−3 can be understood to be mainly due to the effect of O impurity. B and P impurities in FZ–Si have also been found to suppress dislocation generation [6]. However, the critical stresses for dislocation generation in FZ–Si are lower than those in CZ–Si. The suppression of dislocation generation by Sb impurity is not clear because its solubility limit into Si is lower than those of B, P and As impurities. In Ge-doped Si, the magnitude of the critical stress for dislocation generation is 8 MPa, i.e., the same as the critical stress for undoped CZ–Si, and increases slightly to ≈10 MPa when the Ge concentration exceeds 1020 cm−3 . However, Ge impurity even at a high concentration of 2.5 × 1020 cm−3 is not effective for suppression of dislocation generation. Indeed, in the dilute SiGe alloys with Ge content of 0.004, strong suppression of dislocation generation has not been observed [8]. Contrarily, in (Ge + B)
Fig. 2. Stressing temperature dependence of release stress τ R for dislocations aged at 900 ◦ C for 15 min in various types of CZ–Si. (Ge + B) denotes the results for CZ–Si co-doped with Ge and B at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
co-doped CZ–Si, the critical stress of dislocation generation is higher than that in Si independently doped with either B or Ge. This shows the effect of (Ge + B) co-doping effect on the suppression of dislocation generation, though such effect is weaker than that observed at 800 ◦ C [5]. In N-doped CZ–Si, the critical stress for dislocation generation is 9 MPa, comparable to or somewhat higher than that in undoped CZ–Si. 3.2. Dislocation immobilization The absence of dislocation generation from a scratch or surface flaw under low stress has been observed for dislocations in several semiconductors doped with certain kinds of impurity (see review [1]). Dislocations are nucleated around a scratch/surface flaw and immobilized due to the impurity segregation along the dislocations even while the crystal is being heated to the test temperature [1,5,6]. The observed critical stress for dislocation generation should be understood as the stress required to release a dislocation from the immobilized state and to penetrate into the matrix crystal, which can be detected macroscopically as dislocation generation from the scratch. This stress is termed release stress τ R . The characteristic features of dislocation–impurity interaction can be evaluated through the analysis of the stressing temperature dependence of the release stress of aged dislocations. Fig. 2 shows the release stress against the stressing temperature for dislocations in various Si crystals aged at 900 ◦ C for 15 min. The release stress decreases linearly with an increase in the stressing temperature, showing that the process is thermally activated. A theory of the thermally activated release of dislocations from locking agents gives the following relation between the release stress τ R and the temperature T: τR =
Fig. 1. Variation in the critical stress for generation of 60◦ dislocations at 900 ◦ C against the concentration of N, B, P, As, Sb, Ge and O impurities in CZ–Si crystals. The ellipse denotes the critical stress in Ge and B co-doped Si at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
[E − kB T ln(LNν/Γ )]N , b2
(1)
where E is the maximum interaction energy between a dislocation and a locking agent, L the length of the dislocation, N the mean density of locking agents along the dislocation line,
I. Yonenaga / Materials Science and Engineering B 124–125 (2005) 293–296
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Table 1 Magnitudes of E and N for dislocations in the impurity-doped CZ–Si crystals
3.3. Dislocation velocity
Impurity species and concentration (cm−3 )
Dislocation velocity v in high purity FZ–Si is described as a function of stress τ and temperature T according to the empirical law m τ Q exp − , (2) v = v0 τ0 kB T
1 × 1018
O: N: 6 × 1015 B: 9 × 1019 P: 3 × 1019 As: 4 × 1019 Ge: 9 × 1019 Ge: 4 × 1019 , B: 9 × 1018
E (eV)
N (cm−1 )
3.6 4.1 4.5 3.6 3.7 3.6 3.8
2.4 × 105 1.0 × 105 1.1 × 105 3.4 × 105 2.8 × 105 2.6 × 105 1.6 × 105
ν the vibration frequency of the dislocation, Γ the release rate of the locked dislocation, kB the Boltzmann constant and b the magnitude of the Burgers vector of the dislocation [1,6,9]. By using Eq. (1), the density of the pinning agents along the dislocation line N and the interaction energy E in the crystals were evaluated as shown in Table 1. The experimentally estimated magnitudes of interaction energy E are 3–4 eV, too high to be interpreted with a model in which the dislocations interact with individual impurity atoms. The magnitudes of line density N are 1–3 × 105 cm−1 , much smaller than that expected from the concentration of the impurity atoms individually dispersed in the matrix. This result indicates the following picture: impurity atoms dispersed within the matrix segregate at dislocations at rest and pipe diffuse along the dislocation line, meeting and coagulating at some discretely separated sites on the dislocation line. As a result, the dislocations are locked/immobilized by such complexes or clusters, which may include a few impurity atoms, intrinsic point defects, or O atoms in CZ–Si, as calculated by Heggie et al. for P impurity [10]. Experimentally, oxygen precipitates have been found to develop along a dislocation line as observed by transmission electron microscopy [11]. As seen in Table 1, B and N impurities have larger interaction energy E and lower density N than do O, Ge, As and P impurities. This suggests that B and N impurities contribute to the prompt formation/development of stronger locking agents with lower density along dislocations. On the other hand, P and As impurities are known to form a high density of locking agents, resulting in high release stress. The magnitudes of the release stress and E and N in Ge-doped CZ–Si are comparable to those in undoped CZ–Si. This supports the experimental result in Fig. 1 that Ge impurity even at a high concentration of 2.5 × 1020 cm−3 does not suppress dislocation generation and confirms that Ge has no effect on dislocation immobilization. In P-doped CZ–Si, the density N is higher than that in Pdoped FZ–Si, which suggests that a combination of a P atom with an O atom leads to the formation of locking agents with higher density along a dislocation line than in the case of an individual P atom. Similarly, in (Ge + B) co-doped Si, the interaction energy E is slightly higher and the density N is lower than that in undoped CZ–Si. Strong locking agents are probably constructed in cooperation with Ge and B atoms, resulting in the immobilization of dislocations. These features indicate that a unique reaction of impurities occurs at a dislocation site.
where v0 , m and Q are material constants, τ 0 is 1 MPa and m ≈ 1 [1,6,12]. Contrarily, the velocity of 60◦ dislocations in CZ–Si with O, N, B, P, As and Ge impurities increases rapidly once the stress exceeds the critical stress value for dislocation generation and then shows a break, which depends on the impurity species and concentration. Such a rapid increase in the velocity is related to the dislocation generation/release process from the impurity-immobilized state. Beyond the break, the velocity increases rather slowly with an increase in the stress at a rate comparable to that of 60◦ dislocations in highly pure FZ–Si. Fig. 3 shows how the velocities of 60◦ dislocations at 900 ◦ C depend on the concentration of impurities in a semi-quantitative manner. The velocities of dislocations shown are those under a stress of 30 MPa where the measured velocities are thought to be free from the influence of impurity immobilization. It is seen that the velocity of dislocations in Si doped with donor impurities (P, As, Sb) increases with an increase in the concentration as reported previously [1,6,12]. Additionally, the dislocation velocity in Si doped with acceptor impurity B increases monotonically from that in undoped Si with an increase in the B concentration [5]. N and Ge impurities have almost no effect on dislocation velocity enhancement/reduction. In (Ge + B) co-doped Si the dislocation velocity at 900 ◦ C is comparable to that in undoped Si. This means that the retardation effect of (Ge + B) co-doping on the dislocation velocity observed in Si at temperatures lower than 800 ◦ C [5] becomes weak at elevated temperatures. Fig. 4 shows the velocities of 60◦ dislocations in CZ–Si doped or co-doped with various impurities at various concentrations under a stress of 30 MPa plotted against the reciprocal temperatures: B (9 × 1019 cm−3 ), P (3 × 1019 ), As
Fig. 3. Velocities of 60◦ dislocations in impurity-doped CZ–Si crystals under a shear stress of 30 MPa at 900 ◦ C: the dependence on the electrical type and concentration of main impurities. The ellipse denotes the critical stress in Ge and B co-doped CZ–Si at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
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where the doping level is extremely high, which can be regarded as being in a rather dilute solid solution. 4. Conclusion
Fig. 4. Velocities of 60◦ dislocations in impurity-doped CZ–Si crystals under a shear stress of 30 MPa against the reciprocal temperature. Numerals show the impurity concentration in a unit of cm−3 . (Ge + B) denotes the results for Ge and B co-doped CZ–Si at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
(4 × 1019 ), Ge (9 × 1019 ), N (6 × 1015 ) and Ge + B (4 × 1019 and 9 × 1018 ). Also shown are the results in undoped CZ–Si (O: 1 × 1018 cm−3 ). The dislocation velocity in motion was found to be unaffected by the doping of Si crystals with N and Ge impurities in the whole temperature range of 650–950 ◦ C. In (Ge + B) co-doped CZ–Si, dislocations move with lower velocity than in undoped CZ–Si in the low temperature range. (Ge + B) co-doping is probably effective at low temperatures. Dislocations move far faster in P- and As-doped Si and slightly faster in B-doped than in undoped CZ–Si at temperatures lower than about 800 ◦ C. The velocity enhancement and weak temperature dependence, i.e., reduction of the activation energy Q for dislocation motion in n-type crystals, are attributed to the electrical effect through the formation and/or migration of kinks as an elementary process of dislocation motion. An acceptor level is thought to be associated with a kink site in Si as proposed by Hirsch [13] and Jones [14]. If the enhanced velocity of dislocations detected in B-doped Si is related to such a mechanism, then a donor level would seem to be associated with a kink site in Si. Surprisingly, even at temperatures higher than 800 ◦ C, the dislocation velocity in Si doped with B, P and As impurities is larger than that of dislocations in undoped CZ–Si. Such enhancement of dislocation velocity observed in heavily impurity-doped Si may not be due to the above mechanism since a break of the temperature dependence of dislocation velocity in B-, P- and As-doped Si is seen in Fig. 4. The kink configuration of a dislocation is probably concerned with the elementary process of dislocation motion in heavily impurity-doped semiconductors,
The dynamic interaction between dislocations and impurities in CZ–Si crystals heavily doped with light impurity (N) and acceptor (B), donor (P, As, Sb) and neutral (Ge) impurities was investigated by means of the etch pit method. Generation of dislocations from a surface scratch is strongly suppressed in Si doped with B, P and As impurities with a concentration higher than 1 × 1019 cm−3 , while Ge impurity does not strongly suppress dislocation generation. The critical stress for dislocation generation increases with B, P and As concentration, which is interpreted in terms of dislocation immobilization/locking due to impurity segregation through a unique reaction at dislocation sites. In the analysis of the thermally activated release process from immobilized states, B and N impurities are evaluated to promptly form strong locking agents, while P and As impurities form high density locking agents along dislocations. (Ge + B) co-doping also effectively promotes the formation of strong locking agents. Dislocation velocity in electrically conductive Si increases with an increase in the concentration of not only the donor (P, As, Sb) but also acceptor (B) impurities at temperatures of 650–950 ◦ C. N and Ge impurities have no or little effect on the dislocation velocity in motion. In (Ge + B) co-doped CZ–Si, dislocations move with lower velocity than in undoped CZ–Si at low temperatures, which means that (Ge + B) co-doping is effective for retarding dislocation velocity at temperatures lower than 900 ◦ C. Acknowledgement The author wishes to thank Dr. T. Taishi and Prof. K. Hoshikawa of Shinshu University for the supply of B-doped CZ–Si crystals. References [1] K. Sumino, I. Yonenaga, Solid State Phenomena 85/86 (2002) 145. [2] K. Jurkschat, S. Senkader, D. Gambaro, R.J. Falster, P.R. Wilshaw, J. Appl. Phys. 90 (2001) 3219. [3] X. Huang, T. Taishi, I. Yonenaga, K. Hoshikawa, J. Cryst. Growth 213 (2000) 283. [4] I. Yonenaga, T. Taishi, X. Huang, K. Hoshikawa, Mater. Sci. Eng. B 91/92 (2002) 192. [5] I. Yonenaga, T. Taishi, X. Hunag, K. Hoshikawa, J. Appl. Phys. 93 (2003) 265. [6] I. Yonenaga, Solid State Phenomena 95/96 (2004) 423. [7] ASTM standard F80-85, ASTM, Philadelphia, PA. [8] I. Yonenaga, J. Cryst. Growth 275 (2005) 91. [9] K. Sumino, M. Imai, Philos. Mag. A 47 (1983) 753. [10] M.I. Heggie, R. Jones, A. Umerski, Philos. Mag. A 63 (1991) 571. [11] I. Yonenaga, K. Sumino, J. Appl. Phys. 80 (1996) 734. [12] M. Imai, K. Sumino, Philos. Mag. A 47 (1983) 599. [13] P.B. Hirsch, J. Phys. Colloq. (Paris) 40 (1979) C6–C117. [14] R. Jones, Philos. Mag. B 42 (1980) 213.
Dislocation–impurity interaction in Si I. Yonenaga ∗ Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
Abstract Dynamic dislocation–impurity interactions in CZ–Si doped with light impurity (N), acceptor (B), donor (P, As, Sb) and neutral (Ge) impurities were investigated in comparison with those in undoped CZ–Si. Dislocation generation was effectively suppressed in B-, P- and As-doped Si when the concentration was higher than 1019 cm−3 , while Ge impurity did not strongly suppress dislocation generation. Dislocations were immobilized by the stable complexes formed through the impurity segregation and reaction. It was found that B and N impurities promptly form strong locking agents, while P and As impurities form highly dense locking agents along dislocations. Dislocation velocity in Si doped with electrically active impurities increased with increasing concentrations of not only the donor (P, As, Sb) but also the acceptor (B) impurities in the temperature range of 650–950 ◦ C. N and Ge impurities had no or little effect on the velocity of dislocations in motion. Co-doping of Si with Ge and B was effective for suppression of dislocation generation and retardation of dislocation velocity at low temperatures. © 2005 Elsevier B.V. All rights reserved. Keywords: Dislocation–impurity interaction; Generation; Immobilization; Velocity; Impurity segregation; Si
1. Introduction Understanding of dislocation–impurity interaction in crystals and wafers with large diameters is important for advanced silicon technology. This interaction has two aspects: (1) the effect of dislocations on the spatial distribution of impurities, as in gettering, defect reaction and complex formation, which is essential for dislocation-engineering; (2) the effect of impurities on the dynamic properties of dislocations, which is essential in the growth of dislocation-free crystals and the suppression of slippage and warpage during wafer processing. However, far less is known about the interaction of dislocations and impurities, except for those of oxygen impurity in Si crystals. The dislocation–oxygen interaction in Si is well known in terms of dislocation immobilization due to preferential segregation [1,2] and, indeed, basic knowledge of this is widely applied in the growth of bulk crystals and thin films and in device fabrication processing. The present author’s group succeeded in growing dislocation-free Si crystals by the Czochralski (CZ) method without the conventional Dash-necking process with heavy doping of boron (B) impurity at a concentration higher than 1018 cm−3 [3] for the growth of heavy Si crystals with large diameter. The present author has previously reported the
∗
Tel.: +81 22 215 2042; fax: +81 22 215 2041. E-mail address: [email protected].
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.08.013
suppression of dislocation generation and the enhancement of dislocation velocities by certain kinds of impurities in Si [4–6]. The present paper details the dynamic interactions between dislocations and impurities in CZ–Si doped with light impurity (N) and acceptor (B), donor (P, As, Sb) and neutral (Ge) impurities at various concentrations up to 2.5 × 1020 cm−3 , as well as those in CZ–Si co-doped with Ge and B, hereafter termed (Ge + B) co-doped. 2. Experimental Specimens were prepared from dislocation-free CZ–Si crystals doped with various concentrations of B, P, As, Sb, N and Ge and co-doped with Ge and B at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively. All the CZ–Si crystals contained oxygen (O) impurity at a concentration of ≈1 × 1018 cm−3 . High purity float-zone-grown (FZ)-Si and undoped CZ–Si were also employed for purposes of comparison. Specimens were sectioned into rectangular shapes 2 mm × 3 mm × 15 mm with the long axis in the [1 1¯ 0] direction and the side surfaces parallel to ¯ planes. Scratches were drawn on the chemthe (1 1 1) and (1 1 2) ¯ surfaces in the [1 1¯ 0] direction at ically polished (1 1 1)/(1¯ 1¯ 1) room temperature with a diamond stylus to introduce preferential dislocation nucleation sites. The specimen was stressed at an elevated temperature by means of three-point bending in a vacuum. The motion of dislocations from the scratch was investigated by observing etch pits detected by a modified
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Sirtl etchant [7]. Details of the experimental procedures and the crystal growth have been described in previous reports [3–5]. 3. Results and discussion 3.1. Critical stress for dislocation generation A certain critical stress exists for generation of dislocations from a scratch in CZ–Si doped with certain impurities. No appreciable critical stress, however, has been measured for dislocation generation in high purity FZ–Si. Fig. 1 shows the dependence of the critical stress for dislocation generation at 900 ◦ C on the concentration of doped impurities in CZ–Si crystals. Data for various concentrations of oxygen (O) impurity are also included in the figure. The critical stress increases with increasing O concentration and becomes 8 MPa at about 1018 cm−3 , the standard level of O concentration in CZ–Si. The critical stress starts to increase remarkably when B, P and As concentrations exceed 1 × 1019 cm−3 . This means that B, P and As impurities at concentrations higher than ≈1 × 1019 cm−3 effectively suppress the generation of dislocations. Thus, the critical stress for dislocation generation observed within crystals doped with concentrations of B, P and As impurities less than 1 × 1019 cm−3 can be understood to be mainly due to the effect of O impurity. B and P impurities in FZ–Si have also been found to suppress dislocation generation [6]. However, the critical stresses for dislocation generation in FZ–Si are lower than those in CZ–Si. The suppression of dislocation generation by Sb impurity is not clear because its solubility limit into Si is lower than those of B, P and As impurities. In Ge-doped Si, the magnitude of the critical stress for dislocation generation is 8 MPa, i.e., the same as the critical stress for undoped CZ–Si, and increases slightly to ≈10 MPa when the Ge concentration exceeds 1020 cm−3 . However, Ge impurity even at a high concentration of 2.5 × 1020 cm−3 is not effective for suppression of dislocation generation. Indeed, in the dilute SiGe alloys with Ge content of 0.004, strong suppression of dislocation generation has not been observed [8]. Contrarily, in (Ge + B)
Fig. 2. Stressing temperature dependence of release stress τ R for dislocations aged at 900 ◦ C for 15 min in various types of CZ–Si. (Ge + B) denotes the results for CZ–Si co-doped with Ge and B at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
co-doped CZ–Si, the critical stress of dislocation generation is higher than that in Si independently doped with either B or Ge. This shows the effect of (Ge + B) co-doping effect on the suppression of dislocation generation, though such effect is weaker than that observed at 800 ◦ C [5]. In N-doped CZ–Si, the critical stress for dislocation generation is 9 MPa, comparable to or somewhat higher than that in undoped CZ–Si. 3.2. Dislocation immobilization The absence of dislocation generation from a scratch or surface flaw under low stress has been observed for dislocations in several semiconductors doped with certain kinds of impurity (see review [1]). Dislocations are nucleated around a scratch/surface flaw and immobilized due to the impurity segregation along the dislocations even while the crystal is being heated to the test temperature [1,5,6]. The observed critical stress for dislocation generation should be understood as the stress required to release a dislocation from the immobilized state and to penetrate into the matrix crystal, which can be detected macroscopically as dislocation generation from the scratch. This stress is termed release stress τ R . The characteristic features of dislocation–impurity interaction can be evaluated through the analysis of the stressing temperature dependence of the release stress of aged dislocations. Fig. 2 shows the release stress against the stressing temperature for dislocations in various Si crystals aged at 900 ◦ C for 15 min. The release stress decreases linearly with an increase in the stressing temperature, showing that the process is thermally activated. A theory of the thermally activated release of dislocations from locking agents gives the following relation between the release stress τ R and the temperature T: τR =
Fig. 1. Variation in the critical stress for generation of 60◦ dislocations at 900 ◦ C against the concentration of N, B, P, As, Sb, Ge and O impurities in CZ–Si crystals. The ellipse denotes the critical stress in Ge and B co-doped Si at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
[E − kB T ln(LNν/Γ )]N , b2
(1)
where E is the maximum interaction energy between a dislocation and a locking agent, L the length of the dislocation, N the mean density of locking agents along the dislocation line,
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Table 1 Magnitudes of E and N for dislocations in the impurity-doped CZ–Si crystals
3.3. Dislocation velocity
Impurity species and concentration (cm−3 )
Dislocation velocity v in high purity FZ–Si is described as a function of stress τ and temperature T according to the empirical law m τ Q exp − , (2) v = v0 τ0 kB T
1 × 1018
O: N: 6 × 1015 B: 9 × 1019 P: 3 × 1019 As: 4 × 1019 Ge: 9 × 1019 Ge: 4 × 1019 , B: 9 × 1018
E (eV)
N (cm−1 )
3.6 4.1 4.5 3.6 3.7 3.6 3.8
2.4 × 105 1.0 × 105 1.1 × 105 3.4 × 105 2.8 × 105 2.6 × 105 1.6 × 105
ν the vibration frequency of the dislocation, Γ the release rate of the locked dislocation, kB the Boltzmann constant and b the magnitude of the Burgers vector of the dislocation [1,6,9]. By using Eq. (1), the density of the pinning agents along the dislocation line N and the interaction energy E in the crystals were evaluated as shown in Table 1. The experimentally estimated magnitudes of interaction energy E are 3–4 eV, too high to be interpreted with a model in which the dislocations interact with individual impurity atoms. The magnitudes of line density N are 1–3 × 105 cm−1 , much smaller than that expected from the concentration of the impurity atoms individually dispersed in the matrix. This result indicates the following picture: impurity atoms dispersed within the matrix segregate at dislocations at rest and pipe diffuse along the dislocation line, meeting and coagulating at some discretely separated sites on the dislocation line. As a result, the dislocations are locked/immobilized by such complexes or clusters, which may include a few impurity atoms, intrinsic point defects, or O atoms in CZ–Si, as calculated by Heggie et al. for P impurity [10]. Experimentally, oxygen precipitates have been found to develop along a dislocation line as observed by transmission electron microscopy [11]. As seen in Table 1, B and N impurities have larger interaction energy E and lower density N than do O, Ge, As and P impurities. This suggests that B and N impurities contribute to the prompt formation/development of stronger locking agents with lower density along dislocations. On the other hand, P and As impurities are known to form a high density of locking agents, resulting in high release stress. The magnitudes of the release stress and E and N in Ge-doped CZ–Si are comparable to those in undoped CZ–Si. This supports the experimental result in Fig. 1 that Ge impurity even at a high concentration of 2.5 × 1020 cm−3 does not suppress dislocation generation and confirms that Ge has no effect on dislocation immobilization. In P-doped CZ–Si, the density N is higher than that in Pdoped FZ–Si, which suggests that a combination of a P atom with an O atom leads to the formation of locking agents with higher density along a dislocation line than in the case of an individual P atom. Similarly, in (Ge + B) co-doped Si, the interaction energy E is slightly higher and the density N is lower than that in undoped CZ–Si. Strong locking agents are probably constructed in cooperation with Ge and B atoms, resulting in the immobilization of dislocations. These features indicate that a unique reaction of impurities occurs at a dislocation site.
where v0 , m and Q are material constants, τ 0 is 1 MPa and m ≈ 1 [1,6,12]. Contrarily, the velocity of 60◦ dislocations in CZ–Si with O, N, B, P, As and Ge impurities increases rapidly once the stress exceeds the critical stress value for dislocation generation and then shows a break, which depends on the impurity species and concentration. Such a rapid increase in the velocity is related to the dislocation generation/release process from the impurity-immobilized state. Beyond the break, the velocity increases rather slowly with an increase in the stress at a rate comparable to that of 60◦ dislocations in highly pure FZ–Si. Fig. 3 shows how the velocities of 60◦ dislocations at 900 ◦ C depend on the concentration of impurities in a semi-quantitative manner. The velocities of dislocations shown are those under a stress of 30 MPa where the measured velocities are thought to be free from the influence of impurity immobilization. It is seen that the velocity of dislocations in Si doped with donor impurities (P, As, Sb) increases with an increase in the concentration as reported previously [1,6,12]. Additionally, the dislocation velocity in Si doped with acceptor impurity B increases monotonically from that in undoped Si with an increase in the B concentration [5]. N and Ge impurities have almost no effect on dislocation velocity enhancement/reduction. In (Ge + B) co-doped Si the dislocation velocity at 900 ◦ C is comparable to that in undoped Si. This means that the retardation effect of (Ge + B) co-doping on the dislocation velocity observed in Si at temperatures lower than 800 ◦ C [5] becomes weak at elevated temperatures. Fig. 4 shows the velocities of 60◦ dislocations in CZ–Si doped or co-doped with various impurities at various concentrations under a stress of 30 MPa plotted against the reciprocal temperatures: B (9 × 1019 cm−3 ), P (3 × 1019 ), As
Fig. 3. Velocities of 60◦ dislocations in impurity-doped CZ–Si crystals under a shear stress of 30 MPa at 900 ◦ C: the dependence on the electrical type and concentration of main impurities. The ellipse denotes the critical stress in Ge and B co-doped CZ–Si at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
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where the doping level is extremely high, which can be regarded as being in a rather dilute solid solution. 4. Conclusion
Fig. 4. Velocities of 60◦ dislocations in impurity-doped CZ–Si crystals under a shear stress of 30 MPa against the reciprocal temperature. Numerals show the impurity concentration in a unit of cm−3 . (Ge + B) denotes the results for Ge and B co-doped CZ–Si at concentrations of 4 × 1019 and 9 × 1018 cm−3 , respectively.
(4 × 1019 ), Ge (9 × 1019 ), N (6 × 1015 ) and Ge + B (4 × 1019 and 9 × 1018 ). Also shown are the results in undoped CZ–Si (O: 1 × 1018 cm−3 ). The dislocation velocity in motion was found to be unaffected by the doping of Si crystals with N and Ge impurities in the whole temperature range of 650–950 ◦ C. In (Ge + B) co-doped CZ–Si, dislocations move with lower velocity than in undoped CZ–Si in the low temperature range. (Ge + B) co-doping is probably effective at low temperatures. Dislocations move far faster in P- and As-doped Si and slightly faster in B-doped than in undoped CZ–Si at temperatures lower than about 800 ◦ C. The velocity enhancement and weak temperature dependence, i.e., reduction of the activation energy Q for dislocation motion in n-type crystals, are attributed to the electrical effect through the formation and/or migration of kinks as an elementary process of dislocation motion. An acceptor level is thought to be associated with a kink site in Si as proposed by Hirsch [13] and Jones [14]. If the enhanced velocity of dislocations detected in B-doped Si is related to such a mechanism, then a donor level would seem to be associated with a kink site in Si. Surprisingly, even at temperatures higher than 800 ◦ C, the dislocation velocity in Si doped with B, P and As impurities is larger than that of dislocations in undoped CZ–Si. Such enhancement of dislocation velocity observed in heavily impurity-doped Si may not be due to the above mechanism since a break of the temperature dependence of dislocation velocity in B-, P- and As-doped Si is seen in Fig. 4. The kink configuration of a dislocation is probably concerned with the elementary process of dislocation motion in heavily impurity-doped semiconductors,
The dynamic interaction between dislocations and impurities in CZ–Si crystals heavily doped with light impurity (N) and acceptor (B), donor (P, As, Sb) and neutral (Ge) impurities was investigated by means of the etch pit method. Generation of dislocations from a surface scratch is strongly suppressed in Si doped with B, P and As impurities with a concentration higher than 1 × 1019 cm−3 , while Ge impurity does not strongly suppress dislocation generation. The critical stress for dislocation generation increases with B, P and As concentration, which is interpreted in terms of dislocation immobilization/locking due to impurity segregation through a unique reaction at dislocation sites. In the analysis of the thermally activated release process from immobilized states, B and N impurities are evaluated to promptly form strong locking agents, while P and As impurities form high density locking agents along dislocations. (Ge + B) co-doping also effectively promotes the formation of strong locking agents. Dislocation velocity in electrically conductive Si increases with an increase in the concentration of not only the donor (P, As, Sb) but also acceptor (B) impurities at temperatures of 650–950 ◦ C. N and Ge impurities have no or little effect on the dislocation velocity in motion. In (Ge + B) co-doped CZ–Si, dislocations move with lower velocity than in undoped CZ–Si at low temperatures, which means that (Ge + B) co-doping is effective for retarding dislocation velocity at temperatures lower than 900 ◦ C. Acknowledgement The author wishes to thank Dr. T. Taishi and Prof. K. Hoshikawa of Shinshu University for the supply of B-doped CZ–Si crystals. References [1] K. Sumino, I. Yonenaga, Solid State Phenomena 85/86 (2002) 145. [2] K. Jurkschat, S. Senkader, D. Gambaro, R.J. Falster, P.R. Wilshaw, J. Appl. Phys. 90 (2001) 3219. [3] X. Huang, T. Taishi, I. Yonenaga, K. Hoshikawa, J. Cryst. Growth 213 (2000) 283. [4] I. Yonenaga, T. Taishi, X. Huang, K. Hoshikawa, Mater. Sci. Eng. B 91/92 (2002) 192. [5] I. Yonenaga, T. Taishi, X. Hunag, K. Hoshikawa, J. Appl. Phys. 93 (2003) 265. [6] I. Yonenaga, Solid State Phenomena 95/96 (2004) 423. [7] ASTM standard F80-85, ASTM, Philadelphia, PA. [8] I. Yonenaga, J. Cryst. Growth 275 (2005) 91. [9] K. Sumino, M. Imai, Philos. Mag. A 47 (1983) 753. [10] M.I. Heggie, R. Jones, A. Umerski, Philos. Mag. A 63 (1991) 571. [11] I. Yonenaga, K. Sumino, J. Appl. Phys. 80 (1996) 734. [12] M. Imai, K. Sumino, Philos. Mag. A 47 (1983) 599. [13] P.B. Hirsch, J. Phys. Colloq. (Paris) 40 (1979) C6–C117. [14] R. Jones, Philos. Mag. B 42 (1980) 213.