N. Zakharov et al Physica E 37(2007)148-152 corresponds to the supersaturation Aoo/kTa002 Such a The minimal radius of the whiskers is determined by low supersaturation will not be sufficient to support interplay between the gain in elastic and the loses in surface whisker growth by classical gas apitaxy. However, the energies rc=2y/Ag ( Gibbs-Tomson effect). The stress presence of the liquid Si/Au phase makes the growth relaxation efficiency decreases with the radius of the possible due to a low nucleation energy in the liquid phase. whisker [18]. This results in the reduction of supersatura Thus, the role of Au droplets in our case is the formation of tion for thicker whiskers with r>R and their growth i/Au liquid phase. The difference between (220) inter- interruption. This also explains the experimental fact that planar distances near the top of the whisker and inin the case of mbe thinner whiskers grow faster. The vergrown layer measured in this investigation in HRTEM whisker growth in our case can be considered as a stress images is AE= AEyya5 x 10. This should be sufficient relaxation mechanism similar to the Stranski-Krastanow to drive the whisker growth. A very similar mechanism of mechanism [19], where stress relaxation occurs by transi- n whisker growth on a stressed Sn surface of Cu-Sn tion from two-dimensional system to three-dimensional bimetallic film was experimentally observed by Tu [17]. In one specimen maintained at room temperature, the Sn and Cu yers were both in compression and tension. The whiskers grew only on compressed Sn film. The driving force of this Acknowledgments process was attributed to the interdiffusion and reaction that occurs in the cu-Sn film The authors would like to thank l. schubert and a The tiny amorphous particles, about 5nm in size, are Frommfeld for the MBE experiments, F. Syrowatka for present on the Si surface at room temperature as can be seen in Fig. 4. They are most probably Si/Au eutectic SEM analysis, S. Hopfe for TEM specimen preparation, phase. The RHEED in situ control of the surface structure and M. Werner for specific TEM analysis. The work was also partially supported by European project NODE (FP6 during the heating of Si wafer deposited by 2 nm Au points /015783)and Russian foundation of basic research(04-02 Above this transition temperature instead of sharp reflec- 16747) tions from the crystalline Si, the diffuse halo appears(s Fig. 5). This is a strong indication that at a growth temperature of 525C the whole specimen is covered by a References thin Si/Au liquid eutectic layer. Using Eq. (5)and remembering that Ls= l,t we can write [Y. Nakajiama, Y. Takahashi, S Horiguchi, K. Iwadate, H. Namatsu, K. Kurihara, M. Tabe, Appl. Phys. Lett. 65(1994)2833 L2Da△ 2 N. Usami, T. Mine, S. Fukatsu, Y. Shiraki, Appl. Phys. Lett. 64 (1994)1126 3]J. L. Liu, Y. Shi, F. Wang, Y. Lu, R. Zhang, P. Han, S.L. Gu,Y D Thus, Eq.(6)and Fig. 2d show that the elongation of Zheng, Appl. Phys. Lett. 68(1996)352. whisker L is controlled by the diffusion of Si ad-atoms and 4] C.M. Lieber, MRS Bull. 28(2003)128 stress in the overgrown layer L, [A.H. Cottrell, in: Dislocations and Plastic Flow in Crystals. Clarendon Press, Oxford, 1953, p. Il 5. Conclusions [6R.S. Wagner, w.C. Ellis, Appl. Phys. Lett. 4(1964)89 964)2907. w.C. Ellis, K. Jackson, S M. Arnold, J. Appl. Phys. 35 It has been shown that the driving force for MBE [8R.s.Wagner, W.C.Ellis, Trans. Metall. Soc. AIME 233(1965)1053 energy stored in an overgrown layer L, due to gold 0 R S Wagner. W.C. Ellis, Appl.Phys. Lett. 4(1964)89 intrusion. The supersaturation is determined by the inter- [12] J.L. Liu, S.J. Gai, G L. Jin, S.G. Tomas, K.L. Wang, J. Cryst play between elastic stresses and surface energy(Eq (3)) Growth200(1999)106. The last one could be considerably decreased due to the [3]Q Tang, X Liu, T.I. Kamins, G.S. Salomon, J.S. Harris, Appl. Phys ett.81(2002)2452 surface. This suggests that in our case the supersaturation [4 L, Schubert Werne N.D lakharov, g Gerth K oIb, L. Long. is not an independent growth parameter. This, however, is [15)S. Takeda, K Ueda, N Ozaki, Y Ohno, Appl. Phys. Lett. 82(2003) lot the case for the CVd growth technique where the supersaturation is determined by vapor pressure and can be []C. Messmer, J.C. Bilello, J Appl. Phys. 52(1981)4623 sily varied as an independent parameter. This approach (7KN. Tu, Acta MetalL. 21(1973)347 allows us to explain quite satisfactorily the growth kinetics (8 N.D. akharov, P: Werre G, Gert, L Schubert, L. Sokolov and the relationship between the radius and the length of [19 I.N. Stranski, L. Krastanow, Sitzungsberichte d. Akad. D. wi senschaften in Wien, Abt IIb, Band 146(1937)797.corresponds to the supersaturation Dso/kTE0.02. Such a low supersaturation will not be sufficient to support whisker growth by classical gas apitaxy. However, the presence of the liquid Si/Au phase makes the growth possible due to a low nucleation energy in the liquid phase. Thus, the role of Au droplets in our case is the formation of Si/Au liquid phase. The difference between {2 2 0} inter￾planar distances near the top of the whisker and in overgrown layer measured in this investigation in HRTEM images is Dezz ¼ DeyyE5  103 . This should be sufficient to drive the whisker growth. A very similar mechanism of Sn whisker growth on a stressed Sn surface of Cu–Sn bimetallic film was experimentally observed by Tu [17]. In specimen maintained at room temperature, the Sn and Cu layers were both in compression and tension. The whiskers grew only on compressed Sn film. The driving force of this process was attributed to the interdiffusion and reaction that occurs in the Cu–Sn film. The tiny amorphous particles, about 5 nm in size, are present on the Si surface at room temperature as can be seen in Fig. 4. They are most probably Si/Au eutectic phase. The RHEED in situ control of the surface structure during the heating of Si wafer deposited by 2 nm Au points to a phase transition which occurred at (360720)1C. Above this transition temperature instead of sharp reflec￾tions from the crystalline Si, the diffuse halo appears (see Fig. 5). This is a strong indication that at a growth temperature of 525 1C the whole specimen is covered by a thin Si/Au liquid eutectic layer. Using Eq. (5) and remembering that Ls ¼ I1t we can write L Ls ¼ 2Da kT Dso lRI 1 1 2g DsR . (6) Thus, Eq. (6) and Fig. 2d show that the elongation of whisker L is controlled by the diffusion of Si ad-atoms and stress in the overgrown layer Ls. 5. Conclusions It has been shown that the driving force for MBE whisker growth is supported by the relaxation of elastic energy stored in an overgrown layer Ls due to gold intrusion. The supersaturation is determined by the inter￾play between elastic stresses and surface energy (Eq. (3)). The last one could be considerably decreased due to the formation of a thin liquid Si/Au eutectic layer on the Si surface. This suggests that in our case the supersaturation is not an independent growth parameter. This, however, is not the case for the CVD growth technique where the supersaturation is determined by vapor pressure and can be easily varied as an independent parameter. This approach allows us to explain quite satisfactorily the growth kinetics and the relationship between the radius and the length of the whiskers. The minimal radius of the whiskers is determined by an interplay between the gain in elastic and the loses in surface energies rc ¼ 2g/Ds (Gibbs–Tomson effect). The stress relaxation efficiency decreases with the radius of the whisker [18]. This results in the reduction of supersatura￾tion for thicker whiskers with R4Rc and their growth interruption. This also explains the experimental fact that in the case of MBE thinner whiskers grow faster. The whisker growth in our case can be considered as a stress relaxation mechanism similar to the Stranski–Krastanow mechanism [19], where stress relaxation occurs by transi￾tion from two-dimensional system to three-dimensional one. Acknowledgments The authors would like to thank L. Schubert and A. Frommfeld for the MBE experiments, F. Syrowatka for SEM analysis, S. Hopfe for TEM specimen preparation, and M. Werner for specific TEM analysis. The work was also partially supported by European project NODE (FP6 /015783) and Russian foundation of basic research (04-02- 16747). References [1] Y. Nakajiama, Y. Takahashi, S. Horiguchi, K. Iwadate, H. Namatsu, K. Kurihara, M. Tabe, Appl. Phys. Lett. 65 (1994) 2833. [2] N. Usami, T. Mine, S. Fukatsu, Y. Shiraki, Appl. Phys. Lett. 64 (1994) 1126. [3] J.L. Liu, Y. Shi, F. Wang, Y. Lu, R. Zhang, P. Han, S.L. Gu, Y.D. Zheng, Appl. Phys. Lett. 68 (1996) 352. [4] C.M. Lieber, MRS Bull. 28 (2003) 128. [5] A.H. Cottrell, in: Dislocations and Plastic Flow in Crystals, Clarendon Press, Oxford, 1953, p. 11. [6] R.S. Wagner, W.C. Ellis, Appl. Phys. Lett. 4 (1964) 89. [7] R.S. Wagner, W.C. Ellis, K. Jackson, S.M. Arnold, J. Appl. Phys. 35 (1964) 2993. [8] R.S. Wagner, W.C. Ellis, Trans. Metall. Soc. AIME 233 (1965) 1053. [9] E.I. Givargizov, J. Cryst. Growth 31 (1975) 20. [10] R.S. Wagner, W.C. Ellis, Appl. Phys. Lett. 4 (1964) 89. [11] H.D. Park, T.P. Hogan, J. Vac. Sci. Technol. B 22 (2004) 237. [12] J.L. Liu, S.J. Gai, G.L. Jin, S.G. Tomas, K.L. Wang, J. Cryst. Growth 200 (1999) 106. [13] Q. Tang, X. Liu, T.I. Kamins, G.S. Salomon, J.S. Harris, Appl. Phys. Lett. 81 (2002) 2452. [14] L. Schubert, P. Werner, N.D. Zakharov, G. Gerth, F. Kolb, L. Long, U. Go¨sele, T.Y. Tan, Appl. Phys. Lett. 84 (2004) 4968. [15] S. Takeda, K. Ueda, N. Ozaki, Y. Ohno, Appl. Phys. Lett. 82 (2003) 979. [16] C. Messmer, J.C. Bilello, J. Appl. Phys. 52 (1981) 4623. [17] K.N. Tu, Acta Metall. 21 (1973) 347. [18] N.D. Zakharov, P. Werner, G. Gerth, L. Schubert, L. Sokolov, U. Go¨sele, J. Cryst. Growth 290 (2006) 6. [19] I.N. Stranski, L. Krastanow, Sitzungsberichte d. Akad. D. Wis￾senschaften in Wien, Abt. IIb, Band 146 (1937) 797. ARTICLE IN PRESS 152 N. Zakharov et al. / Physica E 37 (2007) 148–152