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Evaluation of Strain-Relaxation of Carbon-Doped Silicon Nanowires and Its Crystal Orientation Dependence Using X-Ray Diffraction Reciprocal Space Mapping

  • Topical Collection: 19th Conference on Defects (DRIP XIX)
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Abstract

Carbon-doped silicon (Si:C) thin films with C concentrations of 0.60% and 0.83% were fabricated into nanowires, and the lattice strain relaxation with shrinking the nanowire width, W, was evaluated in detail by x-ray reciprocal lattice space mapping (RSM) measurements. The obtained RSM profiles showed a right-downward distribution. From the RSM profiles, we considered that the lattice relaxation of the Si:C nanowires progressed slowly from the nanowires/substrate interfaces to the nanowire top surfaces. Then, we assumed the lattice strain of the Si:C thin films to be 100% and derived the average lattice strain relaxation of the Si:C nanowires from the RSM profiles. To derive the lattice relaxation, we summed the RSM profiles in the qx or qz directions, respectively, and calculated the average in-plane and out-of-plane lattice parameters. The obtained average lattice strain relaxation became larger with shrinking W, and progressed rapidly at W = 200 nm. Thus, we considered that the large strain relaxation occurs in the region of approximately 100 nm from the edge of the nanowires. In addition, the lattice strain relaxation was smaller for Si:C nanowires fabricated with their long side along the [100] direction than for Si:C nanowires along the [110] direction. We considered this difference of strain relaxation might be due to the crystallographic orientation dependence of Young’s modulus.

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References

  1. E. Ungersboeck, S. Dhar, G. Karlowatz, V. Sverdlov, H. Kosina, and S. Selberherr, The effect of general strain on the band structure and electron mobility of silicon. IEEE Trans. Electron Dev. 54(9), 2183 (2007).

    Article  CAS  Google Scholar 

  2. J.M. Hinckley, and J. Singh, Monte Carlo studies of ohmic hole mobility in silicon and germanium: examination of the optical phonon deformation potential. J. Appl. Phys. 76(7), 4192 (1994).

    Article  CAS  Google Scholar 

  3. M.V. Fischetti, and S.E. Laux, Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys. J. Appl. Phys. 80(4), 2234 (1996).

    Article  CAS  Google Scholar 

  4. S. Reggiani, M. Valdinoci, L. Colalongo, M. Rudan, G. Baccarani, A.D. Stricker, F. Illien, N. Felber, W. Fichtner, and L. Zullino, Electron and hole mobility in silicon at large operating temperatures. I. Bulk mobility. IEEE Trans. Electron Dev. 49(3), 490 (2002).

    Article  CAS  Google Scholar 

  5. M.B. Prince, Drift mobilities in semiconductors. I. Germanium. Phys. Rev. 92(3), 681 (1953).

    Article  CAS  Google Scholar 

  6. M.B. Prince, Drift mobilities in semiconductors. II. Silicon. Phys. Rev. 93(6), 1204 (1954).

    Article  CAS  Google Scholar 

  7. S.G. Volz, and G. Chen, Molecular-dynamics simulation of thermal conductivity of silicon crystals. Phys. Rev. B 61(4), 2651 (2000).

    Article  CAS  Google Scholar 

  8. R. Yokogawa, S. Hashimoto, K. Takahashi, S. Oba, M. Tomita, M. Kurosawa, T. Watanabe, and A. Ogura, Evaluation of laterally graded silicon germanium wires for thermoelectric devices fabricated by rapid melting growth. ECS Trans. 86(7), 87 (2018).

    Article  CAS  Google Scholar 

  9. R. Yokogawa, H. Takeuchi, Y. Arai, I. Yonenaga, M. Tomita, H. Uchiyama, T. Watanabe, and A. Ogura, Anomalous low energy phonon dispersion in bulk silicon-germanium observed by inelastic x-ray scattering. Appl. Phys. Lett. 116, 242104 (2020).

    Article  CAS  Google Scholar 

  10. J.P. Dismukes, L. Ekstrom, E.F. Steigmeier, I. Kudman, and D.S. Beers, Thermal and electrical properties of heavily doped Ge-Si alloys up to 1300°K. J. Appl. Phys. 35, 2899 (1964).

    Article  CAS  Google Scholar 

  11. M.C. Steele, and F.D. Rosi, Thermal conductivity and thermoelectric power of germanium-silicon alloys. J. Appl. Phys. 29(11), 1517 (1958).

    Article  CAS  Google Scholar 

  12. Z. Wang, and N. Mingo, Diameter dependence of SiGe nanowire thermal conductivity. Appl. Phys. Lett. 97, 101903 (2010).

    Article  Google Scholar 

  13. D. Fan, H. Sigg, R. Spolenak, and Y. Ekinci, Strain and thermal conductivity in ultrathin suspended silicon nanowires. Phys. Rev. B 96, 115307 (2017).

    Article  Google Scholar 

  14. S. Zaima, O. Nakatsuka, N. Taoka, M. Kurosawa, W. Takeuchi, and M. Sakashita, Growth and applications of GeSn-related group-IV semiconductor materials. Sci. Technol. Adv. Mater. 16, 043502 (2015).

    Article  Google Scholar 

  15. M. Oehme, E. Kasper, and J. Schulze, GeSn heterojunction diode: detector and emitter in one device. ECS J. Solid State Sci. Technol. 2, R76 (2013).

    Article  CAS  Google Scholar 

  16. S. Gupta, R. Chena, B. Vincent, D. Lin, B. Magyari-Köpea, M. Caymaxb, J. Dekosterb, J.S. Harrisa, Y. Nishia, and K.C. Saraswat, Evaluation of thermal expansion coefficient in Ge1-xSnx nanowire using reciprocal space mapping. ECS Trans. 50, 937 (2013).

    Article  Google Scholar 

  17. Y. Yang, S. Su, P. Guo, W. Wang, X. Gong, L. Wang, K.L. Low, G. Zhang, C. Xue, B. Cheng, G. Han, and Y.-C. Yeo, Towards direct band-to-band tunneling in P-channel tunneling field effect transistor (TFET): technology enablement by Germanium-tin (GeSn). IEDM Tech. Dig. 16(3), 1 (2013).

    Google Scholar 

  18. Y.-C. Fang, K.-Y. Chen, C.-H. Hsieh, C.-C. Su, and Y.-H. Wu, N-MOSFETs formed on solid phase epitaxially grown GeSn film with passivation by oxygen plasma featuring high mobility. ACS Appl. Mater. Interfaces 7(48), 26374 (2015).

    Article  CAS  Google Scholar 

  19. J.P. Dismukes, L. Ekstrom, and R.J. Paff, Lattice parameter and density in germanium-silicon alloys. J. Phys. Chem. 68(10), 3021 (1964).

    Article  CAS  Google Scholar 

  20. G. Celotti, D. Nobili, and P. Ostoja, Lattice parameter study of silicon uniformly doped with boron and phosphorus. J. Mater. Sci. 9, 821 (1974).

    Article  CAS  Google Scholar 

  21. G. Murrieta, A. Tapia, and R. de Coss, Structural stability of carbon in the face-centered-cubic (Fm-3m) phase. Carbon 42(4), 771 (2004).

    Article  CAS  Google Scholar 

  22. M. Berti, D. De Salvador, A.V. Drigo, F. Romanato, J. Stangl, S. Zerlauth, F. Schäffler, and G. Bauer, Lattice parameter in Si1−yCy epilayers: deviation from Vegard’s rule. Appl. Phys. Lett. 72(13), 1602 (1998).

    Article  CAS  Google Scholar 

  23. T.-Y. Liow, K.-M. Tan, D. Weeks, R.T.P. Lee, M. Zhu, K.-M. Hoe, C.-H. Tung, M. Bauer, J. Spear, S.G. Thomas, G. Samudra, N. Balasubramanian, and Y.-C. Yeo, Strained n-channel FinFETs featuring in situ doped silicon-carbon (Si1−yCy) source and drain stressors with high carbon content. IEEE Trans. Electron Dev. 55(9), 2475 (2008).

    Article  CAS  Google Scholar 

  24. S.-M. Koh, X. Wang, K. Sekar, W. Krull, G.S. Samudra, and Y.-C. Yeo, Silicon-carbon formed using cluster-carbon implant and laser-induced epitaxy for application as source/drain stressors in strained n-channel MOSFETs. J. Electrochem. Soc. 156(5), H361 (2009).

    Article  CAS  Google Scholar 

  25. S. Yamamoto, K. Takeuchi, R. Yokogawa, M. Tomita, D. Kosemura, K. Usuda, and A. Ogura, Evaluation of anisotropic biaxial stress in Si1-XGex/Ge mesa-structure by oil-immersion Raman spectroscopy. ECS Trans. 66(4), 39 (2015).

    Article  CAS  Google Scholar 

  26. Y. Takahashi, R. Yokogawa, T. Murakami, I. Hirosawa, K. Suda, and A. Ogura, Evaluation of anisotropic three-dimensional strain relaxation in stripe-shaped Ge1-xSnx mesa structure. ECS Trans. 86(7), 329 (2018).

    Article  CAS  Google Scholar 

  27. K. Yoshioka, R. Yokogawa, and A. Ogura, Anisotropic biaxial stress evaluation in metal-organic chemical vapor deposition grown Ge1-xSnx mesa structure by oil-immersion Raman spectroscopy. Thin Solid Films 697, 137797 (2020).

    Article  CAS  Google Scholar 

  28. H.-S.P. Wong, K. Akarvardar, D. Antoniadis, J. Bokor, C. Hu, T.-J.K. Liu, S. Mitra, J.D. Plummer, and S. Salahuddin, A density metric for semiconductor technology. Proc. IEEE 108(4), 478 (2020).

    Article  Google Scholar 

  29. D.-M. Tang, C.-L. Ren, M.-S. Wang, X. Wei, N. Kawamoto, C. Liu, Y. Bando, M. Mitome, N. Fukata, and D. Golberg, Mechanical properties of Si nanowires as revealed by in situ transmission electron microscopy and molecular dynamics simulations. Nano Lett. 12(4), 1898 (2012).

    Article  CAS  Google Scholar 

  30. C.-L. Hsin, W. Mai, Y. Gu, Y. Gao, C.-T. Huang, Y. Liu, L.-J. Chen, and Z.-L. Wang, Elastic properties and buckling of silicon nanowires. Adv. Mater. 20, 3919 (2008).

    Article  CAS  Google Scholar 

  31. Y.-S. Sohn, J. Park, G. Yoon, J. Song, S.-W. Jee, J.-H. Lee, S. Na, T. Kwon, and K. Eom, Mechanical properties of silicon nanowires. Nanoscale Res. Lett. 5, 211 (2010).

    Article  CAS  Google Scholar 

  32. K. Yoshioka, R. Yokogawa, N. Sawamoto, and A. Ogura, Anisotropic biaxial strain evaluation in carbon-doped silicon using water-immersion Raman spectroscopy. ECS Trans. 92(4), 33 (2019).

    Article  CAS  Google Scholar 

  33. S. Takagi, A. Toriumi, M. Iwase, and H. Tango, On the universality of inversion layer mobility in Si MOSFET’s: part I-effects of substrate impurity concentration. IEEE Trans. Electron Dev. 41(12), 2357 (1994).

    Article  CAS  Google Scholar 

  34. H. Irie, K. Kita, K. Kyuno, and A. Toriumi, In-plane mobility anisotropy and universality under uni-axial strains in n- and p-MOS inversion layers on (loo), (110), and (111) Si. IEDM Tech. Dig. 2004, 225 (2004).

    Google Scholar 

  35. Y.M. Niquet, C. Delerue, and C. Krzeminski, Effects of strain on the carrier mobility in silicon nanowires. Nano Lett. 12, 3545 (2012).

    Article  CAS  Google Scholar 

  36. I. Hirosawa, K. Yoshioka, R. Yokogawa, A. Ogura, and T. Watanabe, 19th International Conference on Defects-Recognition, Imaging and Physics in Semiconductors, WeP-08 (2022)

  37. W.A. Brantley, Calculated elastic constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44(1), 534 (1973).

    Article  CAS  Google Scholar 

  38. J.O. Kim, J.D. Achenbach, P.B. Mirkarimi, M. Shinn, and S.A. Barnett, Elastic constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy. J. Appl. Phys. 72(5), 1805 (1992).

    Article  CAS  Google Scholar 

  39. E. Anastassakis, A. Cantarero, and M. Cardona, Piezo-Raman measurements and anharmonic parameters in silicon and diamond. Phys. Rev. B 41(11), 7529 (1990).

    Article  CAS  Google Scholar 

  40. M.A. Hopcroft, W.D. Nix, and T.W. Kenny, What is the Young’s modulus of silicon? J. Microelectromech. Syst. 19(2), 229 (2010).

    Article  CAS  Google Scholar 

  41. E.J. Boyd, and D. Uttamchandani, Measurement of the anisotropy of Young’s modulus in single-crystal silicon. J. Microelectromech. Syst. 21(1), 243 (2012).

    Article  CAS  Google Scholar 

  42. J.J. Wortman, and R.A. Evans, Young’s modulus, shear modulus, and Poisson’s ratio in silicon and germanium. J. Appl. Phys. 36(1), 153 (1965).

    Article  CAS  Google Scholar 

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Acknowledgments

The synchrotron RSM measurements were performed at the BL19B2 of SPring-8 synchrotron facility with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2020A1748 and 2020A1849).

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Authors and Affiliations

  1. School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama, Kawasaki, 214-8571, Japan

    Kazutoshi Yoshioka, Ryo Yokogawa & Atsushi Ogura

  2. Meiji Renewable Energy Laboratory, Meiji University, 1-1-1 Higashimita, Tama, Kawasaki, 214-8571, Japan

    Kazutoshi Yoshioka, Ichiro Hirosawa, Ryo Yokogawa & Atsushi Ogura

  3. SAGA Light Source, 8-7 Yayoigaoka, Tosu, Saga, 841-0005, Japan

    Ichiro Hirosawa

  4. Japan Synchrotron Radiation Research Institute, 1-1-1 Koto, Sayo, Sayo, Hyogo, 679-5198, Japan

    Takeshi Watanabe

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  1. Kazutoshi Yoshioka
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Yoshioka, K., Hirosawa, I., Watanabe, T. et al. Evaluation of Strain-Relaxation of Carbon-Doped Silicon Nanowires and Its Crystal Orientation Dependence Using X-Ray Diffraction Reciprocal Space Mapping. J. Electron. Mater. 52, 5140–5149 (2023). https://doi.org/10.1007/s11664-023-10497-5

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