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Top-down method to introduce ultra-high elastic strain

  • Thomas Zabel (a1), Richard Geiger (a2), Esteban Marin (a1), Elisabeth Müller (a3), Ana Diaz (a4), Christopher Bonzon (a5), Martin J. Süess (a5), Ralph Spolenak (a6), Jérôme Faist (a5) and Hans Sigg (a1)...


Elastic strain is an effective and thus widely used parameter to control and modify the electrical, optical, and magnetic properties of crystalline solid-state materials. It has a large impact on device performance and enables adjusting the materials functionality. Here, we promote a micromechanical strain enhancement technology to achieve ultra-high strain in semiconductors. The here presented suspended membranes enable the accurate control of the strain on a wafer-scale by standard top-down fabrication methods making it attractive for both device applications and also, thanks to the simplicity of the method, for fundamental research. This review aims at discussing the process of strain enhancement and its usage as an investigation platform for strain-related physical properties. Furthermore, we present design rules and a detailed analysis of fracture effects limiting the strain enhancement.


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1. Moss, S.J. and Ledwith, A.: Chemistry of the Semiconductor Industry (Chapman and Hall, New York, 1987).
2. Shklovskii, B.I. and Efros, A.L.: Electronic Properties of Doped Semiconductors (Springer, Berlin, 2012).
3. Schetzina, J.F. and McKelvey, J.P.: Strain dependence of the minority carrier mobility in p-type germanium. Phys. Rev. Lett. 181, 1191 (1969).
4. Fischetti, M.V. and Laux, S.E.: Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys. J. Appl. Phys. 80, 2234 (1996).
5. Chen, Y.T., Lan, H.S., Hsu, W., Fu, Y.C., Lin, J.Y., and Liu, C.W.: Strain response of high mobility germanium n-channel metal-oxide-semiconductor field-effect transistors on (001) substrates. Appl. Phys. Lett. 99, 022106 (2011).
6. Geiger, R., Zabel, T., and Sigg, H.: Group IV direct band gap photonics: Methods, challenges, and opportunities. Front. Mater. 2, 52 (2015).
7. Ahn, D. and Chuang, S.L.: The theory of strained-layer quantum-well lasers with bandgap renormalization. IEEE J. Quantum Electron. 30, 350 (1994).
8. Ahn, D. and Chuang, S.L.: Optical gain in a strained-layer quantum-well laser. IEEE J. Quantum Electron. 24, 2400 (1988).
9. Garone, P.M., Venkataraman, V., and Sturm, J.C.: Hole confinement MOS-gated Ge x Si1−x /Si heterostructures. IEEE Electron Device Lett. 12, 230 (1991).
10. Nanver, L.K., Jovanović, V., Biasotto, C., Moers, J., Grützmacher, D., Zhang, J.J., Hrauda, N., Stoffel, M., Pezzoli, F., Schmidt, O.G., Miglio, L., Kosina, H., Marzegalli, A., Vastola, G., Mussler, G., Stangl, J., Bauer, G., van der Cingel, J., and Bonera, E.: Integration of MOSFETs with SiGe dots as stressor material. Solid State Electrochem. 60, 7583 (2011).
11. Li, X., Maute, K., Dunn, M.L., and Yang, R.: Strain effects on the thermal conductivity of nanostructures. Phys. Rev. B: Condens. Matter Mater. Phys. 81, 245318 (2010).
12. Huang, B., Yu, J., and Wei, S.H.: Strain control of magnetism in graphene decorated by transition-metal atoms. Phys. Rev. B: Condens. Matter Mater. Phys. 84, 075415 (2011).
13. Braun, A., Briggs, K.M., and Böni, P.: Analytical solution to Matthews’ and Blakeslee’s critical dislocation formation thickness of epitaxially grown thin films. J. Cryst. Growth 241, 231234 (2002).
14. Matthews, J.W. and Blakeslee, A.E.: Defects in epitaxial multilayers: I. Misfit dislocations. J. Cryst. Growth 27, 118125 (1974).
15. Schorer, R., Friess, E., Eberl, K., and Abstreiter, G.: Structural stability of short-period Si/Ge superlattices studied with Raman spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 44, 1772 (1991).
16. Tan, P.H., Brunner, K., Bougeard, D., and Abstreiter, G.: Raman characterization of strain and composition in small-sized self-assembled Si/Ge dots. Phys. Rev. B: Condens. Matter Mater. Phys. 68, 125302 (2003).
17. Brunner, K.: Si/Ge nanostructures. Rep. Prog. Phys. 65, 2772 (2002).
18. Ong, P.L., Wei, J., Tay, F.E.H., and Iliescu, C.: A new fabrication method for low stress PECVD—SiN(x) layers. J. Phys.: Conf. Ser. 34, 764 (2006).
19. El Kurdi, M., Prost, M., Ghrib, A., Checoury, X., Beaudoin, G., Sagnes, I., Picardi, G., Ossikovski, R., and Boucaud, P.: Direct band gap germanium microdisks obtained with silicon nitride stressor layers. ACS Photonics 3, 443448 (2016).
20. Capellini, G., Kozlowski, G., Yamamoto, Y., Lisker, M., Wenger, C., Niu, G., Zaumseil, P., Tillack, B., Ghrib, A., de Kersauson, M., El Kurdi, M., Boucaud, P., and Schroeder, T.: Strain analysis in SiN/Ge microstructures obtained via Si-complementary metal oxide semiconductor compatible approach. J. Appl. Phys. 113, 013513 (2013).
21. Morin, P., Maitrejean, S., Allibert, F., Augendre, E., Liu, Q., Loubet, N., Grenouillet, L., Pofelski, A., Chen, K., Khakifirooz, A., Wacquez, R., Reboh, S., Bonnevialle, A., le Royer, C., Morand, Y., Kanyandekwe, J., Chanemougamme, D., Mignot, Y., Escarabajal, Y., Lherron, B., Chafik, F., Pilorget, S., Caubet, P., Vinet, M., Clement, L., Desalvo, B., Doris, B., and Kleemeier, W.: A review of the mechanical stressors efficiency applied to the ultra-thin body & buried oxide fully depleted silicon on insulator technology. Solid State Electrochem. 117, 100116 (2016).
22. Prost, M., El Kurdi, M., Ghrib, A., Sauvage, S., Checoury, X., Zerounian, N., Aniel, F., Beaudoin, G., Sagnes, I., Boeuf, F., and Boucaud, P.: Tensile-strained germanium microdisk electroluminescence. Opt. Express 23, 6722 (2015).
23. Bhaskar, U.K., Pardoen, T., Passi, V., and Raskin, J-P.: Piezoresistance of nano-scale silicon up to 2 GPa in tension. Appl. Phys. Lett. 102, 031911 (2013).
24. Haque, M.A. and Saif, M.T.A.: Microscale materials testing using MEMS actuators. J. Microelectromech. Syst. 10, 146 (2001).
25. Gravier, S., Coulombier, M., Safi, A., André, N., Boé, A., Raskin, J-P., and Pardoen, T.: New on-chip nanomechanical testing laboratory-applications to aluminum and polysilicon thin films. J. Microelectromech. Syst. 18, 555 (2009).
26. Minamisawa, R.A., Süess, M.J., Spolenak, R., Faist, J., David, C., Gobrecht, J., Bourdelle, K.K., and Sigg, H.: Top-down fabricated silicon nanowires under tensile elastic strain up to 4.5%. Nat. Commun. 3, 1096 (2012).
27. Süess, M.J., Geiger, R., Minamisawa, R.A., Schiefler, G., Frigerio, J., Chrastina, D., Isella, G., Spolenak, R., Faist, J., and Sigg, H.: Analysis of enhanced light emission from highly strained germanium microbridges. Nat. Photonics 7, 466472 (2013).
28. Davis, R.O.: Elasticity and Geomechanics (Cambridge University Press, New York, 1996).
29. Süess, M.J., Minamisawa, R.A., Geiger, R., Bourdelle, K.K., Sigg, H., and Spolenak, R.: Power-dependent Raman analysis of highly strained Si nanobridges. Nano Lett. 14, 12491254 (2014).
30. Gassenq, A., Tardif, S., Guilloy, K., Dias, G.O., Pauc, N., Duchemin, I., Rouchon, D., Hartmann, J.M., Widiez, J., Escalante, J., Niquet, Y.M., Geiger, R., Zabel, T., Sigg, H., Faist, J., Chelnokov, A., Rieutord, F., Reboud, V., and Calvo, V.: Accurate strain measurements in highly strained Ge microbridges. Appl. Phys. Lett. 108, 241902 (2016).
31. Sukhdeo, D.S., Nam, D., Kang, J-H., Brongersma, M.L., and Saraswat, K.C.: Direct bandgap germanium-on-silicon inferred from 5.7% 〈100〉 uniaxial tensile strain. Photon. Res. 2, A8 (2014).
32. Sukhdeo, D.S., Nam, D., Kang, J.H., and Brongersma, M.L.: Bandgap-customizable germanium using lithographically determined biaxial tensile strain for silicon-compatible optoelectronics. Opt. Express 23, 16740 (2015).
33. Gassenq, A., Guilloy, K., Dias, G.O., Pauc, N., Rouchon, D., Hartmann, J-M., Widiez, J., Tardif, S., Rieutord, F., Escalante, J., Duchemin, I., Niquet, Y.M., Geiger, R., Zabel, T., Sigg, H., Faist, J., Chelnokov, A., Reboud, V., and Calvo, V.: 1.9% bi-axial tensile strain in thick germanium suspended membranes fabricated in optical germanium-on-insulator substrates for laser applications. Appl. Phys. Lett. 107, 191904 (2015).
34. Stringfellow, G.B.: The importance of lattice mismatch in the growth of Ga x In1−x P epitaxial crystals. J. Appl. Phys. 43, 3455 (1972).
35. Jain, S.C., Willander, M., and Maes, H.: Stresses and strains in epilayers, stripes and quantum structures of III–V compound semiconductors. Semicond. Sci. Technol. 11, 641671 (1996).
36. Sailer, J., Wild, A., Lang, V., Siddiki, A., and Bougeard, D.: Quantum Hall resistance overshoot in two-dimensional (2D) electron gases: Theory and experiment. New J. Phys. 12, 113033 (2010).
37. Wild, A., Kierig, J., Sailer, J., Ager, J.W. III, Haller, E.E., Abstreiter, G., Ludwig, S., and Bougeard, D.: Few electron double quantum dot in an isotopically purified 28Si quantum well. Appl. Phys. Lett. 100, 143110 (2012).
38. Takagi, S., Mizuno, T., Tezuka, T., Sugiyama, N., Numata, T., Usada, K., Moriyama, Y., Nakaharai, S., Koga, J., Tanabe, A., and Maeda, T.: Fabrication and device characteristics of strained-Si-on-insulator (strained-SOI) CMOS. Appl. Surf. Sci. 224, 241247 (2004).
39. Milanovic, V.: Multilevel beam SOI-MEMS fabrication and applications. J. Microelectromech. Syst. 13, 1930 (2004).
40. Turner, K.T.: Fabricating strained silicon substrates using mechanical deformation during wafer bonding. ECS Trans. 16, 321328 (2008).
41. Geim, A.K.: Graphene: Status and prospects. Science 324, 15301534 (2009).
42. Geiger, R.: Direct Band Gap Germanium for Si-Compatible Lasing (ETH-Zürich, Zurich, 2016).
43. Süess, M.J.: Highly Strained Si and Ge Micro- and Nanobridges for Micro- and Optoelectronic Applications (ETH-Zürich, Zurich, 2014).
44. Etzelstorfer, T., Süess, M.J., Schiefler, G.L., Jacques, V.L.R., Carbone, D., Chrastina, D., Isella, G., Spolenak, R., Stangl, J., Sigg, H., and Diaz, A.: Scanning X-ray strain microscopy of inhomogeneously strained Ge micro-bridges. J. Synchrotron Radiat. 21, 111118 (2014).
45. Robach, O., Micha, J.S., Ulrich, O., Geaymond, O., Sicardy, O., Härtwig, J., and Rieutord, F.: A tunable multicolour rainbow’ filter for improved stress and dislocation density field mapping in polycrystals using X-ray Laue microdiffraction. Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 69, 164170 (2013).
46. Tardif, S., Gassenq, A., Guilloy, K., Pauc, N., Dias, G.O., Hartmann, J-M., Widiez, J., Zabel, T., Marin, E., Sigg, H., Faist, J., Chelnokov, A., Reboud, V., Calvo, V., Micha, J.S., Robach, O., and Rieutord, F.: Lattice strain and tilt mapping in stressed Ge microstructures using X-ray Laue micro-diffraction and rainbow-filtering. J. Appl. Crystallogr. 49, 5 (2016).
47. Okada, Y. and Tokumaru, Y.: Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K. J. Appl. Phys. 56, 314 (1984).
48. Cannon, D.D., Liu, J., Ishikawa, Y., Wada, K., Danielson, D.T., Jongthammanurak, S., Michel, J., and Kimerling, L.C.: Tensile strained epitaxial Ge films on Si(100) substrates with potential application in L-band telecommunications. Appl. Phys. Lett. 84, 906908 (2004).
49. Singh, H.P.: Determination of thermal expansion of germanium, rhodium and iridium by X-rays. Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 24, 469 (1968).
50. Geiger, R., Zabel, T., Marin, E., Gassenq, A., Hartmann, J-M., Widiez, J., Escalante, J., Guilloy, K., Pauc, N., Rouchon, D., Dias, G.O., Tardif, S., Rieutord, F., Duchemin, I., Niquet, Y.M., Reboud, V., Calvo, V., Chelnokov, A., Faist, J., and Sigg, H.: Uniaxially stressed germanium with fundamental direct band gap. arXiv 1603.03454v1 (2015).
51. Ruoff, A.L.: On the ultimate yield strength of solids. J. Appl. Phys. 49, 197 (1978).
52. Ngo, L.T., Almécija, D., Sader, J.E., Daly, B., Petkov, N., Holmes, J.D., Erts, D., and Boland, J.J.: Ultimate-strength germanium nanowires. Nano Lett. 6, 29642968 (2006).
53. Griffith, A.A.: The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. London, Ser. A 221, 163198 (1921).
54. Weibull, W.: A Statistical Theory of the Strength of Materials, Vol. 151 (Generalstabens Litografiska Anstalts Förlag, Stockholm, 1939).
55. Weibull, W.: A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293297 (1951).
56. Afferrante, L., Ciavarella, M., and Valenza, E.: Is Weibull’s modulus really a material constant? Example case with interacting collinear cracks. Int. J. Solids Struct. 43, 51475157 (2006).
57. Wortman, J.J. and Evans, R.A.: Young’s modulus, shear modulus, and Poisson’s ratio in silicon and germanium. J. Appl. Phys. 36, 153 (1965).
58. Jaccodine, R.J.: Surface energy of germanium and silicon. J. Electrochem. Soc. 110, 524527 (1963).
59. Bonzon, C.: Phase and Mode Control of Structured Semiconductor Lasers (ETH-Zürich, Zurich, 2016).
60. Petykiewicz, J., Nam, D., Sukhdeo, D.S., Gupta, S., Buckley, S., Piggot, A.Y., Vuckovic, J., and Saraswat, K.C.: Direct bandgap light emission from strained germanium nanowires coupled with high-Q nanophotonic cavities. Nano Lett. 16, 21682173 (2016).
61. Tsai, E., Diaz, A., Menzel, A., and Guizar, M.: X-ray ptychography using a distant analyzer. Opt. Express 24, 64416450 (2016).
62. Euaruksakul, C., Li, Z.W., Zheng, F., Himpsel, F.J., Ritz, C.S., Tanto, B., Savage, D.E., Liu, X.S., and Lagally, M.G.: Influence of strain on the conduction band structure of strained silicon nanomembranes. Phys. Rev. Lett. 101, 147403 (2008).
63. Cloetens, P., Barrett, R., Baruchel, J., Guigay, J-P., and Schlenker, M.: Phase objects in synchrotron radiation hard x-ray imaging. J. Phys. D: Appl. Phys. 29, 133146 (1996).
64. Luong, G.V., Knoll, L., Blaeser, S., Süess, M.J., Sigg, H., Schäfer, A., Trellenkamp, S., Bourdelle, K.K., Buca, D., Zhao, Q.T., and Mantl, S.: Demonstration of higher electron mobility in Si nanowire MOSFETs by increasing the strain beyond 1.3%. Solid State Electrochem. 108, 1923 (2015).
65. Schmidt, M., Süess, M.J., Barros, A.D., Geiger, R., Sigg, H., Spolenak, R., and Minamisawa, R.A.: A patterning-based strain engineering for sub-22 nm node FinFETs. IEEE Electron Device Lett. 35, 300302 (2014).



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