Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T08:45:11.398Z Has data issue: false hasContentIssue false

Deformation and fracture of single-crystal silicon theta-like specimens

Published online by Cambridge University Press:  11 October 2011

Michael S. Gaither*
Affiliation:
Nanomechanical Properties Group, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Frank W. DelRio
Affiliation:
Nanomechanical Properties Group, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Richard S. Gates
Affiliation:
Nanomechanical Properties Group, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Robert F. Cook
Affiliation:
Nanomechanical Properties Group, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Single-crystal silicon test specimens, fabricated by lithography and deep reactive ion etching (DRIE), were used to measure microscale deformation and fracture properties. The mechanical properties of two specimen geometries, both in the form of a Greek letter Θ (theta), were measured using an instrumented indentation system. The DRIE process generated two different surface structures leading to two strength distributions that were specimen geometry independent: One distribution, centered about 2.1 GPa, was controlled by 35 nm surface roughness of scallops; the second distribution, centered about 1.4 GPa, was controlled by larger, 150 nm, pitting defects. Finite element analyses (FEA) converted measured loads into strengths; tensile elastic measurements validated the FEA. Fractographic observations verified failure locations. The theta specimen and testing protocols are shown to be extremely effective at testing statistically relevant (hundreds) numbers of samples to establish processing–structure–property relationships at ultrasmall scales and for determining design parameters for components of microelectromechanical systems.

Type
Invited Feature Paper
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Gambino, J.P. and Colgan, E.G.: Silicides and ohmic contacts. Mater. Chem. Phys. 52, 99 (1998).CrossRefGoogle Scholar
2.Kim, H.: Atomic layer deposition of metal and nitride thin films: Current research efforts and applications for semiconductor device processing. J. Vac. Sci. Technol. B. 21, 2231 (2003).CrossRefGoogle Scholar
3.Wallace, R.M. and Wilk, G.D.: High-κ dielectric materials for microelectronics. Crit. Rev. Solid State Mater. Sci. 28, 231 (2003).CrossRefGoogle Scholar
4.Spearing, S.M.: Materials issues in microelectromechanical systems (MEMS). Acta Mater. 48, 179 (2000).CrossRefGoogle Scholar
5.Madou, M.J.: Fundamentals of Microfabrication: The Science of Miniaturization, 2nd ed. (CRC Press, Boca Raton, FL, 2002).Google Scholar
6.Soref, R.A.: Silicon-based optoelectronics. Proc. IEEE 81, 1687 (1993).CrossRefGoogle Scholar
7.Yan, R., Gargas, D., and Yang, P.: Nanowire photonics. Nat. Photonics 3, 569 (2009).CrossRefGoogle Scholar
8.Fan, T-X., Chow, S-K., and Zhang, D.: Biomorphic mineralization: From biology to materials. Prog. Mater. Sci. 54, 542 (2009).CrossRefGoogle Scholar
9.Parkin, S., Jiang, X., Kaiser, C., Panchula, A., Roche, K., and Samant, M.: Magnetically engineered spintronic sensors and memory. Proc. IEEE 91, 661 (2003).CrossRefGoogle Scholar
10.Slaughter, J.M.: Materials for magnetoresistive random-access memory. Annu. Rev. Mater. Res. 39, 277 (2009).CrossRefGoogle Scholar
11.Gulyaev, Y.V., Kalinkin, A.N., Mityagin, A.Y., and Khlopov, B.V.: Advanced inorganic materials for hard magnetic media. Inorg. Mater. 46, 1403 (2010).CrossRefGoogle Scholar
12.van Spengen, W.M.: MEMS reliability from a failure mechanisms perspective. Microelectron. Reliab. 43, 1049 (2003).CrossRefGoogle Scholar
13.Lord, J.D., Roebuck, B., Morrell, R., and Lube, T.: Aspects of strain and strength measurement in miniaturized testing for engineering metals and ceramics. Mater. Sci. Technol. 26, 127 (2010).CrossRefGoogle Scholar
14.Durelli, A.J., Morse, S., and Parks, V.: The theta specimen for determining tensile strength of brittle materials. Mater. Res. Standards 2, 114 (1962).Google Scholar
15.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
16.Field, J.S. and Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
17.Field, J.S. and Swain, M.V.: Determining the mechanical properties of small volumes of material from submicrometer spherical indentations. J. Mater. Res. 10, 101 (1995).CrossRefGoogle Scholar
18.Mencik, J., Munz, D., Quandt, E., Weppelmann, E.R., and Swain, M.V.: Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12, 2475 (1997).CrossRefGoogle Scholar
19.Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).CrossRefGoogle Scholar
20.Oyen, M.L. and Cook, R.F.: A practical guide for analysis of nanoindentation data. J. Mech. Behav. Biomed. Mater. 2, 396 (2009).CrossRefGoogle ScholarPubMed
21.Anstis, G.R., Chantikul, P., Lawn, B.R., and Marshall, D.B.: A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurements. J. Am. Ceram. Soc. 64, 533 (1981).CrossRefGoogle Scholar
22.Cook, R.F. and Pharr, G.M.: Direct observation and analysis of indentation cracking in glasses and ceramics. J. Am. Ceram. Soc. 73, 787 (1990).CrossRefGoogle Scholar
23.Bradby, J.E., Williams, J.S., Wong-Leung, J., Swain, M.V., and Munroe, P.: Mechanical deformation in silicon by micro-indentation. J. Mater. Res. 19, 3 (2004).Google Scholar
24.Cook, R.F.: Strength and sharp contact fracture of silicon. J. Mater. Sci. 41, 841 (2006).CrossRefGoogle Scholar
25.Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A.M., and Shen, Y-L.: Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater. 55, 4015 (2007).CrossRefGoogle Scholar
26.Chantikul, P., Anstis, G.R., Lawn, B.R., and Marshall, D.B.: A critical evaluation of indentation techniques for measuring fracture toughness: II, strength method. J. Am. Ceram. Soc. 64, 539 (1981).CrossRefGoogle Scholar
27.Quinn, G.D., Fuller, E., Xiang, D., Jillavenkatesa, A., Ma, L., Smith, D., and Beall, J.: A novel test method for measuring mechanical properties at the small-scale: The theta specimen, in Mechanical Properties and Performance of Engineering Ceramics and Composites, edited by Lara-Curzio, E. (Cer. Eng. Sci. Proc. 26, Westerville, OH, 2005), p. 117.Google Scholar
28.Fuller, E.R. Jr., Henann, D.L., and Ma, L.: Theta-like specimens for measuring mechanical properties at the small-scale: Effects of non-ideal loading. Int. J. Mater. Res. 98, 729 (2007).CrossRefGoogle Scholar
29.Gaither, M.S., DelRio, F.W., Gates, R.S., Fuller, E.R. Jr., and Cook, R.F.: Strength distribution of single-crystal silicon theta-like specimens. Scr. Mater. 63, 422 (2010).CrossRefGoogle Scholar
30.Durelli, A.J. and Parks, V.: Relationship of size and stress gradient to brittle failure stress, in Proceedings of the Fourth U.S. National Congress of Applied Mechanics: Volume Two, edited by Rosenberg, R.M. (The American Society of Mechanical Engineers, New York, 1962), p. 931.Google Scholar
31.Durelli, A.J.: Applied Stress Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1967), pp. 173, 178.Google Scholar
32.Eisner, R.L.: Tensile tests on silicon whiskers. Acta Metall. 3, 414 (1955).CrossRefGoogle Scholar
33.Pearson, G.L., Read, W.T. Jr., and Feldman, W.L.: Deformation and fracture of small silicon crystals. Acta Metall. 5, 181 (1957).CrossRefGoogle Scholar
34.Sylwestrowicz, W.D.: Mechanical properties of single crystals of silicon. Philos. Mag. 7, 1825 (1962).CrossRefGoogle Scholar
35.Hu, S.M.: Critical stress in silicon brittle fracture, and effect of ion implantation and other surface treatments. J. Appl. Phys. 53, 3576 (1982).CrossRefGoogle Scholar
36.McLaughlin, J.C. and Willoughby, A.F.W.: Fracture of silicon wafers. J. Cryst. Growth 85, 83 (1987).CrossRefGoogle Scholar
37.Johansson, S., Schweitz, J-A., Tenerz, L., and Tiren, J.: Fracture testing of silicon microelements in situ in a scanning electron microscope. J. Appl. Phys. 63, 4799 (1988).CrossRefGoogle Scholar
38.Ericson, F. and Schweitz, J-A.: Micromechanical fracture strength of silicon. J. Appl. Phys. 68, 5840 (1990).CrossRefGoogle Scholar
39.Vedde, J. and Gravesen, P.: The fracture strength of nitrogen doped silicon wafers. Mater. Sci. Eng., B 36, 246 (1996).CrossRefGoogle Scholar
40.Wilson, C.J. and Beck, P.A.: Fracture testing of bulk silicon microcantilever beams subjected to a side load. J. Microelectromech. Syst. 5, 142 (1996).CrossRefGoogle Scholar
41.Wilson, C.J., Ormeggi, A., and Narbutovskih, M.: Fracture testing of silicon microcantilever beams. J. Appl. Phys. 79, 2386 (1996).CrossRefGoogle Scholar
42.Schweitz, J-A. and Ericson, F.: Evaluation of mechanical materials properties by means of surface micromachined structures. Sens. Actuators 74, 126 (1999).CrossRefGoogle Scholar
43.Suwito, W., Dunn, M.L., Cunningham, S.J., and Read, D.T.: Elastic moduli, strength, and fracture initiation at sharp notches in etched single crystal silicon microstructures. J. Appl. Phys. 85, 3519 (1999).CrossRefGoogle Scholar
44.Chen, K-S., Ayon, A., and Spearing, S.M.: Controlling and testing the fracture strength of silicon on the mesoscale. J. Am. Ceram. Soc. 83, 1476 (2000).CrossRefGoogle Scholar
45.Namazu, T., Isono, Y., and Tanaka, T.: Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM. J. Microelectromech. Syst. 9, 450 (2000).CrossRefGoogle Scholar
46.Yi, T., Li, L., and Kim, C-J.: Microscale material testing of single crystalline silicon: Process effects on surface morphology and tensile strength. Sens. Actuators 83, 172 (2000).CrossRefGoogle Scholar
47.Chen, K-S., Ayon, A.A., Zhang, X., and Spearing, S.M.: Effect of process parameters on the surface morphology and mechanical performance of silicon structures after deep reactive ion etching (DRIE). J. Microelectromech. Syst. 11, 264 (2002).CrossRefGoogle Scholar
48.Sundararajan, S., Bhushan, B., Namazu, T., and Isono, Y.: Mechanical property measurements of nanoscale structures using an atomic force microscope. Ultramicroscopy 91, 111 (2002).CrossRefGoogle ScholarPubMed
49.Jeong, S-M., Park, S-E., Oh, H-S., and Lee, H-L.: Evaluation of damage on silicon wafers using the angle lapping method and a biaxial fracture strength test. J. Cer. Processing Res. 5, 171 (2004).Google Scholar
50.Tsuchiya, T., Hirata, M., Chiba, N., Udo, R., Yoshitomi, Y., Ando, T., Sato, K., Takashima, K., Higo, Y., Saotome, Y., Ogawa, H., and Ozaki, K.: Cross comparison of thin-film tensile-testing methods examined single-crystal silicon, polysilicon, nickel, and titanium films. J. Microelectromech. Syst. 14, 1178 (2005).CrossRefGoogle Scholar
51.Hoffmann, S., Utke, I., Moser, B., Michler, J., Christiansen, S.H., Schmidt, V., Senz, S., Werner, P., Gosele, U., and Ballif, C.: Measurement of the bending strength of vapor-liquid-solid grown silicon nanowires. Nano Lett. 6, 622 (2006).CrossRefGoogle ScholarPubMed
52.Isono, Y., Namazu, T., and Terayama, N.: Development of AFM tensile test technique for evaluating mechanical properties of sub-micron thick DLC films. J. Microelectromech. Syst. 15, 169 (2006).CrossRefGoogle Scholar
53.Nakao, S., Ando, T., Shikida, M., and Sato, K.: Mechanical properties of a micron-sized SCS film in a high-temperature environment. J. Micromech. Microeng. 16, 715 (2006).CrossRefGoogle Scholar
54.Miller, D.C., Boyce, B.L., Dugger, M.T., Buchheit, T.E., and Gall, K.: Characteristics of a commercially available silicon-on-insulator MEMS materials. Sens. Actuators, A 138, 130 (2007).CrossRefGoogle Scholar
55.Zhu, Y., Xu, F., Qin, Q., Fung, W.Y., and Lu, W.: Mechanical properties of vapor-liquid-solid synthesized silicon nanowires. Nano Lett. 9, 3934 (2009).CrossRefGoogle ScholarPubMed
56.Banks-Sills, L., Shklovsky, J., Krylov, S., Bruck, H.A., Fourman, V., Eliasi, R., and Ashkenazi, D.: A methodology for accurately measuring mechanical properties on the micro-scale. Strain 47, 288 (2011).CrossRefGoogle Scholar
57.Ashby, M.F.: Materials Selection in Mechanical Design, 2nd ed. (Pergamon Press, Oxford, 1999).Google Scholar
58.Davidge, R.W.: Mechanical Behaviour of Ceramics (Cambridge University Press, Cambridge, 1979).Google Scholar
59.Quinn, G.D.: Fractographic analysis of very small theta specimens, in Fractography of Advanced Ceramics III, edited by Dusza, J., Danzer, R., Morrell, R., and Quinn, G.D. (Key Engineering Materials 409, Stafa-Zurich, Switzerland, 2009), p. 201.Google Scholar
60.Lawn, B.: Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, Cambridge, 1993).CrossRefGoogle Scholar
61.Senturia, S.D.: Microsystem Design (Kluwer Academic Publishers, Boston, 2001).CrossRefGoogle Scholar
62.Levengood, W.C.: Effect of origin flaw characteristics on glass strength. J. Appl. Phys. 29, 820 (1958).CrossRefGoogle Scholar
63.Johnson, J.W. and Holloway, D.G.: On the shape and size of the fracture zones on glass fracture surfaces. Philos. Mag. 14, 731 (1966).CrossRefGoogle Scholar
64.Quinn, G.D.: Fractography of Ceramics and Glasses (National Institute of Standards and Technology, Washington, DC, 2007).Google Scholar
65.Tsai, Y.L. and Mecholsky, J.J. Jr.: Fractal fracture of single crystal silicon. J. Mater. Res. 6, 1248 (1991).CrossRefGoogle Scholar
66.McSkimin, H.J. and Andreatch, P. Jr.: Measurement of third-order moduli of silicon and germanium. J. Appl. Phys. 35, 3312 (1964).CrossRefGoogle Scholar
67.Holm, B., Ahuja, R., Yourdshahyan, Y., Johansson, B., and Lundqvist, B.I.: Elastic and optical properties of α- and κ-Al2O3. Phys. Rev. B. 59, 12777 (1999).CrossRefGoogle Scholar
68.Brantley, W.A.: Calculated elastic constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44, 534 (1973).CrossRefGoogle Scholar
69.Yamamoto, Y., Sumi, Y., and Ao, K.: Stress intensity factors of cracks emanating from semi-elliptical side notches in plates. Int. J. Fract. 10, 593 (1974).CrossRefGoogle Scholar
70.Bagdahn, J., Sharpe, W.N. Jr., and Jadaan, O.: Fracture strength of polysilicon at stress concentrators. J. Microelectromech. Syst. 12, 302 (2003).CrossRefGoogle Scholar
71.Boyce, B.L., Grazier, J.M., Buchheit, T.E., and Shaw, M.J.: Strength distributions in polycrystalline silicon MEMS. J. Microelectromech. Syst. 16, 179 (2007).CrossRefGoogle Scholar
72.Boyce, B.L.: A sequential tensile method for rapid characterization of extreme-value behavior in microfabricated materials. Exp. Mech. 50, 993 (2010).CrossRefGoogle Scholar
73.Hazra, S.S., Baker, M.S., Beuth, J.L., and de Boer, M.P.: Demonstration of an in situ on-chip tensile tester. J. Micromech. Microeng. 19, 1 (2009).CrossRefGoogle Scholar
74.Hazra, S.S., Baker, M.S., Beuth, J.L., and de Boer, M.P.: Compact on-chip microtensile tester with prehensile grip mechanism. J. Microelectromech. Syst. 20, 1043 (2011).CrossRefGoogle Scholar
75.Greer, J.R. and Nix, W.D.: Size dependence of mechanical properties of gold at the sub-micron scale. Appl. Phys. A 80, 1625 (2005).CrossRefGoogle Scholar
76.Pecholt, B. and Molian, P.: Nanoindentation of laser machined 3C-SiC thin film micro-cantilevers. Mater. Des. 32, 3414 (2011).CrossRefGoogle Scholar