How To Understand Stress In Thin Film

Transcription

1 Stress Evolution During and After Deposition of Polycrystalline Thin Films Carl V. Thompson, Jeff S. Leib, and Hang Yu Dept. of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA USA A bit about Bill Residual stresses in thin films Stress evolution during growth of polycrystalline films - Coalescence stress - Compressive stress - Reversible stress relaxation

2 Residual Stress in Polycrystalline Thin Films Relevance, for example, in microelectromechanical devices W. Tang - DARPA

3 Effects of Residual Stress on Electrically Actuated Micromachined Beams as Switches Cantilever Doubly Supported Beam

4 Effects of Residual Stress on Electrically Actuated Micromachined Beams as Switches Cantilever A stress gradient causes initial curvature Doubly Supported Beam Compressive stress buckling Tensile stress higher spring constant

5 Polycrystalline Silicon Accelerometer Microsystem Design; S.D. Senturia, Kluwer, Norwell MA, USA (2001).

6 Polysilicon Accelerometer (Novasensor)

7 Residual Stress: Buckling Control in the range of 10 s of MPa is required (Nunan et al, Vacuum Technology and Coating, Jan. 2001, p.27: Analog Devices)

8 Residual Stress in As-Deposited Thin Films Stress in As-Deposited CVD Polysilicon Stress In As-Deposited Sputtered Metallic Films (Hung et al, MRS Symp. Proc. V182, p201, 1990) (From Ohring, after Hoffman)

9 Stress Evolution in Films Deposited via Evaporative Deposition Floro & Chason Measure deflection of cantilever tip Stoney s equation: E ~ h 3E ~ h ) ( s s f f E ~ = biaxial modulus, h =thickness s = substrate, f =film or measure substrate curvature for measured curvature h f f 2 s E ~ sh 6

10 Stress Evolution in Polycrystalline Films via Evaporative Deposition ~1 GPa tensile e.g. Ti, W, Cr e.g. Au, Ag, Cu after R. Abermann, Vacuum 41, 1279 (1990).

11 Behavior Depends on Temperature as well as the Materials average stress (GPa) Low atomic mobility High atomic mobility after R. Abermann, Vacuum 41, 1279 (1990).

12 low atomic mobility => small initial grain size low T dep /T m high T dep /T m low mobility high mobility e.g. Si, Ti, W, Ta, Cr at R.T. e.g. Al, Cu, Au, Ag at R.T. (C.V. Thompson, Ann. Rev. Mat. Sci. 2000)

13 Stress and Structure Co-Evolution During Film Deposition Low mobility Beginning of coalescence High mobility

14 Island Coalescence and Tensile Stress Ag on fused silica S.C. Seel, C.V. Thompson, S.J. Hearne and J.A. Floro, J. Appl. Phys 88, (2000).

15 Stress and Structure Co-Evolution During Film Deposition Completion of coalescence Beginning of coalescence

16 Coalescence Stress The Hoffman Model 2 sv gb E 1 d R.W. Hoffman, Thin Solid Films 34, 185 (1976).

17 Coalescence Stress The Nix and Clemens Model W.D. Nix and B.M. Clemens, Crystallite Coalescence: A Mechanism for Intrinsic Tensile Stresses in Thin Films, J. Mater. Res. 14 (8), (1999).

18 Coalescence Stress The Nix and Clemens Model E 1 2r change in energy after zipping h(2 sv r gb ) E h 1 2r 2 Minimize E to find max and treat as a Griffith crack 1 E 1 1 / 2 2 sv r gb

19 Modified Nix-Clemens: Freund-Chason: Finite Element Model: (Coalescing half-cylinders) 1 E (2 s gb) 9(1 2 ) r 1 2 2(2 s gb r ) W.D. Nix and B.M. Clemens, J. Mater. Res. 14, 3467 (1999). FEM: S.C. Seel, C.V. Thompson, S.J. Hearne and J.A. Floro, J. Appl. Phys 88, (2000). L.B. Freund and E. Chason, J. Appl. Phys. 89, 4866 (2001). Modified N-C: S.C. Seel Ph.D. Thesis, MIT (2002)

20 Direct Comparison with Experiment S. J. Hearne, S. C. Seel, J. A. Floro, C. W. Dyck, W. Fan, and S.R.J. Brueck,, J. of Applied Physics 97, (2005).

21 Stress and Structure Co-Evolution During Film Deposition Completion of coalescence Beginning of coalescence

22 High Mobility vs. Low Mobility Behavior W.D. Nix and B.M. Clemens, J. Mater. Res. 14 (8), (1999).

23 Stress and Structure Co-Evolution During Film Deposition Completion of coalescence Beginning of coalescence

24 Origin of Initial Compressive Stress: Surface Stress Young-Laplace effect: Pressure due surface stress causes a compressive stress when particles are small Gill et al R. Abermann, R. Kramer, and J. Maser, J., 1978, Thin Solid Films 52, 215 (1978). S. P. A. Gill, H. Gao, V. Ramaswamy, and W. D. Nix, J. of Appl. Mech. 69, 425 (2002).

25 Stress and Structure Co-Evolution During Film Deposition Completion of coalescence Beginning of coalescence

26 Origin of Compressive Stress: Young-Laplace Stress? Long term compressive stress arises because the Young-Laplace stress gets locked-in? R.C. Cammarata, T.M. Trimble, and D.J. Srolovitz, J. Mater. Res. 15, 2468 (2000). J. A. Floro, et al, J. Appl. Phys. 89, 4886 (2001).

27 Origin of Compressive Stress: Spaepen Adatoms trapped between coalescing ledges F. Spaepen, Acta Mat. 48, 31 (2000).

28 Origin of Compressive Stress: Chason et al Excess adatoms present during deposition are trapped in grain boundaries during growth. E. Chason, B. W. Sheldon, L. B. Freund, J. A. Floro, and S. J. Hearne, Phys Rev. Lett. 88, (2002).

29 Reversible Stress Relaxation growth interruption J. Leib First seen by Shull and Spaepen, J. Appl. Phys. 80, 6243 (1996).

30 Origin of Reversible Stress: Spaepen Near-surface trapped adatoms are released during a growth interruption F. Spaepen, Acta Mat. 48, 31 (2000).

31 Origin of Compressive Stress: Friesen and Thompson Excess point defects on dynamic surface cause nonequilibrium surface stress C. Friesen and C.V. Thompson, Phys. Rev. Letts. 93, (2004).

32 Origin of Reversible Stress: Chason et al Near-surface excess adatoms diffuse out of grain boundaries E. Chason, B. W. Sheldon, L. B. Freund, J. A. Floro, and S. J. Hearne, Phys Rev. Lett. 88, (2002).

33 Effect of Grain Size on the Reversible Stress Spaepen a surface effect Friesen and Thompson a surface effect Chason et al a grain boundary effect

34 Effect of Grain Size on the Reversible Stress Processes for fixed thickness but different grain sizes + homoepitaxy J. Leib, R. Monig, C.V. Thompson, Phys. Rev. Letters 102, (2009).

35 Effect of Grain Size on the Reversible Stress J. Leib, R. Monig, C.V. Thompson, Phys. Rev. Letters 102, (2009).

36 Effect of Grain Size on the Reversible Stress J. Leib, R. Monig, C.V. Thompson, Phys. Rev. Letters 102, (2009). 1 d

37 Origin of Stress Increase: Koch Recrystallization Occurs During Interruption (in the high mobility case) R. Koch, D. Hu, and A.K. Das, Phys. Rev. Lett. 94, (2005).

38 Grain Growth During Coalescence In situ STM for Ag deposited at room temperature C. Polop et al, New J. Physics 9, 74 (2007).

39 Grain Growth During a Growth Interruption h = 100 nm, 45 min. interrupt h = 100nm, 24 hr. interrupt Au deposited at Room Temperature Leib, MIT PhD thesis

40 Stress and Grain Growth Change of Average stress (MPa) Measured stress Calculated stress based on Bright Field TEM grain size Calculated stress based on Dark Field TEM grain size Time(Hour) Hang Yu, unpublished Grain growth would cause densification without traction at substrate surface a 1 d 1 d 0 E 1 a = excess volume per unit area of grain boundary ~ 0.1nm

41 24 Hour Growth Interruptions Not all the stress is reversible Leib, MIT PhD thesis

42 Long Interrupts vs. Film Thickness Force per Width (N/m) Time (second) 140nm 75nm 45nm 15nm 100nm thick Au at room temperature Two processes: Fast and Slow Effect of slow decreases with decreasing film thickness (grain growth saturation?) (Hang Yu, unpublished)

43 Koch: Multiple Mechanisms R. Koch, D. Hu, and A.K. Das, Phys. Rev. Lett. 95, (2005).

44 Effect of Stress on Relaxation During Growth Interruption Vary initial stress by varying deposition time J. Leib and C.V. Thompson, Phys. Rev. B82, (2010).

45 Effect of Stress on Relaxation During Growth Interruption Change h peak (and 0 ) by varying background pressure Change 0 by varying deposition rate

46 Effect of Stress on Relaxation During Growth Interruption J. Leib and C.V. Thompson, Phys. Rev. B82, (2010).

47 Effect of Stress on Initial Change During Interruption So stress matters, but T does not? J. Leib and C.V. Thompson, Phys. Rev. B82, (2010).

48 Relaxed Stress versus Time and Temperature

49 Summary Diffusion of adatoms to boundaries Grain boundary zipping thickness Young-Laplace effect Young-Laplace? Adatoms trapped - in lattice? - at boundaries? Surface roughening? Recrystallization? Detrapping from - lattice? - grain boundaries?

50 Conclusions Structure and stress evolution are coupled at all stages. The magnitude of the reversible stress depends on the grain size. Grain growth occurs during coalescence and during film growth interruptions in high mobility materials, and affects stress. Multiple mechanisms probably lead to reversible stress phenomenology. One mechanism is fast and one is slow process. - the fast process depends on the grain size and is reversible - the slow process is not reversible and is probably grain growth The initial stress change during an interruption is weakly temperature dependent.

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