Co-Evolution of Stress and Structure During Growth of Polycrystalline Thin Films Carl V. Thompson and Hang Z. Yu* Dept. of Materials Science and Engineering MIT, Cambridge, MA, USA Effects of intrinsic stress and applications (e.g. in MEMs) Focus on evaporative deposition; categories of observed behavior Mechanisms affecting stress evolution - coalescence - adatom trapping - grain growth Generalizations in the form of mechanism maps * Current address: Virginia Tech
Structure Evolution During Deposition of Polycrystalline Thin Films film thickness at coalescence ~1 to a few nm (C.V. Thompson, Ann. Rev. Mat. Sci. 2000)
Microelectromechanical Accelerometers and Gyroscopes are Ubiquitous
Basic Process for Microelectromechanical Devices W. Tang DARPA deposited, patterned and released polycrystalline films
Polycrystalline Silicon Accelerometer Microsystem Design; S.D. Senturia, Kluwer, Norwell MA, USA (2001).
Polycrystalline Silicon Gyroscope
Effects of Residual Stress in MEMS Device Elements micromachined cantilever: e.g. for a voltage actuated mechanical switch micromachined doubly supported beam: e.g. for a voltage actuated mechanical switch
Effects of Residual Stress in MEMS Device Elements cantilever: minor residual stress gradients in the films can cause upward or downward curvature when the beam is released, increasing or decreasing the pull-in voltage, or making device non-functional. doubly supported beam: residual tensile stress in the films leads to an increased stiffness of the beam to be high and increase the pull-in voltage
Effects of Residual Stress in MEMS Device Elements cantilever: minor residual stress gradients in the films can cause upward or downward curvature when the beam is released, increasing or decreasing the pull-in voltage, or making device non-functional. doubly supported beam: residual compressive stress in the films can cause the beam to buckle, and make the device non-functional
Polycrystalline Silicon Accelerometer (Novasensor)
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)
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) dominated by intrinsic stress (From Ohring, after Hoffman)
In-situ Real-Time Intrinsic Stress Monitoring evaporative deposition UHV e-beam deposition system with load-lock, LEED, and stress sensor. Deposit on cantilever. Measure cantilever deflection. Measure capacitance change to monitor tip-displacement Sensitivity: <1ML equivalent at 100Hz
Stoney s Equation: Instantaneous Stress 6 = instantaneous surface stress units stress-thickness or force per width = average stress in the film = film thickness = thickness of the beam = biaxial modulus of the beam
Stress Evolution in Polycrystalline Films via Evaporative Deposition ~1 GPa tensile instantaneous stress e.g. Ti, W, Cr e.g. Au, Ag, Cu after R. Abermann, Vacuum 41, 1279 (1990).
Structure Evolution During Deposition of Polycrystalline Thin Films (C.V. Thompson, Ann. Rev. Mat. Sci. 2000)
Stress and Structure Co-Evolution During Film Deposition Completion of coalescence Type I tensile average stress (GPa) Type II compressive Beginning of coalescence
Aluminum Deposited on Oxidized Silicon stress-thickness (N/m) 0.5 0-0.5-1.0-1.5 25 o C 0.2 nm/sec Al Data collected by J.A. Floro and S.J. Hearne Sandia National Laboratory J. A. Floro, S. J. Hearne, J. A. Hunter, and P. Kotula, E. Chason, S. C. Seel and C. V. Thompson, J. Appl. Phys. 89, 4886 (2001). 0 10 20 30 film thickness (nm) etalon 25 A 40 A 55 A 2.5 nm 4.0 nm 5.5 nm 1000 nm Å
Tensile Stress Generation Due to Island Coalescence Surface Energy s Grain Boundary Energy gb 2 s gb r E 1 1 / 2 W.D. Nix and B.M. Clemens, J. Mater. Res. 14, 3467 (1999).
Comparison of Models for Coalescence Stress Coalescence of Ag islands with 90 0 contact angle with substrate Average stress (GPa) 10 1 0.1 Freund- Chason Nix-Clemens FEM* Modified Nix-Clemens Finite Element Model: (Coalescing half-cylinders) 1 10 100 Island radius (nm) Modified Nix-Clemens: 1 E (2 s gb) 9(1 2) r 1 2 Freund-Chason: 2(2 s gb r ) W.D. Nix and B.M. Clemens, J. Mater. Res. 14, 3467 (1999). Modified N-C: S.C. Seel Ph.D. Thesis, MIT (2002) L.B. Freund and E. Chason, J. Appl. Phys. 89, 4866 (2001). FEM: S.C. Seel, C.V. Thompson, S.J. Hearne and J.A. Floro, J. Appl. Phys 88, 7079-7086 (2000).
Stress and Structure Co-Evolution During Film Deposition Completion of coalescence Type I tensile average stress (GPa) Type II compressive Beginning of coalescence
Data from in-situ Stress Measurements (stress-thickness) Type i: e.g. Pt 300K Type II: e.g. Au 300K Hang Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
The Origin of The Compressive Stress Type II Behavior Trapping of excess adatoms in grain boundaries during deposition W. D. Nix, and B. M. Clemens, J. Mater. Res. 14, 3467 (1999) E. Chason, B.W. Sheldon, and L. B. Freund, J. A. Floro and S. J. Hearne, PRL 88, 156103 (2002). Chason et al: Deposition flux affects adatom population and excess chemical potential. The jump from surface sites into the grain boundary sites is thermally activated.
Data From in-situ Stress Measurements (stress-thickness) Type i: e.g. Pt 300K Type II: e.g. Au 300K H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Intermediate Stress Behavior effect of substrate temperature (stress-thickness) H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
stress-thickness = surface stress = force/width (N/m) Intermediate Stress Behavior effect of deposition rate Ni deposited at 473K H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
What Causes the Stress Turnaround in Intermediate Behavior tensile compressive tensile coalescence stress trapping of excess atoms? film thickening grain growth during deposition
Grain Growth During Film Deposition Ni Ni: T =300K T homologous = 0.17 grain growth occurs at low homologous temperatures in nanocrystalline materials H.Z. Yu, J.S. Leib, S.T. Boles, and C.V. Thompson, J. Appl. Phys. 115, 043251 (2014).
Grain Growth Stress Grain boundaries have excess free volume Grain growth in unconstrained films would lead to densification In films attached to substrates, without sliding, grain growth leads to a tensile stress 1 1 = biaxial modulus = the excess volume per boundary area (~0.1nm) = the initial grain size = the final grain size P. Chaudhari, IBM J. Res. Dev. 197 (1969) C. V. Thompson, and R. Carel, J. Mech. Phys. Solids 44, 657 (1996).
Au films 2 : Stress Evolution During Growth Interruptions A fast process leads to reversible stress evolution during grain growth 1 The fast process is related to surface phenomena (not thickness dependent) 2,3 A slow process leads to irreversible stress 2 The slow process involves a bulk phenomenon (film thickness dependent) 2 (1) A. L. Shull and F. Spaepen, J. Appl. Phys. 80(11), 6243 6256 (1996). (2) H.Z. Yu, J.S. Leib, S.T. Boles, and C.V. Thompson, J. Appl. Phys. 115, 043251 (2014). (3) H.Z. Yu and C.V. Thompson, Appl. Phys. Letts. 104, 141913 (2014).
Grain Growth After Deposition 0.5hrs 10hrs 26hrs 45nm Au 300K H.Z. Yu, J.S. Leib, S.T. Boles, and C.V. Thompson, J. Appl. Phys. 115, 043251 (2014).
Influence of Grain Growth on Stress During Deposition on the Instantaneous Stress During a very small period of time, the bulk stress increases 1 1 Δ The measured force per unit width increases The instantaneous stress is: Δ Δ Δ Δ empirically: so: H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Grain Growth Stress During Deposition of Nanocrystalline Films The grain size at coalescence ~ 1nm Grain growth during film thickening leads yielding Modified expression for instantaneous stress accounting for yielding: Δ 1 1
Three Mechanisms for Stress Evolution coalescence stress: tensile 1 grain growth during deposition: tensile 1 (very approximately) post-coalescence adatom trapping: compressive Chason Model 1
Modification of Chason Model Assume that only adatoms within a diffusion distance can be trapped in the grain boundaries is limited by the steady state ledge spacing, affected by ledge nucleation rate on terraces / D SD = surface diffusivity R = deposition rate = lattice parameter d < 2 collection area is the total area and is fixed 1 d > 2 collection area scales with d independent of d H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Post-Coalescence Stress Transition with Increasing Thickness/Grain Size Δ 1 1 d > 2 tensile d < 2 compressive H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Compressive Component of the Intrinsic Stress ~ dashed line d = 2 Stress measurements with stress due to grain growth removed (based on characterization of post deposition grain growth) H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Activation Energy for Adatom diffusion (200) (111) / 0.035 6 0.21 / 6 The activation energy for adatom diffusion on (111) textured Ni surfaces is 0.21eV. H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Stress Evolution Model both T and R dependencies are captured H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Explanations for Type I and Type II Behavior Type I: Epitaxial inheritance of tensile coalescence stress (no grain growth or trapping) Type II: Turnaround at very large film thickness H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Generalization for fcc Metals H. Yu and C.V. Thompson, Acta Materialia 67, 189 (2014)
Stress Evolution as a Function of Incidence Angle H.Z. Yu and C.V. Thompson, Acta Materialia 77, 284 (2014).
Stress Evolution as a Function of Incidence Angle 115nm Au = 0 o = 60 o roughness H.Z. Yu and C.V. Thompson, Acta Materialia 77, 284 (2014).
Stress Evolution as a Function of Incidence Angle increased shadowing of the gb region reduced compressive component H.Z. Yu and C.V. Thompson, Acta Materialia 77, 284 (2014).
Stress Evolution as a Function of Incidence Angle grain size still scales with film thickness for all s H.Z. Yu and C.V. Thompson, Acta Materialia 77, 284 (2014).
Stress Evolution as a Function of Incidence Angle As tilt angle goes up: Peak tensile thickness goes up (larger coalescence thickness) Less compressive stress H.Z. Yu and C.V. Thompson, Acta Materialia 77, 284 (2014).
Stress Evolution as a Function of Incidence Angle H.Z. Yu and C.V. Thompson, Acta Materialia 77, 284 (2014).
Summary and Conclusions The intrinsic stress in polycrystalline vapor deposited thin films strongly depends on: the deposition technique the film thickness the substrate temperature the deposition rate the deposition angle impurities from the background pressure (not discussed here) In evaporative deposition, stress evolution is affected by three mechanisms coalescence strains (tensile) adatom trapping (compressive) grain growth (tensile) Plasticity plays a critical role in defining the intrinsic stress: due to deformation during coalescence and grain growth.