When Vapor Deforms Metal: Thermodynamics of Deposition Flux Dependent Intrinsic Film Stress M.J. Rost Kamerlingh Onnes Laboratory, Leiden University (NL) Rost@physics.leidenuniv.nl www.physics.leidenuniv.nl/rost Stress Evolution during Film Growth: CTC! stress x thickness Deposition OFF Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 Stress Evolution during Film Growth: CTC! Capillary Forces Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 nucleation & 3D island growth (Volmer-Weber Growth)
Stress Evolution during Film Growth: CTC! Boundary Zipping Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 coalescence & grain boundary formation Stress Evolution during Film Growth: CTC! Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 film growth Further Surprise: Reversible Stress Jumps deposition interrupts Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 film growth
Deposition Interrupt: Tensile Relaxation Deposition OFF deposition interrupts Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 deposition interrupt Deposition Resumption: Jump to Initial Stress State deposition interrupts Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 deposition resumption Why is this happening? pre-coalescence surface tension continuation combined with ongoing grain growth 3
Boundary Adatom Insertion Model: Increase of ace Chemical Potential Diffusion of Atoms into Boundaries (GBs) Deposition OFF ON Development of Compressive Stress in s Boundary Adatom Insertion Model: Decrease of ace Chemical Potential (atoms incorporate at steps and kinks) Deposition OFF Atoms Diffuse out of Boundaries Relaxation of Compressive Stress Can this be true??? Can this be True: Values? ~ 50 MPa ~ 0. ML/s Aim: testing the GB insertion model thermodynamically deposition interrupts Shull & Spaepen, J. Appl. Phys. 80 (996 ) 643 deposition resumption 4
Thermodynamic Equilibrium GB GB GB Thermodynamic Equilibrium GB GB GB deposition interrupts Chemical Potential of the ace O,,,... O,,,... surface adatoms step adatoms kinks steps surface adatoms step adatoms kinks steps 5
Chemical Potential of the ace O,,,... O,,,... surface adatoms step adatoms kinks steps surface adatoms step adatoms kinks steps s N TV, N N N μ due to Adatoms Fs Uadatom Uinter S T q: Coverage Adatom Lattice Model Ad. Latt. Ead ktln Ignoring Interactions between Adatoms D Adatom Gas Model DAG Ead kt ln Aad h thermal de Broglie wavelength mkt μ due to Adatoms Difference in absolute value of entropy Same slope for q < 0.ML Important: interest in Dμ For q < 0.ML: adadtom kt ln Eq. Ad Ead kt. Latt. ln Ead kt ln Aad DAG 6
adadtom kt ln Eq. distribution of during growth? Island Nucleation Kinetic Monte Carlo Simulation of Film Growth: with courtesy of Vladimir Kaganer, Paul-Drude-Institut für Festkörperelektronik (see also https://www.youtube.com/watch?v=nsgrksv8yh8) Step Flow Growth 7
Step Flow Growth Kinetic Monte Carlo Simulation of Film Growth: with courtesy of Vladimir Kaganer, Paul-Drude-Institut für Festkörperelektronik (see also https://www.youtube.com/watch?v=nsgrksv8yh8) Adatom Density on a Terrace E att E form E diff E ES energy landscape θ n Fˆ adatom density 0 V s ν d ν e n N Adatom Density on a Terrace n n n ˆ d V s en F t n n diffusion step movement evaporation deposition flux Simplifications: room temperature: e 0 for typical deposition situations: Vs 0 θ n adatom density 0 E att E form V s Fˆ ν d N E diff ν e E ES energy landscape n 8
Definitions: Result: exp E / kt eq form s s0 exp EES / kt Adatom Density on a Terrace FN ˆ ( an)( sn) Fn ˆ n eq d asn a s d Cu(): 0 Hz E ev 0 0.040 diff s0 5 EES 0.4eV Eatt 0eV E 0.74eV form exp d 0 Ediff kt aexp E / kt att Eq. experimentally determined θ n adatom density 0 E att E form V s Fˆ ν d N E diff ν e E ES energy landscape n adadtom kt ln FN ˆ ( an)( sn) Fn ˆ n eq d asn a s d Eq. Eq. chemical potential of a grain under stress? Wt grain E 0 grain Chemical Potential of Interior stress-strain relation Fgrain W t lim N N t0 TV,, Nt 0 t t ( ) 0 A dl W E lim lim t t grain t0 N t0 t L0 E E grain lim tlim t t0 L t0 0 L0 t L 0 σ Gr σ Gr+ dσ σ Gr+ dσ Eq. 3 grain 9
Chemical Potential of Interior Eq. 3 grain L 0 σ Gr σ Gr+ dσ t σ Gr+ dσ R. Sandström, J. Hallgren, J. Nuc. Mater. 4 (0) 5 adadtom kt ln FN ˆ ( an)( sn) Fn ˆ n eq d asn a s d Eq. Eq. Eq. 3 grain Combining the Equations kt ln ˆ ˆ FN( an )( sn ) Fn n eq asn a s d kt FN ˆ ( an )( sn ) Fn ˆ comp ln asn a s d eq d eq which terrace position n? d 0
ace Equilibrium Structure Phys.Rev.Lett. 9 (003) 060 from 5 0 C to 75 0 C in 394 min. [film coarsening] ace Equilibrium Structure Phys.Rev.Lett. 9 (003) 060 surface in equilibrium grains with convex shape
Ehrlich-Schwoebel barrier / Step Flow 9 9 9 7 7 7 5 5 5 3 3 3 0 0 0 30 40 50 60 70 0 0 0 30 40 50 60 70 0 0 0 30 40 50 60 70 9 9 9 7 7 7 5 5 5 3 3 3 0 0 0 30 40 50 60 70 0 0 0 30 40 50 60 70 0 0 0 30 40 50 60 70 Zeno Effect Phys.Rev.Lett. 99 (007) 660 the last terrace position counts kt FN ˆ ( an )( sn ) Fn ˆ comp ln asn a s d eq d eq n N calculate for different widths N θ n adatom density 0 E att E form V s Fˆ ν d E diff ν e E ES energy landscape n N Boundary
the result the result downward funneling M.Giesen, G. Schulze Icking-Konert, H.Ibach, Phys.Rev.Lett. 8 (999) 30 3
downward funneling DE ES =0 for N 6 M.Giesen & H.Ibach,.Sci. 464 (000) L697 funneling in the vicinity of grain boundaries lowering the barrier for atoms to diffuse towards/into the GB, decreases the stress N kt ln eq DE ES =0.4eV Boundary DE ES =0eV the final result best fit: w eff =5 only last 3 terraces show funneling 4
Roughening instead of Step Flow Growth Kinetic Monte Carlo Simulation of Film Growth: with courtesy of Vladimir Kaganer, Paul-Drude-Institut für Festkörperelektronik (see also https://www.youtube.com/watch?v=nsgrksv8yh8) Roughening instead of Step Flow Growth Summary A.Saedi & M.J. Rost, Nature Communication 06 huge stress entropic effect ~ 50 MPa ~ 0. ML/s 5