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Interface effects on thermophysical properties in nanomaterial systems

Interface effects on thermophysical properties in nanomaterial systems. Patrick E. Hopkins MAE Dept. Seminar March 22, 2007. Moore’s Law. Rocket nozzle 10 7 W/m 2. Nuclear reactor 10 6 W/m 2. hot plate 10 5 W/m 2. Equivalent power density [W/m 2 ]. 45 nm. 100 nm. 500 nm.

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Interface effects on thermophysical properties in nanomaterial systems

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  1. Interface effects on thermophysical properties in nanomaterial systems Patrick E. Hopkins MAE Dept. Seminar March 22, 2007

  2. Moore’s Law Rocket nozzle 107 W/m2 Nuclear reactor 106 W/m2 hot plate 105 W/m2 Equivalent power density [W/m2] 45 nm 100 nm 500 nm Transistor size

  3. Thermal boundary conductance Superlattices Field effect transistors Heat generated Rejected heat Thermal management is highly dependent on the boundary of two materials

  4. Today’s Talk Purpose:Determine the effects that the properties of the interface have on thermal boundary conductance, hBD • Theory of phonon interfacial transport • Measurement of hBD with the TTR technique • Influence of atomic mixing on hBD • Influence of high temperatures (T > qD) on hBD

  5. T Thermal conduction in bulk materials Thermal conduction Microscopic picture L Z l = Mean free path [m] phonon-phonon scattering length in homogeneous material k = thermal conductivity [Wm-1K-1] = thermal flux [Wm-2] What happens if l is on the order of L?

  6. T Z Thermal conduction in nanomaterials Microscopic picture of nanocomposite T Z < ln Ln keffective of nanocomposite does not depend on phonon scattering in the individual materials but on phonon scattering at the interfaces hBD = Thermal boundary conductance [Wm-2K-1] Change in material properties gives rise to hBD

  7. Particle theory of hBD Phonon flux transmitted across interface Phonon distribution Phonon interfacial transmission Projects phonon transport perpendicular to interface Spectral phonon density of states [s m-3] Phonon Energy [J] Phonon speed [m s-1]

  8. Diffuse scattering • Scattering completely diffuse • Elastically isotropic materials • Single phonon elastic scattering Diffuse Mismatch Model (DMM) E. T. Swartz and R. O. Pohl, 1989, "Thermal boundary resistance,“ Reviews of Modern Physics, 61, 605-668. diffuse scattering – phonon “looses memory” when scattered T > 50 K and realistic interfaces Averaged properties in different crystallographic directions Is this assumption valid?

  9. Single phonon elastic scattering events Simplifies transmission coefficient

  10. Single phonon elastic scattering events hBD from DMM limited by f1 f=T/qD f Linear in classical regime (T>qD) *Kittel, 1996, Fig. 5-1

  11. Single phonon elastic scattering Elastic Scattering – hBD is a function of df/dT Df/dT

  12. Today’s Talk Purpose:Determine the effects that the properties of the interface has on thermal boundary conductance, hBD • Theory of phonon interfacial transport • Measurement of hBD with the TTR technique • Influence of atomic mixing on hBD • Influence of high temperatures (T > qD) on hBD

  13. Verdi V10 = 532 nm 10 W RegA 9000 tp ~ 190 fs single shot - 250 kHz 4 mJ/pulse Mira 900 tp ~ 190 fs @ 76 MHz l = 720-880 nm 16 nJ/pulse Verdi V5 = 532 nm 5 W Transient ThermoReflectance (TTR) Probe Beam l/2 plate Beam Splitter Delay ~ 1500 ps Sample dovetail prism lenses Polarizer Detector Pump Beam Variable ND Filter Acousto-Optic Modulator Lock-in Amplifier Automated Data Acquisition System

  14. PROBE HEATING “PUMP” FILM Thermal Diffusion SUBSTRATE Transient ThermoReflectance (TTR) Free Electrons Absorb Laser Radiation Electron-Phonon Coupling (~2 ps) Electrons Transfer Energy to the Lattice Thermal Diffusion by Hot Electrons Thermal Equilibrium Thermal Diffusion within Thin Film Thermal Diffusion (~100 ps) Thermal Conductance across the Film/Substrate Interface Thermal Boundary (~2 ns) Conductance Substrate Thermal Diffusion (~100 ps – 100 ns) Thermal Diffusion within Substrate

  15. Thermal Model Nondimensionalized Temperature Boundary conditions Initial conditions

  16. DMM compared to experimental data Goal: investigate the over- and under-predictive trends of the DMM based on the single phonon elastic scattering assumption Ref 8. Stevens, Smith, and Norris, JHT, 2005 Ref 63. Lyeo and Cahill, PRB, 2006 Ref 65. Stoner and Maris, PRB, 1993

  17. Today’s Talk Purpose:Determine the effects that the properties of the interface has on thermal boundary conductance, hBD • Theory of phonon interfacial transport • Measurement of hBD with the TTR technique • Influence of atomic mixing on hBD • Influence of high temperatures (T > qD) on hBD

  18. DMM Assumptions DMM Assumption Realistic interface

  19. Sample Fabrication

  20. Interface Characterization Auger electron spectroscopy (AES) Relaxation and Auger emission Ionization Electron bombardment Monitor energy e- [3 keV] Vacuum Energy Higher levels Core level

  21. AES Depth Profiling detector e- gun O2 Ar+ gun C Cr dN/dE Si Energy [eV]

  22. AES Depth Profile

  23. AES Depth Profiles Cr/Si mixing layer 9.5 nm Cr-1: no backsputter Si change 9.7 %/nm Elemental Fraction Cr/Si mixing layer 14.8 nm Cr-2: backsputter Si change 16.4 %/nm Depth under Surface [nm] Hopkins, and Norris, APL, 2006

  24. Results from AES Data

  25. TTR Testing

  26. hBD Results DMM predicts a constant hBD = 855 MWm-2K-1

  27. Virtual Crystal DMM Multiple scattering events from interatomic mixing Beechem, Graham, Hopkins, and Norris, APL, 2006

  28. VCDMM Hopkins, and Norris, Beechem, and Graham, JHT, Submitted

  29. Summary • DMM predicts hBD850 MWm-2K-1 at room temperature • Measured data varies from 1-2x108 • Multiple phonon elastic scattering could cause discrepancy • DMM only takes into account single scattering event • DMM assumes perfect interface • Virtual Crystal DMM predicts same values and trends • for Cr/Si at room temperature

  30. Today’s Talk Purpose:Determine the effects that the properties of the interface has on thermal boundary conductance, hBD • Theory of phonon interfacial transport • Measurement of hBD with the TTR technique • Influence of atomic mixing on hBD • Influence of high temperatures (T > qD) on hBD

  31. Single phonon elastic scattering Elastic Scattering – hBD is a function of df/dT

  32. Molecular Dynamics Simulations Stevens, Zhigilei, and Norris, IJHMT, Accepted

  33. Mismatched samples Lyeo and Cahill, PRB, 2006 Stoner and Maris, PRB, 1993

  34. TTR Testing

  35. hBD results Hopkins, Salaway, Stevens, and Norris, IJT, 2007 Ref 65. Stoner and Maris, PRB, 1993

  36. hBD results Hopkins, Stevens, and Norris, JHT, 2007

  37. Analysis • Linear trend in MDS in classical regime • MDS calculates hBD with out assuming only elastic scattering in interfacial phonon transport • Several samples show linear hBD trends around classical regime DMM JOINT FREQUENCY DMM

  38. JFDMM

  39. DMM vs. JFDMM

  40. DMM vs. JFDMM

  41. Summary • Inelastic scattering – DMM does not account for this • Data at solid-solid interfaces taken at temperatures around Debye Temperature show linear trend • DMM predicts flattening of predicted hBDaround Debye Temperature • Accounting for substrate phonon population in DMM improves prediction (JFDMM)

  42. Conclusions & Acknowledgments Purpose:Determine the effects that the properties of the interface have on thermal boundary conductance, hBD • Realistic interfaces – two phase regions, mixing, nonperfect junctions – multiple phonon scattering events that can decrease hBD • Inelastic scattering can occur at elevated temperatures (T > qD), increasing hBD • Thanks for the financial support from NSF GRFP, VSGC, U.Va. Faculty Senate and Double Hoo, and NSF grant CTS-0536744 • Dr. Pam Norris, Dr. Samuel Graham, Thomas Beecham • Microscale Crew: Rich Salaway, Rob Stevens, Mike Klopf, Jenni Simmons, Thomas Randolph, Jes Sheehan

  43. Resolving TBC with TTR Al/Al2O3 interfaces kf = 237 Wm-1K-1 hBD = 2.0 x 108 Wm-2K-1 Resolving TBC with TTR ti tf

  44. Thermal Model Lumped capacitance substrate T film Al/Al2O3 interfaces kf = 237 Wm-1K-1 hBD = 2.0 x 108 Wm-2K-1 Bi<<1 d =75 nm< 120 nm Bi = 1 Bi>>1 x

  45. hBD trends vs. sample mismatch

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