1. Microscale Heat Transfer Lab – University of Virginia Interface effects on thermophysical properties in nanomaterial systems Patrick E. Hopkins MAE Dept. Seminar March 22, 2007

2. Microscale Heat Transfer Lab – University of Virginia Moore’s Law hot plate 10 5 W/m 2 Transistor size Equivalent power density [W/m 2 ] Nuclear reactor 10 6 W/m 2 500 nm 100 nm 45 nm Rocket nozzle 10 7 W/m 2

3. Microscale Heat Transfer Lab – University of Virginia Thermal boundary conductance Superlattices Field effect transistors Heat generated Rejected heat Thermal management is highly dependent on the boundary of two materials

4. Microscale Heat Transfer Lab – University of Virginia Today’s Talk Purpose: Determine the effects that the properties of the interface have on thermal boundary conductance, h BD Theory of phonon interfacial transport Measurement of h BD with the TTR technique Influence of atomic mixing on h BD Influence of high temperatures (T >  D ) on h BD

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

6. Microscale Heat Transfer Lab – University of Virginia Thermal conduction in nanomaterials  n Microscopic picture of nanocomposite LnLn k effective of nanocomposite does not depend on phonon scattering in the individual materials but on phonon scattering at the interfaces T Z Z T h BD = Thermal boundary conductance [Wm -2 K -1 ] Change in material properties gives rise to h BD

7. Microscale Heat Transfer Lab – University of Virginia Particle theory of h BD Phonon flux transmitted across interface Spectral phonon density of states [s m -3 ] Phonon distribution Phonon Energy [J] Phonon speed [m s -1 ] Phonon interfacial transmission Projects phonon transport perpendicular to interface

8. Microscale Heat Transfer Lab – University of Virginia Diffuse 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 Scattering completely diffuse Elastically isotropic materials Single phonon elastic scattering T > 50 K and realistic interfaces Averaged properties in different crystallographic directions Is this assumption valid?

9. Microscale Heat Transfer Lab – University of Virginia Single phonon elastic scattering events Simplifies transmission coefficient

10. Microscale Heat Transfer Lab – University of Virginia Single phonon elastic scattering events h BD from DMM limited by f 1 *Kittel, 1996, Fig. 5-1 Linear in classical regime (T>  D ) f=T/  D f

11. Microscale Heat Transfer Lab – University of Virginia Single phonon elastic scattering Elastic Scattering – h BD is a function of df/dT Df/dT

12. Microscale Heat Transfer Lab – University of Virginia Today’s Talk Purpose: Determine the effects that the properties of the interface has on thermal boundary conductance, h BD Theory of phonon interfacial transport Measurement of h BD with the TTR technique Influence of atomic mixing on h BD Influence of high temperatures (T >  D ) on h BD

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

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

15. Microscale Heat Transfer Lab – University of Virginia Thermal Model Initial conditions Boundary conditions Nondimensionalized Temperature

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

17. Microscale Heat Transfer Lab – University of Virginia Today’s Talk Purpose: Determine the effects that the properties of the interface has on thermal boundary conductance, h BD Theory of phonon interfacial transport Measurement of h BD with the TTR technique Influence of atomic mixing on h BD Influence of high temperatures (T >  D ) on h BD

18. Microscale Heat Transfer Lab – University of Virginia DMM Assumptions DMM AssumptionRealistic interface

19. Microscale Heat Transfer Lab – University of Virginia Sample Fabrication Sample ID Backsputter Etch Heat Treat Prior to Deposition Deposition Notes Cr-1none 50 nm Cr @ 300 K Cr-25 minnone50 nm Cr @ 300 K Cr-35 min20 min @ 873 K50 nm Cr @ 300 K Cr-45 min50 min @ 873 K50 nm Cr @ 300 K Cr-55 min20 min @ 873 K50 nm Cr @ 573 K Cr-65 minnone10 nm of Cr at 300 K; Heating to 770 K; 40 nm of Cr at 300 K

20. Microscale Heat Transfer Lab – University of Virginia Interface Characterization Auger electron spectroscopy (AES) Relaxation and Auger emission Ionization Electron bombardment Higher levels Core level Vacuum Energy e - [3 keV] Monitor energy

21. Microscale Heat Transfer Lab – University of Virginia AES Depth Profiling Ar + gun e - gun detector Si O2O2 Cr C dN/dE Energy [eV]

22. Microscale Heat Transfer Lab – University of Virginia AES Depth Profile

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

24. Microscale Heat Transfer Lab – University of Virginia Results from AES Data Sample ID Cr Film Thickness [nm] Mixing Layer [nm] Slope of Si in Beginning of Mixing Layer [%/nm] Cr-138 ± 2.19.5 ± 0.69.7 ± 0.7 Cr-237 ± 0.414.8 ± 1.016.4 ± 0.7 Cr-335 ± 0.511.5 ± 0.716.6 ± 1.0 Cr-435 ± 2.810.8 ± 0.87.4 ± 1.0 Cr-539 ± 0.55.8 ± 0.524.1 ± 1.0 Cr-645 ± 0.57.0 ± 0.428.1 ± 1.2

25. Microscale Heat Transfer Lab – University of Virginia TTR Testing

26. Microscale Heat Transfer Lab – University of Virginia h BD Results DMM predicts a constant h BD = 855 MWm -2 K -1

27. Microscale Heat Transfer Lab – University of Virginia Virtual Crystal DMM Beechem, Graham, Hopkins, and Norris, APL, 2006 Multiple scattering events from interatomic mixing

28. Microscale Heat Transfer Lab – University of Virginia VCDMM Hopkins, and Norris, Beechem, and Graham, JHT, Submitted

29. Microscale Heat Transfer Lab – University of Virginia Summary DMM predicts h BD 850 MWm -2 K -1 at room temperature Measured data varies from 1-2x10 8 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. Microscale Heat Transfer Lab – University of Virginia Today’s Talk Purpose: Determine the effects that the properties of the interface has on thermal boundary conductance, h BD Theory of phonon interfacial transport Measurement of h BD with the TTR technique Influence of atomic mixing on h BD Influence of high temperatures (T >  D ) on h BD

31. Microscale Heat Transfer Lab – University of Virginia Single phonon elastic scattering Elastic Scattering – h BD is a function of df/dT

32. Microscale Heat Transfer Lab – University of Virginia Molecular Dynamics Simulations Stevens, Zhigilei, and Norris, IJHMT, Accepted

33. Microscale Heat Transfer Lab – University of Virginia Mismatched samples Lyeo and Cahill, PRB, 2006 Stoner and Maris, PRB, 1993

34. Microscale Heat Transfer Lab – University of Virginia TTR Testing

35. Microscale Heat Transfer Lab – University of Virginia h BD results Ref 65. Stoner and Maris, PRB, 1993 Hopkins, Salaway, Stevens, and Norris, IJT, 2007

36. Microscale Heat Transfer Lab – University of Virginia h BD results Hopkins, Stevens, and Norris, JHT, 2007

37. Microscale Heat Transfer Lab – University of Virginia Analysis Linear trend in MDS in classical regime MDS calculates h BD with out assuming only elastic scattering in interfacial phonon transport Several samples show linear h BD trends around classical regime DMM JOINT FREQUENCY DMM

38. Microscale Heat Transfer Lab – University of Virginia JFDMM

39. Microscale Heat Transfer Lab – University of Virginia DMM vs. JFDMM

40. Microscale Heat Transfer Lab – University of Virginia DMM vs. JFDMM

41. Microscale Heat Transfer Lab – University of Virginia 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 h BD around Debye Temperature Accounting for substrate phonon population in DMM improves prediction (JFDMM)

42. Microscale Heat Transfer Lab – University of Virginia Conclusions & Acknowledgments Realistic interfaces – two phase regions, mixing, nonperfect junctions – multiple phonon scattering events that can decrease h BD Inelastic scattering can occur at elevated temperatures (T >  D ), increasing h BD Purpose: Determine the effects that the properties of the interface have on thermal boundary conductance, h BD 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. Microscale Heat Transfer Lab – University of Virginia Resolving TBC with TTR Al/Al 2 O 3 interfaces k f = 237 Wm -1 K -1 h BD = 2.0 x 10 8 Wm -2 K -1 ii ff

44. Microscale Heat Transfer Lab – University of Virginia Thermal Model Lumped capacitance T x Bi<<1 Bi = 1 Bi>>1 film substrate Al/Al 2 O 3 interfaces k f = 237 Wm -1 K -1 h BD = 2.0 x 10 8 Wm -2 K -1 d =75 nm< 120 nm

45. Microscale Heat Transfer Lab – University of Virginia h BD trends vs. sample mismatch