Stephen R. Lee, Doug Medlin, Harlan Brown- Shaklee, Jon F. Ihlefeld Sandia NaConal Labs Strain field and coherent domain wall effects on the thermal conducevity and Kapitza conductance in Bismuth Ferrite Brian M. Foley University of Virginia Patrick E. Hopkins Assistant Professor Dept. Mech. & Aero. Eng. University of Virginia phopkins@virginia.edu patrickehopkins.com Carolina Adamo, Darrell G. Schlom Cornell University Linghan Ye, Bryan Huey University of ConnecCcut Brady Gibbons Oregon State University
Thermal conducevity of Ferroelectrics Ferroelectrics and related materials can have low thermal conductivities Complex phonon spectra Soft modes Anisotropy What role do internal boundaries/structures play?? Tachibani et al. Appl. Phys. Lett. 93, 092902 (2008)
of SrTiO 3. For SrTiO 3, we take the experimentally determined Grain dispersion boundaries: in the [00] SrTiOdirection from Cowley 34 by fitting each of the 5 phonon branches 3 with fourth-order polynomials. We take the total scattering time, s j, as the combination of the scattering times due to both anharmonic phonon-phonon (s a ), and phonon-grain boundary (s gb ), and phonon-film boundary (s fb ) scattering. It should be noted that additional contributions to the reduction in thermal conductivity likely include phonon scattering at internal pore boundaries, which would follow the same dependence as grain boundary scattering. However, since TDTR cannot distinguish between grain boundary scattering and scattering at other internal interfaces, we lump this together as a single boundary scattering term. The total scattering rate is then determined through Matthiessen s rule, 35 given as s j ¼ þ þ s a s gb s fb ¼ BTx 2 j exp C þ v j v j þ T d ; (2) avg FIG. 2. Thermal conductivity of ng-srtio 3 as a function of avera size (hollow 70squares), 0 9 along with the previous data of Wang et al. (fi angles) and bulk SrTiO 3 (solid line). In addition, we plot the predi Eq. (), which is shown to agree well with our data. The agreement our model and data suggests that the frequency dependence of the where d avg is thefoley average et grain al. Appl. sizephys. presented Lett. in0, Table 23908 I and (202)
What about domain boundaries/strain? Grain boundaries = incoherent Ferroelectric domain boundaries = coherent and strained
Outline Domains and domain walls in BiFeO 3 Time domain thermoreflectance (TDTR) Domain effects on thermal transport in BiFeO 3 Domain wall Kapitza conductance phonon-strain field scattering
Coherent interfaces think layers Layered structures can exhibit ultralow thermal conductivity Ex. Sr 2 Nb 2 O 7 Perovskitelike layers SrO layer Thermal Conductivity, W m K 2.8.6.4.2 0.8 0.6 0.4 Kobayashi et al. 5 layer 30 layer Sr 2 Nb 2 O 7 WSe 2 50 300 450 600 Temperature, K Cahill et al. Appl. Phys. Lett. 96, 2903 (200) Chiritescu et al. Science 35, 35 (2007) 0.2 0 CsBiNb 2 O 7 Fig. 2. Summary of measured thermal conductiv-
Coherent interfaces BiFeO 3 domains Domain boundaries other types of coherent interfaces Reactive molecular-beam epitaxy: 30 nm BiFeO 3 films on SrTiO 3 substrates Exact (00) SrTiO 3 BiFeO 3 4 miscut toward [00] BiFeO 3 Slide courtesy of Chang-Beom Eom and Jon Ihlefeld 4 miscut toward [0] BiFe O 3 SrRuO 3 /SrTiO 3 SrRuO 3 /SrTiO 3 SrRuO 3 /SrTi O 3 α e r or r 4 r 2 or r 3 αe α m r r 4 α m r (0) (00) (0) r r 4 r r r 2 r 4 r SrRuO 3 /SrTiO 3 /SrTiO 3 3 SrRuO 3 /SrTiO 3 Ihlefeld et al. Appl. Phys. Lett. 9, 07922 (2007) SrRuO 3 /SrTi O 3
Domain characterizaeon - PFM Prof. Bryan Huey U. Conn. a: normal (z) PFM b: lateral (y) PFM z c: normal (z) PFM d: lateral (x) PFM y x Standard domain imaging not sufficient Require quantification of domain boundaries Vector (angle-resolved) PFM: 2 steps Out-of-plane (normal) z-direction In-plane y-direction Rotate specimen 90 degrees Desmarais et al. Appl. Phys. Lett. 99, 62908 (20)
Domain boundary quaneficaeon Non-vicinal substrate 4-variants Vicinal substrate 2-variants Growth on vicinal substrate results in different domain structure Virtually all 7 deg. domain walls 4 variant: 6 µm domain wall/µm 2 2 variant: µm domain wall/µm 2 Hopkins et al. Appl. Phys. Lett. 02, 2903 (203)
Time domain thermoreflectance (TDTR) Thermal conductivity of series of BiFeO 3 films with different domain structures Nanostructure Semi-infinite substrate Probe Thin metal film transducer Pump Thermal penetration depth TDTR ratio, -X/Y 0 9 8 7 6 5 4 3 2 0 TDTR data, 7 nm Al/Si Thermal model 0 2 3 4 5 Pump-probe time delay, (ns) τ (ps) Can measure thermal conductivity of thin films and substrates (κ) separately from thermal boundary conductance (h K ) Nanometer spatial resolution (~0 s of nm) Femtosecond to nanosecond temporal resolution Noncontact
Domain effects on effec$ve thermal conducevity 20.0 Effective thermal conductivities of BiFeO 3 < 2.5 W m - K - Presence of domain walls reduces κ by ~30% Strain fields from domains are scattering phonons (previous speaker) Thermal conductivity (W m - K - ) 0.0.0 0.5 75 Hopkins et al. Appl. Phys. Lett. 02, 2903 (203) Single variant 2-variant SrTiO 3 4-variant a-sio 2 00 200 300 400500 Temperature (K)
Domain effects Kapitza conductance h K = 4 variant: D = 6 µm domain wall/µm 2 2 variant: D = µm domain wall/µm 2 apple 0 D apple 0 apple Strain fields from coherent domain boundaries can scatter phonons like domain boundaries Coherent domain walls offer as much resistance as 0 nm of SiO 2 Hopkins et al. Appl. Phys. Lett. 02, 2903 (203)
Domain engineering of thermal properees Single Crystalline Pb[Zr x Ti -x ]O 3 (PZT) A LOT OF DOMAINS! Thermal Conductivity of single crystalline PZT films 2.5 More domains and smaller domains at boundaries Thermal Conductivity, W m K 2.5 0.5 0 0 20 40 60 80 00 Mole % PbTiO 3 Domain scattering stronger than alloy scattering Schmitt et al. JAP 0, 07407 (2007)
Conclusions - Appl. Phys. Lett. 02, 2903 (203) Domains boundaries scatter phonons Coherent strain fields have similar effects as incoherent grain boundaries 2.5 Thermal Conductivity of single crystalline PZT films = domain wall v d domain wall Thermal Conductivity, W m K 2.5 0.5 0 0 20 40 60 80 00 Mole % PbTiO 3 Young Investigator Program
Single vs. poly PZT Thermal Conductivity of polycrystalline PZT films 2.5 Thermal Conductivity of single crystalline PZT films 2.5 Thermal Conductivity, W m K 2.5 0.5 Thermal Conductivity, W m K 2.5 0.5 0 0 20 40 60 80 00 Mole % PbTiO 3 0 0 20 40 60 80 00 Mole % PbTiO 3
TDTR sensieviees effeceve thermal conducevity Thermal sensitivity, S 0.30 0.25 0.20 0.5 0.0 0.05 0.00-0.05-0.0-0.5 h K : Pt/BiFeO 3 h K : Pt/SrTiO 3 : BiFeO 3 C: BiFeO 3-0.20 50 500 5000 Pump-probe delay time (ps)
Conductance measurements 400 Thermal conductance (MW m -2 K - ) 00 domain Pt/SrTiO 3 2 domains 4 domains 30 00 50 200 250 300 350 400 Temperature (K)
Reciprocal space mapping G. 4. Reciprocal space mapping of the 03 peaks in 30 nm thick BiFeO3 films grown on (00)-orient TiO3 with (a) 4 domain variants, (b) 2-domain variants and (c) a single domain variant.
Slide courtesy of Coherent interfaces Domain boundaries Chang-Beom Eom and Jon Ihlefeld Domain boundaries other types of coherent interfaces BiFeO 3 domains can be engineered with substrate vicinality Exact (00) SrTiO 3 4 miscut toward [00] 4 miscut toward [0] BiFeO 3 BiFeO 3 BiFeO 3 SrRuO 3 /SrTiO 3 SrRuO 3 /SrTiO 3 SrRuO 3 /SrTiO 3 α e r or r 4 r 2 or r 3 α e α m r r 4 α m r (0) (00) (0) r r 4 r r r r 2 r 4 SrRuO SrRuO 3 /SrTiO 3 /SrTiO 3 3 SrRuO 3 /SrTiO 3 SrRuO 3 /SrTiO 3
BiFeO 3 film growth Reactive molecular-beam epitaxy: 30 nm BiFeO 3 films on SrTiO 3 substrates Phase-pure Smooth surface and interface Crystallinity limited by substrate (SrTiO 3 ) Intensity (arbitrary units) 0 7 0 6 0 5 0 4 0 3 0 2 0 0 0 02 SrTiO 3 00 2024 SrTiO 3 200 20 30 40 50 60 70 80 2θ (degrees) Ihlefeld et al. Appl. Phys. Lett. 9, 07922 (2007) 3036 SrTiO 3 300 Film Intensity (arb. units) 400 200 000 800 600 400 200 2024 BiFeO Peak 3 FWHM = 25 arc sec (0.007 ) 002 SrTiO 3 Peak FWHM = 25 arc sec (0.007 ) 0 0-50 -00-50 0 50 00 50 ω (arc seconds) 8x0 4 6x0 4 4x0 4 2x0 4 Substrate Intensity (arb. units)
Does this make sense? Coherent domain wall scatters phonons like incoherent grain boundary? What s the mechanism??? Attenuation (Akhieser): Rayleigh: /! 2 Akhieser /! 4 impurity Incoherent (like a grain boundary): / grain v d grain