Probing Thin Film Thermophysical Properties using the Femtosecond Transient ThermoReflectance Technique

Transcription

1 Probing Thin Film Thermophysical Properties using the Femtosecond Transient ThermoReflectance Technique Pamela M. Norris Director of the Microscale Heat Transfer Laboratory and The Aerogel Research Lab Department of Mechanical and Aerospace Engineering University of Virginia

2 REPORT DOCUMENTATION PAGE Form Approved OMB No Public reporting burder for this collection of information is estibated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burder to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (74-188), 1215 Jefferson Davis Highway, Suite 124, Arlington, VA Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE Workshop Presentations 4. TITLE AND SUBTITLE Probing Thin Film Thermophysical Properties using the Femtosecond Transient ThermoReflectance Technique Unclassified 6. AUTHOR(S) Norris, Pamela M. ; 7. PERFORMING ORGANIZATION NAME AND ADDRESS University of Virginia Department of Mechanical and Aerospace Engineering Charlottesville, VAxxxxx 9. SPONSORING/MONITORING AGENCY NAME AND ADDRESS Office of Naval Research International Field Office Office of Naval Research Washington, DCxxxxx 3. DATES COVERED (FROM - TO) to a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 8. PERFORMING ORGANIZATION REPORT NUMBER 1. SPONSOR/MONITOR'S ACRONYM(S) 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT APUBLIC RELEASE, 13. SUPPLEMENTARY NOTES See Also ADM1348, Thermal Materials Workshop 21, held in Cambridge, UK on May 3-June 1, 21. Additional papers can be downloaded from: ABSTRACT? Discuss Femtosecond Transient ThermoReflectance (FTTR) technique as a method for measuring the thermophysical properties of thin film materials.? Demonstrate the measurement of the thermal diffusivity, electron-phonon coupling factor, and thermal boundary resistance of thin metallic films using the FTTR technique.? Discuss the importance of considering the nonlinear relationship between reflectance and temperature.? Present experimental results for Femtosecond Transient ThermoTransmittance (FTTT) studies performed on amorphous silicon solar cells. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Public Release a. REPORT Unclassified b. ABSTRACT Unclassified c. THIS PAGE Unclassified 18. NUMBER OF PAGES NAME OF RESPONSIBLE PERSON Fenster, Lynn lfenster@dtic.mil 19b. TELEPHONE NUMBER International Area Code Area Code Telephone Number DSN Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39.18

3 Acknowledgements Students: Dr. John Hostetler (Princeton Lightwave), Dr. Andrew Smith (US Naval Academy), James McLeskey, Michael Klopf This work was funded by: National Science Foundation #CTS #CTS BP Solar

4 Objectives Discuss Femtosecond Transient ThermoReflectance (FTTR) technique as a method for measuring the thermophysical properties of thin film materials. Demonstrate the measurement of the thermal diffusivity, electron-phonon coupling factor, and thermal boundary resistance of thin metallic films using the FTTR technique. Discuss the importance of considering the nonlinear relationship between reflectance and temperature. Present experimental results for Femtosecond Transient ThermoTransmittance (FTTT) studies performed on amorphous silicon solar cells.

5 Transient Thermal Property Measurement Ultrashort Laser Pulse Thin Film Substrate Pulse Duration, t p Thermal Diffusion FWHM t 1-1 nm x

6 Nonequilibrium Energy Deposition Process Free Electrons Absorb Radiant Energy Electrons Transfer Energy to the Lattice Thermal Diffusion by Hot Electrons Electron-Phonon Coupling Factor Thermal Equilibrium (~1 ps) Thermal Diffusion within Thin Film Thermal Conductance across the Film/Substrate Interface Thermal Diffusivity Thermal Boundary Resistance

7 Parabolic Two Step (PTS) Model Electron System: C e (T e ) T e t Lattice System: = x K e (T e ) T e G[ T x e T l ]+ S(x,t) T C l l t = G [ T e T ] l G = Electron Phonon Coupling Factor Electron Heat Capacity: C e ( T e ) = γt e Electron Thermal Conductivity: T K e ( T e,t l ) = K e eq T l C l = Lattice Heat Capacity γ = Electron Heat Capacity Constant S(x,t) = Laser Source Term

8 Transient ThermoReflectance Technique Solid State Diode Pumped Laser λ = 532 nm ~9W Ti:Saph Laser 76 MHz τ p = 2 fs λ = 72 nm - 88 nm (1.4 ev ev) Delay ~ 15 ps Sample λ /2 Plate Probe Beam 5 % Beam Splitter 2 :1 Dove Prism Lens 6 1 µ s Pump Beam 95% Detector Polarizer Variable ND Filter Acousto-Optic 1MHz Lock-in Amplifier- 1MHz

9 Reflectivity as a Function of Temperature and Strain Laser Absorption Nonequilibrium Temperature Rise Thermal Expansion PROBE Electron-Phonon Coupling Compressional "Acoustic" Wave HEATING PUMP Thermal Diffusion DR(h) GENERATION FILM REFLECTION DR(T e,t l ) R R = a T e + b T l +x SUBSTRATE

10 Thermal Diffusivity (W) Signal ( µ V) Tungsten on Silicon 26 nm G = 26( ± 3) x 1 16 W/m 3 K α 3 eff = 27±3 x 1-6 m 2 /s eff α bulk bulk = 67 x 1-6 m 2 /s /s 2 t echo " 9 ps Time (ps) The large initial response represents the initial nonequilibrium electron temperature. The ultrasonic echoes allow for the measurement of the sound velocity and/or elastic constants assuming the film thickness is known. The diffusion of thermal energy allows for determination of the thermal diffusivity.

11 Electron Phonon Coupling Factor (Pt) 4 R/R (x1-6 ) PTS Model - - G G=62±6x1 = 6 ± ±± x W/m 3 K 3 Incident Fluence =.36 J/m 2 2 PTS Model - - G G=59±6x1 ± = ± 6 x W/m 3 K 3 Incident Fluence = J/m 2 2 PTS Model - - G G=58±6x1 = ± 6 x W/m 3 K 3 Incident Fluence ± Incident Fluence =.72 J/m J/m Time (ps) 29 nm Pt on Glass Slower scans of the nonequilibrium period allow for the measurement of electron phonon coupling factor, G. A linear relationship was used, R/R = a T e + b T l.

12 Electron Phonon Coupling Factor (Au) R/R (x1-6 ) nm Au on Glass PTS Model - - G G=3.1±.3x1 = ±± ± x 1 16 W/m 3 K 3 K Incident Fluence Fluence = J/m J/m 2 PTS Model - - G G=2.9±.3x1 ± = ± x 16 W/m 3 K 3 K Incident Fluence Fluence = J/m J/m 2 PTS PTS Model Model - - G G=2.4±.3x1 = ± x W/m W/m 3 K 3 K ± Incident Fluence =.72 J/m J/m Time (ps) Note that the values of the electron-phonon coupling factor determined assuming a linear reflectance model change with the incident fluence.

13 Absorption Mechanisms in Metals E F E o Intraband Transition Conduction Band Interband Transition d-band Intraband Transitions 1) Indirect transitions which require a collision. 2) Strongly influenced by the electron collisional frequency. Interband Transitions 1) Direct transitions from the filled d- band to the conduction band. 2) Strongly influenced by changes in both the Fermi distribution and the interband transition energy.

14 ThermoReflectance Response of Au R/R Rosie Rosei and Lynch, (Interband Transition) Transitions) Drude Model (Intraband Transitions) Au T=1K E IB =2.45 ev tuning range Photon Energy (ev) In the tuning range of the Ti:Saph laser, the thermoreflectance response of Au results from changes in the intraband transition probabilities.

15 Intraband Transitions Drude model for the dielectric function of a nearly free electron metal ε( T e,t l ) = 1 ω p 2 ω ω + iω τ ( T e,t l ) [ ] ω p ω Plasma Frequency Incident Photon Frequency Electron Collisional Frequency: ω τ ( T e,t l ) 1 τ = A ee Te2 + B ep T l R K R/R ev T l =T o =3K T e -T o Nonequilibrium Electron Temperature

16 Intraband Reflectance Model (Au) R/R (x1-6 ) nm Au on Glass PTS Model Model - G - = G=2.1±.2x1 ±± ± x W/m W/m 3 K 3 K Incident Fluence Fluence = J/m J/m 2 PTS PTS Model Model - G - = G=2.2±.2x1 ± ± ± x W/m W/m 3 K 3 K Incident Fluence Fluence = J/m J/m 2 2 PTS PTS Model Model - G - = G=2.1±.2x1 ± x W/m W/m 3 K 3 K ± Incident Fluence = J/m J/m Time (ps) The Drude model was used to relate changes in temperature to reflectance. The electron-electron scattering coefficient was determined to be A ee = 1.4x1 7 1/sK 2.

17 Signal ( µ V) Signal ( µ V) Thermal Boundary Resistance 23 nm Au on SiO2 R b = 1.8±.2 x 1-8 m 2 KW Time (ps) 23 nm Au on Si R b =.84±.7 x 1-8 m 2 KW Time (ps)

18 Transient ThermoTransmittance Technique Solid State Diode Pumped Laser λ = 532 nm ~9W Ti:Saph Laser 76 MHz τ p = 2 fs λ = 72 nm - 88 nm (1.4 ev ev) Probe Beam 5 % Delay ~ 15 ps λ /2 Plate Beam Splitter Sample 2 :1 Dove Prism Lens Polarizer Detector 1 µ s Pump Beam 95% 6 Variable ND Filter Acousto-Optic 1MHz Lock-in Amplifier- 1MHz

19 Probing Amorphous Silicon Solar Cells Light Glass Transparent conducting oxide (SnO 2 ) 6 nm thick Boron doped (p-type) a-si 1 nm thick Intrinsic layer (undoped ) a-si 2 nm thick Phospho rus doped (n-type) a-si 2 nm thick Rear contact (ZnO) 1 nm thick

20 Normalized Transmission (DT / T) Scans of the 2 nm Intrinsic a-si Layer ev Time (ps) ev Increasing Photon Energy ev ev ev ev ev ev ev ev ev 1.7 ev

21 Residual Values for Individual Layers.8 Negative Residual Value at 5 ps a-si:h a-si:p:h(n-layer) a-si:b:h (p-layer) Light Energy (ev)

22 .2 Scan of a Single Junction a-si:h Cell Normalized Transmission (DT / T) ev 1.7 ev ev 1.46 ev ev ev ev ev ev ev ev ev ev ev 1.7 ev Time (ps)

23 Negative Residual Value at 5 ps Residual Value for Junction vs. Model Experimental a-si:h single junction cell Linear Combination Model Rv j = A p *Rv p + A i *Rv i + A n *Rv n A p =.32 A i =.65 A n = Light Energy (ev)

24 Distinguishable Material Parameters Bandgap Sample composition (germanium and carbon alloys) Dopant concentration (phosphorus and boron doping) Hydrogenation level (defect passivation / crystallinity)

25 Conclusions Presented Femtosecond Transient ThermoReflectance (FTTR) technique measurements of the thermal diffusivity, electronphonon coupling factor, and thermal boundary resistance of thin metallic films. Showed that the thermoreflectance response is two orders of magnitude greater when the incident probe energy is near an interband transition, and that the response is only linear for small changes in temperature. Demonstrated that the wavelength dependence of Femtosecond Transient ThermoTransmittance (FTTT) response from an amorphous silicon solar cell can be related to the response of the individual layers.

26 Simplified Band Structure of a-si Parabolic Conduction Band E c - Bottom of Conduction Band Exponential Bandtails E v - Top of Valence Band E g 1.7 ev (a-si) Mobility Gap Parabolic Valence Band Density of States

27 Model Assumptions Change in transmission is entirely due to change in absorption. Band structure is parabolic with exponential band-tails. Absorption before and after spike is interband absorption into band-tails. Difference is due to temperature increase. N = G o G o exp(-αx) α T = α o exp {[hν - (E o - βt)] / 2k B T} Spike is due to intraband absorption of free carriers generated by the pump being excited higher within the conduction band. α fc = λ 2 q3 4π 2 c 3 n * ε ( N n m n 2 µ n + N p m p 2 µ p )

28 Experiment-Model Comparison Normalized Transmission (DT / T) Time (ps) Laser Photon energy ev data 1.62 ev data 1.67 ev data ev data ev model 1.62 ev model 1.67 ev model ev model

29 Effects of Electron-Electron Scattering on Thermal Conductivity Electron Thermal Conductivity K e C e ω τ Electron Heat Capacity C e = γt e Electron Collisional Frequency ω τ = A ee T e 2 + Bep T l Electron Thermal Conductivity, K e (W/m 3 K) neglecting e-e scattering accounting for e-e scattering Electron Temperature, T (K) e Electron-electron scattering becomes important at higher electron temperatures.

30 Predicted Temperature Response, Au J/m 2 3 T e (K) J/m 2.72 J/m T l (K) Time (ps)

31 Predicted Temperature Response, Pt J/m 2 2 T e (K) J/m 2.72 J/m 2 15 T l (K) Time (ps)

32 Interband Transitions Rosei and Lynch, 1972 ( ε 2 E E o) 1/ 2 E e 1 ( ) E E 1 k B T Using the Kramers-Kronig relations this expression can be used to calculate the temperature dependence of the complex dielectric function. 1 R K R/R (arb units) ev T l =T o =3K T e -T o Nonequilibrium Electron Temperature

33 Ultrashort Pulsed Laser Transient Thermal Measurement Tungsten Film: 15 5 τ c Thin Film Substrate Minimum Film Thickness (nm) Parabolic Two Step Model Standard Heat Equation Pulse Duration (ps) Thermal Penetration Depth: δ thermal δ optical + k e τ c C e + k e t pulse C l

34 Interband Effects on Reflectivity Reflectance Reflectance Au 1.55 ev Photon Energy (ev) Al If probe photon energy is near an interband transition, then the bound electron contribution can be significant. Reflectance spectra calculated from the Drude - Lorentz model with constants from Rakic et al., Appl. Optics, 37, 5271, Reflectance Ni Photon Energy (ev) 1.55 ev 1.55 ev Photon Energy (ev)

35 Thermomodulation Critical Points (Scouler, Phys. Rev., Vol. 18, No. 12, p. 445, 1967) Au R R 1 4 R R (12K ) Reflectance 77 K 2.5 ev Photon Energy (ev) Interband effects cause signal polarity reversal.

36 Electron Phonon Coupling Calculated from the electron-phonon collisional equations using the Debye model and assuming that T e > T l > T D U l t ep Wm T e -T l (T l =3K)

37 Ultrashort Pulsed Laser Heating Parabolic: heat propagation is diffusive Hyperbolic: heat propagates at a finite speed One Step: electrons and lattice are in equilibrium Two Step: energy is initially absorbed by electrons then coupled into the lattice Regime Map: (Au) Thermalization Time: τ c = C e C l ( C e + C l )G C e G Characteristic Heating Time, t h (ps) HOS t h = 5τ F Parabolic One Step t h = 5τ c Parabolic Two Step Hyperbolic Two Step Temperature (K)

38 Nonlinear Thermoreflectance Response R/R (x1-6 ) 1 PTS PTS Model Model - G - G=3.1±.3x1 = x 1 16 W/m 3 K ±± ± 16 W/m 3 K Incident Fluence = J/m J/m 22.8 PTS Model - G - G=2.9±.3x1 ± = ± x W/m 3 K 3 K Incident Fluence Fluence = J/m J/m 2 PTS PTS Model Model - G - G=2.4±.3x1 = ± x W/m W/m 3 K 3 K.6 ± Incident Incident Fluence Fluence = J/m J/m Time (ps)