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
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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-998372 #CTS-951911 BP Solar
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.
Transient Thermal Property Measurement Ultrashort Laser Pulse Thin Film Substrate Pulse Duration, t p Thermal Diffusion FWHM t 1-1 nm x
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
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
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 - 1.7 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 Modulator @ 1MHz Lock-in Amplifier- 1MHz
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
Thermal Diffusivity (W) Signal ( µ V) 1 8 6 4 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 1-6 2 bulk = 67 x 1-6 m 2 /s /s 2 t echo " 9 ps 5 1 15 2 25 3 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.
Electron Phonon Coupling Factor (Pt) 4 R/R (x1-6 ) 35 3 25 2 15 PTS Model - - G G=62±6x1 = 6 ± ±± x 16 16 W/m 3 K 3 Incident Fluence =.36 J/m 2 2 PTS Model - - G G=59±6x1 ± = ± 6 x 16 16 W/m 3 K 3 Incident Fluence =.216.22 J/m 2 2 PTS Model - - G G=58±6x1 = ± 6 x 1 16 16 W/m 3 K 3 Incident Fluence ± Incident Fluence =.72 J/m J/m 2 2 1 5.5 1 1.5 2 2.5 3 3.5 4 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.
Electron Phonon Coupling Factor (Au) R/R (x1-6 ) 2 15 1 23 nm Au on Glass PTS Model - - G G=3.1±.3x1 = ±± ± x 1 16 W/m 3 K 3 K Incident Fluence Fluence = 3.6 3.6 J/m J/m 2 PTS Model - - G G=2.9±.3x1 ± = ± x 16 W/m 3 K 3 K Incident Fluence Fluence = 2.16 2.16 J/m J/m 2 PTS PTS Model Model - - G G=2.4±.3x1 = ± x 16 16 W/m W/m 3 K 3 K ± Incident Fluence =.72 J/m J/m 2 5 1 2 3 4 5 6 7 8 Time (ps) Note that the values of the electron-phonon coupling factor determined assuming a linear reflectance model change with the incident fluence.
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.
2.5 1-4 ThermoReflectance Response of Au R/R 2 1-4 1.5 1-4 1 1-4 5 1-5 1 Rosie Rosei and Lynch, 1972 1972 (Interband Transition) Transitions) Drude Model (Intraband Transitions) Au T=1K E IB =2.45 ev -5 1-5 -1 1-4 tuning range -1.5 1-4 1 1.5 2 2.5 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.
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: 1-2 1-4 ω τ ( T e,t l ) 1 τ = A ee Te2 + B ep T l R 1 6 1 K R/R -4 1-4 -6 1-4 -8 1-4 -1 1-3 Au @ 1.5 ev T l =T o =3K 5 1 15 2 25 3 35 4 T e -T o Nonequilibrium Electron Temperature
Intraband Reflectance Model (Au) R/R (x1-6 ) 2 15 1 23 nm Au on Glass PTS Model Model - G - = G=2.1±.2x1 ±± ± x 1 16 16 W/m W/m 3 K 3 K Incident Fluence Fluence = 3.6 3.6 J/m J/m 2 PTS PTS Model Model - G - = G=2.2±.2x1 ± ± ± x 16 16 W/m W/m 3 K 3 K Incident Fluence Fluence = 2.16 2.16 J/m J/m 2 2 PTS PTS Model Model - G - = G=2.1±.2x1 ± x 1 16 16 W/m W/m 3 K 3 K ± Incident Fluence =.72.72 J/m J/m 2 2 5 1 2 3 4 5 6 7 8 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.
Signal ( µ V) Signal ( µ V) 8 6 4 2 6 5 4 3 2 1-1 Thermal Boundary Resistance 23 nm Au on SiO2 R b = 1.8±.2 x 1-8 m 2 KW -1 5 1 15 2 25 3 35 Time (ps) 23 nm Au on Si R b =.84±.7 x 1-8 m 2 KW -1 1 2 3 4 5 6 7 Time (ps)
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 - 1.7 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 Modulator @ 1MHz Lock-in Amplifier- 1MHz
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
Normalized Transmission (DT / T).2 -.2 -.4 -.6 -.8 Scans of the 2 nm Intrinsic a-si Layer -1 1.7 ev -1.2-1 1 2 3 4 5 6 Time (ps) 1.426 ev Increasing Photon Energy 1.426 ev 1.495 ev 1.532 ev 1.571 ev 1.591 ev 1.611 ev 1.632 ev 1.654 ev 1.677 ev 1.7 ev
Residual Values for Individual Layers.8 Negative Residual Value at 5 ps.7.6.5.4.3.2.1 a-si:h a-si:p:h(n-layer) a-si:b:h (p-layer) 1.4 -.1 1.45 1.5 1.55 1.6 1.65 1.7 -.2 Light Energy (ev)
.2 Scan of a Single Junction a-si:h Cell Normalized Transmission (DT / T) -.2 -.4 -.6 -.8-1 1.477 ev 1.7 ev 1.443 ev 1.46 ev 1.477 ev 1.495 ev 1.513 ev 1.532 ev 1.551 ev 1.571 ev 1.591 ev 1.611 ev 1.654 ev 1.677 ev 1.7 ev -1.2-1 1 2 3 4 5 6 Time (ps)
Negative Residual Value at 5 ps.7.6.5.4.3.2 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 =.32.1 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Light Energy (ev)
Distinguishable Material Parameters Bandgap Sample composition (germanium and carbon alloys) Dopant concentration (phosphorus and boron doping) Hydrogenation level (defect passivation / crystallinity)
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.
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
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 )
Experiment-Model Comparison Normalized Transmission (DT / T).2 -.2 -.4 -.6 -.8-1 -1.2-2 2 4 6 Time (ps) Laser Photon energy 1.557 ev data 1.62 ev data 1.67 ev data 1.716 ev data 1.557 ev model 1.62 ev model 1.67 ev model 1.716 ev model
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) 2 15 1 5 neglecting e-e scattering accounting for e-e scattering 4 6 8 1 12 14 16 18 2 Electron Temperature, T (K) e Electron-electron scattering becomes important at higher electron temperatures.
Predicted Temperature Response, Au 35 35 3 3.6 J/m 2 3 T e (K) 25 2 2.1 J/m 2.72 J/m 2 25 2 T l (K) 15 15 1 1 5 5 1 2 3 4 5 6 7 8 Time (ps)
Predicted Temperature Response, Pt 25 25 2.36 J/m 2 2 T e (K) 15.21 J/m 2.72 J/m 2 15 T l (K) 1 1 5 5.4.8 1.2 1.6 2 2.4 2.8 Time (ps)
Interband Transitions Rosei and Lynch, 1972 ( ε 2 E E o) 1/ 2 E 2 1 1+ 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 1 4 1 K R/R (arb units) -2 1-2 -4 1-2 -6 1-2 -8 1-2 -1 1-1 -1.2 1-1 Au @ 2.4 ev T l =T o =3K 5 1 15 2 25 3 35 4 T e -T o Nonequilibrium Electron Temperature
Ultrashort Pulsed Laser Transient Thermal Measurement Tungsten Film: 15 5 τ c Thin Film Substrate Minimum Film Thickness (nm) 145 14 135 13 125 12 115 Parabolic Two Step Model Standard Heat Equation 11.1 1 1 Pulse Duration (ps) Thermal Penetration Depth: δ thermal δ optical + k e τ c C e + k e t pulse C l
Interband Effects on Reflectivity Reflectance Reflectance 1.8.6.4.2 1.8.6.4.2 Au 1.55 ev 5 1 15 2 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, 1998. Reflectance 1.8.6.4.2 Ni 5 1 15 2 Photon Energy (ev) 1.55 ev 1.55 ev 5 1 15 2 Photon Energy (ev)
Thermomodulation Critical Points (Scouler, Phys. Rev., Vol. 18, No. 12, p. 445, 1967) Au R R 1 4 R R (12K ) Reflectance R @ 77 K 2.5 ev Photon Energy (ev) Interband effects cause signal polarity reversal.
Electron Phonon Coupling Calculated from the electron-phonon collisional equations using the Debye model and assuming that T e > T l > T D. 2 1 19 U l t ep Wm 3 1.5 1 19 1 1 19 5 1 18 1 2 3 4 5 6 7 T e -T l (T l =3K)
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) 1 1 1 HOS t h = 5τ F Parabolic One Step t h = 5τ c Parabolic Two Step Hyperbolic Two Step.1 1 1 1 Temperature (K)
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 = 3.6 3.6 J/m J/m 22.8 PTS Model - G - G=2.9±.3x1 ± = ± x 16 16 W/m 3 K 3 K Incident Fluence Fluence = 2.16 2.16 J/m J/m 2 PTS PTS Model Model - G - G=2.4±.3x1 = ± x 16 16 W/m W/m 3 K 3 K.6 ± Incident Incident Fluence Fluence =.72.72 J/m J/m 2.4.2 1 2 3 4 5 6 7 8 Time (ps)