Imaging surface acoustic wave dynamics in semiconducting polymers by scanning ultrafast electron microscopy

Accepted Manuscript

Imaging Surface Acoustic Wave Dynamics in Semiconducting Polymers by Scanning Ultrafast Electron Microscopy Ebrahim Najafi , Bolin Liao , Timothy Scarborough , Ahmed Zewail PII: DOI: Reference:

S0304-3991(17)30041-4 10.1016/j.ultramic.2017.08.011 ULTRAM 12442

To appear in:

Ultramicroscopy

Received date: Revised date: Accepted date:

23 January 2017 14 August 2017 20 August 2017

Please cite this article as: Ebrahim Najafi , Bolin Liao , Timothy Scarborough , Ahmed Zewail , Imaging Surface Acoustic Wave Dynamics in Semiconducting Polymers by Scanning Ultrafast Electron Microscopy, Ultramicroscopy (2017), doi: 10.1016/j.ultramic.2017.08.011

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Highlights • Scanning ultrafast electron microscopy was used to image surface acoustic waves dynamics photo-generated in a polymer. Mechanical properties of the polymer were characterized.

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Numerical simulation was used to validate the observations.

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Imaging Surface Acoustic Wave Dynamics in Semiconducting Polymers by Scanning Ultrafast Electron Microscopy Ebrahim Najafi 1*, Bolin Liao1, Timothy Scarborough2, Ahmed Zewail 1§ 1

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Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125 2 Department of Physics, Ohio State University, Columbus OH, 43210 § Posthumously * Corresponding Author

Abstract

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Understanding the mechanical properties of organic semiconductors is essential to their electronic and photovoltaic applications. Despite a large volume of research directed toward elucidating the chemical, physical and electronic properties of these materials, little attention has been directed toward understanding their thermomechanical behavior. Here, we report the ultrafast imaging of surface acoustic

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waves (SAWs) on the surface of the Poly(3-hexylthiophene-2,5-diyl) (P3HT) thin film at the picosecond and nanosecond timescales. We then use these images to

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measure the propagation velocity of SAWs, which we then employ to determine the Young’s modulus of P3HT. We further validate our experimental observation by performing a semi-empirical transient thermoelastic finite element analysis. Our

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findings demonstrate the potential of ultrafast electron microscopy to not only probe charge carrier dynamics in materials as previously reported, but also to

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measure their mechanical properties with great accuracy.

This is particularly

important when in situ characterization of stiffness for thin devices and

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nanomaterials is required.

Keywords: Ultrafast electron microscopy, surface acoustic waves, Rayleigh waves, mechanical properties, organic thin films.

Author Contributions: The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. 2

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Introduction The exceptional characteristics of organic semiconductors allow their adoption in innovative technologies such as solar cells, microelectronics, and chemical sensors

1-4

. In

comparison with traditional inorganic semiconductors, these materials offer added technological value due to their processability, reduced weight, and low production cost. However, to be fully

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exploited for commercial applications, they must also possess sufficient mechanical strength to retain performance under thermomechanical stresses generated during operation.

The mechanical properties of thin films are different than those of the same materials in the bulk due to their reduced dimensions, enhanced surface effects, and the constraints imposed by the substrate. Thus, in the design of thin devices, such deviations should be included to ensure

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performance and durability 5. The optoelectronic aspects of organic semiconductors have been thoroughly investigated in the past few decades, but their mechanical properties, especially those exclusive to the surface, are generally overlooked. This is particularly troublesome for applications that require these materials to survive prolonged exposures to the harsh outdoor environment. The stiffness of thin films is commonly evaluated by instrumented indentation,

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which induces both elastic and inelastic strain 6. The extraction of information concerning elastic behavior, though, is usually nontrivial and involves the use of intricate mathematical models.

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Surface acoustic wave (SAW) spectroscopy is an alternative approach that derives the stiffness from the velocity of ultrasound waves generated by a piezoelectric device and detected by a

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transducer placed at a preset distance 7. These waves are classified as Rayleigh waves and travel along the surface of the elastic material with an amplitude which exponentially decays into the

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bulk 8. Since the longitudinal and transverse components of Rayleigh waves couple with any medium in contact with the surface, variations in the mass and stiffness caused by the presence of defects are reflected in the SAW profile 9. In addition, SAWs are technologically relevant in a

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variety of applications such as chemical and biological sensors where they are used for accurate analysis of chemical and biological reactions 10-14. They also provide the basis for devices used in high-frequency applications in the range of 100 MHz to a few GHz 15. Acoustic charge transport (ACT) is a relatively recent application of SAWs, which involves coupling between SAWs and the two-dimensional electron gas (2DEG) within a piezoelectric semiconductor

16-18

. SAWs

propagating on a piezoelectric crystal generate electric potential which confines the electrons in

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the 2DEG within the moving quantum wells; thus, allowing quantized and energy efficient charge transport over large distances 16-18. To characterize the mechanical behavior of supported thin films and multilayers, picosecond ultrasonic spectroscopy is usually preferred because it allows a quick, non-invasive and precise measurement by exciting merely a small region of the surface that does not extend 19

. This technique can also characterize the polymer-substrate interaction by

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far into the bulk

comparing the mechanical properties of the thin film at various thicknesses, especially in the nanometer regime where such effects are pronounced. In this technique, a focused ultra-short laser pulse induces transient expansion or ablation of an absorbing material due to an impulsive heating, which results in thermoelastic and elastodynamic responses, respectively. Such

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processes are limited to only a few nanometers in metals, but become volumetric in semiconductors and polymers due to the larger penetration depth of the optical pulse. The propagation of the thermoelastic waves is then probed by measuring the transient reflectivity of a weaker laser pulse hundreds of micrometers away from the laser/sample crossover. The transient change in the reflectivity measures the acoustic strain caused by interface displacement as well

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as variation in the refractive index by the acousto-optic coupling. Since wave propagation is mainly dependent upon material properties near the surface, optically generated SAWs are an

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excellent tool to investigate surface elasticity 9.

The use of SAWs to study organic materials is somewhat challenging because the velocity of these waves is slow and their detection requires a near field detection scheme due to

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their strong attenuation. Thus, there is a need for a time-resolved microscopy technique that will allow the characterization of SAWs in polymers with simplicity and precision. Here, we

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investigate the formation and propagation of optically generated SAWs on the surface of poly(3hexylthiophene-2,5-diyl) (P3HT) thin film by scanning ultrafast electron microscopy (SUEM).

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P3HT is a p-type semiconductor, which is widely used in organic opto-electronic and photovoltaic devices. SUEM, which combines the spatial resolution of the electron probe with the temporal resolution of the femtosecond laser, was previously employed to study charge carriers in semiconductors by imaging their dynamics in both space and time

20-29

. In this work,

we use SUEM to image the spatiotemporal behavior of radially propagating SAWs and we measure their propagation velocity and wavelength to be

⁄

and

,

respectively. By employing the thermoelastic transport equation, we then calculate the Young’s

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modulus to be

GPa, which is in agreement with the reported values in the literature

for P3HT 30. Two-dimensional finite element analysis on a semi-infinite model well mimics the experimental observation and validates the calculated Young’s modulus. This work illustrates the potential of SUEM for the in-situ characterization of organic thin films and nanomaterials. Furthermore, SUEM can operate at low vacuums, allowing a similar study in the presence of

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inert and reactive gasses. Experimental Method For this experiment, P3HT with the average

was purchased from

Sigma-Aldrich and used without further chemical treatments. The powder was fully dissolved in dichlorobenzene at

. The solution was then spun-cast on the surface of a heavily doped p-type silicon

(

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⁄

at

under continuous magnetic stirring to produce a concentrated solution

at

, which resulted in a film with an average thickness of

. Such a

relatively large thickness ensured that the mechanical properties measured in this study were independent of the polymer-substrate interaction and reflected only those inherent to the polymer itself. Due to the small rpm and lower solubility of P3HT in dichlorobenzene at room

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temperature during spin coating, the thickness was not visually uniform. The role of p-type silicon was to assist the discharging of the excess electrons into its positively charged surface in the vacuum to

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during SUEM measurements. The sample was annealed overnight at

relieve the residual stress and to evaporate the remaining solvent. Finally, the sample was transferred into the SUEM chamber where the pressure was maintained at

torr. The

31, 32

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technical detail of SUEM was reported previously, but a short description is as the following

22,

. In SUEM, a femtosecond fiber laser system (Impulse by Clark-MXR Inc.) generates

green

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infrared (IR) pulses

and UV

at

repetition rate. The IR is split to produce

pulses through harmonic generation. The green, with an

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elliptical profile

, pumps the sample whereas the UV produces

electron pulses from the field emission tip that probe the dynamics. A mechanical delay line allows the delay between the green and electron pulses from The primary electron pulses, accelerated to

to

at

steps.

, scan the surface and produce secondary

electrons (SEs) from the top few nanometers of the surface. These SEs are then collected by an Everhart-Thornley detector to form images at different time delays. The measurement of the rise time in intrinsic silicon determined the temporal resolution of SUEM to be

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.

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Results and Discussions Figure 1 schematically shows our experimental setup for the generation and detection of SAWs on the P3HT surface. First, the green pulse at impulsively increases the local temperature

excites the sample and

, whose extent depends on the optical absorption

. The thermal response of the sample is described by the heat diffusion equation

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coefficient

⁄

33, 34

:

(1)

where , ,

are density, heat capacity and heat conductivity, respectively, and Q is the local

displacement

by the sudden temperature increase:

(

)

and

are the Lamé elastic constants and

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where

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rate of heat generation. The thermoelastic wave equation characterizes the generated mechanical

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of the sample:

(3)

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√

is the linear thermal expansion coefficient.

of photo-generated SAWs depend on the Young’s modulus

The propagation velocity and Poisson’s ratio

(2)

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Such surface displacements are imaged by SUEM because of the geometrical contrast that results from more electrons emitting at the peaks than from the valleys. The spatial resolution of SUEM

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is better than 10 nm and

31, 35, 36

. However, in the current work, we focused the electron probe into

spots for low and high magnification imaging, respectively, which were

sufficient to image the wave pattern on the surface. To characterize polymers in a conventional SEM, they are usually coated with a thin metallic layer to prevent charging. In SUEM, the beam current is significantly smaller than in SEM. In addition, there is 1 microsecond delay between two consecutive electron pulses which provides sufficient time for electrons to discharge into the ground; thus, we generally observe no significant charging in semiconducting polymers.

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Figure 1- Schematic of SUEM and imaging of surface acoustic waves on P3HT. The 515-nm

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optical pump impulsively heats the crossover, which incudes mechanical displacements on the surface emanating in radial direction. The scanning electron probe then measures the resulting

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changes at 0.1 ns and 3.4 ns by emitting secondary electrons from the surface. The chemical

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structure of P3HT is shown in the lower right corner of the figure.

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Figure 2A shows the SUEM image of the P3HT thin film, recorded

after optical

excitation. The image displays the topographical structure of the surface resulting from the thickness variation in the film and the presence of thermoelastic waves. The dotted ellipse highlights the crossover which is partially damaged by the laser pulse; the radiation damage is

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usually attributed to the thermal degradation of chemical bonds whose bonding characteristics were previously weakened by the pumping of their bonding electrons into anti-bonding orbitals. Since the damage is negligible and localized, it can be ignored for the study of thermoelasticity in P3HT, especially in the far field where the sample is not impacted by the beam and only experiences the energy transfer by thermomechanical waves. To clearly observe the wave

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pattern, we removed the background by performing principal components analysis (PCA) using the classical nonlinear iterative partial least squares (NIPALS) algorithm

37, 38

. PCA, which is

routinely employed in image processing, is a multivariate statistical tool that decomposes the variations in large datasets into orthogonal components. Here, the first PC captures the surface topography as the primary source of intensity variation in the image, mostly caused by

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inhomogeneous thickness. The second PC, as shown in Figure 2B, extracts the wave pattern generated by the thermoelastic response of P3HT to the laser excitation. The image shows the

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waves emanating from the crossover and extending up to a few hundreds of micrometers away. The far field observation of SAWs only after

is not due to their rapid propagation; rather,

it indicates that those generated by earlier pulses survive long enough to be imaged within our

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experimental timeframe. Therefore, these waves collectively elucidate the chronological response of the surface excited by successive pulses. The smeared appearance of SAWs in the

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near field is due to the excitation of a large set of acoustic modes, whose constructive and destructive interferences produce disorganized waves invisible to SUEM at such a low

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magnification 19, 34, 39. At the far field, SAWs become spatially resolved and well-structured. The waves do not appear to be present outside of the frame, implying that they strongly attenuate only after travelling for a few hundred micrometers from the crossover. The surface returns to the unperturbed state as soon as the pump pulse is turned off and the sample is imaged in the ground state, i.e. imaging in the static mode where there is no excitation. This further confirms the thermoelastic nature of the deformation.

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Figure 2- Snapshot of SAWs on the P3HT surface recorded

after optical excitation.

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(A) The waves in the near field are not resolved at such a low magnification, whereas they combine and form relatively uniform waves at the far field, making their detection by SUEM

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simpler. (B) PCA processed image that removes the thickness contribution to further improve the

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visualization of the wave pattern.

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To estimate the propagation velocity of SAWs, we recorded two images at

and

, as shown in Figure 3A and B, respectively. These images were recorded from the highlighted rectangle in Figure 2A where the waves appear relatively uniform and wellstructured. The limitation of the current mechanical stage in SUEM does not allow us to explore . However, these waves travel at a low acoustic velocity and decay

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the dynamics beyond

relatively slowly within the region of interest, making this timeframe suitable to estimate the distance SAWs travel within

. We used PCA filter to remove random noises from the

images and improve the appearance of SAWs. The spatial profile of SAWs at

ns and

were extracted along the line in

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Figure 2A and plotted in Figure 2C (solid dots). The harmonic damping function appears to fit the experimental data reasonably well (solid lines), which is in agreement with the attenuation of SAWs at the far field due to material and geometric damping, as described by

where

and

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( )

are wave amplitudes at distances for a circular source), and

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damping coefficient (

and

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:

(1)

from the crossover,

geometric

the material damping coefficient. We also

see oscillations with smaller amplitudes that do not fit into a single sinusoidal fit; these are residual waves generated by preceding laser pulses. By using Equation 4,

is estimated to be

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for P3HT, suggestive of a relatively high surface elasticity. The propagation

velocity was calculated as the sonic distance divided by time of travel and estimated to be

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. We note that this calculation is valid, although the wave pattern observed here

results from the accumulation of responses from multiple laser pulses, if we assume the system is

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linear and time-invariant (see Supplementary Information). By entering the propagation velocity and the empirical Poisson’s ratio (0.33 for typical polymers) into Equation 3, we determined the elastic Young’s modulus to be 1.03

, which is close to the literature value 41; the FFT

of the spectra is suggestive of the presence of only a few acoustic modes with the dominant wavelength of

.

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Figure 3- SAW dynamics on the P3HT surface. Figures (A) and (B), recorded from

the rectangle in Figure 2A at 0.1 ns and 3.4 ns, show the spatiotemporal dynamics of SAWs on the surface. (C) plots the spatial profile (solid dots) at 0.1 ns and 3.4 ns along the line in (A), fitted with the sinusoidal decay function (solid lines).

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To validate the experimental observation, we used the transient thermomechanical finite element method (FEM) in the commercial code, Ansys. We designed a 2D geometry whose thickness and length were

and

, respectively. The top surface was set free

whereas the bottom surface was assigned fixed to mimic the substrate effect; the length was intentionally chosen to be large to prevent the interference between the primary and boundary dimensions near the

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reflected SAWs at extended times. We used fine elements with

surface to provide sufficient spatial resolution and capture all possible acoustic modes. For this analysis, we used the elastic modulus and damping coefficient obtained from the experimental calculations. We then excited the model with a spatiotemporally Gaussian pulse (FWHM: and

), which deposited

at the center of the model. Given the experimentally

and wave velocity , we can calculate the relaxation time of

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measured damping coefficient

⁄

SAWs as  r  1  c   200 ns . Therefore, the contribution to the observed pattern from the response of the second pulse is only roughly 0.6% of the first-pulse response. So we only simulate the response to a single laser pulse, which is sufficient for a qualitative comparison to the experiment.

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Figure 4A shows the transient and steady-state thermal behavior of the model at the center, whose temperature increases from

to

after impulsive excitation and then

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cools down exponentially to recover the ground state. Due to the low thermal conductivity of P3HT, the decay process is rather slow and requires tens of microseconds to reach the initial

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room temperature. In the actual experiment, the crossover is illuminated by millions of pulses at intervaals; this forces the crossover to equilibrate at a higher steady-state temperature. In

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fact, the simulation of the same system excited with 16 successive pulses shows that the equilibrium temperature increases from

to

; this in return, may induce non-linear

effects, especially at the near field close to the crossover where the material is in a quasi-

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equilibrium state.

Figure 4B plots the calculated surface displacement versus time for a region

wide and

away from the epicenter; this region was selected to mimic the experimental

conditions presented previously. The initial wave front enters this region excitation; the cross-correlation indicates that these waves initially travel at wavelength of

after optical ⁄ with a

; these are fairly close to our experimental observation. However, at

extended times, both the wavelength of velocity of these waves change to 12

and

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⁄ , due to continuous wave interference and the loss of energy as these waves propagate. This simulation captured the overall behavior of SAWs as observed by SUEM. In conclusion, four-dimensional electron microscopy was used to image the formation and propagation of SAWs on the P3HT surface. The characteristics of these waves were then employed to calculate the elastic behavior exclusive to the surface, which is particularly

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important when the mechanical properties of thin devices and interfaces are desired. Since SUEM can operate at low vacuum, similar investigation can be done under the exposure of different gasses, which will help optimize the performance of such devices used in different

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environment.

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Figure 4- Finite element analysis of SAWs. Figure (A) shows the transient temperature at the crossover after each excitation. (B) Surface displacement at the far field, which shows wellstructured waves with the dominant wavelength of

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Acknowledgements This work was supported by NSF grant DMR-0964886 and Air Force Office of Scientific Research grant FA955011-1-0055 in the Physical Biology Center for Ultrafast Science and Technology at California Institute of Technology, which is supported by the Gordon and Betty

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Moore Foundation.

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References

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

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22.

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9.

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8.

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6. 7.

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2. 3. 4. 5.

Chua, L. L.; Zaumseil, J.; Chang, J. F.; Ou, E. C.; Ho, P. K.; Sirringhaus, H.; Friend, R. H. Nature 2005, 434, (7030), 194-9. Mazzio, K. A.; Luscombe, C. K. Chem Soc Rev 2015, 44, (15), 5744. Muccini, M. Nat Mater 2006, 5, (8), 605-13. Zhang, C.; Chen, P.; Hu, W. Chem Soc Rev 2015, 44, (8), 2087-107. Ohring, M., The materials science of thin films : deposition and structure. 2nd ed.; Academic Press: San Diego, CA, 2002; p xxi, 794 p. VanLandingham, M. R. J Res Natl Inst Stand Technol 2003, 108, (4), 249-65. Leroy, O.; Breazeale, M. A., Physical Acoustics Fundamentals and Applications. Springer US,: Boston, MA, 1991; p 1 online resource (724 pages). Viktorov, I. A., Rayleigh and Lamb waves: physical theory and applications. Plenum Press: New York,, 1967; p x, 154 p. Aggelis, D. G.; Hemelrijck, D. v.; Vanlanduit, S.; Anastasopoulos, A.; Philippidis, T., Emerging technologies in non-destructive testing VI. CRC Press, an imprint of the Taylor & Francis Group, an Informa business,: Boca Raton, 2016; p 1 online resource (525 pages). Ferreira, G. N.; da-Silva, A. C.; Tome, B. Trends Biotechnol 2009, 27, (12), 689-97. Gronewold, T. M. Anal Chim Acta 2007, 603, (2), 119-28. Lange, K.; Rapp, B. E.; Rapp, M. Anal Bioanal Chem 2008, 391, (5), 1509-19. Lee, H. J.; Namkoong, K.; Cho, E. C.; Ko, C.; Park, J. C.; Lee, S. S. Biosens Bioelectron 2009, 24, (10), 3120-5. Rocha-Gaso, M. I.; March-Iborra, C.; Montoya-Baides, A.; Arnau-Vives, A. Sensors (Basel) 2009, 9, (7), 5740-69. Campbell, C., Surface acoustic wave devices for mobile and wireless communications. Academic Press: San Diego, 1998; p xxvi, 631 p. Fourikis, A.; Mahler, G. Phys Rev B Condens Matter 1987, 36, (18), 9649-9656. Shilton, J. M.; Talyanskii, V. I.; Pepper, M.; Ritchie, D. A.; Frost, J. E.; Ford, C. J.; Smith, C. G.; Jones, G. A. J Phys Condens Matter 1996, 8, (38), L531-9. Zhang, C. Y.; Gao, J.; Li, H.; Song, L.; Lu, C. IEEE Trans Ultrason Ferroelectr Freq Control 2011, 58, (7), 1452-9. Cheeke, J. D. N., Fundamentals and applications of ultrasonic waves. 2nd ed.; CRC Press,: Boca Raton, 2012; pp 1 online resource. Cho, J.; Hwang, T. Y.; Zewail, A. H. Proc Natl Acad Sci U S A 2014, 111, (6), 2094-9. Sun, J.; Adhikari, A.; Shaheen, B. S.; Yang, H.; Mohammed, O. F. J Phys Chem Lett 2016, 7, (6), 985-94. Sun, J.; Melnikov, V. A.; Khan, J. I.; Mohammed, O. F. J Phys Chem Lett 2015, 6, (19), 3884-90. Yang, D. S.; Mohammed, O. F.; Zewail, A. H. Angew Chem Int Ed Engl 2013, 52, (10), 2897-901. Najafi, E.; Scarborough, T. D.; Tang, J.; Zewail, A. Science 2015, 347, (6218), 164-7. Najafi, E.; Ivanov, V.; Zewail, A.; Bernardi, M. Nat Commun 2017, 8. Liao, B. L.; Zhao, H.; Najafi, E.; Yan, X. D.; Tian, H.; Tice, J.; Minnich, A. J.; Wang, H.; Zewail, A. H. Nano Lett 2017, 17, (6), 3675-3680. Liao, B.; Najafi, E.; Li, H.; Minnich, A. J.; Zewail, A. H. Nat Nanotechnol 2017.

CE

1.

23. 24. 25. 26. 27.

16

ACCEPTED MANUSCRIPT

30. 31. 32. 33. 34. 35. 36. 37. 38.

AC

CE

PT

ED

M

39. 40. 41.

CR IP T

29.

Sun, J. Y.; Adhikari, A.; Shaheen, B. S.; Yang, H. Z.; Mohammed, O. F. J Phys Chem Lett 2016, 7, (6), 985-994. Sun, J. Y.; Melnikov, V. A.; Khan, J. I.; Mohammed, O. F. J Phys Chem Lett 2015, 6, (19), 3884-3890. Arnaud Maillard, A. R. Physical Review B 2009, 79, (11), 7. Yang, D. S.; Mohammed, O. F.; Zewail, A. H. Proc Natl Acad Sci U S A 2010, 107, (34), 14993-8. Bolin Liao, E. N. Materials Today Physics 2017, 2, 8. Jiang, S.; Racke, R., Evolution equations in thermoelasticity. Chapman & Hall/CRC: Boca Raton, 2000; p x, 308 p. Nowacki, W., Thermoelasticity. 2nd ed.; Pergamon Press; PWN: Oxford ; New York Warszawa, 1986; p xi, 566 p. Mohammed, O. F.; Yang, D. S.; Pal, S. K.; Zewail, A. H. J Am Chem Soc 2011, 133, (20), 7708-11. Ortalan, V.; Zewail, A. H. J Am Chem Soc 2011, 133, (28), 10732-5. Jolliffe, I. T., Principal component analysis. 2nd ed.; Springer: New York, 2002; p xxix, 487 p. Vidal, R.; Ma, Y.; Sastry, S. S., Generalized principal component analysis. In Interdisciplinary applied mathematics,, Springer,: New York, NY, 2016; pp 1 online resource (xxxii, 566 pages). Li, C.; Guan, G.; Li, S.; Huang, Z.; Wang, R. K. J Biomed Opt 2012, 17, (5), 057002. Dong-Soo Kim, J.-S. L. Soil Dynamics and Earthquake Engineering 2000, 19, (2), 12. Caironi, M.; Noh, Y.-Y., Large area and flexible electronics. Wiley-VCH,: Weinheim, 2015; p 1 online resource (588 pages).

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28.

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