Supporting Information for

Transcription

1 Supporting Information for Enhancing the Thermal Conductance of Polymer and Sapphire Interface via Self-Assembled Monolayer Kun Zheng,,+ Fangyuan Sun,,+ Jie Zhu, *,, Yongmei Ma, *, Xiaobo Li, Dawei Tang, Fosong Wang, Xiaojia Wang S-1

2 1. Ellipsometry of silane layer on silicon As shown in Figure S1, the thicknesses of the silane layers on silicon ranges from 0.7 to 1.0 nm, which is consist with the thickness of mono layer reported in literatures, 1-3 indicating the monolayer SAMs of our samples had been formed. Figure S1. The ellipsometric signals and their best fits for silane layers. The obtained thicknesses are listed under each plot. 2. TDTR measurements and uncertainty analysis Time-domain thermoreflectance (TDTR) method is used to measure the thermal conductivities and interfacial thermal conductance of all the samples involved in this paper. TDTR method is a well-accepted pump-probe measurement technique for characterizing thermal properties of bulk and thin film materials. During the measurement, sample surface is heated by a serial of pump laser pulses and the surface temperature is monitored with picosecond resolution based on thermoreflectance phenomenon. The pump pulses are modulated at 1 MHz with an S-2

3 electro-optic modulator. A lock-in amplifier is used to detect the intensity change of the reflected probe beam. The ratio of the in-plane to out-of-plane signal (-V in /V out ) is fitted to a thermal diffusion model to extract unknown thermal properties. Usually, one or two unknown parameters can be obtained if all the other parameters are known accurately. For our system, a ~100 nm Al film is deposited on the top of the samples as a transducer layer, which heat the sample surface by converting the absorbed pump laser energy and monitor the surface temperature due to the reflectivity change with the temperature. Since acoustic waves travel at a few nanometers per picosecond, the depth resolution of TDTR is approximately the same as the SAM thickness (~1 nm). Thus, we treat the SAM layer as an abrupt interface in the thermal model and its conductance is assumed to be the interfacial thermal conductance (G) at the PS/sapphire interface. To extract the interfacial thermal conductance between PS and sapphire, the thickness, thermal conductivity, and heat capacity for all other layers and must be known. The heat capacity for Al, 4 PS 5 and sapphire 6 is taken from literature values. The thickness of Al transducer layer is measured by AFM, and TDTR acoustic echo method and the thickness of PS films is measured by ellipsometry, please refer to thickness measurement part in this SI for further information. All the thermal conductivities and interfacial thermal conductance of the samples are measured by TDTR method. We summarize the modeling parameters in Table S1, and the superscript number represent the thermal property extract order. S-3

4 Table S1: Parameters used in thermal conductivity model to fit TDTR data. Al transducer layer Layer thickness (d) Measured by AFM/TDTR Thermal conductivity or interfacial thermal conductance (k or G) Heat capacity (C p ) Four probe type measurement J/cm 3 K Al/PS interface - Fitting parameter 3 - PS PS/SAM/Sapphire interface Measured by ellipsometry Fitting parameter J/cm 3 K - Fitting parameter 4 - Sapphire Semi-infinite Fitting parameter J/cm 3 K 2.1 Thickness of Al transducer layer TDTR signals usually contain information beyond thermal properties, such as the acoustic echoes generated by stress pulses induced in the metal film by the laser pulse. When the reflected pulses reach the surface of the Al, they produce a bump in the signal, and if the pulse makes multiple trips through the film then multiple echo bumps will be visible in the signal. Figure S2 shows the acoustic echoes in a 100 nm Al film on one of the samples. Each echo results from the sound pulse making one round trip through the Al film, and so the film thickness can be determined from: = (S1) where is the film thickness, is the time between echoes and is the longitudinal sound speed in the medium, 7-9 which is 6260 m/s for Al. The typical S-4

5 TDTR signals contains picosecond acoustic echoes are shown in Figure S2 where the averaged is ps, thus the calculated Al thickness is nm for this transducer layer. All the Al thicknesses are measured by TDTR picosecond acoustic echo method, and used in the TDTR data fitting process. As shown in Figure S3, the discrepancy of the thicknesses obtained from AFM and TDTR picosecond acoustic echo methods is within 2 nm. Figure S2. Measurement of the round-trip time of a sound pulse in an Al film on PS sample. Figure S3 Al transducer thicknesses measured by both AFM and picosecond acoustic methods S-5

6 2.2 Thermal conductivity of Al transducer layer In-plane electrical conductivity of the Al transducer layer is measured by 4-point probes method and then used to calculate the thermal conductivity by the Wiedemann-Franz law. And this thermal conductivity is considered as the know parameter in the following TDTR fitting process. 2.3 Thermal conductivity of sapphire substrate An Al/sapphire sample is used to measure the thermal conductivity of the sapphire substrate. In this step, the thermal conductivity of sapphire substrate and the interfacial thermal conductance is the fitting parameter. The measured thermal conductivity is about 35.5 W m -1 K -1 and used in the following TDTR fitting process as a known parameter. 2.4 Thermal conductivity of PS and interfacial thermal conductance of Al/PS interface In order to calibrate the thermal conductivity of PS films and the ITC of Al/PS, thicker PS films are good references since the PS/sapphire ITC will not affect the measurement signal significantly enough. On the other hand, since the thermal penetration depth decreases with increased modulation frequency in TDTR, we do the measurements and analysis at 8 MHz to achieve a relatively smaller thermal S-6

7 penetration depth (~60 nm). Figure S4 shows the maximum sensitivity (This maximum sensitivity is the peak value during the entire delay time between 200 ps to 4 ns in our TDTR measurements.) of interfacial thermal conductance as a function of PS thicknesses. Both the sensitivities of Al/PS and PS/sapphire interfaces decrease with the increase of the PS thickness, and maintain a constant when the PS is thicker than ~200 nm. In addition, the sensitivity of PS/sapphire interface drops to zero after ~200 nm, which mean the excitation heat cannot reach the interface and the PS can be considered as a bulk substrate without significant error. A series of Al/PS/sapphire (without SAMs) samples with the thickness of PS films between 50 and 500 nm have been prepared, and several samples with PS thickness between 250 and 500 nm are measured to extract the PS thermal conductivity and Al/PS interfacial thermal conductance. The result shows that the PS thermal conductivity falls into a narrow range between 0.14 to 0.16 W m -1 K -1 and the Al/PS interfacial thermal conductance falls into a narrow range between 18 to 20 MW/m 2 K. Since the PS thermal conductivity is nearly constant when thicker than its radius gyration (~7 nm in the this work), 10 which means all the samples used in this paper has almost the same PS thermal conductivity. We take the average value for PS thermal conductivity (0.15 W m -1 K -1 ) and Al/PS interfacial thermal conductance (20 MW m -2 K -1 ) as known parameters in the data analysis for other measurements. S-7

8 Figure S4. -V in /V out signal sensitivity for an Al/PS/sapphire sample. The blue line and the green line represent the interfacial thermal conductance sensitivity of the Al/PS and PS/sapphire ITC, respectively. 2.5 Interfacial thermal conductance of PS/SAM/sapphire interface Now in the thermal modeling, all the parameters except the PS/SAM/sapphire ITC are known after step 1. To achieve a higher sensitivity, we are seeking an optimized modulation frequency with the highest signal sensitivity to the PS/SAM/sapphire ITC. Figure S5. -V in /V out signal sensitivity for an Al/PS/SAM/sapphire sample, ITC Al/PS = 20 MW m -2 K -1 and ITC PS/sapphire = 30 MW m -2 K -1 are used in the calculation here. The blue line represent the interfacial thermal conductance sensitivity of the PS/SAM/sapphire interface. As shown in Figure S5, the calculated sensitivity to PS/SAM/sapphire ITC (at 2 S-8

9 ns delay time) reaches its highest value around 1 MHz, which is thus applied in this step for the ITC measurement of PS/SAM/sapphire. 2.6 Uncertainty analysis The largest uncertainty source of the experiments comes from the Al thickness, PS thickness and Al thermal conductivity. As shown in Figure S6, we exam the relative error of PS/sapphire interfacial thermal conductance caused by these parameters, and the results shows that the relative errors increase with the PS/sapphire interfacial thermal conductance and the uncertainty of Al thermal conductivity is the main error source. We calculate the total relative error by propagation of uncertainty which is between 5.1% and 26.4%. Figure S6. Relative error of PS/sapphire interfacial thermal conductance considering the uncertainty of Al thickness, PS thickness and Al thermal conductivity. TDTR measurements are repeated 3 times on difference locations for each sample and the results are average to remove the uncertainty comes from the uniformity of the interfaces and surfaces of the samples. S-9

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