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Research Papers: Conduction

# Criteria for Cross-Plane Dominated Thermal Transport in Multilayer Thin Film Systems During Modulated Laser Heating

[+] Author and Article Information
Patrick E. Hopkins2

Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346pehopki@sandia.gov

Justin R. Serrano, Leslie M. Phinney, Sean P. Kearney, Thomas W. Grasser

Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346

C. Thomas Harris3

Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346

2

Corresponding author.

3

Joint appointment with the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139-4307.

J. Heat Transfer 132(8), 081302 (May 20, 2010) (10 pages) doi:10.1115/1.4000993 History: Received August 24, 2009; Revised December 02, 2009; Published May 20, 2010; Online May 20, 2010

## Abstract

Pump-probe transient thermoreflectance (TTR) techniques are powerful tools for measuring the thermophysical properties of thin films, such as thermal conductivity, $Λ$, or thermal boundary conductance, $G$. This paper examines the assumption of one-dimensional heating on, $Λ$ and $G$, determination in nanostructures using a pump-probe transient thermoreflectance technique. The traditionally used one-dimensional and axially symmetric cylindrical conduction models for thermal transport are reviewed. To test the assumptions of the thermal models, experimental data from Al films on bulk substrates (Si and glass) are taken with the TTR technique. This analysis is extended to thin film multilayer structures. The results show that at 11 MHz modulation frequency, thermal transport is indeed one dimensional. Error among the various models arises due to pulse accumulation and not accounting for residual heating.

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## Figures

Figure 1

Transient thermoreflectance setup at Sandia National Laboratories

Figure 2

Sensitivities of the Axf to G and Λ of the substrate in 100 nm Al/Si and Al/SiO2 systems

Figure 3

TTR data from scans on 100 nm Al films evaporated on Si (circles) and glass (squares) substrates along with the best fit from the Axf model scaled at 400 ps. Using the best fit values of G and Λ2 from the Axf, the 1Dt is calculated and scaled to the data showing that the 1Dt fails to capture some aspects of the data. The thermophysical properties determined from Axf model best fits are G=90 MW m−2 K−1 for the Al/Si interface, Λ=142 W m−1 K−1 for Si, and G=40 MW m−2 K−1 and Λ=1.0 W m−1 K−1 for the glass substrate. The measured thermal conductivity of the glass substrate is lower than that of pure SiO2 since the substrate in this case is a glass microscope slide, so the various impurities will reduce the thermal conductivity below that of pure SiO2.

Figure 4

Comparison of 1Df and Axf for a 100 nm Al film on a Si and glass substrate using the material properties determined from the fit in Fig. 3. The 1Dt and Axf are identical for these two material systems.

Figure 5

Ratio of the 1Df signal to the Axf signal as a function of heating event modulation frequency where the signals are defined as the ratio of the real to imaginary temperature rises predicted from the models, −TRe/TIm. An acceptable range to assume one-dimensional cross-plane transport is defined as when the 1Df signal ratio is within 90% of the Axf signal ratio as indicated by the horizontal dashed line. (a) Calculations assuming a 1:1 pump/probe radius ratio (i.e., 15 μm pump radius) shows that one-dimensional transport is achieved at modulation frequencies above 500 kHz except when the substrate material has diffusivities comparable to that of diamond (D∼1×10−3 m2 s−1) , in which case radial transport must be taken into account at modulation frequencies as high as 2 MHz. (b) Calculations assuming a 5:1 ratio (i.e., 75 μm pump radius). Radial heating is less apparent as the pump spot size increases. The inset of (b) shows the 1Df/Axf ratio for an 100 nm Al film on graphite for three pump-probe spot size ratios—10:1, 5:1, and 1:1.

Figure 6

Sensitivities of the Axf as a function of pump-probe delay time for four different Pt films of varying thickness and thermal conductivity. The various conductivities assumed for the Pt films are listed in the figures. Other parameters used for these calculations are GAl/Pt=500 MW m−2 K−1, CPt=2.85 MJ m−3 K−1 , and GPt/Si=140 MW m−2 K−1 . The properties used for the Al film and bulk Si substrate are listed in Table 1.

Figure 7

Sensitivities of the Axf as a function of pump-probe delay time for two SiO2 films with thicknesses of (a) 50 nm and (b) 250 nm. The thermal response with these insulative films is relatively insensitive to the thermal conductivity of the substrate over the pump-probe delay time. For comparison, the sensitivity of using a conductive Pt film of 250 nm is shown in (c). The thermal properties for the 250 nm Pt film are assumed bulk (see Fig. 5), and the other parameters assumed for these calculations were GAl/Pt=500 MW m−2 K−1, CPt=2.85 MJ m−3 K−1 , and GPt/Si=140 MW m−2 K−1.

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