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Research Papers: Thermal Systems

On the Steady-State Temperature Rise During Laser Heating of Multilayer Thin Films in Optical Pump–Probe Techniques

[+] Author and Article Information
Jeffrey L. Braun, Chester J. Szwejkowski, Ashutosh Giri

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904

Patrick E. Hopkins

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904;
Department of Materials
Science and Engineering,
University of Virginia,
Charlottesville, VA 22904;
Department of Physics,
University of Virginia,
Charlottesville, VA 22904
e-mail: phopkins@virginia.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 22, 2017; final manuscript received October 26, 2017; published online February 6, 2018. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(5), 052801 (Feb 06, 2018) (10 pages) Paper No: HT-17-1363; doi: 10.1115/1.4038713 History: Received June 22, 2017; Revised October 26, 2017

In this study, we calculate the steady-state temperature rise that results from laser heating of multilayer thin films using the heat diffusion equation. For time- and frequency-domain thermoreflectance (TDTR and FDTR) that rely on modulated laser sources, we decouple the modulated and steady-state temperature profiles to understand the conditions needed to achieve a single temperature approximation throughout the experimental volume, allowing for the estimation of spatially invariant thermal parameters within this volume. We consider low thermal conductivity materials, including amorphous silicon dioxide (a-SiO2), polymers, and disordered C60, to demonstrate that often-used analytical expressions fail to capture this temperature rise under realistic experimental conditions, such as when a thin-film metal transducer is used or when pump and probe spot sizes are significantly different. To validate these findings and demonstrate a practical approach to simultaneously calculate the steady-state temperature and extract thermal parameters in TDTR, we present an iterative algorithm for obtaining the steady-state temperature rise and measure the thermal conductivity and thermal boundary conductance of a-SiO2 with a 65-nm gold thin film transducer. Furthermore, we discuss methods of heat dissipation to include the use of conductive substrates as well as the use of bidirectional heat flow geometries. Finally, we quantify the influence of the optical penetration depth (OPD) on the steady-state temperature rise to reveal that only when the OPD approaches the characteristic length of the temperature decay does it alter the temperature profile relative to the surface heating condition.

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Figures

Grahic Jump Location
Fig. 1

Temperature profile as a function of radius and depth for a 100 nm Al/a-SiO2 sample subjected to a radially symmetric Gaussian surface heating event with 1/e2 radius of 15 μm and an average absorbed power of 1 mW. The heating event is modulated sinusoidally at 10 MHz; the temperature profile is decoupled to display the (a) constant component from the unmodulated (steady-state) response and (b) the magnitude of temperature rise from the modulated component.

Grahic Jump Location
Fig. 2

(a) Temperature rise due to pump beam heating as a function of radius. TPA is the probe-averaged temperature rise, shown for the cases when the probe radius is equal to pump radius, half the pump radius, and a quarter of the pump radius. (b) Normalized temperature (defined as probe averaged temperature rise divided by maximum temperature rise from pump heating) as a function of normalized probe radius (defined as the ratio of probe to pump radii).

Grahic Jump Location
Fig. 3

Steady-state temperature rise as a function of radius for (a) bulk amorphous SiO2 and a 100 nm Al film on a SiO2 substrate, (b) bulk polymer and a 100 nm Al film on a polymer substrate, and (c) bulk disordered C60, a 100 nm Al film on a C60 substrate, and a 100 nm Al film on a 100 nm C60 film on a Si substrate

Grahic Jump Location
Fig. 4

Heat flux vector field resulting from steady-state heating in (a) bulk a-SiO2 and (b) 100 nm Al on a-SiO2 when r0 = 1 μm and αA = 1 mW. The magnitude of the heat flux is shown as a contour.

Grahic Jump Location
Fig. 5

(a) Ratio of the steady-state temperature rise for a thin film of disordered C60 on Si and SiO2 (Tfilm) to that of bulk C60 (Tbulk) as a function of the ratio of C60 film thickness (d) to heater radius (r0). (b) Ratio of the steady-state temperature rise for 100 nm Al on a thin film of disordered C60 on Si (Tfilm) to that of 100 nm Al on bulk C60 (Tbulk) as a function of C60 thickness (d). In all cases, r1 = r0.

Grahic Jump Location
Fig. 6

Sensitivity of the magnitude of surface temperature rise to thermal parameters as determined by Eq. (4) for the (a) 10 MHz modulated frequency response and (b) steady-state unmodulated response for a 65-nm Au on a-SiO2 sample. Thermal parameters considered include in-plane and cross-plane thermal conductivities (κr and κz, respectively) for both the Au and a-SiO2 layers, volumetric heat capacities (Cv) for both layers, and thermal boundary conductance across the Au/a-SiO2 interface (hAu/a-SiO2).

Grahic Jump Location
Fig. 7

Experimentally determined thermal conductivities of a-SiO2 measured with TDTR when a 65 nm Au transducer layer is used. Solid squares denote the fitted values with temperatures based on calculations that include the Au transducer layer, while solid circles denote the fitted values using temperature rise calculations without including the Au transducer. In both cases, an iterative method was used as described by the inset, whereby input thermal parameters were chosen based on the steady-state temperature rise calculated, the TDTR data were used to fit the a-SiO2 thermal conductivity and the Au/a-SiO2 thermal boundary conductance, and all thermal parameters were then used to recalculate the steady-state temperature rise. This process is repeated until convergence is reached. Literature values are taken from Ref. [31].

Grahic Jump Location
Fig. 8

Temperature distributions for the bidirectional heat flow geometry consisting of transparent substrate/100 nm Al/polymer where laser irradiation occurs at the Al surface adjacent to the transparent substrate. For the case of this transparent substrate being (a) Al2O3 and (b) SiO2, the steady-state (unmodulated) temperature profile is displayed as a contour in radius and depth, while the solid line is the magnitude of modulated temperature at r = 0 μm for a modulation frequency of 10 MHz. In both cases, positive depth depicts the Al/polymer side, while negative depth depicts the transparent substrate side. (c) depicts the steady-state surface temperature rise for the same bidirectional heat flow geometry where the transparent substrate is varied to span a wide range of thermal conductivities from Si (140 W m−1 K−1) to complete insulation. All thermal parameters used for these calculations are listed in Table 1.

Grahic Jump Location
Fig. 9

Sensitivity of the magnitude of modulated surface temperature rise (10 MHz modulation frequency) to thermal parameters as determined by Eq. (4) for the (a) Al2O3/100 nm Al/polymer and (b) a-SiO2/100 nm Al/polymer in the case of laser irradiation at the Al surface adjacent to Al2O3 (a-SiO2). Thermal parameters considered include cross-plane thermal conductivities (κz) for Al, Al2O3 (a-SiO2), and polymer layers and thermal boundary conductances across the Al/Al2O3 (SiO2) interface (hAl/Al2O3(a-SiO2)) and across the Al/polymer interface (hAl/polymer).

Grahic Jump Location
Fig. 10

Effect of optical penetration depth on the heating of bulk materials: (a) and (b) depict the steady-state temperature profile and heat flux for a bulk a-Si film when r0 = 15 μm and αA = 1 mW and the optical penetration depth is 300 nm. (c) Maximum temperature rise for the same sample. The normalized temperature, defined as the ratio of maximum temperature with a finite optical absorption depth to the maximum temperature assuming all optical absorption occurs at the surface, is also plotted as a function of normalized optical penetration depth, defined as the ratio of optical penetration depth to pump radius.

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