Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions

Abstract

This paper describes the instrumentation for broadband frequency domain thermoreflectance (BB-FDTR), a novel, continuous wave laser technique for measuring the thermal conductivity accumulation function. The thermal conductivity accumulation function describes cumulative contributions to the bulk thermal conductivity of a material from energy carriers with different mean free paths. It can be used to map reductions in thermal conductivity in nano-devices, which arise when the dimensions of the device are commensurate to the mean free path of energy carriers. BB-FDTR uses high frequency surface temperature modulation to generate non-diffusive phonon transport realized through a reduction in the perceived thermal conductivity. By controlling the modulation frequency it is possible to reconstruct the thermal conductivity accumulation function. A unique heterodyning technique is used to down-convert the signal, therein improving our signal to noise ratio and enabling results over a broader range of modulation frequencies (200 kHz-200 MHz) and hence mean free paths. © 2013 AIP Publishing LLC. [http://dx

Compact stochastic models for multidimensional quasiballistic thermal transport

“…Key examples of scalable sources include laser interference patterns used by transient thermal grating (TTG) [2][3][4], metal nanogratings employed by soft x-ray metrology [5,6] and two-tint time domain thermoreflectance (TDTR) [7], and TDTR laser spot diameter [8,9]. The characteristic length scale of the thermal gradient can also be varied indirectly, as is done in time/frequency domain thermoreflectance (TDTR/FDTR) through the pump laser modulation frequency [9][10][11][12][13].…”

“…However, BTE solutions are formulated in terms of a wide spectrum of phonon modes and as such are too intricate and inflexible for direct processing of experimental data. Instead, nearly all measurements of inherently nondiffusive heat dynamics are analysed using conventional diffusive theory and interpreted in terms of 'effective' Fourier thermal conductivities/resistivities [3][4][5][6][7][8][9][10][11][12]. Several of our prior works [13,25] have pointed out substantial artifacts induced by this methodology, and other community members have joined in expressing the growing need for 'beyond Fourier' characterisation frameworks [6,26].…”

Experimental estimates of in-plane thermal conductivity in FePt-C granular thin film heat assisted magnetic recording media using a model layered system

“…Likewise, the k th values of Au were calculated from the Au sheet resistance as measured by 4-point probe measurements for separate Au films deposited on 1 lm-thick thermally grown SiO 2 films on Si substrates following the Weidemann Franz Law. The k th value of n-type Si substrates were found to be 95 6 10 W/m-K, which appears low relative to the bulk value (143 W/m-K) for Si, but is reasonably attributed to the known suppression in k th observed by high frequency FDTR measurements 17,18 paired with effects of added phonon scattering due to phosphorous dopant concentration of about 10 15 Table I. These values were averaged over 3 measurements at 3 locations on the samples.…”

“…The thermal conductivities of the film stacks in the direction normal to the layers were characterized using the FrequencyDomain Thermoreflectance (FDTR) technique, [16][17][18][19] as illustrated in Figure 1(c), and we take those to be representative of the in-plane thermal conductivity of granular films when the lateral grain size is similar to the FePt thickness in the model samples. To estimate the effect of media grain size on the inplane lateral thermal conduction, the thickness of FePt layer was varied from 14.5 nm to 29 nm.…”

“…( In the FDTR method, 16,18,19 schematically illustrated in Figure 2(a), two continuous wave lasers periodically heat the sample and measure its thermal response to determine the unknown thermal transport properties of the FePt/C stack. The 1/e 2 effective radius of the Gaussian laser spots on the sample surface was measured by knife-edge to be 2.6 6 0.2 lm.…”