Phase-controlled, heterodyne laser-induced transient grating measurements of thermal transport properties in opaque material

Abstract

The methodology for a heterodyned laser--induced transient thermal grating technique for non-contact, non--destructive measurements of thermal transport in opaque material is presented.Phase--controlled heterodyne detection allows us to isolate pure phase or amplitude transient grating signal contributions by varying the relative phase between reference and probe beams.The phase grating signal includes components associated with both transient reflectivity and surface displacement whereas the amplitude grating contribution is governed by transient reflectivity alone. By analyzing the latter with the two--dimensional thermal diffusion model, we extract the in--plane thermal diffusivity of the sample. Measurements on a 5 µm thick single crystal PbTe film yielded excellent agreement with the model over a range of grating periods from 1.6 to 2.8 µm. The measured thermal diffusivity of 1.3 × 10 --6 m 2 /s was found to be slightly lower than the bulk value.

Compact stochastic models for multidimensional quasiballistic thermal transport

“…Note that our reasoning deviates from the result given by Minnich [24], who incorporated an additional factor (1 + ξ 2 z d 2 opt ) −1 to account for cross-plane weighing of the thermal field by the probe beam. However, we argue that no such weighing takes place since the probe reflection is normally considered to originate at the actual sample surface [2]. Modelling the thermal transport with a 3D isotropic Poissonian process P (ζ, t) = exp[−ψ 3 (ζ) t] we obtain…”

“…2. For perfect surface heating (d opt → 0) the diffusive response obeys M ∝ (Dt) −1/2 exp(−4π 2 Dt/λ 2 ); conventional analyses fit this simple form to the measured transients to extract an effective diffusivity D eff (λ) [3,4].…”

“…TTG analysis of GaAs TTG experiments use interference of two laser beams to subject the sample to a heating pulse that is spatially periodic (grating period λ) in one in-plane direction (x) [2]. The induced power density p is assumed to extend uniformly across the other in-plane direction (y) and decays exponentially in the cross-plane direction (z) with the optical penetration depth d opt of the pump laser:…”

“…Some measurements induce nondiffusive behaviour directly by altering the physical size of the heat source. 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].…”

Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance

“…Furthermore, direct calculations of k accum at the phonon mode level by molecular dynamic simulations or lattice dynamics calculations 1,2,10 yield different behaviours for k accum than the analytical approaches. Discrepancies among predictions and a lack of information from conventional thermal conductivity measurements have motivated innovative experiments to probe phonon MFP spectra 1,[16][17][18][19][20] . Koh and Cahill 16 found that the thermal conductivities of InGaP, InGaAs and SiGe alloys measured by time domain thermoreflectance (TDTR) depend on the surface heat flux modulation frequency (f).…”