Embedded nanoparticles have been shown to reduce thermal conductivity of semiconductors below the alloy limit while preserving electron mobility and the thermoelectric power factor. A wide distribution of phonon mean free paths contribute to thermal conductivity of III-V alloys such as InGaAlAs. Changing the modulation frequency in time domain thermoreflectance (TDTR) has been used to extract contribution of ballistic phonons as the phonons with mean free path larger than the thermal penetration depth don’t contribute to the “apparent” thermal conductivity of the material. The apparent thermal conductivity of InGaAlAs alloy (20% Al, lattice matched to InP substrate) reduces by more than 40% when the modulation frequency is increased from 1MHz (~ 1 microns thermal penetration length) to 10MHz (~0.3 microns thermal penetration length). This explanation is based on quasi-ballistic description that considers “ballistic” heat transport near the metal transducer and a transition to pure “diffusive” transport at larger distances. An alternative explanation is based on truncated Levy flight where ballistic “jumps” and Brownian “diffusion” are mixed. This gives rise to a fractional diffusion at early times (short distances). The transition to regular diffusion happens after a ballistic-diffusive transition length. While modified Fourier and truncated Levy can both explain the top transducer temperature profile accurately, their prediction for internal temperature distribution inside the semiconductor alloy can be significantly different. In this study, TDTR is used to investigate the effect of embedded nanoparticles on the Levy random walk as well as the thermal conductivity. Six samples of randomly distributed ErAs nanoparticles in InGaAlAs matrix with nanoparticles concentration ranging from 0.01 to 10% were characterized.
Consistent with previous observations , a drop in the thermal conductivity by a factor of 2.5 is observed with an increase in the nanoparticles concentration. More nanoparticles leads to more phonon scattering which reduces the effective phonon mean free path as well as the thermal conductivity. By varying the nanoparticles concentration from 0.01% to 10%, the extracted ballistic to diffusive transition length is reduced by almost an order of magnitude. This confirms that transition length is correlated to the effective phonon free path. On the other hand, the Levy exponent is almost constant (~1.55-1.67) in all of the samples. This suggests that superdiffusive exponent is inherent to the properties of the host material.
W. Kim, J. Zide, A. Gossard, D. Klenov, S. Stemmer, A. Shakouri and A. Majumdar, "Thermal Conductivity Reduction and Thermoelectric Figure of Merit Increase by Embedding Nanoparticles in Crystalline Semiconductors," Physical Review Letters, vol. 96, 2006.
Birck Nanotechnology center, Purdue University
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