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With the advent of nanotechnology, silicon nanoparticles have shown promising applications in the manufacturing sector. In this letter, we examine the lattice thermal conductivity predictions for a silicon nanoparticle using three popular formulations of the Boltzmann transport equation. The models as proposed by Klemens, Callaway and Holland, essentially differ in the phonon scattering mechanisms and the vibrational modes considered in the respective formulations. At low temperatures, results from all three models show strong agreement with experimental measurements, but deviate significantly with increasing temperatures. Estimates from the Holland model, which explicitly accounts for the normal and Umklapp scattering processes of the transverse and longitudinal modes, concur with the measured values. Similar predictions are obtained from both Holland and Callaway models at high temperatures since phonon transport is dominated by longitudinal modes, as revealed from our analyses of the relaxation times. In conclusion, the letter infers the importance of mode dependent thermal conduction in silicon nanoparticle at elevated temperatures. • Klemens, Callaway and Holland formulations of BTE differ in the phonon scattering mechanisms considered. • Holland model thermal conductivity predictions account for the normal and Umklapp scattering and concur with experiments. • All models show similar evolution at low, but not at high, temperatures. [ABSTRACT FROM AUTHOR]

• The multidimensional phonon Boltzmann Transport Equation (BTE) is solved. • A frequency domain thermo-reflectance experiment is simulated. • Phase lag is computed with and without optical phonons and compared to experiments. • Thermal conductivity is extracted and shows suppression. The multidimensional phonon Boltzmann Transport Equation (BTE) was solved numerically in cylindrical coordinates and in time domain to simulate a Frequency Domain Thermo-Reflectance (FDTR) experimental setup. The phase lag between the pump and probe laser signals were computed for a pump laser modulation frequency ranging from 20 to 200 MHz. Results were obtained both with and without the inclusion of optical phonons, as well as with two different relaxation time-scale expressions (Holland versus Broido) for scattering, obtained from the literature for silicon. It was found that inclusion of optical phonons significantly improved the agreement between the measured and the computed phase lag. Subsequently, the thermal conductivity was extracted by fitting the Fourier heat conduction equation results—also solved numerically in time domain—to the measured and computed (using BTE) phase lag values. While both relaxation time-scales exhibited thermal conductivity suppression, a clear superiority of one time-scale expression over the other could not be established. With the Broido time-scale, the thermal conductivity extracted from BTE calculations overpredicted the value extracted from experiments regardless of whether optical phonons were included in the calculations. In contrast, with the Holland time-scale, the extracted thermal conductivity value overpredicted the value extracted from experiments when optical phonons were included, but underpredicted the value when optical phonons were excluded. [ABSTRACT FROM AUTHOR]