The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T>200 K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures.

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We have fabricated ballistic cavities from a two-dimensional GaAs electron gas in which the Fermi energy can be varied independent of cavity shape. For each cavity, we have measured the magnetoconductance G(B) of many individual members of an ensemble, with each member labeled by its Fermi energy. We find that G(B) of a single ensemble member does not always display the minimum at Bϭ0 which is the signature of weak localization. By averaging over our ensemble, we have obtained the energy-averaged weak-localization effect for each cavity shape. The average result does display the expected minimum at Bϭ0. We compare our results with recent analytical theories and numerical simulations of weak localization in cavities with chaotic classical scattering and find good quantitative agreement.Two quantum interference effects due to multiply scattered electron waves, conductance fluctuations 1 and weak localization, 2 have been studied extensively in diffusive conductors, where electron scattering occurs on a length scale much smaller than the system size. Both effects have more recently been observed in ballistic cavities fabricated from the two-dimensional ͑2D͒ electron gas of a GaAs/Al x Ga 1Ϫx As heterostructure, where large angle scattering is dominated by the edges of the cavities rather than by impurities. Ballistic quantum interference effects involving a magnetic field are governed by the distribution of enclosed areas in the classical analog of the cavity, according to a semiclassical analysis. 3 The area distribution is determined by the shape of the cavity and the size of the leads. For shapes in which classical particles scatter chaotically, the probability that a particle encloses an area A before escape is given by P(A)ϰe Ϫ2␣͉A͉ . 3 The inverse area ␣ determines the magnetic-field scale of the conductance fluctuations and the weak localization. For nonchaotic cavities the area distribution is not exponential and the semiclassical theory predicts the quantum interference will differ from that found in chaotic cavities. Experimental studies of conductance fluctuations as a function of magnetic field in chaotic cavities 4,5 agree well with the predictions of the semiclassical theory, and evidence for a difference between chaotic and nonchaotic shapes has been reported in one case. 4 Here we focus on weak localization ͑WL͒ in ballistic cavities. We demonstrate that ballistic conductors do not ''self-average'' as do typical diffusive conductors used for the study of WL. This points out the need to average over an ensemble of cavities. We describe the fabrication of cavities in which the Fermi energy can be varied without changing the cavity shape. These cavities allow us to create many ensemble members and to construct the ensemble-averaged ballistic WL explicitly from the behavior of the individual members. Our results for three cavities with different shapes are in good quantitative agreement with theoretical predictions. We also discuss using the comparison with theory to estimate the amount of electron phase...

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