Phonon–phonon interactions are a key intrinsic mechanism governing energy dissipation in resonators operating in the GHz to THz range, directly limiting the attainable quality factor (Q). In this work, a computational framework is established that integrates density functional theory (DFT), machine-learning-based Deep Potential (DP) training, and large-scale molecular dynamics (MD) simulations to investigate phonon–phonon interactions in single-crystalline silicon length extensional resonators. A DP model trained on DFT data is shown to reproduce forces and energies with high accuracy while enabling simulations at nanometer to sub-micrometer length scales. Within this framework, the dependence of f × Q on resonant frequency, temperature, and crystal orientation is systematically quantified. As the frequency increases from the GHz to the THz regime, Q exhibits a moderate decrease whereas f × Q increases. This behavior can be traced to a pronounced reduction in the phonon relaxation time. For a 74.7 GHz resonator, Q follows an approximate 1/T scaling, consistent with significant Akhiezer-like phonon–phonon damping, while possible boundary and finite-size contributions cannot be completely excluded in the present nanometer-scale geometries. Orientation dependent simulations further reveal that resonators aligned along the 〈110〉 crystal orientation exhibit systematically lower Q and smaller f × Q than those aligned along the 〈100〉 crystal orientation, due to enhanced phonon anisotropy and stronger coupling between acoustic and thermal phonons. These results provide an atomistic and quantitative picture of phonon–phonon interactions in silicon resonators and demonstrate that the proposed framework offers a general route for predicting and optimizing intrinsic damping in resonators based on silicon and other crystalline materials with diverse device geometries.
Chen et al. (Mon,) studied this question.
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