The thermal conductivity of silicon nitride membranes is not sensitive to stress

We have measured the thermal properties of suspended membranes from 10 K to 300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and for two different thicknesses (50 nm and 100 nm). The use of the original 3 \omega -Volklein method has allowed the extraction of both the specific heat and the thermal conductivity of each SiN membrane over a wide temperature range. The mechanical properties of the same substrates have been measured at helium temperatures using nanomechanical techniques. Our measurements show that the thermal transport in freestanding SiN membranes is not affected by the presence of internal stress. Consistently, mechanical dissipation is also unaffected even though Qs increase with increasing tensile stress. We thus demonstrate that the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] does not apply to this amorphous material in this stress range. On the other hand, our results can be viewed as a natural consequence of the "dissipation dilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544 (1998)] which has been introduced in the context of mechanical damping.Comment: 15 pages, 6 figures. Submitted to PR

Evidence for the role of normal-state electrons in nanoelectromechanical damping mechanisms at very low temperatures

We report on experiments performed at low temperatures on aluminum covered silicon nanoelectromechanical resonators. The substantial difference observed between the mechanical dissipation in the normal and superconducting states measured within the same device unambiguously demonstrates the importance of normal-state electrons in the damping mechanism. The dissipative component becomes vanishingly small at very low temperatures in the superconducting state, leading to exceptional values for the quality factor of such small silicon structures. A critical discussion is given within the framework of the standard tunneling model

A Second Order Sliding Mode Controller with Predefined-Time Convergence

This paper presents the basis to design a well-suited control law which guarantees predefined-time convergence for a class of second-order systems. In contrast to the case of finite-time and fixed-time controllers, a predefined-time controller allows to set the bound of the convergence time, explicitly during the control design. Furthermore, in the case of no disturbance, the least upper bound of the convergence time can be predefined directly from the control definition. A Lyapunov-like characterization for predefined-time stability is performed. Numerical results are discussed to show the reliability of the proposed method.Consejo Nacional de Ciencia y Tecnologí