First and second orders temperature-compensated resonator

The resonator has a micro electro-mechanical system body i.e. bar, with a core formed of a plate formed at a cut angle in a quartz crystal determining first and second orders temperature coefficients. The body includes a coating deposited partially on the core, where the cut angle of the plate and thickness (d) of the coating are adapted according to thermoelastic coefficients of the coating to obtain first and second orders temperature coefficients of the resonator in order to render the temperature coefficients to be zero. The coating is made of germanium oxide and tantalum oxide.