Oven controlled N⁺⁺ [1 0 0] length-extensional mode silicon resonator with frequency stability of 1 ppm over industrial temperature range

This paper presents an oven controlled N⁺⁺ [1 0 0] length-extensional mode silicon resonator, with a lookup-table based control algorithm. The temperature coefficient of resonant frequency (TCF) of the N⁺⁺ doped resonator is nonlinear, and there is a turnover temperature point at which the TCF is equal to zero. The resonator is maintained at the turnover point by Joule heating; this temperature is a little higher than the upper limit of the industrial temperature range. It is demonstrated that the control algorithm based on the thermoresistor on the substrate and the lookup table for heating voltage versus chip temperature is sufficiently accurate to achieve a frequency stability of  ±0.5 ppm over the industrial temperature range. Because only two leads are required for electrical heating and piezoresistive sensing, the power required for heating of this resonator can be potentially lower than that of the oscillators with closed-loop oven control algorithm. It is also shown that the phase noise can be suppressed at the turnover temperature because of the very low value of the TCF, which justifies the usage of the heating voltage as the excitation voltage of the Wheatstone half-bridge. (paper)