Temperature compensation of silicon MEMS Resonators by Heavy Doping

Passive temperature compensation of silicon MEMS resonators based on heavy n- and p-type doping is studied. Resonators are fabricated utilizing silicon with phosphorus doping level of 5·10¹⁹ cm^-3 and boron doping levels of 5·10¹⁹ cm^-3 and 2 · 10²⁰ cm^-3, the latter being stress compensated with germanium. The temperature behavior of the resonance frequencies of Lamé and square extensional (SE) modes is measured. Depending on the vibration mode and crystal orientation, significant temperature compensation effects are observed: as a result of heavy n-type doping the temperature coefficient of frequency (TCF) of the SE mode is reduced from -32 ppm/K to ca. -1 ppm/K, while a Lamé mode resonator exhibits an overcompensated TCF of +18 ppm/K. In p-type resonators a TCF of ca. -2 ppm/K is observed in a Lamé-mode. Keyes´ [1] theory of free carrier contribution to the elastic constants of many-valley semiconductors is used to predict the temperature behavior of the n-type resonators. Good agreement is obtained between predicted and observed temperature behavior. The n-type doping can be applied to the TCF reduction of a large class of resonators and shows great potential in improving Si resonator performance.