Bulk modes in silicon crystal silicon

Bulk dilation modes in rectangular plates of particular orientations in single crystal silicon are found to have distinct advantages over to those in isotropic materials. Finite element modeling using an anisotropic model reveals plates aligned to the <;110>; direction in (100) silicon have modes which offer excellent capacitive coupling and good isolation to the supports. Low impedance and high Q are predicted for select geometries. Experimental results are included, showing a 100-MHz resonator having an unloaded Q of 90,000, which demonstrate an f-Q product of ~1×10¹³.