Microelectromechanical resonator
A method for manufacturing microelectromechanical flexural resonators with a deforming element that has an elongate body extending along a spring axis. A deforming element is positioned on the semiconductor wafer with a defined nominal n-type doping concentration such that a crystal orientation angle is formed between the spring axis of the deforming element and a crystal axis of the silicon semiconductor wafer. The combination of the crystal orientation angle and the nominal n-type doping concentration is adjusted to a specific range, based on total frequency error of the deforming element in a broad temperature range. The combination is optimized to a range where also sensitivity to variations in the material properties is minimized.
1. A method for manufacturing microelectromechanical resonators, wherein a microelectromechanical resonator comprises a deforming element with an elongate body that extends along a spring axis, and the method comprises:
providing a semiconductor wafer that has a nominal n-type doping concentration, a plane of the semiconductor wafer being aligned to a crystal plane of a semiconductor crystal;
positioning the deforming element on the semiconductor wafer such that a crystal orientation angle is formed between the spring axis of the deforming element and a <100> crystal axis of the semiconductor crystal lattice;
determining, for said crystal orientation angle and said nominal n-type doping concentration, a total frequency error value of the deforming element within a defined temperature range; and
manufacturing the deforming element using the crystal orientation angle if the determined total frequency error value is below a predefined error threshold value.
2. A method according to claim 1 , wherein the determining comprises determining the value for the total frequency error from the largest difference in frequency to the frequency at the reference temperature over the whole operational temperature range.
3. A method according to claim 1 , wherein the providing comprises providing a silicon semiconductor wafer, a plane of which is aligned to a crystal plane of a silicon crystal.
4. A method according to claim 1 , wherein the positioning comprises positioning the deforming element on the semiconductor wafer such that predefined error threshold value is 300 ppm and the nominal crystal orientation angle Θ and the nominal n-type doping concentration C of the deforming element in units of 1·10 19 cm −3 are in a range defined by equation:
C>k 1*Θ 3 +k 2*Θ 2 +k 3*Θ+ k 4, when Θ≧13 deg
where k1=0.0027 deg −3 cm −3
k2=−0.886 deg −2 cm −3
k3=1.1667 deg −1 cm −3
k4=−2.2624 cm −3 .
5. A method according to claim 1 , further comprising forming the elongate body such that the dimension of the body along the spring axis is at least three times the dimensions of the body in a direction traverse to the spring axis.
6. A method according to claim 1 , further comprising forming the elongate body into a beam, wherein the dimension of the beam along the spring axis is at least ten times the dimensions of the beam in a direction traverse to the spring axis.
7. A method according to claim 5 , further comprising anchoring the deforming element via an anchoring point to the microelectromechanical resonator for in-plane or out-of-plane flexure in respect to the plane of the semiconductor wafer.