Microelectromechanical resonator and a method for producing the same
The invention relates to temperature compensated micro-electro-mechanical (MEMS) resonators ( 300 ) preferably made of silicon. Prior art MEMS resonators have a significant temperature coefficient of resonance frequency, whereby it is difficult to achieve a sufficiently good frequency stability. The inventive MEMS resonator has a resonance plate ( 310 ) which resonates in Lamé mode. The resonance plate is p+ doped material, such as silicon doped with boron, and the concentration of the p+ doping is such that the plate has a temperature coefficient of resonance frequency near to zero. The tensile stress and the second order temperature coefficient can further be reduced by doping the plate with germanium.
1. Micro-electro-mechanical (MEMS) resonator comprising:
a substrate; and
a resonator plate which is anchored to the substrate and which is arranged to resonate in a Lamé mode,
wherein the resonator plate is comprised of a material p+ doped in such a quantity that the temperature coefficient of the resonance frequency of the plate is close to zero,
wherein the resonator plate material is p+ doped with an element of boron group of the periodic table of elements, and
wherein the p+ doping concentration in the resonator plate is between 5*10 19 cm −3 and 3*10 20 cm −3 thereby rendering the temperature coefficient of the resonance frequency of the plate close to zero.
2. MEMS resonator according to claim 1 , wherein the basic form of the resonator plate is square.
3. MEMS resonator according to claim 1 , wherein the basic form of the resonator plate comprises n×m squares, wherein n and m are integers.
4. MEMS resonator according to claim 1 , wherein a side of the resonator plate has a crystal orientation <110>.
5. MEMS resonator according to claim 1 , further comprising another of said resonator plate so as to define a first resonator plate and a second resonator plate, wherein said first resonator plate diagonal is oriented along <110> direction and said second resonator plate diagonal is oriented along <100> direction.
6. MEMS resonator according to claim 1 , wherein the resonance mode is characterised by the equation
f
=
1
2
L
c
44
ρ
wherein L stands for the length of the side of a square or a sub square when the resonance plate is formed of a square or sub squares, c44 is an elastic constant of the resonator plate material, ρ stands for density of the resonator plate material, and f is resonance frequency.
7. MEMS resonator according to claim 1 , wherein the side of a resonator plate has a crystal orientation <100>.
8. MEMS resonator according to claim 1 , characterised in that the resonance mode is characterised by the equation
f
=
1
2
L
c
11
-
c
12
ρ
wherein L stands for the length of the side of a square or a sub square when the resonance plate is formed of a square or sub squares, c 11 and c 12 are elastic constants of the resonator plate material, and ρ stands for density of the resonator plate material, and f is resonance frequency.
9. MEMS resonator according to claim 1 , wherein the resonator plate material is p+ doped with boron.
10. MEMS resonator according to claim 1 , wherein the resonator plate material is additionally doped with a further element for reducing the tensile stress of the resonator plate material.
11. MEMS resonator according to claim 10 , wherein the further element is germanium.
12. MEMS resonator according to claim 1 , wherein the resonator plate material is additionally doped with a further element for reducing the second order temperature coefficient of the resonator plate material.
13. MEMS resonator according to claim 1 , wherein it comprises electrodes adjacent to the sides of the resonance plate for actuating the resonator plate to resonate in Lamé mode.
14. MEMS resonator according to claim 1 , wherein the resonance plate comprises a layer of silicon dioxide for increasing the absolute value of the temperature coefficient of the resonance plate.