Methods of Forming Micromechanical Resonators Having High Density Trench Arrays Therein that Provide Passive Temperature Compensation
First Claim
1. A method of forming a micromechanical resonator operable in a bulk acoustic mode, comprising:
- forming a resonator body anchored to a substrate by at least a first anchor, said resonator body comprising a first material having a negative temperature coefficient of elasticity (TCE) and an array of spaced-apart trenches filled with a second material having a positive TCE, said array of spaced-apart trenches having a sufficient density in the resonator body to meet the following relationship;
1≦
−
RV(TCEI/TCES)[(EI/ES)+(ρ
I/ρ
S)1/2(EI/ES)−
1/2]≦
3,where RV=(VI/VS);
TCES, ES, ρ
S and VS represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and volume of the first material in the resonator body, respectively; and
TCEI, EI, ρ
I and VI ρ
represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and total volume of the second material in the array of spaced-apart trenches, respectively.
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Abstract
A method of forming a micromechanical resonator includes forming a resonator body anchored to a substrate by at least a first anchor. This resonator body may include a semiconductor or other first material having a negative temperature coefficient of elasticity (TCE). A two-dimensional array of spaced-apart trenches are provided in the resonator body. These trenches may be filled with an electrically insulating or other second material having a positive TCE. The array of trenches may extend uniformly across the resonator body, including regions in the body that have relatively high and low mechanical stress during resonance. This two-dimensional array (or network) of trenches can be modeled as a network of mass-spring systems with springs in parallel and/or in series with respect to a direction of a traveling acoustic wave within the resonator body during resonance.
52 Citations
23 Claims
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1. A method of forming a micromechanical resonator operable in a bulk acoustic mode, comprising:
-
forming a resonator body anchored to a substrate by at least a first anchor, said resonator body comprising a first material having a negative temperature coefficient of elasticity (TCE) and an array of spaced-apart trenches filled with a second material having a positive TCE, said array of spaced-apart trenches having a sufficient density in the resonator body to meet the following relationship;
1≦
−
RV(TCEI/TCES)[(EI/ES)+(ρ
I/ρ
S)1/2(EI/ES)−
1/2]≦
3,where RV=(VI/VS);
TCES, ES, ρ
S and VS represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and volume of the first material in the resonator body, respectively; and
TCEI, EI, ρ
I and VI ρ
represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and total volume of the second material in the array of spaced-apart trenches, respectively.- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. A method of forming a micromechanical resonator operable in a bulk acoustic mode, comprising:
-
forming a resonator body having upper and lower surfaces thereon, said resonator body comprising a first material having a negative temperature coefficient of elasticity (TCE) and an array of spaced-apart trenches filled with a second material having a positive TCE, said array of spaced-apart trenches having a sufficient density in the resonator body to meet the following relationship;
0.5≦
−
RV(TCEI/TCES)[(EI/ES)+(ρ
I/ρ
S)1/2(EI/ES)−
1/2],where RV=(VI/VS);
TCES, ES, ρ
S and VS represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and volume of the first material in the resonator body, respectively; and
TCEI, EI, ρ
I and VI represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and total volume of the second material in the array of spaced-apart trenches, respectively; andwherein a density of the filled trenches in the upper surface of the resonator body is at least five trenches/square for each square region on the upper surface having an area equal to t2, where t is a thickness of the resonator body as measured between the upper and lower surfaces. - View Dependent Claims (14, 15, 16)
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17. A method of forming a micromechanical resonator operable in a bulk acoustic mode, comprising:
-
forming a resonator body having upper and lower surfaces thereon, said resonator body comprising a first material having a negative temperature coefficient of elasticity (TCE) and a two-dimensional array of spaced-apart through-body holes filled with a second material having a positive TCE, said through-body holes having minimum and maximum lateral dimensions in a range from about 0.1 T to about 0.2 T, where T is a thickness of the resonator body and T is greater than about 10 microns; and wherein a density of the filled through-body holes is at least five trenches/square for each square region on the upper surface having an area equal to t2, where t is a thickness of the resonator body as measured between the upper and lower surfaces. - View Dependent Claims (18, 19, 20, 21, 22)
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23. A method of forming a micromechanical resonator operable in a bulk acoustic mode, comprising:
-
forming a resonator body having upper and lower surfaces thereon, said resonator body comprising a first material having a negative temperature coefficient of elasticity (TCE) and an array of spaced-apart trenches filled with a second material having a positive TCE, said array of spaced-apart trenches having a sufficient density in the resonator body to meet the following relationship;
0.5≦
−
RV(TCEI/TCES)[(EI/ES)+(ρ
I/ρ
S)1/2(EI/ES)−
1/2],where RV=(VI/VS);
TCES, ES, ρ
S and VS represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and volume of the first material in the resonator body, respectively; and
TCEI, EI, ρ
I and VI represent the temperature coefficient of elasticity, Young'"'"'s modulus, density and total volume of the second material in the array of spaced-apart trenches, respectively; andwherein a density of the filled trenches in the upper surface of the resonator body is at least one trench/square for each square region on the upper surface having an area equal to t2, where t, which is a thickness of the resonator body as measured between the upper and lower surfaces, is in a range from about 2 microns to about 10 microns.
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Specification