CN101947819B - Method for processing small-size quartz crystal substrate for manufacturing resonator - Google Patents

Abstract

The invention discloses a method for processing a small-size quartz crystal substrate for manufacturing a resonator. The method has the advantages that: because a relation between vibration frequency omega and size of the quartz crystal substrate is set by the method, the relationship between the vibration frequency and the size of the crystal substrate can be obtained through the relation, the size of the small-size quartz crystal substrate can be determined according to the pre-designed frequency, and the size and the vibration frequency of a large-size quartz crystal substrate to be processed can be further determined so that the vibration frequency of the small-size quartz crystal substrate obtained by cutting meets the designed frequency requirement and the finally obtained small-size quartz crystal substrate is ensured to be a qualified wafer; and the method improves the processing efficiency, and reduces the processing difficulty of the small-size quartz crystal substrate at the same time.

Description

A kind of processing method of the small size quartz crystal substrate for the manufacture of resonator

Technical field

The present invention relates to a kind of shearing-type quartz-crystal resonator, relate in particular to a kind of processing method of the small size quartz crystal substrate for the manufacture of resonator.

Background technology

In the design and manufacturing of quartz-crystal resonator, the vibration frequency of resonator is most important performance parameter, the vibration frequency of general shear type resonator and thickness and the size of quartz crystal substrate have relation, and the size of quartz crystal substrate (length and width and thickness) increase can make the vibration frequency of resonator reduce.

The processing of traditional quartz-crystal resonator is generally finished at a wafer, and we are mainly used in design and the processing of resonator to the estimation of wafer frequency.In the calculating of the vibration frequency of quartz crystal substrate, owing to considered that length is far longer than width usually, so use craspedodrome ripple solution (supposing that namely elastic wave only changes a direction of propagation) to analyze relation between the size of vibration frequency and quartz crystal substrate usually.But along with the size of quartz crystal product constantly diminishes, significant change has also taken place in the processing mode of resonator, one of them obvious variation is: because wafer size diminishes, monolithic method for processing efficient is not high, difficulty increases, so can at first select a bigger wafer is processed, cuts after some important process are finished as operations such as polishing, cleaning and back of the body silver again, thereby can merge many technologies, realize improving the target of working (machining) efficiency.But because the frequency parameter of the frequency parameter of wafer and the little wafer that finally obtains is different, we can't guarantee the accurate estimation to the little wafer frequency parameter that obtains through cutting according to present method, thereby also can't guarantee to be qualified wafer through the little wafer that cutting obtains.

Summary of the invention

Technical problem to be solved by this invention provides a kind of vibration frequency of the little wafer that obtains of cutting that makes and satisfies the design frequency requirement, guarantees that namely little wafer that cutting obtains is the processing method for the manufacture of the small size quartz crystal substrate of resonator of the qualified wafer of design.

The present invention solves the problems of the technologies described above the technical scheme that adopts: a kind of processing method of the small size quartz crystal substrate for the manufacture of resonator may further comprise the steps:

(1), setting the vibration frequency Ω of quartz crystal substrate and the relational expression between its size is:

In the formula: a is the length of quartz crystal substrate, and c is the width of quartz crystal substrate, and b is the thickness of quartz crystal substrate, and α, β, γ, δ and ε are the coefficient relevant with the material property of quartz crystal;

(2), obtain the value of factor alpha, β, γ, δ and ε, and in the relational expression with the value substitution step (1) of factor alpha, β, γ, δ and ε;

(3), set the target vibration frequency Ω of the small size quartz crystal substrate that finally will obtain _Little, length a _LittleWith width c _Little, obtain the thickness b of small size quartz crystal substrate then by relational expression _Little

(4), measure the length a of large scale quartz crystal substrate to be processed _GreatlyWith width c _Greatly, and the processing thickness b of setting large scale quartz crystal substrate _GreatlyThickness b with small size quartz crystal substrate _LittleEquate, utilize the length a of large scale quartz crystal substrate then _Greatly, width c _GreatlyWith processing thickness b _GreatlyObtain the theoretical vibration frequency Ω of large scale quartz crystal substrate by relational expression _Reason

(5), the processing thickness b that configures according to step (4) _GreatlyMachining large-sized quartz crystal substrate, and the actual vibration frequency omega of the large scale quartz crystal substrate after the detection processing _Real, then with the actual vibration frequency omega of large scale quartz crystal substrate _RealVibration frequency Ω theoretical with it _ReasonCompare, if both error is in ± 0.5%, then large scale quartz crystal substrate is certified products;

(6), to qualified large scale quartz crystal substrate by the length a that configures _LittleWith width c _LittleCut, obtain meeting target vibration frequency Ω _LittleSmall size quartz crystal substrate, i.e. qualified small size quartz crystal substrate.

The value of factor alpha, β, γ, δ and ε described in the step (2) is tried to achieve by following step:

(1-1), use with large scale quartz crystal substrate identical materials to be processed and produce some quartz crystal check-out consoles with different size, and the vibration frequency Ω of described quartz crystal check-out console is in vibration frequency under the optimum thickness scissoring vibration state for it, and measures length a, width c, thickness b and the vibration frequency Ω of these quartz crystal check-out consoles respectively;

(1-2), with the vibration frequency Ω of some bauerite crystal check-out consoles of obtaining in the step (1-1) and dimensional parameters a, c, b respectively at relational expression:

Carry out the curve match based on least square method, obtain the value of factor alpha, β, γ, δ and ε in the relational expression.

Determine that the concrete steps whether described quartz crystal check-out console is in optimum thickness scissoring vibration state are: the design frequency with described quartz crystal check-out console encourages this quartz crystal check-out console, the parameter curve of at least one is determined the principal mode of this quartz crystal check-out console in the quality factor of this quartz crystal check-out console or these two parameters of electric capacity then, be its thickness shear mode of oscillation, if there is not other mode near principal mode, then this thickness shear mode of oscillation is optimum thickness scissoring vibration mode.

Compared with prior art, advantage of the present invention is: because this method has been set the vibration frequency Ω of quartz crystal substrate and the relational expression between its size, can draw the vibration frequency of crystal substrate and the relation between its size by this relational expression, can determine the size of small size quartz crystal substrate according to design frequency in advance, and further determine size and the vibration frequency of large scale quartz crystal substrate to be processed, make the vibration frequency of cutting the small size quartz crystal substrate that obtains satisfy the design frequency requirement, guarantee that the small size quartz crystal substrate that finally obtains is qualified wafer; This method has improved working (machining) efficiency, has also reduced the difficulty of processing of small size quartz crystal substrate simultaneously.

Description of drawings

Fig. 1 cuts quartz crystal plate in the embodiment of the invention for the used rectangle AT of derivation relational expression.

The specific embodiment

Below the present invention is described in further detail.

A kind of processing method of the small size quartz crystal substrate for the manufacture of resonator may further comprise the steps:

(1), setting the vibration frequency Ω of quartz crystal substrate and the relational expression between its size is:

In the formula: a is the length of quartz crystal substrate, and c is the width of quartz crystal substrate, and b is the thickness of quartz crystal substrate, and α, β, γ, δ and ε are the coefficient relevant with the material property of quartz crystal;

(1-1), use with large scale quartz crystal substrate identical materials to be processed and produce some quartz crystal check-out consoles with different size, and encourage this quartz crystal check-out console with the design frequency of quartz crystal check-out console, the parameter curve of at least one is determined the principal mode of this quartz crystal check-out console in the quality factor of this quartz crystal check-out console or these two parameters of electric capacity then, be its thickness shear mode of oscillation, when not having other mode near principal mode, this quartz crystal check-out console is in optimum thickness scissoring vibration mode;

(1-2) measure these length a that is in the quartz crystal check-out console under the optimum thickness scissoring vibration mode, width c, thickness b and vibration frequency Ω respectively;

(1-3), with the vibration frequency Ω of some bauerite crystal check-out consoles of obtaining in the step (1-2) and dimensional parameters a, c, b respectively at relational expression: Carry out the curve match based on least square method, obtain the value of factor alpha, β, γ, δ and ε in the relational expression, and in the relational expression with the value substitution step (1) of factor alpha, β, γ, δ and ε;

(2), set the target vibration frequency Ω of the small size quartz crystal substrate that finally will obtain _Little, length a _LittleWith width c _Little, obtain the thickness b of small size quartz crystal substrate then by relational expression _Little

(3), measure the length a of large scale quartz crystal substrate to be processed _GreatlyWith width c _Greatly, and the processing thickness b of setting large scale quartz crystal substrate _GreatlyThickness b with small size quartz crystal substrate _LittleEquate, utilize the length a of large scale quartz crystal substrate then _Greatly, width c _GreatlyWith processing thickness b _GreatlyObtain the theoretical vibration frequency Ω of large scale quartz crystal substrate by relational expression _Reason

(4), the processing thickness b that configures according to step (3) _GreatlyMachining large-sized quartz crystal substrate, and the actual vibration frequency omega of the large scale quartz crystal substrate after the detection processing _Real, then with the actual vibration frequency omega of large scale quartz crystal substrate _RealVibration frequency Ω theoretical with it _ReasonCompare, if both error is in ± 0.5%, then large scale quartz crystal substrate is certified products;

(5), to qualified large scale quartz crystal substrate by the length a that configures _LittleWith width c _LittleCut, obtain meeting target vibration frequency Ω _LittleSmall size quartz crystal substrate, i.e. qualified small size quartz crystal substrate.

In above-described embodiment, the value of factor alpha, β, γ, δ and ε also can be tried to achieve by other computational methods.

Below be the derivation of the relational expression that sets in the step (1) to this processing method:

The rectangle AT that gets as shown in Figure 1 cuts quartz crystal plate, sets up its vibration equation according to the basic theories of Elasticity,

And the equation of motion of being write as the displacement form is:

$c_{11}{u}_{\mathrm{1,11}}+c_{12}{u}_{\mathrm{2,21}}+c_{13}{u}_{\mathrm{3,31}}+c_{14}(u_{\mathrm{3,21}}+u_{\mathrm{2,31}})+c_{55}(u_{\mathrm{3,13}}+u_{\mathrm{1,33}})+c_{56}(u_{\mathrm{2,13}}+u_{\mathrm{1,23}})$

$+c_{65}(u_{\mathrm{3,12}}+u_{\mathrm{1,32}})+c_{66}(u_{\mathrm{2,12}}+u_{\mathrm{1,22}})=\mathrm{\ρ}\frac{{\∂}^2{u}_1}{\∂t^2},$

$c_{21}{u}_{\mathrm{1,12}}+c_{22}{u}_{\mathrm{2,22}}+c_{23}{u}_{\mathrm{3,32}}+c_{24}(u_{\mathrm{3,22}}+u_{\mathrm{2,32}})+c_{41}{u}_{1,13}+c_{42}{u}_{\mathrm{2,23}}+c_{43}{u}_{\mathrm{3,33}}+c_{44}(u_{\mathrm{2,33}}+u_{\mathrm{3,23}})$

$+c_{65}(u_{\mathrm{3,11}}+u_{\mathrm{1,31}})+c_{66}(u_{\mathrm{2,11}}+u_{\mathrm{1,21}})=\mathrm{\ρ}\frac{{\∂}^2{u}_2}{\∂t^2},---\left(1\right)$

$c_{31}{u}_{\mathrm{1,13}}+c_{32}{u}_{\mathrm{2,23}}+c_{33}{u}_{\mathrm{3,33}}+c_{34}(u_{2,33}+u_{3,23})+c_{41}{u}_{\mathrm{1,12}}+c_{42}{u}_{\mathrm{2,22}}+c_{43}{u}_{\mathrm{3,32}}+c_{44}(u_{\mathrm{2,32}}+u_{\mathrm{3,22}})$

$+c_{55}(u_{\mathrm{3,11}}+u_{\mathrm{1,31}})+c_{56}(u_{\mathrm{2,11}}+u_{\mathrm{1,21}})=\mathrm{\ρ}\frac{{\∂}^2{u}_3}{\∂t^2},$

(1) in the formula: ρ is the density of material of quartz crystal plate, u _j(j=1,2,3) are the mechanical displacement of quartz crystal plate, c _Pq(p, q=1,2,3,4,5,6) are the elastic constant of quartz crystal plate.

The general type of supposing the elastomer distortion is:

$u_j=A_j{e}^{i(\mathrm{\ξ}{x}_1+\mathrm{\η}{x}_2+\mathrm{\ζ}{x}_3-\mathrm{\ωt})},j=\mathrm{1,2,3},---\left(2\right)$

(2) in the formula: A _j(j=1,2,3) expression amplitude, ξ represents x ₁Wave number on the direction, η represents x ₂Wave number on the direction, ζ represents x ₃Wave number on the direction, x _j(j=1,2,3) denotation coordination, ω represents vibration frequency, t represents the time.

For reduced equation, vibration frequency, wave number and elastic constant normalization are obtained:

$\mathrm{\Ω}=\frac{\mathrm{\ω}}{\frac{\mathrm{\π}}{2b}\sqrt{\frac{c_{66}}{\mathrm{\ρ}}}},X=\frac{\mathrm{\ξ}}{\frac{\mathrm{\π}}{2b}},Y=\frac{\mathrm{\η}}{\frac{\mathrm{\π}}{2b}},Z=\frac{\mathrm{\ζ}}{\frac{\mathrm{\π}}{2b}},C_{\mathrm{pq}}=\frac{c_{\mathrm{pq}}}{c_{66}}.---\left(3\right)$

With the equation of motion of the corresponding normalization wave number of (1) formula form be:

[C ₁₁X ²+Y ²+C ₅₅Z ²+(C ₆₅+C ₅₆)YZ-Ω ²]A ₁+[(C ₁₂+1)XY+(C ₁₄+C ₅₆)XZ]A ₂

+[(C ₁₃+C ₅₅)XZ+(C ₁₄+C ₆₅)XY]A ₃＝0，

[(1+C ₂₁)XY+(C ₆₅+C ₄₁)XZ]A ₁+[X ²+C ₂₂Y ²+C ₄₄Z ²+(C ₂₄+C ₄₂)YZ-Ω ²]A ₂ (4)

+[C ₆₅X ²+C ₂₄Y ²+C ₄₃Z ²+(C ₂₃+C ₄₄)YZ]A ₃＝0，

[(C ₅₆+C ₄₁)XY+(C ₅₅+C ₃₁)XZ]A ₁+[C ₅₆X ²+C ₄₂Y ²+C ₃₄Z ²+(C ₄₄+C ₃₂)YZ]A ₂

+[C ₅₅X ²+C ₄₄Y ²+C ₃₃Z ²+(C ₃₄+C ₄₃)YZ-Ω ²]A ₃＝0.

When rectangular crystal plate shown in Figure 1 was done free vibration, its boundary condition that need satisfy was:

T ₂＝T ₄＝T ₆＝0，x ₂＝±b，

T ₁＝T ₅＝T ₆＝0，x ₁＝±a， (5)

T ₃＝T ₄＝T ₅＝0，x ₃＝±c.

(5) in the formula: T _p(p=1,2,3,4,5,6) expression stress.

The operation mode that fundamental frequency AT cuts quartz-crystal resonator is the vibration of fundamental frequency thickness shear, and the displacement form of this mode of oscillation is:

(6)

At thickness x ₂Dominant mode on the direction is thickness shear mode, and it is that its boundary condition is about the antisymmetric distortion of thickness:

T ₂＝T ₄＝T ₆＝0，x ₂＝±b. (7)

Only consider leading boundary condition T ₂=0, can obtain:

cosηb＝0 (8)

Solve thus:

$\mathrm{\η}=\frac{\mathrm{\π}}{2b},---\left(9\right)$

Can be obtained by (3) formula again:

$Y=\frac{\mathrm{\η}}{\frac{\mathrm{\π}}{2b}}=1.---\left(10\right)$

At length x ₁Leading thickness shear mode on the direction need satisfy symmetrical distribution, and its boundary condition is:

T ₁＝T ₅＝T ₆＝0，x ₁＝±a. (11)

Satisfying main boundary condition T ₁Under=0 situation, can obtain:

sinξa＝0 (12)

Solve thus:

$\mathrm{\ξ}=\frac{\mathrm{\π}}{a},---\left(13\right)$

Can be obtained by (3) formula again:

$X=\frac{\mathrm{\ξ}}{\frac{\mathrm{\π}}{2b}}=\frac{2b}{a}.---\left(14\right)$

At width x ₃Leading thickness shear mode need satisfy symmetrical distribution on the direction, and its boundary condition is:

T ₃＝T ₄＝T ₅＝0，x ₃＝±c. (15)

Satisfying T ₃Under=0 situation, can obtain:

sinζc＝0 (16)

Solve thus:

$\mathrm{\ζ}=\frac{\mathrm{\π}}{c},---\left(17\right)$

Can be obtained by (3) formula again:

$Z=\frac{\mathrm{\ζ}}{\frac{\mathrm{\π}}{2b}}=\frac{2b}{c}.---\left(18\right)$

First equation of representative thickness scissoring vibration in (4) formula is rewritten as:

${\mathrm{\Ω}}^2=C_{11}{X}^2+Y^2+C_{55}{Z}^2+(C_{65}+C_{56})\mathrm{YZ}+\frac{A_2}{A_1}[(C_{12}+1)\mathrm{XY}+(C_{14}+C_{56})\mathrm{XZ}]---\left(19\right)$

$+\frac{A_3}{A_1}[(C_{13}+C_{55})\mathrm{XZ}+(C_{14}+C_{65})\mathrm{XY}],$

Again (10) formula, (14) formula, (18) formula substitution (19) formula can be obtained:

${\mathrm{\Ω}}^2=1+2[\frac{A_2}{A_1}(C_{12}+1)+\frac{A_3}{A_1}(C_{14}+C_{65})]\frac{b}{a}+4C_{11}{\left(\frac{b}{a}\right)}^2+4[\frac{A_2}{A_1}(C_{14}+C_{56})+\frac{A_3}{A_1}(C_{13}+C_{55})]\frac{b^2}{\mathrm{ac}}---\left(20\right)$

$+2(C_{65}+C_{56})\frac{b}{c}+{4C}_{55}{\left(\frac{b}{c}\right)}^2,$

And note:

$H=2[\frac{A_2}{A_1}(C_{12}+1)+\frac{A_3}{A_1}(C_{14}+C_{65})]\frac{b}{a}+{4C}_{11}{\left(\frac{b}{a}\right)}^2+4[\frac{A_2}{A_1}(C_{14}+C_{56})+\frac{A_3}{A_1}(C_{13}+C_{55})]\frac{b^2}{\mathrm{ac}}---\left(21\right)$

$+2(C_{65}+C_{56})\frac{b}{c}+{4C}_{55}{\left(\frac{b}{c}\right)}^2,$

Cut quartz crystal for AT, the normalization elastic constant value that occurs in (21) formula is:

C ₁₁＝2.99，C ₁₂＝-0.2845，C ₁₃＝0.9359，C ₁₄＝-0.1262，C ₅₅＝2.3719，C ₅₆＝C ₆₅＝0.0873。

Because the mode of shaking that thickness shear mode is the master of resonator, its amplitude is far longer than other mode, i.e. A during resonance ₁＞＞A ₂And A ₁＞＞A ₃, general total can the assurance | H|＜＜1.

Therefore, can be obtained by (20) formula and (21) formula:

$\mathrm{\Ω}=\sqrt{1+H}\≈1+\frac{1}{2}H.---\left(22\right)$

Obtain finally considering that the thickness shear vibration resonance frequency computation part formula of planar dimension is:

$\mathrm{\Ω}=1+[\frac{A_2}{A_1}(C_{12}+1)+\frac{A_3}{A_1}(C_{14}+C_{65})]\frac{b}{a}+{2C}_{11}{\left(\frac{b}{a}\right)}^2+2[\frac{A_2}{A_1}(C_{14}+C_{56})+\frac{A_3}{A_1}(C_{13}+C_{55})]\frac{b^2}{\mathrm{ac}}---\left(23\right)$

$+(C_{65}+C_{56})\frac{b}{c}+2C_{55}{\left(\frac{b}{c}\right)}^2,$

By material constant etc. is reduced to a coefficient, we can determine that the pass between resonant frequency Ω and length of side parameter a, c, the b is:

$\mathrm{\Ω}=1+\mathrm{\α}\frac{b}{a}+\mathrm{\β}{\left(\frac{b}{a}\right)}^2+\mathrm{\γ}\frac{b}{a}\frac{b}{c}+\mathrm{\δ}\frac{b}{c}+\mathrm{\ϵ}{\left(\frac{b}{c}\right)}^2.---\left(24\right)$

(24) in the formula: the value of α, β, γ, δ and ε is relevant with the material property of quartz crystal.

Claims (2)

1. processing method for the manufacture of the small size quartz crystal substrate of resonator is characterized in that may further comprise the steps:

(1), setting the vibration frequency Ω of quartz crystal substrate and the relational expression between its size is:

In the formula: a is the length of quartz crystal substrate, and c is the width of quartz crystal substrate, and b is the thickness of quartz crystal substrate, and α, β, γ, δ and ε are the coefficient relevant with the material property of quartz crystal;

(2), the value of described factor alpha, β, γ, δ and ε is tried to achieve by following step:

(2-1), use with large scale quartz crystal substrate identical materials to be processed and produce some quartz crystal check-out consoles with different size, and the vibration frequency Ω of described quartz crystal check-out console is in vibration frequency under the optimum thickness scissoring vibration state for it, and measures length a, width c, thickness b and the vibration frequency Ω of these quartz crystal check-out consoles respectively;

(2-2), with the vibration frequency Ω of some bauerite crystal check-out consoles of obtaining in the step (2-1) and dimensional parameters a, c, b respectively at relational expression:

Carry out the curve match based on least square method, obtain the value of factor alpha, β, γ, δ and ε in the relational expression, and in the relational expression with the value substitution step (1) of factor alpha, β, γ, δ and ε;

(3), set the target vibration frequency Ω of the small size quartz crystal substrate that finally will obtain _Little, length a _LittleWith width c _Little, obtain the thickness b of small size quartz crystal substrate then by relational expression _Little

(4), measure the length a of large scale quartz crystal substrate to be processed _GreatlyWith width c _Greatly, and the processing thickness b of setting large scale quartz crystal substrate _GreatlyThickness b with small size quartz crystal substrate _LittleEquate, utilize the length a of large scale quartz crystal substrate then _Greatly, width c _GreatlyWith processing thickness b _GreatlyObtain the theoretical vibration frequency Ω of large scale quartz crystal substrate by relational expression _Reason

(5), the processing thickness b that configures according to step (4) _GreatlyMachining large-sized quartz crystal substrate, and the actual vibration frequency omega of the large scale quartz crystal substrate after the detection processing _Real, then with the actual vibration frequency omega of large scale quartz crystal substrate _RealVibration frequency Ω theoretical with it _ReasonCompare, if both error is in ± 0.5%, then large scale quartz crystal substrate is certified products;

(6), to qualified large scale quartz crystal substrate by the length a that configures _LittleWith width c _LittleCut, obtain meeting target vibration frequency Ω _LittleSmall size quartz crystal substrate, i.e. qualified small size quartz crystal substrate.

2. the processing method of a kind of small size quartz crystal substrate for the manufacture of resonator as claimed in claim 1, it is characterized in that the concrete steps whether definite described quartz crystal check-out console is in optimum thickness scissoring vibration state are: the design frequency with described quartz crystal check-out console encourages this quartz crystal check-out console, the parameter curve of at least one is determined the principal mode of this quartz crystal check-out console in the quality factor of this quartz crystal check-out console or these two parameters of electric capacity then, be its thickness shear mode of oscillation, if there is not other mode near principal mode, then this thickness shear mode of oscillation is optimum thickness scissoring vibration mode.

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