CN100498803C - Reusable parameter module model building method for space continuous deformation MEMS - Google Patents

Abstract

A modeling method of reusable parameterized component for space continuous deformation MEMS includes confirming each dynamic control equation and boundary condition equation of MEMS device, carrying out space discretization on dynamic control equation and converting said control equation to be constant-differential equation set, utilizing hardware description language of analog and mixed signal to carry out coding for realizing function description, plotting schematic diagram of MEMS device and connecting said diagram with code to form MEMS device being called in system modeling and in simulation analysis.

Description

The reusable parametrization assembly modeling method of space continuous modification MEMS

Technical field

The present invention relates to the method for establishing model of a kind of MEMS (micro electro mechanical system) (MEMS) device, belong to computer-aided design (CAD) (MEMS CAD) field of MEMS (micro electro mechanical system).

Background technology

Along with the raising of integrated level, the demand of MEMS system level design can be more and more urgent.System level design is paid close attention to whole micro-system (comprising physical construction, circuit and multiple domain coupling unit etc.) is carried out modeling and performance simulation on the whole.Because related work exists certain difficulty and complexity, therefore how to set up and can either more accurately express the device behavior and can realize that again reusable parametrization component model becomes key issue, for development MEMS cad technique, improve the MEMS design efficiency and the research and development level most important.

Nodal analysis can be set up the parametrization component model of MEMS device in the existing MEMS system-level modeling method, has obtained using widely.For example, the NODAS (Design ofActuators andSensors) of external Carnegie Mellon university exploitation, the SUGUR in the ARCHITECT of Coventor company, Berkeley branch school, University of California and the multiport three-dimensional micromodule modeling method of domestic Northwestern Polytechnical University etc. grows up on the nodal analysis basis basically.Its basic thought is that the device with labyrinth is decomposed into unit one by one, each unit is corresponding units corresponding storehouse respectively, be equivalent to primary element such as resistance, electric capacity and inductance etc. in the circuit, link to each other by node between the unit, and the quality and the rigidity of unit focused on the node deformation result the unknown between the node.Usually at the characteristics of MEMS device, system is divided into primary elements such as beam, stiffener plate, electrostatic gap, broach and anchor point.To primary element, methods such as apply materials mechanics and Structural Dynamics are set up the analytic model of lumped parameter.

Nodal analysis is by the end points concentrated reflection distortion situation of each MEMS functional structure.But for having space continuous modification behavior MEMS device, this method can not be described its deformational behavior in detail, i.e. the unknown as a result of the continuous modification in zone between the end points.In fact, most MEMS structure, as diaphragm, semi-girder, bridge etc., its deformational behavior all is that the space is continuous, these structures often relate to the height coupling of many physical domain such as static territory, domain, fluid territory, must obtain space continuous modification result to carry out directly related with it multiple domain coupling behavioural analysis.Therefore, at MEMS device, be necessary to set up special modeling method with space continuous modification behavioural characteristic.

Summary of the invention

Be not useable for describing deficiency in order to overcome prior art, the present invention proposes a kind of method for building up of the reusable parametrization component model at space continuous modification MEMS device with space continuous modification behavioural characteristic MEMS device.

The method for building up of the reusable parametrization component model of the space continuous modification MEMS device that the present invention proposes comprises the steps:

Step 1: energy territory and coupling scheme definite dynamic control equation, the boundary condition equation of describing each energy territory and couple state thereof thereof related according to the MEMS device.For most of MEMS devices such as semi-girder (single-ended fixing), bridge (two ends are fixed) and diaphragm (periphery is fixing) etc., owing to itself can not be approximately rigid body, its distortion has the continuous feature in space, so the dynamic control equation of such MEMS device is generally partial differential equation, its dynamic deformation amount is not only relevant with the time, and relevant with the locus.

Step 2: in conjunction with boundary condition, dynamic control equation to definite each the energy territory of description of step 1 carries out spatial discretization, on each Spatial Dimension, the MEMS device is carried out uniform grid and divide, replace partial differential with differential type then, thereby partial differential equation is converted to the ordinary differential equation group.

Step 3: according to the determined ordinary differential equation group of step 2, be input variable, adopt simulation and mixed signal hardware descriptive language (MAST, VHDL-AMS etc.) to encode, realize the functional description of device with MEMS size of devices parameter and technological parameter.

Step 4: draw MEMS assembly synoptic diagram, be connected, form the MEMS assembly, call during for system-level modeling and simulation analysis with coding.

Beneficial effect of the present invention has been to propose the method for building up of the reusable parametrization component model of a kind of space continuous modification MEMS device, and the component model that obtains can carry out system emulation with circuit.This method has reflected the basic characteristics of the space continuous modification that the many functional structures of MEMS are had, and the different types of reusable parametrization component model that has space continuous modification behavioral characteristic for foundation has directive function.For setting up models such as semi-girder, bridge, diaphragm fast, further make up the model of the device that comprises these unit or system and finish relevant overall permanence simulation analysis etc. easily and have important support effect.

The present invention is further described below in conjunction with drawings and Examples.

Description of drawings

Fig. 1: the system-level modeling process flow diagram of space continuous modification MEMS device.

Fig. 2: both-end is the little beam synoptic diagram of electrostatically actuated fixedly;

Among the figure, the 1-anchor point; The 2-bottom crown; The 3-substrate; The little beam of 4-.

Fig. 3: one-dimensional discrete process grid dividing figure.

Fig. 4: the little beam parametrization of electrostatically actuated assembly synoptic diagram.

Fig. 5: (a) vertical view of capacitance pressure transducer; (b) side view of capacitance pressure transducer.

Fig. 6: two-dimensional discrete process grid dividing figure.

Fig. 7: capacitance pressure transducer, parametrization assembly synoptic diagram.

Embodiment embodiment 1: the component model method for building up of the little beam of electrostatically actuated.

Step 1: energy territory and coupling scheme definite dynamic control equation, the boundary condition equation of describing each energy territory and couple state thereof thereof related according to the little beam of electrostatically actuated.

Accompanying drawing 2 is fixedly synoptic diagram of electrostatically actuated micro girder construction of a kind of both-end, and this structure is the common structure in the MEMS system, all is widely used in devices such as RF switch, micro-acceleration gauge, pressure transducer.When applying voltage V between upper/lower electrode, top electrode deforms under the effect of electrostatic attraction, and the amount of deflection that the size of the electrostatic force that each point is subjected on the beam is put therewith is relevant.The axis of beam when not being out of shape, promptly the straight line that is linked to be of each cross section centre of form is got and is made the x axle, does not consider the influence that rotate around neutral axis in detrusion and cross section.If the amount of deflection of beam each point is that (x, t), promptly the point at x place departs from the displacement of equilibrium position to w constantly on the beam at t.According to Euler's beam theory and static theory structure analysis being obtained the dynamic control equation of beam element under electrostatic force drives is:

$\mathrm{EI}\frac{{\&PartialD;}^{4}w}{{\&PartialD;x}^4}-S\frac{{\&PartialD;}^{2}w}{\&PartialD;x^2}+b\frac{\&PartialD;w}{\&PartialD;t}+\mathrm{\&rho;Wh}\frac{{\&PartialD;}^{2}w}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="C200710017305E00082.png,C200710017305E00093.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=-\frac{1}{2}\mathrm{\&epsiv;W}\frac{V^2\left(t\right)}{{(d+w)}^2}---\left(1\right)$

In the formula, L, W, h are respectively length, width and the thickness of beam, and d is an initial separation between pole plate.EI is called bendind rigidity, and E is the Young modulus of beam, and I is the moment of inertia of beam: I=Wh ³/ 12.

Boundary condition equation is:

w| _x＝0x＝L＝0

The electricity behavior of the little beam of electrostatically actuated can by under the description that establishes an equation:

$i=\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{dC}}{\mathrm{dt}}V+C\frac{\mathrm{dV}}{\mathrm{dt}}---\left(3\right)$

Wherein, Q is the quantity of electric charge of capacitor stores, and V is the voltage between two electrodes, and C is the electric capacity between the upper/lower electrode of beam distortion back:

$C=\mathrm{\&epsiv;}\underset{x=0}{\overset{L}{\&Integral;}}\frac{W}{d+w(x,y)}\mathrm{dx}---\left(4\right)$

Step 2: in conjunction with boundary condition, dynamic control equation to definite each the energy territory of description of step 1 carry out one-dimensional discreteization, on each Spatial Dimension, the MEMS device is carried out uniform grid and divide, replace partial differential with differential type then, thereby partial differential equation is converted to the ordinary differential equation group.

At first must carry out discretize, be translated into the form of ordinary differential equation group partial differential equation (1), (2).Here adopt finite difference method, its process is that little beam is evenly divided grid, replaces partial differential with differential type then, and promptly the inclined to one side subitem of each node represents that with Centroid and its displacement of 4 nodes on every side as shown in Figure 3, used difference formula is as follows:

$\frac{\&PartialD;w}{\&PartialD;x}\&ap;\frac{1}{2t}(w_{i+1}-w_{i-1})$ $\frac{{\&PartialD;}^{2}w}{\&PartialD;x^2}\&ap;\frac{1}{t^2}(w_{i-1}-2w_i+w_{i+1})$

$\frac{{\&PartialD;}^{3}w}{\&PartialD;x^3}\&ap;\frac{1}{{2t}^3}(-w_{i-2}+2w_{i-1}-2w_{i+1}+w_{i+2})$

$\frac{{\&PartialD;}^{4}w}{\&PartialD;x^4}\&ap;\frac{1}{t^4}(w_{i+2}-4w_{i+1}+6w_i-4w_{i-1}+w_{i-2})$

Just can set up an equation at each node like this, thereby partial differential equation just is converted into the system equation that adopts the ordinary differential equation group to represent:

$M\stackrel{..}{w}+K\stackrel{.}{w}+\mathrm{Cw}=F---\left(5\right)$

M wherein, K, C are system matrixes, w and F are amount of deflection and the load vectors that node (i) is located.

Step 3: according to the determined ordinary differential equation group of step 2, dimensional parameters and technological parameter with the little beam of electrostatically actuated are input variable, adopt simulation and mixed signal hardware descriptive language (MAST, VHDL-AMS etc.) to encode, realize the functional description of device.

Step 4: draw the little beam assembly synoptic diagram of electrostatically actuated, be connected, be embedded in the Component Gallery, for system-level calling with coding.The reusable parametrization assembly behavior model of the little beam of electrostatically actuated as shown in Figure 4.This assembly is made up of 4 ports, and two electric ports are top crown voltage v_t, and bottom crown voltage v_b, output port are capacitor C ap and central point displacement Z_mid.Structural parameters comprise the long L of little beam, wide W, and thick h, initial separation d etc. can pass through the graphical interfaces typing between pole plate.

Embodiment 2: the component model method for building up of capacitance pressure transducer.

Step 1: energy territory and coupling scheme definite dynamic control equation, the boundary condition equation of describing each energy territory and couple state thereof thereof related according to capacitance pressure transducer.

Accompanying drawing 5 is structural representations of a kind of capacitance pressure transducer,, and its flexible member is made of the diaphragm that props up admittedly all around.The deformation equation that diaphragm bears behind ambient pressure and the static pressure can be described as:

$D\frac{{\&PartialD;}^{4}w}{\&PartialD;x^4}+2D\frac{{\&PartialD;}^{4}w}{\&PartialD;x^2\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="C200710017305E00082.png,C200710017305E00093.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}+D\frac{{\&PartialD;}^{4}w}{\&PartialD;{\mathrm{<figure-callout\; id="4"\; label="y"\; filenames="C200710017305E00101.png"\; state="\{\{state\}\}">y</figure-callout>}}^4}={\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="C200710017305E00101.png"\; state="\{\{state\}\}">p</figure-callout>}}_0+\frac{\mathrm{\&epsiv;}{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="C200710017305E00082.png,C200710017305E00093.png"\; state="\{\{state\}\}">V</figure-callout>}}^2}{2{(d-w(x,y))}^2}-b\frac{\mathrm{dw}}{\mathrm{dt}}-\mathrm{\&rho;h}\frac{d^{2}w}{{\mathrm{dt}}^2}---\left(6\right)$

Wherein: w is that (x, y are volume coordinates for x, displacement y), and D is bending stiffness D=Eh on the diaphragm ³/ 12/ (1-v ²), E is an elastic modulus, and v is a Poisson ratio, and ρ is a diaphragm density, and h is the thickness of diaphragm.

Boundary condition equation is:

w| _x＝0x＝L＝0

w| _y＝0y＝L＝0 (7)

The electricity behavior of capacitance pressure transducer, can by under the description that establishes an equation:

$i=\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{dC}}{\mathrm{dt}}V+C\frac{\mathrm{dV}}{\mathrm{dt}}---\left(8\right)$

Wherein, Q is the quantity of electric charge of capacitor stores, and V is the voltage between two electrodes, and C is the electric capacity behind the diaphragm deformation:

$C=\mathrm{\&epsiv;}\underset{x=0}{\overset{L}{\&Integral;}}\underset{y=0}{\overset{W}{\&Integral;}}\frac{\mathrm{dxdy}}{d-w(x,y)}---\left(9\right)$

Step 2: in conjunction with boundary condition, dynamic control equation to definite each the energy territory of description of step 1 carry out two-dimensional discreteization, on each Spatial Dimension, the MEMS device is carried out uniform grid and divide, replace partial differential with differential type then, thereby partial differential equation is converted to the ordinary differential equation group.

At first must carry out discretize, be translated into the form of ordinary differential equation group partial differential equation (6), (7).Here adopt finite difference method, its process is that diaphragm is evenly divided grid, replaces partial differential with differential type then, and promptly the inclined to one side subitem of each node represents that with Centroid and its displacement of 12 nodes on every side as shown in Figure 6, used difference formula is as follows:

$\frac{\&PartialD;w}{\&PartialD;x}\&ap;\frac{1}{2t}(w_{i+1,j}-w_{i-1,j})$

$\frac{{\&PartialD;}^{2}w}{\&PartialD;x^2}\&ap;\frac{1}{t^2}(w_{i-1,j}-2w_{i,j}+w_{i+1,j})$

$\frac{{\&PartialD;}^{4}w}{\&PartialD;x^4}\&ap;\frac{1}{t^4}(w_{i+2,j}-4w_{i+1,j}+6w_{i,j}-4w_{i-1,j}+w_{i-2,j})$

$\frac{{\&PartialD;}^{4}w}{\&PartialD;x^2\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="C200710017305E00082.png,C200710017305E00093.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}\&ap;\frac{1}{t^4}(w_{i-1,j-1}-2w_{i-1,j}+w_{i-1,j+1}-2w_{i,j-1}+4w_{i,j}-2w_{i,j+1}+w_{i+1,j-1}-2w_{i+1,j}+w_{i+1,j+1})$

Just can set up an equation at each node like this, thereby partial differential equation just is converted into the system equation that adopts the ordinary differential equation group to represent:

$M\stackrel{..}{w}+K\stackrel{.}{w}+\mathrm{Cw}=F---\left(10\right)$

M wherein, K, C are system matrixes, w and F are node (i, amount of deflection of j) locating and load vectors.

Step 3: according to the determined ordinary differential equation group of step 2, dimensional parameters and technological parameter with capacitance pressure transducer, are input variable, adopt simulation and mixed signal hardware descriptive language (MAST, VHDL-AMS etc.) to encode, realize the functional description of device.

Step 4: draw capacitance pressure transducer, assembly synoptic diagram, be connected, be embedded in the Component Gallery, for system-level calling with coding.The reusable parametrization assembly behavior model of capacitance pressure transducer,, as shown in Figure 7.This assembly is made up of 5 ports, and input port is ambient pressure P, and two electric ports are top crown voltage V2, and bottom crown voltage V1, output port are capacitor C ap and central point displacement Z_mid.Structural parameters comprise the long L of diaphragm, wide W, and thick h, initial separation d etc. can pass through the graphical interfaces typing between pole plate.

Claims (1)

1, the reusable parametrization assembly modeling method of a kind of space continuous modification MEMS is characterized in that comprising the steps:

Step 1: energy territory and coupling scheme definite dynamic control equation, the boundary condition equation of describing each energy territory and couple state thereof thereof related according to the MEMS device;

Step 2: in conjunction with boundary condition, dynamic control equation to definite each the energy territory of description of step 1 carries out spatial discretization, on each Spatial Dimension the MEMS device being carried out uniform grid divides, replace partial differential with differential type then, thereby be dynamic control equation ordinary differential equation group form by the partial differential equation formal transformation;

Step 3: according to the determined ordinary differential equation group of step 2, be input variable, adopt simulation and mixed signal hardware descriptive language MAST or VHDL-AMS to encode, realize the functional description of device with MEMS size of devices parameter and technological parameter;

Step 4: draw MEMS assembly synoptic diagram, be connected, the MEMS assembly that calls when forming for system-level modeling and simulation analysis with coding.

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