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Method for Automated Synthesis of Micromodels of Plate Based Elements of MEMS
Vasyl Teslyuk, Rostyslav Kryvyy
Abstract - In the article the method for automated design of micromodels of MEMS’ elements based on developed micromodels on the basis of thin plates theory, developed algorithms and production rules is developed.
Keywords: MEMS, automated synthesis, пластинчаст елементи МЕМС.
I. Introduction
Nowadays interdisciplinary scientific fields are actively developed. One of such fields is the microelctromechanic systems [1-3]. The peculiarity of these devices is the micron sizes that greatly complicate the process of their projection, testing, making experiments, production etc. That is why the programming systems, technologies, methods and models become playing essential role, enabling to obtain modeling and projection results with high accuracy and to automate the design of different functional appointment models.
TABLE I
№
Type of differential equation
Code
d4w(x, y) d4w(x, y) d4w(x, y) P
dx4
dx2dy2
dy4
D
d2 + 1 d У d2w(r) + 1 dw(r) | _ P(r)
dr2
D
- k
d x4
d w (x,y,t )
dt
r dr A dr
4
+ 2D "
dr
D
d4w(x,y,t ) „„ d w(x,
d4w(x,y,t ) + d d 4w(x,y,t )
— ph
dx2dy2 dw2 (x,y,t ) Э?
d y4
P (t)
D d4w(x,y) + 2D d4w(x,y) + D d4w(x,y)
—(1—u)
dx4
f X 2 no2,.
dx2dy2
dy4
d2D d2w(x, y) 2 d2D d2w(x, y) + d2D d2w(x, y)
dy2 dx2 dvdy dxxdy dx2 dy2
Riv 1
Riv 2
Riv 3
Riv_4
_ P
D,
d2 w(x, y) dx4
+ 2(D0 + 2Dy)
d2 w(x, y) d4 w(x, y)
dx2dy2
+D
dy2
Riv n
1
2
r
3
4
P
n
II. Design of synthesis algorithm of micromodels of PLATE CONSTRUCTION OF MEMS ELEMENTS
Micromodels of plate constructions of MEMS elements are developed and presented in a number of scientific studies [1, 4, 5]. Mostly, they all are based on thin plate theory, where differential equations are used for their description. They are grouped in the Table I. The code is assigned to every differential equation, and their physical processes are described too. The analogical procedure is carried out to critical (Table II) and initial conditions (Table III).
The synthesis process of micromodels of MEMS acoustic elements is in sequent choice of appropriate elements from presented tables. The algorithm of differential equations choice of critical and initial conditions is illustrated at Fig. 1. The choice is implemented on the basis of production rules, the general structure of which is viewed below. These rules are located in appropriate library and used by analysis block of proposed algorithm.
TABLE II
№ Type of critical conditions Code
1 w\~ _ £ II О £ Gran 1
\AD
dw _ 0
2 — Gran 2
dn AD
dw
dy
_ qM’My _—D
f 2 d w
гр
~\2 } d w
2 +V 2
^ dy dx 2
m
Gran _m
TABLE III
№ Type of initial conditions Code
1 * II 0) _ Poch_1
2 dw(x, y, t _ 0) о Poch 2
к dt dw(R, t _ 0) dn _ 0 гр Poch _к
Manuscript received November 3, 2012.
Rostyslav Kryvyy is with the CAD department, National University “Lvivska Politekhnika”, Bandery Str., 12, Lviv, 79053, Ukraine (corresponding author to provide e-mail: rostyslav.kryvyy@gmail.com).
Vasyl Teslyuk is with the CAD department, National University “Lvivska Politekhnika”.
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Fig. 1. Algorithm for automated synthesis of model plate MEMS elements
III. Design the algorithm of micromodels use of MEMS PLATE ELEMENTS
The realization of previously mentioned models at your computer and their application for analysis and synthesis of MEMS plate elements requires the design of appropriate algorithms. At Fig. 2 the developed block-scheme of the algorithm of automated micromodel choice is presented for analysis and synthesis of microelectromechanic systems’ elements.
During the first stage of algorithm usage some data should be inputted: basic construction, applied materials etc.
The basic construction and applied materials are choosing accordingly to Data base. on the basis of input task analysis and selected constructions and materials the micromodel code is formed. The further calculation of output parameters is carried out based on the micromodel.
However, within the use of crystalline silicon plates as material, which is anisotropic material, we ought to apply the appropriate micromodel (differential equation (Riv_n) with conditions (Gran_1); if it is necessary to increase the results acurancy we use the critical conditions of type (Gran_m)). In case of changeable of plate thickness of applied elements we use the differential equation (Riv_4) with critical conditions (Gran_1) or (Gran_m). If necessary to take into account the dynamics of output parameters
change we use transitional micromodels. Dependently on plate construction it is used model based on differential equation (Riv_3) and appropriate critical and initial conditions.
In necessary to use the stationary model dependently on plate construction: for circular we use differential equation (Riv_2) with critical conditions (Gran_1 and Gran_2), and for orthogonal - the critical conditions (Gran_1), (Gran_2).
After analysis the results are presented at the monitor or in the suitable file for user
The offered algorithm makes possible in automated regime to analyze plate construction of MEMS elements, which use the thin plate as working elastic element
IV. Design of production rules
During the choice of differential equations of micromodels we use such type of production rules [6]: PravRiv1: when U1 = A1, then Code _ Riv = Riv _ 1; PravRiv2: when U 2 = A2, then Code _ Riv = Riv _ 2;
PravRivn: when Un = An, then Code _ Riv = Riv _ n,
where An - linguistic terms ; Riv _ n - code of differential equation.
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( End )
Fig.2. Algorithm for automatic selection of models
In case of choosing the critical conditions of micromodels it is used the analogical production rules: PravGran1: when Z1 = B1, then Code _ Gran = Gran _ 1; PravGran2: when Z2 = B2, then Code _ Gran = Gran _ 2;
PravGranm: when Zm = Bm , then Code _ Gran = Gran _ m , where Bm - linguistic terms; Gran _ m - code of critical condition.
For example, for calculation of material anisotropy it is
PravPochk: when Xk = Ck , then Code _ Poch = Poch _ k, де Ck - linguistic terms; Poch _ к - coed of initial condition.
In some cases, it is used more comprehensive construction of production rules, which can used for micromodel synthesis within several critical and initial conditions:
PravGran_m+1: if Zm+1 = Bm+1, then
Code _ Gran = Gran _ 1, Code1 _ Gran = Gran _ 4.
used such production rule: if U1 = An then
Code _ Riv = Riv _ n, Code _ Gran = Gran _1..
Besides, we can change the critical condition if it is needed to raise the output results’ accuracy.
For transitional micromodels it is necessary to add initial condition, selected with help of such production rules: PravPoch1: when X1 = C1, then Code _ Poch = Poch _ 1; PravPoch2: when X2 = C2, then Code _ Poch = Poch _ 2;
For description of MEMS elements construction and micrimodels we built information model of XML format [7, 8]. The example of file with micromodel description of MEMS acoustic element is viewed at Fig. 3-4.
In illustrated example (Fig. 3) 1 and 2 strings describe the type of project. The 3-8 strings define the model, methods and main parameters of modeling. The 9-23 strings describe the microelements‘ sizes and the step mesh partitioning at finite differences.
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<task name=' Прогин Меморани">
<с1е5спрпоп>Визначення перемшень та напружекь у MeopanK'd escripti on>
<raodel> Акусгичний ел ем ент А'т о d el>
<method> сюннчених р1.знш1ь</т et h. о d > simulation id— ПрогинМембрани3' type="state analysis'> <parameter name=”BottomBoundaiy”> Normal cxiHHHeHiPisHi-mi <.'parameter>
<pro.peny name-"MeshAccuiacy">0.01</property> <propertv rLame=,,ConvergenceAccuiacy,>0.01<.',property>
01:
02:
03;
04
05
06
07
08
09
10 11 12
13
14
15 16; 17: 18;
19
20 21 22
23:
24: <space>
25: </simuiaiion>
26: </task>
Fig. 3..An example of the formalization of structure MEMS acoustic element using XML-format
The information model at Fig. 4 describes the micromodel of MEMS acoustic elements. The 1-st, 2-d strings have the model name and its description. The 3-6 strings are viewing the microsystem type. The construction of modeling device is described by 7-11strings., where the construction type, material and its sizes are presented. The 12-24 strings display the used mathematical model for modeling (coeds of initial and critical conditions, coed of differential equation).
<space type="re <x> gular gnd">
<b egm>CH7begm> <end>2E -3</end>
<&> <step>lE-5</'step>
<y> <b egui>0</beg in> <end>2E -3</end>
<fy> <7> <step>lE-5</step>
<b egin>0</beg in> <end>5E -5</end>
<iz?-
<Model name = Acusl>
<description> Model Acustyka MEM SI </description> <typeMEMS>
type = (electrostatic); clear ance=5E-6;
</typeMEMS>
<konstruct >
kon_typ=2;
material=Si02;
rozmir (S,D,H) •= ‘C:\Docmnents\kons_vl.xmr; </konstmct >
<poch>
H);
</poch>
<gran>
x: {Granl. Gran_2}; y: {Granl, Gran_2);
</gran>
<matem>
modl=Riv_l; g_x: mod2=Riv_5; g_y: mod3=Riv_6; t_xy: mod4=Riv_7;
</matem>
</Model>
Fig. 4. Example descriptions model MEMS acoustic element using XML -forma
V. Conclusion
Method for automated synthesis of micromodels of basic elements of MEMS plate design based on thin plates theory and designed production rules based. Structure of output files (designs and micromodels) with the description of synthesized model with XML representation has been designed.
References
[1] Teslyuk V.M. models and information fusion technology microelectromechanical systems. Monograph. - Lviv Tower and Co., 2008. - 192 p.
[2] Lysenko IE Design of sensor elements and actuator microsystem technology. - Taganrog TSURE. 2005. - 103 с.
[3] Varadan V.K., Varadan V.V. Microelectro- mechanical Systems
(MEMS), 2000.
[4] Tariq (Moh'd Taysir) Ali Al Omari, Teslyuk V.M., Miller M.R. Algorithmic models of acoustic microphones for information technology analysis and synthesis of MEMS at the component level / / Modelling and Information Technologies. Collection. Science. Avenue IPPME im.H.Ye.Puhova NAS of Ukraine. - Kyiv, 2009, Vol. 51. - P.182 - 188.
[5] Teslyuk V.M., Denysyuk P.U. mathematical model of fluid actuators termoelastychnoho member / / Bulletin of the National University "Lviv Polytechnic": CAD Systems. Theory and Practice. - 2004. - № 522. - S. 181 - 185.
[6] V.O. Tarasov, Gerasimov B.M., Levin V.A., V.A. Korniichuk Intelligent Decision Support Systems: Theory, synthesis efficiency. - K. MAKNS, 2007. - 336 p.
[7] Denysyuk P., Teslyuk V., Khimich I.,Farmaga I. XML application for microfluidic devices description // Proc of the IX-th Intern. Conf. on The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM’2007). - Lviv - Polyana, Ukraine, 2007. - P. 567 - 569.
[8] Denysyuk P.Y. The use of XML-format to describe the hydraulic structures of MEMS / / Proceedings of the Ukrainian Academy of Printing "Computer Printing Technology", № 17 - Lviv, 2007., - S. 65 - 71.
Vasyl Teslyuk., Professor of CAD department Research interests: Computer-aided design and
modeling of microelectromechanical systems and integrated circuits.
E-mail: vtesliuk(at)polynet.lviv.ua
Rostyslav Kryvyy, Assistant professor, Research interests: Genetic algorithms, Matlab, optimization problem, object-oriented programming,
E-mail: rostyslav.kryvyy (at) gmail.com
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