Effects of etching holes on complementary metal oxide semiconductor microelectromechanical systems capacitive structure

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1 Article Effects of etchin holes on complementary metal oxide semiconductor microelectromechanical systems capacitive structure Journal of Intellient Material Systems and Structures 24(3) Ó The Author(s) 2012 Reprints and permissions: saepub.co.uk/journalspermissions.nav DOI: / X jim.saepub.com Wei-Hsian Tu 1, Wen-Chan Chu 2, Chih-Kun Lee 1,2,3, Pei-Zen Chan 2 and Yuh-Chun Hu 4 Abstract Etchin the lare area of sacrificial layer under the microstructure to be released is a common method used in microelectromechanical systems technoloy. In order to completely release the microstructures, many etchin holes are often required on the microstructure to enable the etchant to completely etch the sacrificial layer. However, the etchin holes often alter the electromechanical properties of the micro devices, especially capacitive devices, because the frine fields induced by the etchin holes can sinificantly alter the electrical properties. This article is aimed at evaluatin the frine field capacitance caused by etchin holes on microstructures. The authors aim to find a eneral capacitance compensation formula for the frine capacitance of etchin holes by the use of ANSYS simulation. Accordin to the simulation results, the desin of a capacitive structure with small etchin holes is recommended to prevent an extreme capacitance decrease. In conclusion, this article provides a frinin field capacitance estimation method that shows the capacitance compensation tendency of the desin of etchin holes; this method is expected to be applicable to the desin in capacitive devices of complementary metal oxide semiconductor microelectromechanical systems technoloy. Keywords Actuator, sensor, autonomic structures Introduction To date, there have been numerous hih-performance and low-cost microsensors or microactuators fabricated by microelectromechanical systems (MEMS) technoloy applied to the automobiles, biomedicine, and electronics industries. In the fabrication process of micro devices, it is enerally required to etch the sacrificial layer under the microstructure to form a movable sensin or actuatin microstructure: such a method is called the release process. To completely and rapidly etch the sacrificial layer, enerally a lot of etchin holes are made on the microstructure to be released, which enables the etchant to uniformly and rapidly permeate into the sacrificial layer. The arranement of etchin holes, includin the density, size, shape, etc, depends on the properties of the etchant, namely the etchin rate and selectivity between the materials of the microstructure and the sacrificial layer. However, etchin holes may alter the characteristics of the device, such as mechanical properties, manetic field, and electrical field, which will sinificantly decrease the fabrication yield of the micro devices. Some of the literature discusses the effect of etchin holes. Rabinovich et al. (1997) employed the so-called effective medium method to investiate the effect of etchin holes on the mechanical properties of microstructures. They made two identical sized unit modules, one with etchin holes and the 1 Department of Enineerin Science and Ocean Enineerin, National Taiwan University, Taipei, Taiwan 2 Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 3 President of Institute for Information Industry, Taipei, Taiwan 4 Department of Mechanical and Electromechanical Enineerin, National Ilan University, Ilan, Taiwan Correspondin author: Yuh-Chun Hu, Department of Mechanical and Electromechanical Enineerin, National Ilan University, No. 1, Sec. 1, Shen-Lun Road, Ilan 26041, Taiwan. ychu@niu.edu.tw

2 Tu et al. 311 other without, and compared the force displacement behaviors of the two modules by exertin a series of normal and shear forces on them. Their results showed that the mechanical properties of structures are hihly affected by etchin holes. Fan et al. (2001) published a theoretical model that showed that the size and density of etchin holes have a tremendous influence on the coercivity of a microstructure. Elshurafa and El-Masry (2006) employed a commercial finite element packae COMSOL to analyze the influence of the size and density of etchin holes on the tunable rane of MEMS parallel plate variable capacitors. Their results showed that the deviation of the tunable rane affected by etchin holes is around 16%. Elshurafa and El-Masry (2007) discussed the effects of etchin holes within one plate in a parallel plate varactor or in a two-plate varactor; their results showed the effect of etchin holes in two-plate varactors is not extreme in reard to the capacitance value. Fan et al. (2010) discussed the effect of etchin holes on variable capacitors and issued an analytical model to compute the effect of etchin holes on pull-in voltae and capacitance. Accordin to the aforementioned literature, the influence of etchin holes on the characteristics of the devices needs to be considered in desin and fabrication. For a lon, flat plate whose lenth dimension is much reater than its width, we can consider it as a two-dimensional problem, Fiure 1 shows a crosssectional view and eometric parameters of a lon parallel plate capacitor. Apart from the uniform electrical field under the plate, illustrated as the blue field lines in Fiure 1, frine fields come from its top surface and two sides, illustrated as red and reen field lines in Fiure 1. Chan (1976) derived a frine capacitance equation via two times Schwartz Christoffel conformal mappin process and asserted that its deviation could be less than 1% to the finite element method as the ratio of thickness to ap is larer than 1, namely b/. 1. Vandermeijs and Fokkema (1984) offered an empirical formula by curve-fittin Chan s equation as follows C unitlenth =e " b +0:77+1:06 b 0:25 +1:06 h # 0:5 Fiure 1. Schematic diaram and eometric parameters of two-dimensional frine fields. ð1þ Fiure 2. Schematic diaram and eometric parameters of three-dimensional frine fields. where b is the width of the plate, h is the thickness of the plate, is the ap between two electrodes, and e is the permittivity. Compared with Chan s equation, its deviation is within 2% as b/. 1 and 0.1 \ h/ \ 4, and within 6% as b/. 0.3 and h/ \ 10. If the plate s lenth and width are not different, then three-dimensional (3D) frine fields should be taken into consideration. As shown in Fiure 2, not only the frine fields from the top surface and the lenth sides but also the ones from the width sides should be considered. Sakurai and Tamaru (1983) utilized the subarea method to develop an empirical formula for 3D frine capacitance C = 1:15 ð area of the plate Þ e + 1:40 h 0:222 ðcircumference of the plateþ + 4:12 h 0:728 ð2þ Its deviation is within 10% under the condition of 0 \ b/l \ 1, 0.5 \ b/ \ 40, and 0.4 \ h/ \ 10. Vandermeijs and Fokkema (1984) presented a formula for calculatin 3D frine capacitance; yet it is imprecise. After surveyin many literatures, we found that no literature mentioned how to calculate the frine fields caused by etchin holes, and only a few literatures mentioned the effects of etchin holes on the variable capacitor (Elshurafa and El-Masry, 2006, 2007; Fan et al., 2010). Fiure 3 shows the schematics of etchin holes throuh which the field lines of the top surface, as well as the field lines from its inner-edes, pass. The etchin holes make the electrical fields much more complicated than the case of a parallel plate capacitor and cause a nonideal electrical field, which is difficult for capacitance assessment and invalidatin of foreoin formulas. Therefore, this article provides a compensative

3 312 Journal of Intellient Material Systems and Structures 24(3) where C T is the total capacitance; C p is an ideal capacitance of parallel plate, which can be calculated by the well-known equation C p = ea=; and C f is the frine field capacitance caused by the thickness and upper surface of a parallel plate capacitor. Similarly, the capacitance (CT e ) of a parallel plate capacitor with etchin holes can be expressed as Fiure 3. Schematic diaram of the frine fields of etchin holes. formula of assessment of etchin hole capacitance for a plate capacitor structure. For a capacitive MEMS device, ANSYS is utilized to simulate the capacitance under different sizes of etchin holes, and an empirical formula is derived. We expect that this result can provide desiners with a rule to precisely estimate the capacitance of a plate capacitor with etchin holes. Methodoloy There are three parts to this research. First, the authors comprehend the difference between a parallel plate capacitor and parallel plate capacitor with etchin holes, and define the quantity of difference as capacitance correction term. Second, the authors employ ANSYS to compute the capacitance of a parallel plate capacitor and a parallel plate capacitor with etchin holes with different dimensions, and ain the capacitance correction term that is necessary for compensatin the difference. Finally, the authors utilize the capacitance correction term obtained under different dimensions to acquire the relation between capacitance correction and dimension via curve fittin, and provide an empirical formula. Analysis of capacitance The literatures show that the frine fields of a parallel plate capacitor cannot be nelected in a micro scale. The frine field from the thickness and upper surface of a parallel plate capacitor needs to be considered. For this reason, the capacitance of micro parallel plate capacitor can be expressed as C T = C p + C f ð3þ C e T = Ce p + Ce f ð4þ where C e p and Ce f are the ideal capacitance and the total frine capacitance, respectively, for the parallel plate with etchin hole. C e p can be represented as C e p = C p C p removed where C p removed is the ideal capacitance of the etchin hole area. C e f can be represented as C e f = C f + C f hole where C f hole is the frine capacitance from the etchin hole. A correction term will be carried out between capacitors with etchin holes and those without etchin holes. The formula of capacitance correction can be sinified as follows Simulation DC = C e T C T = C p removed + C f hole ð5þ The effect of etchin holes is nonidentical under different dimensions, sizes, and densities of etchin holes. Hence, this research employs ANSYS to simulate the influence of etchin holes on the capacitance throuh desinin different sizes of plates and etchin holes. Usually, the alinment is an array, as shown in Fiure 4(a), so a unit module of an etchin hole can be taken out and simulated alone, as shown in Fiure 4(b). Furthermore, the structure of an etchin hole is symmetric, so the simulation can function by merely usin a quarter of the structure and field. Table 1 shows the dimensions for simulation. The size of the etchin hole is defined as the liament efficiencies (m) meanin line width divided by the pitch of the etchin hole. As shown in Fiure 5, the m is expressed as m = l pitch ð6þ The value of m is within 0 1; the bier the m value, the smaller the size of the etchin hole. Simulation of the parallel plate structure capacitor without etchin holes (m=1) is conducted under three different Fiure 4. (a) Schematic diaram of the capacitive structure and (b) schematic diaram of unit module.

4 Tu et al. 313 Table 1. Structure dimensions for simulation. Lenth of the square 4, 8, and 16 unit module (mm) Thickness (mm) 0.5 Gap (mm) 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5, 2.0, and 4.0 Liament efficiencies 1, 0.7, 0.5, and mm 3 ). For the settin of c =8mm, h = 0.5 mm, m = 0.5 mm, and = 1 mm, the amount of element is around 95,000. After simulation, characteristics of the structure s electrical field and whole capacitance can be obtained. The whole plate capacitance, C T, correspondin to various sizes, can be obtained via simulation, and you can compute the ideal plate capacitance, C P, to solve frine field capacitance, C f, as shown in Table 3. Equivalently, the plate capacitance with etchin holes, CT e, the ideal plate capacitance that subtracted the area of the etchin holes from the full plate, Cp e, and the frine field capacitance caused by the thickness of the etchin hole frine can be obtained, as shown in Table 4. Fiure 5. Schematic of liament efficiencies. conditions (c = 4, 8, and 16), and the dimensions of the plate structure capacitor with etchin holes for simulation are m = 0.7, 0.5, and 0.3. The thickness of the plate (h) is 0.5 mm. The variable ap between two plates () is within mm. ANSYS element Solid122 is employed in the electrical field analysis. Due to the symmetry of the structure, the simulation can be processed by takin just 1/4 of the model to build the electrical field. The analyzed electrical field is a cube with side lenths of 2c. The upper electrode is involved in the field, and the lower electrode is the bottom of the simulated field, as shown in Fiure 6(a). The settin for the mesh size is shown in Fiure 6(b) and Table 2 (e.. the element size of X reion from 0 to c/ , Y reion from + h to + h + 2.1, and Z reion from c/ to 2c is Results and discussion Based on the results of the simulations, when the ap increases, the ideal plate capacitance in the whole capacitance decreases, and the frine field capacitance in the whole capacitance increases; this indicates that the effect of the frine field is more prevalent. Afterward, just like the procedure for the capacitance correction, the plate structure capacitance with etchin holes, C e T, and whole plate structure capacitance, C T, can be resolved, and the subtraction of these two values is the capacitance correction term DC. As shown in Fiure 7, under identical liament efficiencies (m = 0.5), the larer the unit module, the reater the capacitance correction. Takin into account the relation with the ap of electrodes, the capacitance correction and ap are rouhly in inverse proportion. Considerin the same area of square plates and cuttin out the same area of etchin holes with different sizes and densities, liament efficiencies of m = 0.5, the samples include 16 unit modules with 4 mm for each Fiure 6. (a) Scheme of analyzed electrostatic field and (b) scheme of mesh size distribution.

5 314 Journal of Intellient Material Systems and Structures 24(3) Table 2. Mesh size in three distributions. X reion Y reion Z reion Mesh size (mm 3 ) 0 c/ c/ c/ c/ c 0 + h h h h c 0 + h h h h c 0 + h h h h c 0 c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c c/ c/ c/ c/ c Table 3. Simulation results of parallel plate capacitor. Lenth of square unit module (mm): 16 mm Gap (mm) C P (ff) C T (ff) C f (ff) side lenth, 4 unit modules with 8 mm for each side lenth, and 1 unit module with 16 mm for its side lenth, as shown in Fiure 8. The total capacitance correction has been discussed under different circumstances (hih density, small etchin holes, and low density, lare etchin holes). The result shown in Fiure 9 is that the loner the lenth of unit etchin holes, the larer the capacitance correction. In contrast, even thouh it takes more small etchin holes to attain the same area, the summation of all capacitance corrections is still less. Thus, a result can be inferred that the influence of small etchin holes on the whole capacitance is small. When the ap between the electrodes Table 4. Simulation results of parallel plate capacitor with etchin hole. Lenth of square unit module (mm): 16 mm and liament efficiencies (m): 0.5 Gap (mm) CP e (ff) Ce T (ff) Ce f (ff) increases, the summation of capacitance correction in these three conditions is decreasin. Curve fittin In the above-mentioned simulation for the effect of etchin holes, this research employs Mathematica to curve-fit the results of the simulation. The empirical formula of capacitance correction term of unit etchin hole plate capacitor is deduced as follows

6 Tu et al. 315 C (ff) c = 4 (µm) c = 8 (µm) c = 16 (µm) Gap (µm) Fiure 7. Capacitance correction term DC with m = 0.5; c = 4, 8, and 16; and variable ap. Capacitance difference (ff) c = 4 (µm) c = 8 (µm) c = 16 (µm) Gap (µm) Fiure 9. Capacitance correction term DC with the same area of square plates, cuttin out the same area of etchin holes with different sizes and densities. C EH = Cð1 mþ ð7þ DC = e C2 EH + 44:940C h 0:025 EH 41:314C EH! ð8þ The first term indicates the plate capacitance of the area of etchin holes. The second term indicates the capacitance caused by the frine field on the thickness of the etchin holes. When the structure is without etchin holes (C EH = 0), the capacitance correction is zero. Because a small plate capacitor has small etchin holes, the capacitance correction is small. The plate capacitance is smaller when the plate ap is larer and the capacitance correction decreases. Accordin to the literature (Rebeiz, 2003), when the diameter of the etchin hole less than 3 4 times the ap of the electrodes, the effect of the etchin holes can be inored, owin to the compensation of the frine electric field for etchin holes. Synthesizin all the above factors, this research C (ff) μ = 0.7, 2.5<h/<5 Simulation μ = 0.7, 2.5<h/<5 Empirical formula μ = 0.5, 1.25<h/<5 Simulation μ = 0.5, 1.25<h/<5 Empirical formula μ = 0.3, 1<h/<5 Simulation μ = 0.3, 1<h/<5 Empirical formula h/ Fiure 10. Comparison of analytical solution and ANSYS simulation with c = 4. nelects small and trivial values. Fiures 10 to 12 show the comparison of results between the analytical solution of formula and the simulation of ANSYS. Fiure 8. Schematic of square plates, cuttin out the same area of etchin holes with different sizes and densities.

7 316 Journal of Intellient Material Systems and Structures 24(3) C (ff) μ = 0.7, 1.25<h/<5 Simulation μ = 0.7, 1.25<h/<5 Empirical formula μ = 0.7, 0.67<h/<5 Simulation μ = 0.7, 0.67<h/<5 Empirical formula μ = 0.7, 0.5<h/<5 Simulation μ = 0.7, 0.5<h/<5 Empirical formula h/ Capacitance (ff) Simulation Ideal parallel plate (Chuan, 2011) This work h/ Fiure 11. Comparison of analytical solution and ANSYS simulation with c = 8. Fiure 13. Comparison of capacitance with different aps obtained from different models. C (ff) μ = 0.7, 0.67<h/<5 Simulation μ = 0.7, 0.67<h/<5 Empirical formula 8 μ = 0.5, 0.33<h/<5 Simulation μ = 0.5, 0.33<h/<5 Empirical formula 10 μ = 0.3, 0.25<h/<5 Simulation μ = 0.3, 0.25<h/<5 Empirical formula h/ Fiure 12. Comparison of analytical solution and ANSYS simulation with c = 16. This empirical formula of capacitance correction can be combined with 3D plate capacitance computation. Then, the 3D plate capacitance with etchin holes can be appraised as follows ( " b C Total = e 1:06 + 3:31 h 0:23 + 0:73 b # 0:23 " h L + e 4:2 h 0:18 b + 2:74 h #) 0:86 ( + e C EH 2 ) h 0: :940C EH 41:314C EH! n ð9þ The first term comes from the literature (Chuan et al., 2011), empirical formula for computin plate capacitance. The second term is the capacitance correction in this research. The n is the quantity of etchin holes. The alinment of etchin holes is usually an array; therefore, the quantity of etchin holes can easily be calculated. Assumin there is a sample of unit etchin holes (lenth of 16 mm, thickness of 0.5 mm, and liament efficiencies m = 0.5). Now the sample is computed by three methods as follows: 1. Ideal capacitance formula; 2. 3D structure capacitance formula; 3. 3D structure capacitance with effect of etchin holes. Then, we compare these with the results of an ANSYS simulation, as shown in Fiure 13 and Table 5. Accordin to the results, the best appraisal of etchin hole structure is with the third method (error \ 1%); the smaller the ap, the better the appraisement compared with other methods. Conclusion This research utilized ANSYS to simulate the effect of etchin holes for plate capacitor structures with etchin holes. Under the conditions of cuttin the same areas for etchin holes, the small size of an etchin hole means a hih etchin hole density, which causes minor capacitance chanes. When dimension ranes m = 0.7, 4 \ c \ 16, and 0.25 \ h/ \ 5, the capacitance variation is less than 10%. This research also provides an empirical formula for the compensation of etchin hole capacitance, combined with a 3D true thickness formula of plate capacitance. The mean error is less than 1%, which shows that this formula can be more accurate than other formulas (mean error. 10%). This empirical formula is able to provide desiners with a criterion to appraise the effect of etchin holes promptly and precisely.

8 Tu et al. 317 Table 5. Comparisons of capacitances between simulation and formulae. h/ Simulation Chuan (2011) Ideal parallel plate This study ff ff Error % ff Error % ff Error % Mean error % Fundin This study was supported by the National Science Council of Taiwan throuh rant number NSC E MY3. References Chan WH (1976) Analytical IC metal-line capacitance formulas. IEEE Transactions on Microwave Theory and Techniques 24: Chuan WC, Hu YC, Wan CW, et al. (2011) A frinin capacitance model for electrostatic microstructure. In: 13th international conference on mesomechanics, Vicenza, Italy, 6 8 July. Elshurafa AM and El-Masry EI (2006) Effects of etchin holes on capacitance and tunin rane in MEMS parallel plate variable capacitors. In: 6th IEEE international workshop on system on chip for real time applications (IWSOC), Cairo, Eypt, December, pp , Inst. of Elec. and Elec. En. Computer Society. DOI: /IWSOC Elshurafa AM and El-Masry EI (2007) Desin consideration in MEMS parallel plate variable capacitors. In: 50th IEEE Midwest symposium on circuits and systems (MWSCAS), 5 8 Auust, pp , Institute of Electrical and Electronics Enineers Inc. DOI: /MWSCAS Fan DM, Li XH, Yuan QA, et al. (2010) Effect of etch holes on the capacitance and pull-in voltae in MEMS tunable capacitors. International Journal of Electronics 97: Fan X, Myun N, Nobe K, et al. (2001) Modelin the effect of etch holes on ferromanetic MEMS. In: 8th joint manetism and manetic materials international manetic conference (MMM-Interma), San Antonio, TX, 7 11 January, 37(4): , Institute of Electrical and Electronics Enineers Inc. DOI: / Rabinovich VL, Gupta RK and Senturia SD (1997) The effect of release-etch holes on the electromechanical behaviour of MEMS structures. In: International conference on solid state sensors and actuators, TRANSDUCERS 97, Chicao, IL, June, 2: IEEE. Rebeiz GM (2003) RF MEMS: Theory, Desin, and Technoloy. Hoboken, NJ: John Wiley & Sons, Inc. Sakurai T and Tamaru K (1983) Simple formulas for twodimensional and three-dimensional capacitances. IEEE Transactions on Electron Devices 30: Vandermeijs NP and Fokkema JT (1984) VLSI circuit reconstruction from mask topoloy. Interation-the VLSI Journal 2: