Manufacture of Hemispherical Shell and Surrounding Eave-Shaped Electrodes
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micromachines Article Manufacture of Hemispherical Shell and Surrounding Eave-Shaped Electrodes Renxin Wang † , Bing Bai † , Wendong Zhang , Huiliang Cao * and Jun Liu * State Key Laboratory of Dynamic Testing Technology, North University of China, Taiyuan 030051, China; wangrenxin@nuc.edu.cn (R.W.); 15135173839@163.com (B.B.); wdzhang@nuc.edu.cn (W.Z.) * Correspondence: caohuiliang@nuc.edu.cn (H.C.); liuj@nuc.edu.cn (J.L.); Tel.: +86-351-3920-350 (J.L.) † These authors contributed equally to this work. Abstract: A hemispherical resonator consists of a hemispherical shell and the surrounding circular electrodes. The asymmetry of a hemispherical shell has influence on the vibrating mode and quality factor. The gap distance from shell to electrode is critical for the capacitance and sensitivity of a hemispherical resonator. To realize a symmetric shell and a small gap, a kind of micro-hemispherical resonator (µHR) structure including sandwich-shaped stacks and eave-shaped electrodes has been developed using a glassblowing process. The blowing process could bring favorable surface rough- ness and symmetry. The locations of the hemispherical shell and surrounding electrodes can be precisely controlled by the designs of sandwich-shaped stacks and eave-shaped electrodes, making it feasible to realize uniform and small gaps. In addition, electrical insulation between the hemi- spherical shell and eave-shaped electrodes can be guaranteed owing to eave-shaped structure. The fabrication process and results are demonstrated in detail. Furthermore, an estimation method of shell thickness in a nondestructive manner is proposed, with deviation below 5%. Taking asymmetry, surface roughness, and gap into consideration, these results preliminarily indicate this structure with a hemispherical shell and surrounding eave-shaped electrodes is promising in hemispherical resonator applications. Citation: Wang, R.; Bai, B.; Zhang, W.; Cao, H.; Liu, J. Keywords: hemispheric shell; eave-shaped electrodes; blowing; nondestructive estimation; asymme- Manufacture of Hemispherical Shell try; surface roughness and Surrounding Eave-Shaped Electrodes. Micromachines 2021, 12, 815. https://doi.org/10.3390/ mi12070815 1. Introduction Received: 12 June 2021 A hemispherical resonator is a kind of axisymmetric shell resonator with advantages Accepted: 6 July 2021 of high reliability, long life, and stable physical properties [1]. However, the presently used Published: 12 July 2021 hemispherical resonator has a relatively large size and high manufacturing cost. In recent years, micro-hemispherical resonators (µHRs) have been developed. The µHR consists of a Publisher’s Note: MDPI stays neutral 3D micro-hemispherical shell structure and circular electrodes around the hemispherical with regard to jurisdictional claims in shell [2]. Geometric imperfection characterization of the shell and electrodes is crucial for published maps and institutional affil- the quality of resonators [3]. Therefore, there are two difficult issues: how to fabricate a iations. uniform hemispherical shell, and how to fulfill the alignment of the shell and surrounding circular electrodes. As for the first issue, with the development of 3D MEMS techniques, the fabrication of a 3D micro-hemispherical shell structure has become feasible, for example, via chemical vapor deposition (CVD) on the hemispherical cavity [4] or a blowing process [5,6]. Copyright: © 2021 by the authors. The asymmetry of the shell influences the wineglass mode [7], frequency mismatch [8], Licensee MDPI, Basel, Switzerland. and quality factor [2]. Therefore, a uniform and symmetric hemispherical shell is required. This article is an open access article For the second issue, the essence of alignment is the realization of assembly with a distributed under the terms and uniform and small gap. When the µHR is in working mode, it is excitated by electrostatic conditions of the Creative Commons force, and the change of capacitance is detected to distinguish resonant frequency. There- Attribution (CC BY) license (https:// fore, the gap between shell and electrode is critical for the intensity of driving and detection creativecommons.org/licenses/by/ of signal. 4.0/). Micromachines 2021, 12, 815. https://doi.org/10.3390/mi12070815 https://www.mdpi.com/journal/micromachines
Micromachines 2021, 12, 815 2 of 10 There are two dominant approaches to fabricate µHR. One is via chemical vapor depo- sition (CVD) on the hemispherical cavity, the other is via a blowing process. As for the CVD approach, a 3D micro-hemispherical shell structure could be fabricated by depositions of polysilicon [9], diamond [10], and silicon oxide [4] on isotropically etched cavities, or poly- crystalline diamond [11] on a micro-electro-discharge machining cavity. The gap between the shell and electrode is usually determined by the thickness of the sacrifice layer, which can be precisely controlled. Therefore, the gaps of structures fabricated by the CVD approach are usually small, ranging from 1.7 µm to 20 µm. However, the asymmetry of shells severely depends on the isotropic etching or micro-electro-discharge machining process. 3D blowtorch molding [5,12], chemical foaming [13], and glassblowing [6,14] have been developed with favorable roughness and symmetry. These approaches are based on the blowing process under high temperature close to the film material softening point. Assembly with a locating stem is usually undertaken to align the independently fabricated shell and electrode, where a gap has been reported as 10.3–16.3 µm [5]. Various glass- Micromachines 2021, 12, x FOR PEER REVIEW 3 of 10 blowing processes with integrated electrodes have been developed with a wide range of capacitive gaps. A thermal coefficient mismatch between the blown shell and the cavity mold was used to create a gap of about 8 µm [7]. Deep glass dry etching was carried out K. Najaf et to define the gapOn (>30 followed µm),sili- vertical by glassblowing Assemble with and XeF2 releasing [15]. A kind of Fused silica fuel-oxygen blowtorch -- / 2500 10.3–16.3 al. [5,12] out-of-plane electrode architecture con sidewall has been locating stemproposed, using photoresist as the sacrificial B. Sarac et al. Metallic layers, whose thickness defined the gap (10.7 µm) [2,16]. Satellite spheres were fabricated Blow Molding No electrode -- 30 et.al. [15] resonator would be interfered glass sidewallwith. Therefore, though favorable symmetry and roughness A. Shkel could be achieved by the blowing process, the gap is still relatively high. Overall, it is hard Fused silica Glassblowing Plane on silicon Integration 0.23 / 3500 10.7 et.al. [2,16] to realize a balance in both the symmetry and the gap. In this paper,Satellite a new µHR spherestructure fabricated by a blowing process is proposed, which A. Shkel et 5 (mini- Pyrex glass Glassblowing fabricated includes sandwich-shaped stacks by Integration and eave-shaped0.85 0.05% electrodes, as shown500in Figure 1. The al. [6,14] mum) glassblowing blowing process leaves the shell with favorable surface roughness and symmetry. In addition, R. Wang et sandwich-shaped Annular stacks and elec-eave-shaped electrodes make it feasible to realize uniform Pyrex glass Glassblowing Integration 0.22 / 500 73 al. [17] and small gaps. Therefore, trode the asymmetry, surface roughness, and gap could be kept at a low level, throughOn vertical the novelsili-design in structure and fabrication process. Moreover, the This work Pyrex glass Bonding, glassblowing Integration 0.26 0.04% 275 5.9 electrical insulationconof sidewall the shell and silicon-based electrodes could be guaranteed, owing to “--” represents “Not mentioned in structure. the eave-shaped the paper”.The “/” represents “could Not obtained various hemispherical from shells are the paper”. illustrated in Table 1. Figure 1. Figure 1. μHR structure illustration. µHR structure illustration. 2. Design To investigate the influence of dimension parameter on the performance, simulation models are established by COMSOL Multiphysics® 5.6 (COMSOL, Inc., Burlington, MA, USA). The dimensional sketch of the hemispherical shell is illustrated in Figure 2. The bottom cross-section is circular.
Micromachines 2021, 12, 815 3 of 10 Table 1. Various hemispherical shells. Micromachines 2021, 12, x FOR PEER REVIEW 3 of 10 Fabrication Alignment Surface Typical Shell Electrode Capacitive Source Method of of Shell and Roughness Asymmetry Hemisphere Material Shape Gap (µm) Shell Electrode (nm) Radius (µm) K. Najaf et isotropic On vertical sili- Assemble with X. Zhuang Fused silica fuel-oxygen etching, blowtorch Synclastic -- / 2500 10.3–16.3 al.al. [5,12] Polysilicon Integration locating –stem con sidewall 0.55% 650 1.7 et [9] CVD, hemisphere B. Sarac et al. Metallic sacrificing Blow Molding No electrode --
Micromachines 2021, 12, 815 4 of 10 Finite Micromachines 2021, 12, x FOR PEER REVIEW element modal analysis is undertaken to find the vibrating-mode shapes of 4 of 10 shells and the resonant frequency. When the shell works in 1st m = 2 wineglass mode, there Micromachines 2021, 12, x FOR PEER REVIEW 4 of 10 are four uniformly distributed polar zones, as shown in Figure 3. The thickness of the shell is set as 50 µm. The resonant frequency of the hemispherical shell with different radius could be simulated, as shown in Table 2. (a) (b) Figure 3. 1st m =(a) 2 mode of HRG (a) inclined view (b) overview. (b) Figure 3. 1st m = 23.mode Table Figure 2. mof= HRG 1stResonance (a)of 2 mode inclined HRG of frequency view (a) (b) inclined shell overview. withview (b) overview. different radius. Bottom Radius ofTable Table 2. Resonance Shell2.(μm) Resonance 500frequency frequency of shell of shell with 525 withradius. different different radius. 550 575 600 1st m = 2 mode resonance fre- Bottom Radius of Shell Bottom (μm) Radius of Shell (µm) 500 1.58 500 10525 3 1.49 525 10550 3 1.40 550 10575 3 1.33 575103600 1.26 600103 quency(kHz) 1st m =1st2 m mode resonance = 2 mode fre- frequency (kHz) 3 1.58 × 103 resonance 1.49 × 103 1.40 × 103 1.33 × 103 1.26 × 103 1.58 10 1.49 103 1.40 103 1.33 103 1.26 103 quency(kHz) The structure consists of a 3D micro-hemispherical shell and 16 surrounding discrete The structure consists of a 3D micro-hemispherical shell and 16 surrounding discrete electrodes, as shown in Figure 4. This part will focus on the silicon-based electrodes. Here, electrodes, The structure as shown consists of ain3D Figure 4. This part will shell micro-hemispherical focusand on the silicon-baseddiscrete 16 surrounding electrodes. Here, annular electrodes [17] and silicon-based electrodes are compared. electrodes, annular electrodes as shown [17] in Figure and silicon-based 4. This part will focuselectrodes are compared. on the silicon-based electrodes. Here, annular electrodes [17] and silicon-based electrodes are compared. (a) (b) Figure Figure 4. 4. Comparison Comparison (a) of of μHRs µHRswith with annular annular electrodes electrodesand and silicon-based silicon-basedelectrodes (b) (a) electrodes (a)annular annularelectrodes; electrodes;(b) (b)silicon- silicon- based based electrodes. electrodes. Figure 4. Comparison of μHRs with annular electrodes and silicon-based electrodes (a) annular electrodes; (b) silicon- based electrodes. Thecapacitor The capacitorcould couldbe besimplified simplifiedas astwo twoparallel parallelplate plateelectrodes electrodes which which are areseparated separated byaavacuum. by vacuum. The capacitor could be simplified as the twocapacitor parallel plate valueelectrodes which are separated Forthe For the annular annular electrode, electrode, the capacitor value a could C couldbebeexpressed expressedas:as: by a vacuum. h For the annular electrode, the capacitor Zh value couldε w be expressed as: C h Ca =a = 0 dd00+ p 2 +RRε−−0 w R R2 − ε 00w − yy22 ++ rr−− rr22 − p − yy22 dy dy (1) (1) Ca = 0 + R − of Rthe 0 d 0height 2 y 2 + r − r 2 −is ythe −electrodes, 2 dy (1) where h is the effective permittivity of the medium in vacuum, w is the effective width of the electrodes, and is the gap between the bottom where h is the effective height of the electrodes, is the permittivity of the medium in of electrodes, R is the radius of hemispherical shell, r is the radius of annular electrode, y vacuum, w is the effective width of the electrodes, and is the gap between the bottom represents the variable symbol along the coordinate axes of electrode height. of electrodes, R is the radius of hemispherical shell, r is the radius of annular electrode, y
Micromachines 2021, 12, 815 5 of 10 Micromachines 2021, 12, x FOR PEER REVIEW 5 of 10 where h is the effective height of the electrodes, ε 0 is the permittivity of the medium in vacuum, w is the effective width of the electrodes, and d0 is the gap between the bottom Correspondingly, of electrodes, the capacitor R is the radius value forshell, of hemispherical the silicon-based r is the radius electrode of annular electrode, could be ex-y pressed as: represents the variable symbol along the coordinate axes of electrode height. Correspondingly, the capacitor value h for the silicon-based electrode Cs could be ε0w expressed as: Cs = Zh 0 d + R − R 2 − y 2 dy (2) 0 ε0w Cs = p dy (2) d0 + − Rthan 2 − y2 It should be noted that would 0 beRlarger , assuming the dimensional pa- rameters h, w,beand R are theCsame. The radius of annular electrode r is set to be a relatively It should noted that s would be larger than Ca , assuming the dimensional parame- small value, to guarantee that ters h, w, and R are the same. The radius the resonant frequency of annular of the electrode r is annular set to be electrode a relativelyissmall much biggertothan value, that of that guarantee the hemispherical shell [17]. of the annular electrode is much bigger the resonant frequency than that of the hemispherical shell [17].the eave-shaped electrode. The top silicon layer of Next is the fabrication process of the Next sandwich-shaped is the fabricationstacks (anodically process of thebonded silicon–glass–silicon) eave-shaped electrode. The top aresilicon etchedlayer by deep of reactive ion etching (DRIE) technique to form the silicon electrode. the sandwich-shaped stacks (anodically bonded silicon–glass–silicon) are etched by After that, the wafer deepis soaked ion reactive in the HF (40%) etching (DRIE)totechnique form an eave-shaped structure to form the silicon owingAfter electrode. to isotropic that, theetching wafer isof glass, in soaked as the shown in Figure HF (40%) to form 5. an There are two reasons eave-shaped structuretoowing design eave-shaped to isotropic silicon etching elec- of glass, astrodes. shownOne is that5.silicon in Figure There arecan two be fabricated reasons to in an anisotropic design eave-shaped way. Therefore, silicon the shape electrodes. One isand thatdimension silicon canofbethe electrodeincan fabricated an be preciselyway. anisotropic determined, Therefore,which is favorable the shape for reduc- and dimension of the electrode can be precisely determined, which is favorable for reducing the ing the gap between the shell and eave-shaped electrodes. The other is that the eave- gap shaped structure could be easily formed because silicon could be between the shell and eave-shaped electrodes. The other is that the eave-shaped structure bonded with glass, and the etch could solution be easily of glass formed is notsilicon because reactive withbesilicon. could bonded Therefore, with glass,self-insulting and the etchof electrodes solution of could glass is be notrealized. reactive with silicon. Therefore, self-insulting of electrodes could be realized. Figure 5. Illustration of the eave-shaped structure. Figure 5. Illustration of the eave-shaped structure. 3.3.Fabrication FabricationProcess Process The Theforming formingprocess processofofthethehemispherical hemisphericalshell shellresonator resonatorusesusesthe thedifferent differentpressure pressure between betweenthe theinside insideand andoutside outsideofofthe thehermetic hermeticcavity cavityandandthe thesurface surfacetension tensionforces forcesfrom from the softened glass. The fabrication of the hemispherical shell resonator the softened glass. The fabrication of the hemispherical shell resonator with integrated with integrated silicon-based silicon-basedelectrodes electrodes is illustrated as is illustrated asFigure Figure6:6: (a) (a) A 500A 500 µm-thick μm-thick silicon silicon waferwafer is is etched etched using the DRIE technique with 7 µm-thick AZ4620 photoresistor using the DRIE technique with 7 μm-thick AZ4620 photoresistor (Microchemicals GmbH, (Microchemicals GmbH, D-89079, D-89079, Ulm, Germany) Ulm, Germany) as a pattern as a pattern mask,mask, to form to form a 100a 100 µm-deep μm-deep circular circular cavity. cavity. (b) (b) After After removing removing thethe photoresistor photoresistor andand cleaning cleaning the silicon the silicon wafer, wafer, anodic anodic bonding bonding of of a new a525 newμm-thick 525 µm-thick PyrexPyrex 7740 wafer 7740 glass glass wafer (Corning (Corning Inc., York, Inc., New New York, NY, USA) NY, USA) and and the the silicon silicon wafer is performed, where the circular cavities are encapsulated with atmospheric air. wafer is performed, where the circular cavities are encapsulated with atmospheric air. Then, Then,thetheglass glasswafer waferisisground groundand andpolished polishedusing usinga achemical chemicalmechanical mechanical polishing polishing(CMP) (CMP) technique until the thickness reaches 100 μm. Lithography is performed on the backside silicon surface and a 10 μm-deep cross channel is formed by DRIE, to provide an
Micromachines 2021, 12, 815 6 of 10 Micromachines 2021, 12, x FOR PEER REVIEW 6 of 10 technique until the thickness reaches 100 µm. Lithography is performed on the backside silicon surface alignment labeland for asubsequent 10 µm-deepprocesses. cross channel is formed (c) Another newby DRIE, to provide 400 μm-thick an alignment silicon wafer is label for subsequent anodically bonded with processes. the glass(c) Another surface new of the 400 µm-thick former siliconThe stacked wafer. wafertop is anodically silicon layer bonded with the glass surface of the former stacked wafer. is ground and polished by CMP until the thickness reaches 100 μm. (d) a 7 μm-thickThe top silicon layer is ground and polished AZ4620 by CMP until photoresistor the thicknessGmbH, (Microchemicals reachesD-89079, 100 µm. (d)Ulm,a 7 Germany) µm-thick AZ4620is spunphotore- on the sistor top (Microchemicals silicon GmbH, D-89079, layer, and lithography Ulm, out is carried Germany) is spunthe by aligning onbackside the top silicon cross layer, and channel. lithography Then the topissilicon carried out by layer aligning is etched bythe backside DRIE, until cross channel. the Pyrex glass Then layertheistop silicontolayer exposed formis etched by DRIE, silicon-based until theAfter electrodes. Pyrexthat, glassthelayer is exposed to photoresistor is form silicon-based removed. The wafer electrodes. is immersedAfter that, the photoresistor is removed. The wafer is immersed in the in the HF (40%) for 8 minutes to etch the glass beneath the silicon-based electrodes andHF (40%) for 8 min to etch the glass beneath the silicon-based electrodes and form the eave-shaped form the eave-shaped structure; (e) then, vacuum annealing is conducted, with a vacuum structure; (e) then, vacuumofannealing degree 20 m Torr, is conducted, with a vacuum furnace temperature of 770 degree °C andof 20 m Torr, furnace a remaining time temperature of 2 minutes, of 770 ◦ C and a remaining time of 2 min, and then the furnace temperature is slowly decreased and then the furnace temperature is slowly decreased to 200 °C in 5 minutes. The glass to 200 ◦ C in 5 min. The glass film is blown and solidified to form a hemispherical shell. film is blown and solidified to form a hemispherical shell. (f) 50 nm/100 nm-thick Cr/Au is(f)deposited 50 nm/100onnm-thick the whole Cr/Au wafer is deposited surface usingon thethewhole wafer surface magnetron using sputtering the magnetron technique, thus sputtering technique, thus the silicon-based electrodes and the silicon-based electrodes and shell metals are automatically separated owing shell metals are automatically to the separated owing non-conformal to the metal non-conformal deposition on themetal deposition eave-shaped on the eave-shaped structure. The challengestructure. The of the fabri- challenge of the fabrication technology is to control the parameter of blowing process to cation technology is to control the parameter of blowing process to realize a uniform shell realize a uniform shell and small gap. The annealing temperature and vacuum degree of the and small gap. The annealing temperature and vacuum degree of the blowing process blowing process should be delicately investigated. should be delicately investigated. Figure Figure6.6.Fabrication Fabricationprocess processsketch. sketch. 4.4.Fabrication FabricationResult Result Thekey The keyprocess process is the formation formationof ofthe thesurrounding surroundingeave-shaped eave-shaped electrodes. The electrodes. Thelateral lat- etching eral volume etching of theofPyrex volume glass glass the Pyrex beneath the eave-shaped beneath electrodes the eave-shaped should should electrodes be well manipu- be well lated. If the eave manipulated. is too If the shallow, eave is toothe metal may shallow, be conformally the metal deposited ondeposited may be conformally the glass sidewall, on the resulting in short-circuiting between the electrodes. If the eave is too deep, the glass sidewall, resulting in short-circuiting between the electrodes. If the eave is too deep, contact area between the eave-shaped electrodes and the glass would be dramatically the contact area between the eave-shaped electrodes and the glass would be dramatically reduced due to double-side etching. This is unfavorable when conducting glassblowing reduced due to double-side etching. This is unfavorable when conducting glassblowing experiments. The etching rate of Pyrex glass in HF solution (40%) is measured as 3.7 µm/min. In experiments. addition, the appropriate The etching lateralglass rate of Pyrex etching width in HF is designed solution (40%) isto measured be about 30asµm, 3.7 which μm/min. could In be realized after immersing the wafer in HF solution for 8 min. The SEM addition, the appropriate lateral etching width is designed to be about 30 μm, which could pictures of the eave-shaped be structure realized after immersingare shown in Figure the wafer in HF7.solution for 8 minutes. The SEM pictures of the eave-shaped structure are shown in Figure 7.
Micromachines 2021, 12, 815 7 of 10 Micromachines 2021, Micromachines 2021, 12, 12, xx FOR FOR PEER PEER REVIEW REVIEW 77 of of 10 10 Figure 7. Figure 7. SEM SEM pictures pictures of of the the eave-shaped eave-shaped structure. structure. The big The big challenge challenge in in the the process process is to blow up the glass glass to to form form aa hemispheric hemispheric shell shell with an extremely small gap in the eave-shaped eave-shaped electrode. electrode. The shell shape is determined by the internal–external by internal–externalpressure pressuredifference differenceand andthe annealing the annealing temperature. temperature. Vapor pressure Vapor pres- force,force, sure interfacial force,force, interfacial and gravity force contribute and gravity to the to force contribute blowing process. the blowing The vacuum process. The vac-of the annealing furnacefurnace is kept is at kept 20 matTorr. ◦ C, close uum of the annealing 20 mThe temperature Torr. is raised The temperature up to 770 is raised up to 770 °C, to thetosoftening close temperature the softening of Pyrex temperature 7740 glass, of Pyrex and maintained 7740 glass, for 2 min. and maintained for 2Then, the minutes. temperature slowly falls to 200 ◦ C over 5 min. The fabricated µHR is illustrated in Figure 8, Then, the temperature slowly falls to 200 °C over 5 minutes. The fabricated μHR is illus- with a in trated gap down8,to Figure 5.9 µm with a gapfrom down shell to to 5.9electrode. μm from shell to electrode. Figure 8. Figure 8. SEM SEM pictures pictures of of μHR. μHR. µHR. physical photo of the A physical the µHR μHR after wire-bonding is shown in Figure 9. The micro- hemispherical hemispherical shell and 16 surrounding discrete electrodes electrodes can can be be clearly clearly observed. observed. After wire-bonding, the wire-bonding, the electrodes electrodes are connected connected to the ceramic package package forfor signal signal processing, processing, which are which are verified verified to to have have insulated insulated each each other. other. The surface The surface roughness roughness of of the the hemispherical hemispherical shell shell is is crucial crucial for for the the vibration vibration quality quality factor. An factor. An atomic atomicforce forcemicroscope microscope(AFM) (AFM) measurement measurement waswasperformed performed to characterize the to characterize surface roughness after glassblowing and metal deposition, as shown the surface roughness after glassblowing and metal deposition, as shown in Figure 10. in Figure 10. The roughness The valuevalue roughness was 0.26 wasnm ± nm 0.26 0.06 ±nm, which 0.06 nm, was which comparable to the previously was comparable reported to the previously values ranging from 0.22 nm to 2 nm, achieved via the glassblowing process, reported values ranging from 0.22 nm to 2 nm, achieved via the glassblowing process, and this was and priorwas this to those prior of to other those molding processes, of other molding as mentioned processes, in Table 1. as mentioned in Table 1.
Micromachines 2021, 12, 815 8 of 10 Micromachines 2021, 12, x FOR PEER REVIEW 8 of 10 Micromachines 2021, 12, x FOR PEER REVIEW 8 of 10 Figure 9. Physical Physical photo of of μHR after after wire-bonding. Figure 9. Physical photo Figure 9. μHR after wire-bonding. photo of µHR wire-bonding. Figure 10. Atomic force microscopy (AFM) graph of surface. Figure 10. Atomic force microscopy (AFM) (AFM) graph graph of of surface. surface. 5. Nondestructive 5. Nondestructive Estimation Estimation of Shell Shell Thickness 5. Nondestructive Estimation of of Shell Thickness Thickness The blowing The blowingprocess processisisusually usually performed performed to fabricate to fabricate a glass a glass hemispherical hemispherical shell. shell.shell. The The blowing process is usually performed to fabricate a glass hemispherical The thickness thickness of the spherical shell is critical to the resonant frequency and sensitivity of The thickness of the spherical shell is critical to the resonant frequency and sensitivitythe of the spherical shell is critical to the resonant frequency and sensitivity of of the μHR. However, However, to to measure measure the the thickness, thickness, the glass the glass shell would have to be broken µHR. the μHR. However, to measure the thickness, theshell would glass shell have would to be broken have to bealong its broken along itssection. vertical verticalHerein, section.it Herein, is necessaryit is necessary to develop toandevelop an estimating estimating method in method a in a non- nondestructive along its vertical section. Herein, it is necessary to develop an estimating method in a non- destructive manner. manner.that We manner. assume We assume that the volume glass of theisblowing glass is constant. That destructive Wethe volume assume thatof the the blowing volume of constant.glass the blowing Thatis means the plane constant. That means the volume is plane to equal volume the is equalshell spherical to theone, spherical which shell could one, be which consideredcouldtobebeconsidered the volume to means the plane volume is equal to the spherical shell one, which could be considered to be the volume difference of twodifference of two sphericalofcaps. spherical caps. be the volume difference two spherical caps. 22 ππ 2 ππ T )T2 )] 2−] − π 2 2 2 π R2tt== π6 HH[ H[ H+22 +3(3( πR RR ++ −T ( H( H −)[( H− T )[( H T−)T+ + 3]R22 ] )2 3R (3) (3) π R t = 6 H [ H + 3( R + T ) ] − 6 ( H − T )[( H − T ) + 3R ] 2 6 (3) The parameters are6labeled in Figure 2. This could 6 be simplified as the cubic equation: The parameters are labeled 3 T + (3H in 2Figure 2. This 2could be simplified + 6HR ) T − be 2 as the cubic equation: The parameters are labeled in Figure 2. +This3Rcould t=0 6Rsimplified as the cubic equation: (4) 3 2 2 2 The positive solution T + (3cubic of this H + equation 6 HR + 3 R can)Tbe−taken 6 R t as = 0the estimated thickness (4) T 3 + (3 H 2 + 6 HR + 3 R 2 )T − 6 R 2 t = 0 value, noted as Tf . Typical shell thickness Tm can be measured via SEM, as shown in (4) Figure The positive 11,positive where the solution of this cubic hemispherical shellsequation are destroyed.can be taken as the estimated thickness The solution of this cubic equation can be taken as the estimated thickness value, noted as Tf. Typical shell thickness Tm can be measured via SEM, as shown in Figure value, noted as Tf. Typical shell thickness Tm can be measured via SEM, as shown in Figure 11, where the hemispherical shells are destroyed. 11, where the hemispherical shells are destroyed.
Micromachines 2021, 12, 815 9 of 10 Micromachines 2021, 12, x FOR PEER REVIEW 9 of 10 Figure 11. SEMs of broken hemispherical shells. The The parameters parameters are are compared compared inin Table Table3. 3. The The cavity cavity radius radius “R” “R” can can be be extracted extracted from from the layout design, which can also be confirmed by optical microscopy. The height the layout design, which can also be confirmed by optical microscopy. The height of shell of shell “H” “H” and and the the initial initial thickness thickness of of glass glass “t” “t” can can be be measured measured byby optical optical microscopy microscopy via via the the focusing method. The deviations between estimated thickness value (T focusing method. The deviations between estimated thickness value (Tff) and measured) and measured value value (T (Tmm)) are are within within thethe acceptable acceptable range. range. These These results results demonstrate demonstrate that that the the estimation estimation method method cancan realize realize nondestructive nondestructive testing testing of of hemispheric hemispheric shell shell thickness thickness with with deviation deviation below 5%. below 5%. Table 3. Parameter list and comparison. Table 3. Parameter list and comparison. RR H H t t Tm Tm Tf Tf Deviation Deviation 550 550 455 455 109 109 67.5 67.5 65.2 65.2 3.4% 3.4% 550 550 321 321 120 120 97.5 97.5 95.3 95.3 2.2% 2.2% 550 648 120 53.1 50.6 4.7% 550 600 648 464 120 120 53.1 76.6 50.6 76.2 4.7% 0.5% 600 464 120 76.6 76.2 0.5% 6. Conclusions 6. Conclusions This µHR structure based on a hemispherical shell and surrounding eave-shaped elec- trodesThis μHR structure is presented based on in this paper. a hemispherical It possesses low asymmetryshell andandsurrounding eave-shaped surface roughness, and a electrodes is presented in this paper. It possesses low asymmetry uniform and small gap, compared to the previously reported µHR structure fabricated and surface roughness,by and a uniform molding and small deposition, precisegap, comparedand machining, to the previously reported glassblowing. μHR structure The fabrication process isfabri- pre- cated byincluding sented, moldingthe deposition, formationprecise machining, of eave-shaped and glassblowing. silicon-based electrodes The andfabrication pro- a hemispheric shell. The shape and dimensions of the electrode can be precisely determined, making thea cess is presented, including the formation of eave-shaped silicon-based electrodes and hemispheric gap between the shell. The shell andshape and dimensions eave-shaped electrodesofcontrollable. the electrode Thecan be precisely eave-shaped deter- structure mined, making the gap between the shell and eave-shaped electrodes is formed to obtain self-insulting of electrodes, where the appropriate lateral etching width controllable. The eave-shaped structure is formed to obtain self-insulting of electrodes, is about 30 µm. The hemispheric shell is blown, with a small capacitor gap down to 5.9 µm, where the appro- priate is which lateral etchingamong competitive width theis about 30 μm. reported µHRThe hemispheric s via shell is blown, a blowing process. with a small The asymmetry and capacitor gap down to 5.9 μm, which is competitive among the reported surface roughness after glassblowing were measured as 0.04% and 0.26 nm, respectively, μHR s via a blow- ing process. which The asymmetry are comparable and surface to the reported valuesroughness after glassblowing via the glassblowing were process. measured Finally, as an esti- 0.04% and mation method0.26 of nm, respectively, shell thickness inwhich are comparable a nondestructive manner to is the reported with developed, values via the deviation glassblowing below 5%. These process. Finally, results an estimation preliminarily method indicate that of shell this thickness structure within a nondestructive hemispherical manner is developed, with deviation below 5%. These results shell and surrounding eave-shaped electrodes is promising in µHR application. preliminarily indicate that Further this structure with a hemispherical shell and surrounding investigation of the performance characterization of µHRs should be carried out. eave-shaped electrodes is promising in μHR application. Further investigation of the performance characterization of μHRs should be carried out.
Micromachines 2021, 12, 815 10 of 10 Author Contributions: Conceptualization, R.W. and J.L.; Data curation, B.B.; Investigation, W.Z. and H.C.; Validation, B.B.; Writing—original draft, B.B.; Writing—review and editing, R.W. and B.B. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Program of China, Grant number 2020YFC0122102 and the National Natural Science Foundation of China, Grant number 51875535, 61927807 and by 1331KSC. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to technique privacy. Acknowledgments: The authors would like to thank Jun Tang from North University of China for his suggestion in device design. Conflicts of Interest: The authors declare no conflict of interest. References 1. Xu, Z.; Zhu, W.; Yi, G.; Fan, W. Dynamic modeling and output error analysis of an imperfect hemispherical shell resonator. J. Sound Vib. 2021, 498, 115964. [CrossRef] 2. Senkal, D.; Ahamed, M.J.; Ardakani, M.H.A.; Askari, S.; Shkel, A.M. Demonstration of 1 Million Q—Factor on Microglassblown Wineglass Resonators with Out-of-Plane Electrostatic Transduction. J. Microelectromech. Syst. 2014, 24, 29–37. [CrossRef] 3. Shi, Y.; Lu, K.; Xi, X.; Wu, Y.; Xiao, D.; Wu, X. Geometric Imperfection Characterization and Precise Assembly of Micro Shell Resonators. J. Microelectromech. Syst. 2020, 29, 480–489. [CrossRef] 4. Pai, P.; Chowdhury, F.K.; Pourzand, H.; Tabib-Azar, M. Fabrication and Testing of Hemispherical MEMS Wineglass Resonators. In MEMS 2013; IEEE: Taipei, Taiwan, 2013; pp. 677–680. 5. Cho, J.Y.; Woo, J.-K.; Yan, J.; Peterson, R.L.; Najafi, K. Fused-Silica Micro Birdbath Resonator Gyroscope (µ-BRG). J. Microelectromech. Syst. 2014, 23, 66–77. [CrossRef] 6. Prikhodko, I.P.; Zotov, S.A.; Trusov, A.A.; Shkel, A.M. Microscale Glass-Blown Three-Dimensional Spherical Shell Resonators. J. Microelectromech. Syst. 2011, 20, 691–701. [CrossRef] 7. Kanik, M.; Bordeenithikasem, P.; Kim, D.; Selden, N.; Desai, A.; M’Closkey, R.; Schroers, J. Metallic Glass Hemispherical Shell Resonators. J. Microelectromech. Syst. 2015, 24, 19–28. [CrossRef] 8. Huo, Y.; Ren, S.; Yi, G.; Wang, C. Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity. Chin. J. Aeronaut. 2020, 33, 2660–2669. [CrossRef] 9. Zhuang, X.; Chen, B.; Wang, X.; Yu, L.; Wang, F.; Guo, S. Microsacle PolySilicon Hemispherical Shell Resonating Gyroscopes with Integrated Three-dimensional Curved Electrodes. J. Phys. Conf. Ser. 2018, 986, 012022. [CrossRef] 10. Bernstein, J.J.; Bancu, M.G.; Cook, E.H.; Chaparala, M.V.; Teynor, W.A.; Weinberg, M.S. A MEMS diamond hemispherical resonator. J. Micromech. Microeng. 2013, 23, 125007. [CrossRef] 11. Heidari, A.; Chan, M.; Yang, H.; Jaramillo, G.; Fonda, P.; Najar, H.; Yamazaki, K.; Lin, L.; Horsley, D.A. Micromachined polycrystalline diamond hemispherical shell resonators. In Transducers; IEEE: Barcelona, Spain, 2013; pp. 2415–2418. 12. Cho, J.Y.; Yan, J.; Gregory, J.A.; Eberhart, H.W.; Peterson, R.L.; Najafi, K. 3-Dimensional Blow Torch-Molding of Fused Silica Microstructures. J. Microelectromech. Syst. 2013, 22, 1276–1284. [CrossRef] 13. Xie, J.; Chen, L.; Xie, H.; Zhou, J.; Liu, G. The Application of Chemical Foaming Method in the Fabrication of Micro Glass Hemisphere Resonator. Micromachines 2018, 9, 42. 14. Zotov, S.A.; Trusov, A.A.; Shkel, A.M. Three-Dimensional Spherical Shell Resonator Gyroscope Fabricated Using Wafer-Scale Glassblowing. J. Microelectromech. Syst. 2012, 21, 509–510. [CrossRef] 15. Senkal, D.; Ahamed, M.J.; Trusov, A.A.; Shkel, A.M. Achieving Sub-Hz Frequency Symmetry in Micro-Glassblown Wineglass Resonators. J. Microelectromech. Syst. 2013, 23, 30–38. [CrossRef] 16. Senkal, D.; Raum, C.R.; Trusov, A.A.; Shkel, A.M. Titania silicate/fused quartz glassblowing for 3-d fabrication of low internal loss wineglass micro-structures. In Solid—State Sensors, Actuators, Microsystems Work; IEEE: Krakow, Poland, 2012; pp. 267–270. 17. Wang, R.; Bai, B.; Feng, H.; Ren, Z.; Cao, H.; Xue, C.; Zhang, B.; Liu, J. Design and Fabrication of Micro Hemispheric Shell Resonator with Annular Electrodes. Sensors 2016, 16, 1991. [CrossRef] [PubMed] 18. Sarac, B.; Kumar, G.; Hodges, T.; Ding, S.; Desai, A.; Schroers, J. Three-Dimensional Shell Fabrication Using Blow Molding of Bulk Metallic Glass. J. Microelectromech. Syst. 2010, 20, 28–36. [CrossRef]
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