A Multi-Fork Z-Axis Quartz Micromachined Gyroscope

Transcription

1 Sesors 03, 3, ; doi:0.3390/s30948 Article OPEN ACCESS sesors ISSN A Multi-Fork Z-Axis Quartz Micromachied Gyroscope Lihui Feg *, Ke Zhao, Yua Su, Jiami Cui, Fag Cui ad Aiyig Yag School of Optoelectroics, Beijig Istitute of Techology, Beijig 0008, Chia; s: kirt@bit.edu.c (K.Z.); sy@bit.edu.c (Y.S.); cueijiami@bit.edu.c (J.C.); cf@bit.edu.c (F.C.); yagaiyig@bit.edu.c (A.Y.) * Author to whom correspodece should be addressed; lihui.feg@bit.edu.c; Tel.: ; Fax: Received: 4 July 03; i revised form: 9 August 03 / Accepted: September 03 / Published: 7 September 03 Abstract: A ovel multi-fork z-axis gyroscope is preseted i this paper. Differet from traditioal quartz gyroscopes, the lateral electrodes of the sese beam ca be arraged i simple patters; as a result, the fabricatio is simplified. High sesitivity is achieved by the multi-fork desig. The workig priciples are itroduced, while the fiite elemet method (FEM) is used to simulate the modal ad sesitivity. A quartz fork is fabricated, ad a prototype is assembled. Impedace testig shows that the drive frequecy ad sese frequecy are similar to the simulatios, ad the quality factor is approximately 0,000 i air. The scale factor is measured to be 8.34 mv/( /s) ad the oliearity is 0.40% i a full-scale iput rage of ±50 /s. Keywords: quartz micromachied gyroscope; multi-fork; coriolis force; aisotropic etchig. Itroductio The quartz gyroscope is a importat sesor used i various civil ad military applicatios [ 6]. For most quartz gyroscopes, the drive mode is the fork or beam s vibratio i the x-axis orietatio ad the sese mode is the vibratio i the z-axis orietatio, while the iput agular rate is i the y-axis orietatio. The drive mode, sese mode ad electrode distributio of a typical quartz gyroscope are show i Figure a c.two parallel idepedet sese electrodes o each sidewall of the sese beam (i Figure c, parts 5 ad 8 as well as 6 ad 7 are separated) are required to gather the charges iduced by the sese mode. However, the whole thickess of the quartz tuig fork is about several

2 Sesors 03, hudred micrometers, so performace of the sesors is affected by fabricatio errors ad it is difficult to deposit complicated electrode patters [3,4]. Therefore, may researchers are workig to explore a comprehesive approach to reduce the process difficulties ad to improve the performace of the sesors [7 9]. I this paper, a type of z-axis gyroscope is itroduced. It is fabricated usig the quartz aisotropic wet etchig process. Details about the structure desig, fabricatio process, readout circuit, ad characterizatio of this kid of gyroscope are preseted. Figure. Vibratio modes ad electrode distributio of a traditioal gyroscope. (a) Drive mode (b) Sese mode ad (c) Electrode distributio. The orgaizatio of the paper is as follows: first a brief descriptio of the priciple ad structure is provided i the Itroductio sectio. Device modelig is discussed i Sectio. Theoretical aalysis ad simulatio are itroduced i Sectio 3. Fabricatio ad sigal detectio methods are described i Sectio 4, while experimetal test results are preseted i Sectio 5, ad the summary ad coclusios are give i the last sectio.. Desig Cocept.. Structure of the Z-Axis Multi-Fork Gyroscope ad Workig Priciple The workig priciple of a quartz gyroscope is based o the Coriolis effect. I this paper, we preset a z-axis gyroscope. The structure of the drive fork ad sese fork are show i Figure a. Four drive forks ad four sese forks are arraged symmetrically. The electrode distributio of the left part of the gyroscope is show i Figure b, while the right part is symmetrical to the left part. Whe the drive forks are drive, a vibratio is iduced alog the x-axis based o the iverse piezoelectric effect, while a opposite vibratio occurs o the four drive forks i x-axis directio. The drive mode is show i Figure 3a. Whe the agular rate is applied o the z-axis, the Coriolis force ca make the cross beam move up or dow leadig to vibratio i the sese mode as show i Figure 3b. The bedig of the sese forks i the x-axis ca geerate a charge because of the piezoelectric effect,

3 Sesors 03, which is proportioal to the Coriolis force ad detected by the sesee electrode. The agular rate ca be obtaied by demodulatig this charge sigal. Figure. Structure ad electrode distributio. ( a) The structure of the gyroscope ad (b) The electrode distributio of the left part. (a) (b) Figure 3. Vibratio modes of the gyroscope. (a) Drive mode ad (b) Sese mode. (a) (b) Therefore, the followig beefits ca be determied whe comparig the gyroscope preseted i this paper with a traditioal y-axis gyroscope:. The fabricatio of the electrode is easy: it ca sese the agular rate without complex electrodes.. The thickess of the wafer has little effect o the mode frequecy; thus, the wafer ca be made thier, but the shock resistace should be cosidered. 3. The symmetry of this structure ca suppress the effects of the liear acceleratio ad cross-couplig, etc. I additio, whe compared to other z-axis gyroscopes [7 9], the sesitivity will be greater due to the icrease of the vibratio amplitude of the sese forks.

4 Sesors 03, Desig Rules The most basic desig goal is to obtai the appropriate resoat frequecy; Oe beam of the drive mode is show i Figure 4a ad a simplified drivig fork is show i Figure 4b. The modal coordiate Equatio is expressed as [0]: ξ = ( μ y) cos( μ y) α [ sih( μ y) si( μ y) ] cosh () where, μ ad α ca be obtaied by: α = ( μ l) cos( μ l ) ± 0 cosh = [ cosh ( μ l) ± cos( μ l) ] [ sih( μ l) ± si( μ l) ] From this equatio, it is possible to express the resoat equatio, as below: () (3) ω = i EI ρ Al 4 ( μ l) i (4) where E ad ρ represet the Youg s modulus ad the desity of the quartz, respectively. The sese mode icludes the vibratio of the cross beam, drive fork, ad sese fork, it show i Figure 4c. To simplify this model, it is cosidered that the sese fork ad drive fork have the masses m ad m (where m = desity volume), based o which the model ca be expressed as i Figure 4d, where l ad l represet the legth of the left ad right parts of the cross beam. The Trasfer Matrix Method [,] ca be used solve the modal coordiate equatios of this structure that have bee separated ito several limited uits from a complex system. The dimesio chages of the drive fork ad sese fork ca chage the m ad m values. The chages i m, m, l ad l ca cause a resoat frequecy chage i the sese mode. The differet beam has four elemets x = [ω, θ, M, Q] T, which are lateral displacemet, cross sectio agle of decliatio, bedig momet, ad shear force respectively. The stiffess of the bedig momet is EI. Figure 4d shows that the sese beam ca be cosidered as two poit masses (m, m) ad two beams ((), ()). We desigate the quatities of the left ad right of the mass by superscripts L ad R, respectively. First, cosiderig the beam sectio from poit 0 to poit, the followig equatios ca be derived []: 3 l l L l ω EI 6EI ω θ l l θ = 0 * M EI EI M Q 0 0 l Q R (5-a) Next, cosiderig the poit mass from the left of poit to the right of poit, the followig equatios ca be obtaied:

5 Sesors 03, R ω ω θ θ = * M M Q mω 0 0 Q L (5-b) Figure 4. (a) Oe beam of the drive mode; (b) Simplified model of the drive fork; (c) Right side of the sese mode; (d) Simplified model of the right side i the sese mode. (a) (b) (c) (d) From Equatios (5-a) ad (5-b), we ca get the Equatio (5-c): 3 l l l R El 6E R ω ω l 0 l θ θ = El El * M M 0 0 l Q Q 0 l l m ω lm ω mω mω + El 6El (5-c) x = [ω θ M Q] T, Equatio (5-c) ca be simplified as:

6 Sesors 03, R R Gx 0 x =, where: 3 l l l El 6El l l 0 G = El El 0 0 l l l l El 6El m ω m ω m ω m ω + (5-d) x Usig the same method, the relatioship from poit to poit ca be writte as R = Gx, where: R 3 l l l EI 6EI l l 0 G = EI EI 0 0 l l l mω lmω mω mω + EI 6EI Usig the boudary coditios of the beam, which are expressed i Equatio (6): ω = 0, θ = 0 M 0 0 = 0, Q = 0 (5-e) (6) The state vector of the left poit o the beam ca be expressed as i Equatio (7): Thus, Equatio (8) is obtaied: 0 R [ ω0 θ0 ] T [0 0 ] T X = M Q = M Q (7) R R Gx x 3 l l M + Q EI 6EI l l R R M + Q x = Gx0 = EI EI M + lq l l Mmω + Q( mω + ) EI 6EI l ll l l l l l ll l ω l M( mω ) + Q( m ) EI EI EI 6EI EI 6EI EI EI 6EI 6EI 3 l l l l l ll l M( + + mω ) + Q( + + mω + ) EI EI EI EI EI EI 6EI l l = = M( + l + mω ) + Q( l+ l( mω + )) EI 6I 3 l l l 4 ll l M( mω + lmω + mω + mmω + m ω ) EI EI EI E I I EI 3 3 l l ll 4 ll l l + Qm ( ω + lm ω + mω + mm ω m + ω + mω + ) 6EI EI EI 36E II 6EI 6EI (8-a) (8-b)

7 Sesors 03, A system of homogeeous Equatios ca be obtaied from the above result that are expressed i Equatio (9): l l + + ω + + ω + = EI 6I 3 l l l 4 ll l ω + ω + ω + ω + ω + EI EI EI E II EI 3 3 l l ll 4 ll l l ω + ω + ω + ω + ω + ω 6EI EI EI 36E I 6EI I 6EI M( l m ) Q( l l ( m )) 0 M( m l m m m m m ) Qm ( lm m mm m m + ) = 0 The determiat is assumed to be zero, ad ω i (i is the order of the modal) ca be obtaied. The results calculated i MATLAB are show i Figure 5a c, where E = /S, m = ρ l w t, 3 w t I =. Figure 5. The relatioship betwee frequecy ad various dimesios, (a) The legth; (b) The width, ad (c) The ratio of the l :l. (9) (a) (b) From the above aalysis, it is possible to draw a couple of coclusios. (c). As the legth of the cross beam icreases the sese mode frequecy will decrease. As the width icreases the sese mode frequecy will icrease. As the l :l ratio icreases the sese mode frequecy will icrease.. As the distace betwee the drive fork ad the sese fork decreases, the sese mode frequecy will become higher.

8 Sesors 03, Simulatio 3.. Structure Simulatio Fiite elemet method (FEM) aalysis is used to perform modellig ad simulatio. The frequecy chage with differet dimesio of the fork is simulated as show i Figure 6a f. Figure 6. The effect of differet fork dimesio o the frequecy. (a) Frequecies versus legth of drive fork; (b) Frequecies versus width of drive fork; (c) Frequecies versus legth of sese fork; (d) Frequecies versus width of sese fork; (e) Frequecies versus legth of cross beam, ad (f) Frequecies versus width of cross beam. (a) (b) (c) (d) (e) (f)

9 Sesors 03, It ca be see from Figure 6a,b that the dimesio chage will affect the drive mode frequecy ad sese mode frequecy. The drive mode is more sesitive to the dimesio chage tha the sese mode. Figure 6c,d show that the dimesio chages i the fork affects the frequecies. A chage i the sese legth has o ifluece o the drive frequecy, but it chages the equivalet mass ad sese frequecy. I Figure 6e,f the results of the chage i the cross beam dimesios o the frequecy are show. The dimesio chages of the cross beam have a greater effect o the sese mode frequecy tha o the drive mode frequecy. These results ca be used to desig the dimesios of a structure. From the simulatio, the dimesios of the chip are set as show i Table ad Figure 7. Table. The dimesios of the chip (μm). Item Value Item Value Legth of drive fork 7,030 Width of drive fork 790 Legth of sese fork 6,400 Width of sese fork 800 l,30 l,40 Thickess of fork 500 Figure 7. The dimesios of the chip. From the above aalysis, the followig coclusios ca be draw:. The drive mode frequecy is determied by the drive fork dimesios.. Sese mode frequecy is domiated by the width ad legth of the cross beam. 3. Chages i the drive fork ad sese fork will chage the equivalet mass, ad affect the frequecy of the sese mode. 4. The positio of the sese fork will chage the frequecy of the sese mode. 3.. Sesitivity of the Quartz Gyroscope To obtai the highest sesitivity, the sesitivity ca be expressed by Equatios (0-a) ad (0-b), i which ωr = ωd [3]: S = ω s ω ξ d x0 d ωd s ωsqd ω + ω (0-a)

10 Sesors 03, 3 49 ωω d s φs = arcta ( ω ω ) Q s s d (0-b) where, S is the sesitivity amplitude, φ s is the sesitivity phase, ω r is the drive mode frequecy ad ω d is the drive voltage sigal frequecy, ξ x0 is the drive displacemet, ad ω s is the sese mode frequecy. The output of the gyroscope is the charge sigal; so, the result ca be simulated i ANSYS software. The voltage sesitivity result is show i Table ad Figure 8, from which it is possible to determie the charge sesitivity, where the amplitude is 0.0 fc/( /s) ad the phase is Table. Simulatio data with differet agular rates. Agular rate ( /s) Amplitude of Voltage Sesitivity (V) Phase of Voltage Sesitivity ( ) Figure 8. Simulatio of voltage sesitivity. 4. Fabricatio ad Sigal Detectio 4.. Fabricatio Process The fabricatio process is show i Figure 9 [4]. The prototype gyroscope is fabricated usig a surface polishig z-cut quartz wafer with a thickess of 500 μm. Two masks are prepared for the quartz fork figure ad the electrode figure, called the quartz fork mask ad the electrode mask respectively. The quartz gyroscope ca be realized by the quartz aisotropic wet etchig process. After the quartz wafer is cleaed (Figure 9a), Cr/Au films are deposited o the double surface, i which Cr film is used to add the adhesive force (Figure 9b). Double side photolithography ad etchig are used to make the Cr/Au mask, ad the quartz fork mask is used durig the photolithography (Figure 9c f). The double side photolithography method is used agai to form the electrode patter. The electrode mask will be used (Figure 9g,h) durig the photolithography. A mixture of HF (40 wt % aqueous solutio) ad NH 4 F (40 wt % aqueous solutio) (cocetratio ratio of the HF ad NH 4 F is :) is used

11 Sesors 03, 3 49 to etch the quartz at 50 C for 48 h. Log etchig time ca give rise to good etch result, while it is limited by the Cr/Au films adhesive force o the quartz wafer (Figure 9i). After the Cr/Au films are etched to form the electrode patter, photoresist is removed (Figure 9j,k). The side electrodes are deposited by vacuum sputterig coatig with a agle (Figure 9l,m). Fially, the structure is mouted o a pedestal with epoxy ad electrically coected to the surroudig electroics with Au wire bodig. The whole fabricated device is show i Figure 0. Figure 9. Fabricatio process. Figure 0. Packaged device. 4.. Impedace Testig From Figure, it ca be see that the drive mode frequecy F d ad the sese mode frequecy F s are measured to be.85 khz ad.30 khz, which are similar to the theoretical aalysis ad simulatio results. The Q factor of the drive mode ad the sese mode is calculated to be,735 ad 7,697 without vacuum packagig. The values of the drive mode ad sese mode are show i Table 3. Frequecy (khz) Table 3. Values of the drive mode ad sese mode of the fork. Q Factor Static Capacitace C 0 (pf) Dyamic Capacitace C (pf) Dyamic Resistor R (kω) Dyamic Iductace L (kh) Drive mode.85, Sese mode.34 7,

12 Sesors 03, Figure. Impedece testig. (a) Impedace characteristic of drive mode ad (b) Impedace characteristic of sese mode. (a) (b) 4.3. Sigal Detectio The sigal detectio method is show i Figure [5]. The differetial amplifier is used to elimiate commo mode oise. The optimal phase relatioship betwee referece ad iput sigals ca be obtaied i the phase compesatio; while, the agular rate sigal is demodulated usig phase sesitive demodulators (PSD). Figure. Sigal detectio process; (a) Drive part ad (b) Detect part. (a) (b)

13 Sesors 03, Performace Testig The testig system is show i Figure 3. The prototype is put o the rate table, the data is obtaied by the data acquisitio device at a samplig rate of 0 times the badwidth, ad the data is averaged to oe value per secod. The differet iput rates were from ±0. /s to ±50 /s, ad the output voltages are recorded. The measured scale factor was 8.37 mv/( /s) ad the oliearity was 0.40% uder a full-scale iput rage of ±50 /s. The test results are show i Figure 4 ad statistical results are show i Figure 5. The output with ±0.05 /s agular rate iput i show i Figure 6, showig that the sesitivity is higher tha 0.05 /s. Figure 3. Testig system. Figure 4. Output with differet iput agular rate with ±0. /s, ±0.5 /s, ± /s, ±5 /s, ±0 /s, ±0 /s, ±40 /s, ±60 /s, ±80 /s, ±00 /s, ±0 /s, ±40 /s, ±60 /s, ±80 /s, ±00 /s, ±0 /s, ±40 /s, ±50 /s. Figure 5. Statistical output with differet iput agular rate.

14 Sesors 03, Figure 6. Sesitivity test. 5. Coclusios I this paper, the modelig, simulatio, fabricatio, ad performace characterizatio of a kid of multi fork z-axis quartz gyroscope are preseted. With the proposed scheme, the fabricatio process o the lateral electrode ca be simplified compared to traditioal quartz gyroscopes. Beefitig from the multi fork desig, a higher sesitivity tha possible with some other z-axis quartz gyroscopes is obtaied. The structure is etched from a z-cut quartz wafer. The drive mode frequecy is measured to be about khz ad the quality factor is about 0,000 i air at atmospheric pressure, idicatig the gyroscope ca fuctio i air without the eed for a vacuum package. The experimetally obtaied scale factor is 8.37 mv/( /s) ad the oliearity is 0.40% i the rage of ±50 /s. The sesitivity is higher tha 0.05 /s at the badwidth of 50 Hz. Ackowledgmets Thaks for the grats of School of Optoelectroics i Beijig Istitute of Techology. This work is supported by Natural Sciece Foudatio of Chia (Grat No ). Coflicts of Iterest The authors declare o coflict of iterest. Refereces. Madi, A.M.; Wa, L.A.; Hammos, S. A Microelectromechaical Quartz Rotatioal Rate Sesor for Iertial Applicatios. I Proceedigs of the IEEE Aerospace Applicatios Coferece, Aspe, CO, USA, 3 0 February 996; pp Acar, C.; Schofield, A.R.; Trusov, A.A.; Costlow, L.E.; Shkel, A.M. Evirometally robust MEMS vibratory gyroscopes for automotive applicatios. IEEE Ses. J. 009, 9, Barbour, N.; Schmidt, G. Iertial sesor techology treds. IEEE Ses. J. 0, 8, Madi, A.M.; Costlow, L.E.; Kowles, S.J. Commo desig techiques for BEI GyroChip quartz rate sesors for both automotive ad aerospace/defese markets. IEEE Ses. J. 003, 3,

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