Monolithic microbridges in silicon using laser machining and anisotropic etching

661

Sensors and Actuators A, 37-38 (1993) 661-665

Monolithic microbridges in silicon using laser machining and anisotropic etching M Alavl, Th Fabula, A Schumacher and H -J Wagner Instltut fur Mrkro- und Injormat~onstechmk der Hahn-Schlckard-Gesellschajt Wrlhelm-Schlckard-Strut 10, D-7730 Ydhngen-Schwennmgen (Germany)

fur angewandte Forschung e V,

Abstract Mlcrobndges m slhcon can be used as resonatmg elements for the realization of mechamcal sensors A method for the fabrication of monohttic mlcrobndges m slhcon urlth tnangular cross sectlons and a thickness up to 200 pm IS presented This method combines laser machmmg with wet anisotropIc etchmg The prmclple of thus technique IS based on the local destructlon of lumtmg {111) crystal planes by laser melting and amsotroplc etchmg of the molten zones The geometry of the nucrobndges produced by this method m (110) slhcon wafers IS determmed by the parameters of the masking layer and the laser beam Fmite element analysis IS used to estunate the static and dynanuc behavior of the tnangular mlcrobndges v&h regard to then apphcatlon as resonators of nucromechamcal force or pressure sensors The results of analytical and numerical calculations were expenmentally venfied by means of laser Doppler techmque

Intmductlon Resonant sensors have several advantages m the field of preclslon measurement technique because of their

high sensltlvlty, high resolution and senu-dlgtal output These structures can be reahzed m silicon by means of photolithography and amsotroplc etchmg [l] Several cr&na have to be considered m deslgmng microresonators for sensor apphcatlons (1 e , force, pressure and temperature) hke shift of the resonance frequency due to change of the stress state m the resonator, excitation and detection of specific vlbratlon modes and the mechamcal quality factor For apphcatlon as force sensor the mlcroresonator of the sensor device has usually the form of a vlbratmg beam clamped at both ends These nucrobndges are monohthlcally fabricated by amsotroplc etching of &con doped urlth high concentrations of ad&tlves to achieve an etch stop However, the thickness of the doped beams 1s hrmted to few nucrons due to the specific doping technique Undoped nucrobndges wth higher thickness can be formed non-monohttically by bonding of two separate silicon structures including the vlbratmg beam and the supportmg p&us [2] With this method the bonding of small beams seems to be quite sophisticated for fabrication m batch processes Another conventional technology to produce monohthlc nucrobrldges IS backside-etching the silicon wafer to the desired thickness followed by separation (wet anlsotroplc etching or plasma etching techmques) of the vibrating elements Although this method yields re-

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markable results [3] the wafer has to be photohthographically patterned on both sides and therefore beamon-diaphragm structures [4] cannot be reahzed Ths paper presents a method for the fabncatlon of monohthlc rmcrobndges m s&con urlth a thickness up to 200 m by combmatlon of laser machlmng and wet amsotroplc etching In contrast to the conventional technologes mentloned above this new method allows the fabncatlon of monohthlc beam-on-diaphragm structures for sensor applrcatlons with tnangular nucrobridges as resonating elements

Principle of the method The combmatlon of laser machlmng and amsotroplc etchmg of single crystal silicon leads to a fabncatlon of new types of nucrostructures [5] The details of the processmg method and the experimental setup are described elsewhere [6] The absorbed energy of the laser beam causes a local temperature nse leadmg to a melting and/or evaporation of slhcon accompamed by a local destruction of {Ill} crystal planes in a defined regon around the molten zones If these zones are extended along the [ 1101 direction for a (110) onented silicon wafer, the followmg amsotroplc etchmg provides nucrochannels which are hrmted by the undamaged {111) planes determmed by the maskmg layers We already applied this method m our laboratory to the fabncatlon of rmcrochannels wth high aspect ratios

@ 1993 -

Elsevler Sequoia All nghts reserved

662

Fig 1 Schematlc diagram of a triangular mlcrobrldge formed by laser machmmg and amsotroplc etching of (1 IO) srhcon

m (110) s~llcon wafers [7] and also m (111) oriented srhcon wafers [8] The partially-closed forms of the mrcrochannels (‘bottle neck’) m (110) and (100) silicon wtth an aspect ratio depending on the parameters of the laser beam are well adapted for thrs new apphcatron of fabrtcatmg monolithic mrcrobndges described m this work If the lateral distance between two neighboring mrcrochannels 1s less than a certam value determmed by theta aspect ratios, microbridges with tnangular cross sections can be realized as schematically shown m Fig 1 by the example of (110) onented shcon wafers

Experimental, results and measurements

The expenmental setup conststs of a cw-pumped Nd YAG laser system wtth Q-swatch and a computercontrolled x-y table The pulsed laser beam (wavelength 1064~1, pulse length 200ns, pulse frequency 1 kHz, maxrmum average power 10 W, mnumal beam spot size 8 pm) 1s well suited for sthcon mtcromachmmg because the photon energy (1 17 eV) exceeds the band gap of srhcon ( 1 12 eV) The laser parameters can be varied to obtain a damaged zone of the desired depth Three mch (110) silicon wafers (thickness = 380 pm) covered wrth a thermally-grown 1 5 gm SrO, layer were used for this mvestrgatron Arrays of mtcrobndges have been produced by photohthographrcally patterning the &02 layer and precise computer-controlled movement of the s&con wafer along the [liO] respectively [OOl] drrectron dunng the laser machmmg process A timecontrolled etch process was developed to prevent an overetchmg of the mrcrobrrdges from the convex backside edges The depth of the damaged zones was set variably up to 300 pm The SEM nucrograph of Fig 2 shows an array of tnangular nncrobndges in a (110) &con wafer after laser treatment m [liO] drrectron, amsotroptc etchmg m KOH solutron and removal of the SrO, maskmg layer The wrdth of the rmcrobndges 1s 200 pm determmed by the photohthographrcally-patterned masking layer The SEM mrcrograph of Ag 3 shows the end of a beam ur (110) srllcon with a thickness of about

Fig 2 Array

of tnangular

mxrobndges

in (1 IO} sihcon

(110) Wafer Surface Fig 3 SEM nucrograph showing the clampmg monohthtc tnangular mlcrobndge

region of a (1 IO)

30 pm monohthrcally clamped to the bulk material The cross-sechonal shape of these beams IS limited by slow etching {11 l} crystal planes It 1s a trrangle wrth a theoretical slope angle of 35 26” (for further dtscussron 35”) to the wafer surface, verrfled by measured data of fabncated mrcrobndges Processmg the (110) or-rented wafers m [OOl] due&on mrcrobndges wrth an experrmentally-measured slope angle of 48” (for further dtscussron 50”) have been realized as shown m Ag 4 The shape-hmrtmg planes are here near

Fig 4 Cross se&on of a three mch (1 IO) sdlcon wafer with two opposite monohthlc tnangular nxcrobndges (slope angles = 50”) after laser machmmg, amsotroplc etchmg and removmg of the maskmg layer

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probe The Doppler shift of the reflected laser light 1s measured to generate a real time analogous velocity output signal An absolute displacement output via counting the interference rmgs Hrlth a resolution of 8 nm 1s also available The output signal of the vlbrometer 1s fed to a computer-controlled spectrum analyzer (Hewlett-Packard 3588A) with a personal computer as data acqulsltlon system which directly displays the frequency spectrum With this method we measured the resonance frequencies of triangular slhcon mlcrobndges The first column of Table 1 shows the frequencies of a mlcrobndge (a = 35”, length (I) = 2800 pm, width (w) = 180 km and thickness (t) = 64 pm) The fundamental flexure mode Zl occurs at 60 9 kHz with a mechanical quality factor of 420 at normal air pressure and room temperature The deflection amplitude at resonance depends on the efficiency of the plezoceramlc excltatlon Amplitude values are typical m the nanometer range Figure 6 shows the frequency spectrum of the first three out-of-plane flexure vibration modes (Zl, 22 and 23) In order to resolve the higher vibration modes a velocity spectrum was recorded The maxunum velocity of about 11 mm/s occurred at the fundamental mode Z 1

Fig 5 Companson of cross-se&tonal shapes of mlcrobndges fabncated by (a) laser machmmg and amsotroplc etchmg wth angle 6: = 35”, (b) laser machlmng and amsotroplc etchmg wth a = 50” and (c) convenhonal etching technology wth b = 55

(100) planes The angle of 50” can be theoretically explained by the graphical forecast method of Jaccodme [9] based on experimental etch rate data We fabncated nucrobndges m various dnnenslons using different masking patterns, laser parameters and etch steps Single crystal llcon is a nonplezoelectnc material The exatatlon and detection of the resonating element can be reahzed by plezoelectnc thin-film multilayer systems, e g , ZnO [lo] or AlN For an optunal excltatlon/detectlon efficiency the relation of the active transducer area on the resonator surface to the cross-sectional area of the resonatmg beam has to be as large as possible A comparison of cross-sectional shapes of beams fabncated with angles of 35”, 50” (tnangular mlcrobndges) and 55” (pnsmatlc mlcrobndges) IS shown m Rg 5 For testing the dynamic behavior the tnangular nucrobndges were excited by a plezoelectnc ceranuc disk and interrogated optically by a laser vlbrometer (POLYTEC OFV 1102) This laser vlbrometer 1s based on a fiber optic heterodyne Mach-Zehnder mterferometer and comprises a velocity and amphtude demodulator Using laser Doppler technique the vlbrometer evaluates the out-of-plane motions of the reflecting

Finite element modeling The primary intention of the finite element analysis m this work 1s a comparison of nucrobndges m slhcon with tnangular and pnsmatlc cross sections mth constant width regarding resonant force sensor apphcatlons Due to the slope angles of 35” and 50” and the constant width w = 200 pm, the tnangular rmcrobndges have thicknesses of 71 and 120 pm, respectively, wth a beam length of 3000 pm To determine the resonance frequencies and the mode shapes of the different &con mlcrobndges we used a modal analysis The ANSYS finite element program code offers the Householder and the subspace iteration method for solving the elgenvalue problem [ll] Here we used the Householder method urlth reduced matrices system The finite element models have about 720 to 1400 3-D lsoparametrlc solid elements (STIF45) with 8 nodes and 300 master degrees of freedom for translation m space The models are based on the assumption of free, undamped vibrations and an elastic isotropic matenal behavior of slhcon For modeling the dynanuc behavior rmth boundary condltlons the mcrobndges were assumed to be fully clamped on both sides Table 1 shows the expenmental and numencally-calculated resonance frequencies of the different nucrobndges for the out-of-plane tlexure modes m Z direction, the m-plane flexure modes m Y dlrectlon and

664

TABLE 1 Comparisonof experImentameasuredZ-flexuremodes (first column) and transversal flexure modes (Zl , 22 , Yl) and the torsIonal wbration mode 7’1

numencal-computedresonant frequenciesfor

Resonance frequencies (kHz) Length Width ‘IInckness

2800 pm 18Op1-n 64 pm (35”)

2OOw 71 pm (35”)

Mode

V Experiment

Trmngle V

Pnsma B

Tnangle V

Pnsma

ZI

609

56 6

68 5

94 3

(1 w

(1 w

(100)

(100)

114 I (1W

3000 pm 120 pm (SO”)

22

1682

155 5

1883

258 1

3115

23

(2 76) 327 8

(2 75) 303 9

(2 75) 368 0

(2 74) 5013

(2 73) 603 9

24

(5 38) 536 0

(5 38) 500 6

(5 37) 606 2

(5 32) 819 8

(5 29) 986 9

z5

(8 80) 749 0

(8 85) 7448

(12 3) Yl

(13 2) 1362

(8 85) 9019 (132) 238 8

(8 69) 12090 (128) 1361

Tl

(241) 595 6

(3 49) 4910

(144) 749 7

(8 65) 14600 (12 8) 274 8 (2 41) 634 5

(10 5)

(7 17)

(7 95)

(5 56)

velocity

[mm/a]

120

51 100

22

80

60

40

20

00 I

length of 3000 pm and thickness of 71 and 120 pm, respectively, assummg a value of 1 696 x 10” Pa for reduced Young’s modulus and a material density of 2329 kg/m3 The results of 69 1 and 116 7 kHz, respectively, are m good agreement urlth the resonance frequencles Zl of the prismatic beams m Table 1 The mismatch 1s approximately 1 to 2% The higher vlbratlon modes (harmomcs) are normalized to the specific flexure modes Zl m order to compare the resonance frequencies of the nucrobndges with different cross-sectlonal shapes These values are also listed m Table 1 m parentheses Although the results of the fimte element calculations are approxlmative, there 1s good agreement between the expenmental values (first column) and the snnulated data (next columns) By utdlang a combmed static-dynanuc analysis we calculated the force sensltivltles to determine the effect of an external axial load Due to an apphed force at the ends of the mlcrobndges, a tennle stress will occur m the resonatmg beams leadmg to a stress stiffemng and, therefore, to a shift m resonance frequency A static finite element solution run 1s apphed to determine the displacements and stresses m the rmcrobndges by use of the ANSYS geometnc nonhneanty option (stress sttienmg) In a subsequent modal analysis the shifts of resonance frequencies are determmed The maxlmum stress consldered m the snnulatlons 1s the fracture strength of &con (-200 MPa) The relative change flfO of the fundamental flexure mode Zl depending on

%FT&T& frequency

[kHz]

Fig 6 OptIcally-measured frequency spectrum of the first three out-of-plane flexure modes of a tnangular slhcon nucrobndge wth a length of 2800 pm, a wdth of 180 pm and a tluckness of 64 pm

the first torsional mode (Tl) The frequency of the fundamental flexure mode (Zl) depends mainly on the dimensions of the nucrobndge (length and tickness), the matenal parameters (Young’s modulus, Poisson’s ratio) and the boundary conditions The fundamental resonance frequencies were analytically calculated [ 121 for a fully-clamped rectangular s&on beam urlth a

665

71 /ml

compared with the prismatic structures produced wth conventional processing techniques These nucrobrldges can, therefore, be preferentially used as resonating elements of mechanical nucrosensors mth senudlgtal output The batch compatlhhty of the described method has to be investigated further regarding to thin-film technology for plezoelectnc exatatlon/detectlon of the resonating elements

120 @m

References

tens11e stress [MPa] Fig 7 Comparison of the relative frequency changes f/&, of the fundamental flexure mode Zl due to tensde stress subjected to the

&con microbridge

the tensile stress m the nncrobndge 1s demonstrated m Fig 7 The highest sensltlvlty at equal mechanical stress IS obtamed evidently by the tnangular mlcrobndges Tnangular nncrobndges have about 30% higher sensetlvltles for an applied load compared ulth conventional prismatic structures

A method for the fabrication of triangular-shaped monohthlc rmcrobrldges wth thicknesses up to 200 pm by combination of laser machmmg and followmg anlsotroplc etching of photohthographlcally patterned (110) oriented silicon wafers was presented Dependmg on the direction of the laser treatment on the wafer surface, two types of tnangular nucrobndges wth an angle of 35 and 50”, respectively, are reahzed without any use of dopmg or bondmg techniques Fmlte element calculations were carned out to detennme the resonance frequencies of the rmcrobndges for several vlbratlon modes as well as the sensltlvlties of these mlcrostructures due to an apphed mechamcal load The results gve evidence to h@er force sensltlvlty respondmg to an axial load of the tnangular nucrobndges

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