1994-10_Monolithic-BOD-Microstructure

 Abstract

 Monolithic bridge-on-diaphragm (BOD) microstructures for sensor applications were
 fabricated by means of laser machining and anisotropic etching techniques. The
 pressure-frequency-characteristic was measured by acoustical excitation of the
 microbridge to resonant vibrations and optical detection of the resonance frequency.
 In the pressure range between  0.8 bar and +1.0 bar the pressure-frequency-char
 acteristic is almost linear with a sensitivity of about 4.5 kHz/bar and with a fundamen
 tal bridge resonance frequency of 82.08 kHz. Finite element analysis was used to
 optimize the geometrical dimensions of the sensor structure with respect to maximum
 sensitivity and pressure range. With the same BOD sensor layout it is possible to
 realize pressure sensors for the range between 0.5 and 12 bar only by variing the
 thickness of the diaphragm. BOD sensors with smaller dimensions can be operated
 up to 100 bar with a pressure sensitivity of about 141 Hz/bar.


 1.  Introduction

 Micromechanical sensors based on resonating elements have become important in
 the field of precision measurement technique because of their high sensitivity, high
 resolution, and semi-digital output. Resonant beams are well suited for the detection
 of forces, as the resonance frequency depends on the mechanical stress which is
 induced by an applied axial force. For the realization of pressure sensors a resonat-
 ing beam connected to a diaphragm at both ends ("bridge-on-diaphragm") is pre-
 ferred. In this case the pressure sensitive element (diaphragm) and the resonator
 (bridge) are separated. The resonating element can therefore be encapsulated in
 vacuum to get higher Q-factors in order to increase the resolution.

 In recent years several bridge-on-diaphragm (BOD) pressure sensors were realized.
 Greenwood and Satchell [1] have produced 6 um thin resonating structures on a
 6 um thin diaphragm of highly boron doped silicon by selective and anisotropic
 etching techniques. Thornton et al. [2] fabricated 2 um thin boron-doped silicon
 resonator structures on a 30 um thick silicon diaphragm. Due to this fabrication
 technique the thickness of the resonator is limited to few microns. Furthermore, the
 high dopant concentration causes intrinsic stresses which determines the sensor
 characteristics. Buser et al. [3] used Si-Si bonding techniques to produce silicon
 beams with lower dopant concentrations and higher thickness on a silicon dia-
 phragm. However, for the bonding procedure high temperatures are necessary.
 Furthermore, the resonator has to be separated manually from the supporting frame,
 so that batch processing is not feasible. In addition, any electrical contact of the
 beam is difficult to realize.

 In the following we present a novel
 BOD microstructure for sensor applica
 tions, which has been fabricated mo
 nolithically in silicon without any use of
 bonding or doping techniques. The
 microbridge is clamped between two
 supporting piers which are connected
 directly to the diaphragm (see Fig. 1).
 A pressure applied to the BOD struc-
 ture leads to a deformation of the dia-
 phragm and therefore to an axial
 stress in the microbridge. For sensor
 applications, the BOD structure can be
 operated with piezoresistors on the bridge surface to obtain analog output signals.
 Alternatively, the microbridge can be excited to resonant vibrations either by piezo-
 electric thin films or electrothermally by diffused resistors, for example, and the
 change of the resonance frequency induced by the axial stress can be detected.
 Electrical interconnection between the microbridge and external bonding pads is
 established via the supporting piers.



 2.  Experimental


 2.1 Fabrication process

     The monolithic BOD microstructure has been fabricated by combination of
      laser micromachining and anisotropic etching techniques. The principle of this
      fabrication method is based on the local destruction of {111} crystal planes by
      a laser beam. During the laser treatment the silicon wafer is precisely moved
      by a computer controlled xy-table. Following anisotropic etching in KOH
      solution leads to the formation of new types of microstructures [4]. In <110>
      oriented silicon wafers microbridges with triangular cross sections have been
      produced [5].
 
     For the fabrication of the monolithic BOD microstructures three inch <110>
      silicon wafers with a thickness
      of 380 æm covered with a ther
      mally-grown 1.5 æm SiO2 layer
      were used. In a standard photo
      lithographic process the SiO2
      layer was patterned to define
      the dimensions of the micro-
      bridge, the supporting piers,
      and the diaphragm. In a second
      step the crystal order of the sili
      con substrate was locally dam-
      aged down to a defined depth
      by scanning the focused beam
      of a Nd:YAG laser across the
      wafer surface. During the follow-
      ing anisotropic etching in KOH
      solution the monolithic BOD
      microstructure was formed.
 
     Fig. 2 shows the total view of a
      monolithic BOD microstructure.
      The dimensions of the dia-
      phragm are 5 mm   5 mm
      150 um. The microbridge is ap
      proximately 2 mm long and ori-
      ented parallel to the [10] direc-
      tion. Its sidewalls are consisting
      of {111} planes with an angle of
      35ø to the (110) wafer surface
      resulting in a triangular cross
      section (width = 120 um,
      thickness ÷ 37 um). Fig. 3
      shows the clamping region of
      the microbridge with one supporting pier (left) and the end of the bridge
      (right). At both bridge ends {111} planes vertical to the substrate surface were
      additionally left to minimize the mechanical stress in the clamping region if the
      sensor structure is loaded with pressure.  
 
 
 2.2 Measurements and results
 
     To characterize the dynamic behavior of the BOD structure it is excited to
      resonant vibrations by a piezoelectric ceramic disk and interrogated optically
      by a laser vibrometer (POLYTEC OFV 1102 HR). The output signal of the
      vibrometer is fed to a computer-controlled spectrum analyzer (Hewlett-Packard
      3588A) with a personal computer data acquisition system which directly dis
      plays the frequency spectrum.
 
     The BOD structures were mounted on a test equipment, where air pressure or
      vacuum can be introduced to the back side of the diaphragm while the front
      side including the supporting piers and the microbridge remains at atmos-
      pheric pressure. The frequency of the first fundamental bridge flexure mode
      was measured in dependence of the pressure difference (back side to front
      side) in the range between  0.8 bar (vacuum) and +1.0 bar. Fig. 4 shows the
      pressure-frequency characteristic of the monolithic BOD microstructure. The
      fundamental resonance frequency has been determined to 82.08 kHz, and the
      pressure sensitivity is approximately 4.5 kHz/bar, related to the investigated
      pressure range. At atmospheric pressure a Q-factor of about 500 was
      achieved.


 3.  Optimization of the sensor characteristics

 The following investigations were accomplished to optimize the sensor geometry with
 respect to the sensor characteristics, relating the pressure sensitivity and the maximal
 load which can be introduced to the sensor structure without break or damage. Due
 to the detecting principle it is evident, that the pressure sensitivity will be enhanced
 if the stress in the microbridge is increased at constant pressure difference. As there
 are no analytical formulas available concerning the dynamic behavior of this complex
 sensor geometry, finite-element (FE) analysis was used to predict the sensor charac
 teristics and to analyse geometric modifications on the sensor performance. 
 
 3.1 Simulation of the BOD sensor structure
 
     A three dimensional FE model of the sensor structure was created with I-DEAS
      (SDRC), and FE simulations were carried out with ANSYS using one quarter of
      the BOD sensor structure and considering anisotropic material properties of
      single crystal silicon. For these calculations a bridge length of 1.95 mm and a
      thickness of 42.4 æm were assumed. In Fig. 5 the geometry of the quarter
      model and the results of the FE calculations are presented. In the upper left
      window (1) the displacements uz of the sensor structure caused by a pressure
      difference acting on the diaphragm are shown. By applying a pressure differ-
      ence of 1 bar the maximum displacement of the diaphragm is about 1 æm.
      Due to the leverage principle a stress concentration occurs in the microbridge
      resulting in a maximum tensile stress åy of about 24.7 MPa as shown in win-
      dow (2). The finite element mesh was refined in the bridge and in the clamp-
      ing region as shown in window (3) to get a better stress resolution. Due to the
      complex geometry the BOD structure is able to vibrate in several different
      flexure modes. For the following calculations only the first fundamental flexure
      mode of the bridge and the first antisymmetric coupled mode of the bridge
      and the diaphragm were considered (4).


 3.2 Variation of the diaphragm thickness

     As a strong influence on the pressure sensitivity is expected, the diaphragm
      thickness was varied in the range between 50 and 300 æm while the remaining
      geometrical dimensions were kept constant. The corresponding resonance
      frequencies of the diaphragm (f_diaphragm) and the bridge (f_bridge) were calculated.
      While the frequency of the first fundamental bridge flexure mode is nearly
      independent of the diaphragm thickness, the frequency of the diaphragm is
      approximately proportional to its thickness as shown in Fig. 6. At a thickness
      of about 130 um there is a cross-over of the resonance frequencies. This
      geometrical constellation should be avoided, because the vibration energy of
      the bridge will be transferred into the diaphragm due to mode coupling lead-
      ing to a reduction of the Q-factor. Additionally, the unimodality of the BOD
      sensor structure is drastically decreased.



     The resonance frequencies of the microbridges were calculated in depend-
      ence of the pressure difference in the region between 0 and 1 bar for different
      diaphragm thicknesses. The frequency-pressure-characteristics for the first
      fundamental bridge flexure mode is shown in Fig. 7. As expected, the pressure
      sensitivity decreases with increasing diaphragm thickness. The pressure
      difference pmax, where the stress åmax in the bridge amounts to a quarter of the
      break stress of single crystal silicon, had not been exceeded. For diaphragm
      thicknesses below 130 æm the pressure range is reduced, because the stiff
      nesses of the supporting piers and the diaphragm become comparable resul
      ting in a weakening of the levering mechanism, accompanied with a decrease
      of the resonance frequency. With this BOD sensor geometry it is possible to
      realize pressure sensors in the region between 0.5 and 12 bar with identical
      layout only by adapting the diaphragm thickness.


     The fundamental bridge resonance frequency has been calculated to 95.4 kHz
      which differs from the experimental value (82.1 kHz). This difference is caused
      by the fact, that for the simulation an ideal triangular bridge with a thickness of
      42.4 um and with a length of 1.95 mm has been assumed. In contrast, the
      fabricated bridge is (1.99 +/- 0.04) mm long. Additionally, its thickness is re-
      duced to (37 +/- 5) um, because the convex edge at the bottom of the bridge
      has been attacked by the etchant.


 3.3 Variation of the diaphragm side length

     By reducing the diaphragm side length higher pressures can be detected. FE
      calculations were carried out for a 2 mm   2 mm   300 um diaphragm in
      combination with a 1 mm   120 um   42.4 um microbridge. The fundamental
      resonance frequency has been calculated to 386 kHz, and the pressure sensi
      tivity is about 141 Hz/bar in the range between 0 and 100 bar. At the maximum
      pressure difference pmax = 100 bar a tensile stress of max ÷ 60 MPa will occur
      in the microbridge.



 4.  Conclusions

 Monolithic bridge-on-diaphragm microstructures for sensor applications were fabri-
 cated by means of laser machining and anisotropic etching techniques. The fabri-
 cation procedure of the sensor structure is reproducible and suited for batch proc-
 essing. As the excellent mechanical properties of single crystal silicon are preserved,
 sensors based on this structure have high sensitivity combined with high linearity.
 Furthermore, extremely high Q-factors can be achieved by vacuum encapsulation of
 the bridge resonator. By variation of the geometrical dimensions pressure sensors
 based on BOD structures can be fabricated for a wide pressure range.



 5.  References

 [1] J. C. Greenwood, D. W. Satchell, Miniature silicon resonant pressure sensor,
      IEE Proceedings, Vol. 135, No. 5 (1988) 369 372.

 [2] K. E. B. Thornton, D. Uttamchandani, B. Culshaw, A sensitive optically excited
      resonator pressure sensor, Sensors and Actuators A, 24 (1990) 15 19.

 [3] R. A. Buser, L. Schultheis, N. F. de Rooij, Silicon pressure sensor based on a
      resonating element, Sensors and Actuators A, 25 27 (1991) 717 722.

 [4] M. Alavi, S. Bttgenbach, A. Schumacher, H.-J. Wagner, New microstructures
      in silicon using laser machining and anisotropic etching, Proc. Micro System
      Technologies '91, Berlin, Oct. 29 Nov. 1, 1991, pp. 322 324.

 [5] M. Alavi, Th. Fabula, A. Schumacher, H.-J. Wagner, Monolithic microbridges in
      silicon using laser machining and anisotropic etching, Sensors and Actuators
      A, 37 38 (1993) 661 665.