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MEMS Actuators and Sensors Coursework Design of a Micromachined Accelerometer CAO Zhuo zc2e09 ecs soton ac uk PART1 Theoretical background Micromachined Accelerometers MechanismPiezoresistiveCapacitive PrincipleThe suspension beams are fabricated by piezorisistive material When the proof mass moves relative to the fixed frame the deformation in the suspension beams will generate stress profile hence change the resistivity of the embedded piezoresistors When external acceleration applied on the capacitive accelerometer the relative displacement between the proof mass and the fixed conductive electrode frame will change hence changing the capacitance Advantagessimply structure and readout circuitThey have high acceleration sensitivity low temperature sensitivity good noise performance and low power consumption Drawbacksrelatively large temperature sensitivity and small output signal Must be properly packaged because of their high sensitivity to the electromagnetic interference EMI MechanismTunnellingResonantThermal PrincipleUsing a constant tunnelling current between one tunnelling tip attached to a movable microstructure and its counterelectrode to sense displacement transferring the proof mass inertial force to axial force on the resonant beams and hence shifting their frequency The temperature flux from a heater to a heat sink plate is inversely proportional to their separation The change in separation between the plates can be measured by thermopiles AdvantagesVery high resolution and sensitivity direct digital outputApplied in the environment with large temperature gradient DrawbacksHigh supply voltage is required Not clearNot clear Table 1 the main accelerometer mechanism and their characteristic Although several types of MEMS accelerometers have been reported in the literature the basic structure consists of a proof mass that is attached by a mechanical suspension system to a fixed frame Theoretically the mechanical transfer function of this system in Laplace domain is 1 2 1 2 2 1 In this equation M refers to the proof mass K refers to the effective spring constant of the suspension beams D is the damping factor affecting the dynamic movement of the mass MEMS Actuators and Sensors Coursework is the natural resonance frequency and the quality factor is The static sensitivity of the accelerometer is defined by 1 2 2 According to equation 2 for all micromechined accelerometers a position measuring interface circuit is needed to measure the displacement of the mass due to the acceleration and then it is converted to electrical signal The different types of MEMS accelerometer mechanisms and their characteristics can be summarized in table 1 Nowadays the main challenge of commercial accelerometers is development of low cost inertial grade productions with sub ug noise levels good long term stability and low temperature sensitivity Micromachined Gyroscopes All gyroscopes use vibration mechanical elements to sense rotation When applied a rotation Coriolis acceleration will generate the energy transfer between two vibration modes Based on the performance the gyroscopes can be classified into three categories inertial grade tactical grade and rate grade Among these three different gyroscope types rate grade devices attracted most attention because of their application in automotive Generally the specifications of gyroscope include resolution drift zero rate output ZRO and scale factor The classic structure of gyroscopes is tuning fork which consists of two tines connecting to a junction bar When the device rotate a differential sinusoidal force will developed on the individual tines orthogonal to the main vibration The main mechanisms used to drive the vibration structure into resonance are piezoelectric electrostatic and electromagnetic After that piezoelectric piezoresistive and capacitive are three main methods to detect the Coriolis induced vibrations The characteristics of each mechanism can be concluded in the following tables Vibration excitation mechanismcharacteristics piezoelectricvery high quality factors at atmospheric pressure with improved level of performance batch processing is now compatible with IC fabrication technology electrostaticconstant amplitude maximum resolution is obtained when the outer gimbal is driven at the resonant frequency of the inner gimbal electromagneticlarge amplitude of motion Table 2 different excitation mechanisms of gyroscopes Detection mechanismcharacteristics piezoresistiveeasy to fabricate only require a simpler electronic interface due to their lower output impedance large temperature variation of offset poor resolution capacitiveLarge zero rate output can be easily integrated high sensitivity Table 3 different detection mechanisms of gyroscopes Similarly with accelerometers the pick off circuit of gyroscope can be either open loop or close loop But this is still a trade off between commercial cost and device performance MEMS Actuators and Sensors Coursework PART2 capacitive accelerometer design Micromachined fabrication I Brief process of proof mass fabrication In order to form the proof mass and suspension beams system structure unnecessary materials should be removed from the bulk substrates Hence bulk micromachining is applied in the fabrication process Firstly etch away the material in the gap of figure 1 b For micromachining etching both wet etching and dry etching can be applied to the process However the etchant KOH used in wet etching lead to an anisotropic surface Then the area in the top and the bottom of the proof mass will be different which make the calculation of proof mass and other parameters more complicated Hence Deep Reactive Ion Etching DRIE one type of dry etching technologies is applied in this process because of its very high aspect ratio and more vertical sidewall compared to other etching methods Secondly etching the suspension beams area using DRIE from both front and back side The reason of adopt DRIE is similar as the discussion above At the last the proof mass with a cube structure is obtained a b c Fig 1 Schematic of proof mass fabrication process a Silicon bulk material b top view after etch through the gap 3 diagonal cross section view of the proof mass and suspension beams The process of DRIE can be seen from the following figures MEMS Actuators and Sensors Coursework a photoresistor spin on b expose c pattern develop d DIRE process use SF6 for isotropic etching and C4F8 for wall passivation in turns e strip the photo resistor f do the same process in the back side of the wafer Fig 2 process flow of proof mass and connecting beams fabricaton II Brief process of electrode fabrication Because the electrode is thin surface micromachining is used for top and bottom electrode fabrication Firstly etch the central region of the bulk silicon to make the border district thicker than the centre Secondly deposited copper Cu as the electrode material in square as well as the conducting wire Schematics are shown in figure 3 And the detail of the Cu deposition flow is illustrated in figure 4 III Wafer bonding Wafer bonding is an assembly technique where two or more precisely aligned wafers are bonded together By applying a high voltage to the stacked wafers that induce migration of ions form both wafer will be bonded allowing a strong field assisted bond to form between silicon atoms The final accelerometer cross section schematic is illustrated in figure 5 MEMS Actuators and Sensors Coursework a b c Fig 3 schematic of electrodes fabrication process a silicon bulk material b cross section view of the bottom electrode c top view of the bottom electrode a Deposit and expose the photoresistor b Develop the photoresistor c Dry etch the silicon wafer by SF6 d strip the photo resistor e deposit another photoresister layer MEMS Actuators and Sensors Coursework f expose g develop h Cu depositing i Lift off the photoresistor and Cu on it Fig 4 process flow of electrode fabrication a b Fig 5 cross section view of accelerometer bonding process a before bonding b after bonding Parameter calculation The specifications required for the accelerometer are Bandwidth BW 500 Hz 3141 6 rad sec Sensitivity 0 1 pF g Dynamic range 10g Minimum detectable acceleration 1mg Some already know constants Density of silicon 2300 3 Young s modulus for silicon 160 109 2 Permittivity of air 0 8 85 10 12 Dynamic viscosity of air 1 85 10 5 N m2 s MEMS Actuators and Sensors Coursework Sensitivity For the sensitivity defined in the text book 1 is S M K Here the unit of sensitivity is pF g Based on the uniform of units there is 2 0 0 1 3 And A a2 is the area of the proof mass The differential capacitive sensing C1 C2 Vs Vs Vo Fig 6 Schematic of equivalent circuit for accelerometer When there is a acceleration applied the displacement of the capacitor gaps will lead to a change in the capacitance They are Thus change the output voltage 1 0 0 0 2 0 0 0 0 1 1 2 2 0 4 The output voltage is proportional to the displacement x Assumptions and Limitations From the equation 1 it is obvious that when critical damping has only one 2 2 0 solution Then Q 1 2 which means the accelerometer is critical damped Hence three different cases can be distinguished Under damped systemQ 1 2 2 Critically damped systemQ 1 2 2 Over damped systemQ 2 Table 4 three different cases of damping When the system is over damped the bandwidth will be much smaller than the natural resonant frequency Moreover Higher Q factor indicates a lower rate of energy loss relative to the stored energy So under damper system is expected in this design If the nature resonant frequency equals to the bandwidth required And Making the quality factor equals to 1 2 respectively the bode plot obtained is shown in the following figure MEMS Actuators and Sensors Coursework Bode Diagram Frequency rad sec 10 2 10 3 10 4 10 5 180 135 90 45 0 Phase deg 200 190 180 170 160 150 140 130 120 System sys Frequency rad sec 1 82e 003 Magnitude dB 137 Magnitude dB System sys Frequency rad sec 3 14e 003 Magnitude dB 134 resonant frequency BW Fig 7 Bode plot of 500 Obviously when Q 2 the BW 1820 rad sec cannot satisfy the required bandwidth Hence make an assumption that the natural resonant frequency is slight bigger than the required band width In this design make equals to 5700 rad sec 907 Hz and Q 5 the relevant bode plot is shown in figure 8 From the plot it can be seen that the natural resonant frequency is not just the same with the peak value of the transfer function but it is higher than the frequency relevant to the peak When doing the optimization of wr and Q it is observed that the higher the Q factor the peak will be sharper And the bandwidth will increase with the increasing of the natural resonant frequency wr The assumptions made here will be used to calculate the rest parameters of the capacitance accelerometer MEMS Actuators and Sensors Coursework 10 2 10 3 10 4 10 5 180 135 90 45 0 Phase deg Bode Diagram Frequency rad sec 200 190 180 170 160 150 140 130 System sys Frequency rad sec 3 14e 003 Magnitude dB 147 System sys Frequency rad sec 114 Magnitude dB 150 Magnitude dB BW 3dB Wr 5700 rad sec Fig 8 Bode plot of BW 500 Hz Maximum detection situation When applying a constant acceleration it means that s 0 in equation 1 hence a x wr2 Suppose that the maximum measurable acceleration is which equals to 10 g then the maximum capacitance displacement is given by So 2 3 10 7 From the text book 1 the gap of the capacitor d0 should be at least three times bigger than Thus d0 should be at least 0 9 um Minimum detection situation Suppose that the minimum measurable acceleration is which equals to 1 10 3 g then the minimum capacitance displacement is given by So 2 3 10 11 Noise In the specification the noise power spectral density of the front end amplifier is given to be 5nV Thus the voltage noise of the interface circuit 5 500 111 0 1 In the accelerometer system in order to detect the minimum output voltage the noise voltage of the amplifier circuit should be smaller than the output voltage of the capacitors MEMS Actuators and Sensors Coursework Calculation Supposed that the minimum output voltage is which is higher than the voltage noise of the 0 2 amplifier circuit According to equation 4 and the source voltage is 5V 0 5 7 5 10 4 Furthermore considering the following equation group 2 0 1 2 0 2 0 42 2 3 0 0 42 1 0 2 0 2 In this equation group the value of and D were assumed And the value of and are constants Thus it can be solved that The width of cube mass a 0 0013m 1 5 mm The weight of proof mass M 3 7 0196 10 6 The damping coefficient D 0 0080 N m The effective spring constant K 228 0661 N m When there is no accelerometer the gap between the proof mass and the electrodes will not change Hence The nominal capacitance 2 4828e 014 F 0 1 2 0 0 Geometries of suspension beams For the structure designed in this report has for suspension beams hence the effective spring constant K is given by 4 3 3 Here w is the width of beam t is the thickness of beam L is the length of the beam Giving any two values of these three parameters will get the rest one Considering the limitation of the geometries the final values of w t L are Thickness t 50 um Length L 4 mm Weight w 182 um MEMS Actuators and Sensors Coursework For present fabrication technology these geometries can be achieved However in practical the industry will optimize the geometries from a cost point of view Open loop interface circuit design Fig 9 Charge amplifier circuit for measuring the change in capacitance Here is a simple pick off circuit for the accelerometer designed in this report C1 and C2 represent the variable capacitors of the sensing element C3 is the parabolic capacitor between amplifier and sensor R1 keeps the seismic mass at a defined potential and has to be sufficiently large For the values of C3 and C4 it should be the same order with the value of C1 and C2 Hence the value around pF should be suitable And the gain of the amplifier is decided by R2 To extent the open loop interface design an oscillator can be added to synchronize the system An LPF in the end of the circuit can filter the high frequency noise generated by the circuit A Am mp p L LP PF F S Se en ns so or r O Os sc ci il ll la at to or r o ou ut tp pu ut t S Sy yn nc ch hr ro on no ou us s D De em mo od du ul la at to or r Fig 10 block diagram of the open loop circuit MEMS Actuators and Sensors Coursework Closed loop force feedback system H s Input force Pick off x feedback force Fig 11 schematic of closed loop force feedback system For close loop accelerometers the output signal of the position measurement circuit can be used together with a suitable controller to steer an actuation mechanism that forces the proof mass back to its rest position The electrical signal proportional to this feedback force provides a measure of the input acceleration This process is simply shown is figure 11 From the textbook 1 the feedback force It is clear that the feedback force is 2 0 2 0 proportional to the feedback input voltage Using the set up in figure 12 the same electrodes used for feedback can be used for read out of the mass position AC AC V0 Vfb V0 Vfb Fig 12 schematic view of the capacitance accelerometer with force feedback The feedback system is shown in figure 13 This kind of force feedback system is based on sigma delta modulation M The feedback force is a digital value instead of a analogue value which means the force is quantized to just two levels And the magnitude of the force is not the measurement of acceleration The pulse density determine the response of the acceleration MEMS Actuators and Sensors Coursework Sensor O Os sc ci il ll la at to or r o ou ut tp pu ut t S Sy yn nc ch hr ro on no ou us s D De em mo od du ul la at to or r Pick Off Clock compensator comparatorDigital bitstream Vf GND Vf GND Vout Fig 13 closed loop force feedback control system for accelerometer Discussion From YAZDI 2 the open loop sensitivity of a capacitive accelerometer is proportional to the proof mass size and capacitance overlap area and inversely proportional to the spring constant and air gap squared This also proves the derivation of equation 3 Also it can be understood that S M K is the mechanical sensitivity and can be considered