Electrostatic Feedback for Mems Sensor : Development of in situ TEM instrumentation

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Institutionen för fysik, kemi och biologi

ELECTROSTATIC FEEDBACK FOR MEMS

SENSOR –

D

EVELOPMENT of

In Situ

T

EM

I

NSTRUMENTATION

Huai-Ning Chang

Nanofactory Instruments AB

2008 April

Handledare

Alexandra Nafari & Johan Angenete

Examinator

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Upphovsrätt

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Datum Date 2008-04-22 Avdelning, institution Division, Department Physics

Department of Physics, Chemistry and Biology Linköping University

URL för elektronisk version

ISBN

ISRN: LITH-IFM-EX--08/1927--SE

_________________________________________________________________

Serietitel och serienummer ISSN

Title of series, numbering ______________________________

Språk Language Svenska/Swedish Engelska/English ________________ Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport _____________ Titel Title

ELECTROSTATIC FEEDBACK FOR MEMS SENSOR – DEVELOPMENT of In Situ TEM INSTRUMENTATION

Författare

Author

Huai-Ning Chang

Nyckelord

Keyword

Electrostatic force modeling, Force feedback, Force sensor

Sammanfattning

Abstract

This thesis work is about further developing an existing capacitive MEMS sensor for in situ TEM nanoindentation developed by Nanofactory Instrument AB. Today, this sensor uses a parallel plate capacitor suspended by springs to measure the applied force. The forces are in the micro Newton range. One major issue using with this measurement technique is that the tip mounted on one of the sensor plates can move out of the TEM image when a force is applied. In order to improve the measurement technique electrostatic feedback has been investigated. The sensor’s

electrostatic properties have been evaluated using Capacitance-Voltage measurements and a white light interferometer has been used to directly measure the displacement of the sensor with varying voltage. Investigation of the sensor is described with analytical models with detailed treatment of the capacitive response as function of electrostatic actuation. The model has been tested and refined by using experimental data. The model showed the existence of a serial capacitor in the sensor. Moreover, a feedback loop was tested, by using small beads as load and by manually adjusting the voltage. With the success of controlling the feedback loop manually, it is shown that the idea is feasible, but some modifications and improvements are needed to perform it more smoothly.

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Abstract

This thesis work is about further developing an existing capacitive MEMS sensor for in situ TEM nanoindentation developed by Nanofactory Instrument AB. Today, this sensor uses a parallel plate capacitor suspended by springs to measure the applied force. The forces are in the micro Newton range. One major issue using with this measurement technique is that the tip mounted on one of the sensor plates can move out of the TEM image when a force is applied. In order to improve the measurement technique electrostatic feedback has been investigated. The sensor’s electrostatic properties have been evaluated using Capacitance-Voltage measurements and a white light interferometer has been used to directly measure the displacement of the sensor with varying voltage. Investigation of the sensor is described with analytical models with detailed treatment of the capacitive response as function of

electrostatic actuation. The model has been tested and refined by using experimental data. The model showed the existence of a serial capacitor in the sensor. Moreover, a feedback loop was tested, by using small beads as load and by manually adjusting the voltage. With the success of controlling the feedback loop manually, it is shown that the idea is feasible, but some modifications and improvements are needed to perform it more smoothly.

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Abbreviations

ADC – Analog to Digital Converter

CAPDAC – Computer-Aided Piping Design & Construction CDC – Capacitance to Digital Converter

DOF – Degree of Freedom DUT – Device under Test

MEMS – Microelectromechanical Systems PSU – Power Supply Unit

SOI – Silicon on Insulator

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Chapter 1 Introduction

1.1 Microengineering

Mankind has always been curious of the mini-world. The desire to go beyond to nano world devices could trace back to the second half of the 20th_{century, envisioned by Feynman:}

“What are the possibilities of small but movable machines? They may or may not be useful,

but they surely would be fun to make” [1]. It seemed to be quite obvious that it is not only fun

to miniaturize machines but would also be useful in many fields like industries and medical applications. The small miniaturized world revealed exciting possibilities in engineering, or a new paradigm: Microengineering.

Though small in size, the background disciplines and the potential applications developed by microengineering techniques are enormous. The involved knowledge comes in many fields where multiple physical domains (electrical, mechanical, thermal, optical, chemical, and magnetic) meet in the micro scale range. A collection of technological capabilities are involved in this engineering field. One of the branches that has emerged within

microengineering was MEMS. Microelectromechanical systems (MEMS) refer to mechanical devices that have a characteristic size smaller than millimeter but more than microns. In MEMS electrical and mechanical components are fabricated using integrated circuit batch-processing technologies. Feynman’s vision has become a reality and this multidisciplinary field has witnessed explosive growth during the last decade.

MEMS possess big potential for innovation. However, the actual implementation is hampered by the multidisciplinary complexity, which results in an approach that is best described by leap forward rather than being able to comprehend theories and disciplines behind. MEMS techniques have not yet matured which might result in risks and even failures in some application; however, some successful and encouraging achievements have opened up a prosperous market for MEMS techniques [2], e.g. micromachined ultrasonic transducer, optical MEMS devices and RF MEMS technology in wireless application.

1.2 Electro-Mechanical MEMS sensor

The strong coupling of various domains involved in MEMS devices is a distinct characteristic. When the characteristic dimensions of the device element decreases from the macro scale level to the micro scale, some effects might become minor or negligible such as gravity whereas some might be comparatively dominant like adhesive and friction effects. This implies that the experiences and disciplines based on the macro scale level are no longer

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Chapter 1. Introduction

always valid. The coupling between domains can therefore be much stronger than at macro scale and can be incentive to new innovative applications [2].

The coupling between the electrical and mechanical domain is not exclusive of the MEMS field, but there are characteristics that are unique when it is applied in MEMS. Besides, the electrostatic force has stronger effect in miniaturized devices than in the devices in macro scale, which enables the electrostatic force to be used in actuation. Some examples of

electrical and mechanical coupling applications are electrical motors, air compressors as well as true RMS-to-DC converters. The last one is a very good example of the coupling between the electrical and mechanical domains at the macro level [2].

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Chapter 2 The Nanoindenter and Motivation

2.1 Nanoindenter Sensor

Indentation is a straight forward method to test the mechanical properties of materials. The basic principle which lies behind indentation is to apply a load to deform the testing materials and intrinsic material properties such as hardness and elastic modulus can be obtained [3]. In the indentation process, the displacement and the applied load are required information in order to perform further investigation. For example, the hardness and the effective elastic modulus can be calculated from:

A P H ₌ max dh dP A E_eff π 2 1 =

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Chapter 2. The Nanoindenter and Motivation

H is the hardness, Pmax is the maximum applied load, A is the contact area. Eeff is the effective

elastic modulus and dh dP

is the derivative of the unloading curve.

In the original design of the nanoindenter sensor developed by Nanofactory Instrument AB [4], the load applied could be obtained from the capacitance readout, calibration was done before the testing, and precise value of the applied load could be obtained. The displacement of the experiment is measured by using a piezoelectric positioning system on which the sample is mounted.

For small volume test, in situ TEM nanoindentation was often applied. Since TEM gives a good real time imaging, the indentation depth and the contact area could be precisely obtained. The TEM holder and the positioning setup designed by Nanofactory Instruments AB are shown in Fig. 1.2.

Figure 1.2: Specimen holder and a detailed sketch for sample and sensor relative positions. In the indenting process, an indenter tip is mounted on the sensor holder to indent sample. The tip is designed as a cylindrical base with various kinds of tip. Different types of tips are chosen for different purposes.

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2.1. Nanoindenter Sensor (b) The sensor in cross section. The arrow _↨ indicates that the motion of the plate is restricted

to up and down.

This thesis work is focused on electrical and mechanical coupling of an electrostatic actuated parallel-plate capacitive sensor. Moreover, there were some work of testing pre-loaded sensors and use parallel plate capacitor models for analysis. Besides, different masses of small beads were placed on the sensor holders to simulate the load which applies when the diamond tip indents a sample.

The sensors used in the experiment were developed by Nanofactory Instruments AB [3], Fig. 1.4. The sensors functions as a capacitive sensor. The parallel plate capacitor consists of two plates, one upper plate connected through the springs to a Si membrane and a lower Al electrode deposited on glass.

The fabrication methods include photolithography, deep reactive ion etching and anodic bonding [3]. The upper plate of the capacitive sensor is made of p+_{doped silicon, and the}

lower electrode is made of aluminum, Fig. 1.4.

Figure 1.4: Materials of the sensor. The upper electrode is p+ doped Si and the lower electrode is Al. The springs are also made of p+ doped Si.

2.2 Motivation for the Feedback Loop Control

For the indenting process, the load and the indentation depth are fundamental information, Fig. 1.1. The applied load is obtained from the capacitance readout. The indentation depth is

supposed to be the same as the extension or contraction of the piezo-tube. However, the actual indentation depth is more complicated. When the indenter tip starts indenting the sample, the tip bounces back due to the elastic force of the connected springs, which leads to errors in the indentation depth.

The concept for the feedback loop is to apply voltages on the plates and then produce an electrostatic force [5]. Since the main displacement errors were due to the spring’s elastic force, the idea of using electrostatic force to balance elastic force was developed and tested. The basic feedback loop is shown in fig. 1.5; the piezo-tube movement h is the distance of the piezo-tube extension, which is used to push the tip; δ is the compression of the sensor

plates and ∆ is the indentation depth. In the indentation process, the tip is moving toward the

sample, Fig. 1.5 (a).When the tip encounters sample, the tip deforms the sample with indentation depth ∆ and the sensor plates are compressed with δ at the same time. The

extension of piezo-tube h is used for both indentation depth and the compression of the sensor. Thus _h₌_∆₊δ_{. In order to make the feedback loop, the applied voltage V}₁_{is turned down to}

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Chapter 2. The Nanoindenter and Motivation

V2 is less than the force at V1, and this will release the compression of the two plates and

decrease the capacitance. Once the capacitance drops back to the original value, there is no change of the gap, i.e. δ =0, and one loop is completed.

If the capacitance feedback and the voltage control respond fast enough, there would be almost no change of the plates’ distance at any time, and thus the goal of recording the indentation depth of the tip is accurately reached.

Figure 1.5: Indentation process diagram. (a) The indenter tip is moving toward the sample, the actuation voltage is V1. (b) The tip is pushed forward by piezo-tube of extension h. (c) Tip

is in contact with sample surface and starts deforming the sample with indentation depth ∆. The capacitor’s electrodes were also pushed together. (d) Use voltage V2 tocontrol the

feedback loop (V1>V2). V2 was chosen to keep the electrode distance constant, i.e. δ=0; and

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Chapter 3 System Modeling and Analysis

3.1 Introduction

In this section, an overview of some parameter models for the surface micro systems will be presented. Micromechanical equations of motion, spring constants, and capacitive position sensing will be discussed.

3.2 Spring Constant

In the original sensor spring design, there were 3 types of serpentines structures [3]; in this thesis work, two types of springs were chosen for testing, Fig. 2.1, Appendix C

Figure 2.1: Sketch of the sensor spring design. (a) Type II spring, designed with two turns. (b)

Type I spring, designed with one turn.

For the spring constants of the serpentine structure, the conditions will be different in the three directions of motion. The nanoindenter sensor is designed to be very stiff in both x- and y- direction, thus only the motion in z-direction needs to be considered. The model for

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Chapter 3. System Modeling and Analysis

Figure 2.2: Two turns serpentine spring schematic.

By using free-body diagrams for calculation of the z-directed spring constant, Fig. 2.3, the results show that the spring constants are 1000 N/m for the type I, 1 turn spring design and 430 N/m for type II, 2 turns spring design. Detailed analysis and calculation are in Appendix A.

Figure 2.3: Free-body diagram of a serpentine spring.

3.3 Elastic Force on Electrostatic Actuation

Consider a device which is a two parallel plate capacitor with one plate connected through the springs to the upper plate, Fig. 2.4. The plate’s movement is designed to be in the normal direction. Once a voltage is applied on the electrodes, the electrostatic force pulls the two plates closer and connects the plate to the spring is affected by the elastic force. If the plate displacement is noted as δ, thus the force exerted on the plates could be expressed as below [5]:

k e F

F

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3.3. Elastic Force on Elastic Actuator

Figure 2.4: Parallel plate capacitor with displacement by electrostatic force.

where Fe is the electrostatic force and Fk is the elastic force. When the system is at

equilibrium, the total force is zero:

0 = + =Fe Fk

F _{( 2.2 )}

Therefore, the equation becomes:

0 ) ( 2 2 0 2 0 ₋ ₌ − = εε _δ kδ d V A F _{( 2.3 )}

A is the electrode area, 12 1 2 2 0 =8.854×10− N−m− C

ε _{is the dielectric constant and}ε ₌₁_since the dielectric permittivity of air is very close to vacuum at room temperature, V is the applied voltage, d is the original distance between two plates without applying any voltage or force ₀

and k is the spring constant.

The plot of Fe and Fk versus the displacement, δ, are shown below, Fig. 2.5. It is worth

noting that the displacement range is limited to be less than d0; as it is physically unfeasible if

the displacement goes beyond this range, solutions beyond this range are out of consideration. The equilibrium position for the system can be obtained from solutions of Eq. (2.3). Fig. 2.5 shows the plot of the two forces with the displacement. The intersection points are the solutions to the system [2, 5].

Figure 2.5: Dependence of electrostatic force and elastic force on displacement. The intersections indicate equilibriums. Intersection c is an invalid solution since it is not a

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As we can see from the graph, two solutions are of the equilibrium positions in the range of [0, d0]. The first one is a stable solution; the second one is an unstable solution. If a small

perturbation of displacement is applied on the system around equilibrium positions, the elastic force restoring to the equilibrium position is larger than the pushing–away electrostatic force at position a, therefore, the system intends to remain at the equilibrium position. On the other hand, it is the opposite case at the equilibrium position b, a small displacement at b will push the displacement even further until the movable plate failing into contact with the fixed electrode.

To describe the equilibrium position mathematically, 0 < ∂ ∂ δ F _{( 2.4 )} That is: 0 ) ( 3 0 2 0 ₋ _< − k d V A δ εε (2.5 )

Combine with Eq. (2.3), we then have

0 3 1_d < δ ( 2.6 )

This means that the displacement for stable conditions is when the displacement is less than one third of its original distance from the fixed electrode.

The pull-in (or snap-in) voltage Vpo is the minimal applied voltage to reach the critical

displacement, ₀ 3

1_d _{. For}

po

V

V > , Fe is larger than Fk . The movable plate will therefore fall

into contact with the fixed electrode.

The pull-in effect of the microstructure sets the limit for the device operation at a micro scale. This special property is due to Paschen’s law [2, 7]. The value of the pull-in voltage

po

V can be calculated from Eq. (2.3). Following notations are used:

2 0 2 0 0 0 2 , , ~ d V A F kd F d y kd eo εε δ = − = = and kd eo F F p = Then we have p F F y y kd eo ₌ = −~)2 1 ( ~ ( 2.7 )

For the critical displacement ₀ 3 1_d =

δ _,~ =_y ₁_/₃_{, and}~_y₍₁ ~_y₎2

− is 4/27 . Therefore, the condition for a stable solution is:

27 4 ≤ = kd eo F F p ( 2.8 )

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3.3. Elastic Force on Elastic Actuator 0 3 0 27 8 εε A kd Vpo= ( 2.9 )

3.4 Electrostatic Micromechanical Actuator with Extended Travel Range

According to the above discussion, the travel range of the movable plate in the normal direction is limited to one third of the initial gap. The movable electrode will be pulled into contact with fixed electrode when the voltage is higher than the pull-in voltage. However, the first test, which is presented in Section 4.2, show that the model discussed above does not describe our MEMS system good enough, and some experimental results, e.g. higher snap-in voltage and lower capacitance readouts can not be explained by the simple model. Therefore a more complex model which includes serial and parallel capacitors is assumed.

Several methods have been suggested to extend the travel range for the electrostatic actuators. The manufacturing solution to increase the entire initial gap is preferable for optical applications. Other methods include closed-loop voltage control, series feedback capacitance and leveraged bending [8]. The following is a detailed discussion of the MEMS system with serial capacitor [5].

Figure 2.6: Extended travel range by a serial capacitor.

Use the notation C_Mfor the capacitance of the mechanical structure of the sensor andC_S

for the capacitance due to the serial capacitor. Since

S M C C C 1 1

1 ₌ ₊ _{, where C is the total}

capacitance being measured, the resulting capacitance is

S M S M C C C C C + = . Moreover, denoting 0 ~ d y= δ and 0 0 0 d A

C = εε , gives that the mechanical structure capacitance between the plates A and B is ) ~ 1 ( ) ( 0 0 0 y C d A C_M − ≡ −

= εε_δ . For capacitors in series, the amount of charge Q is the same over each plate, Q=CSVS =CMVM, where VS is the voltage drop on the serial capacitor

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Chapter 3. System Modeling and Analysis 0 0 ) ~ 1 ( ) ~ 1 ( ~ 1 1 C y C V y C y C C V C V s s s s M = ₋− ₊ − + = ( 2.10 )

When the elastic force of springs and the electrostatic force are in equilibrium, it requires δ δ εε k d V A _M = − 2 0 2 0 ) ( 2 ( 2.11 )

Suppose that Cs =bC0 and _b y

b

y ~

1 ˆ

+

≡ , b is a factor to simplify the equations below, we then have: 3 0 3 2 0 3 2 ) 1 ( 2 ) ˆ 1 ( ˆ kd b V A b y y + = − εε _{( 2.12 )}

From Eq. (2.12), the maximum stable region for yˆ ranges from 0 to 1/3 before the pull-in effect occurs.

However, the original mechanical sensor and series capacitor form a voltage divider circuit; thus, higher voltage needs to be applied in order to compensate the bias drop over the serial capacitor C . Therefore, a higher driving voltage is needed to achieve the same displacement S

in the MEMS capacitor CM. According to Eq. (2.12), the voltage V for the maximum M

displacement (i.e.,~ =y 1) is:

2 0 3 0 2 b A kd V_M εε = _{( 2.13 )}

Compare the pull-in voltageVpo and the bias on the sensorV , from Eq. (2.9), the relation M

between V_poand V is [6]: _M po m V b V ₂ 4 27 = _{( 2.14 )}

3.5 Extra Capacitors

From the comparison of theoretical fitting and experimental result, it is suspected that besides the sensor capacitance existed, there are also serial and parallel capacitances. When analyzing the capacitive sensor in detail, a serial capacitor can be expected at the connection point from the Al electrode to the upper plate in Si, Fig. 2.7.

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3.5. Extra Capacitors

Figure 2.7: Schematic plot for sensor electrodes connection. (a) Press contact is used to connect one electrode to the Si plate. (b) The lower electrode is an integrated design; no extra

connection between the electrode and the Al plate is needed.

Fig. 2.7 shows the electrode connection. The serial capacitor is believed to exist at the press contact. Press contact was used to connect one electrode to the upper plate, it consists of three layers, p+_{doped silicon, aluminum and glass. It is well-known that aluminum oxidizes}

easily and quickly once it is exposed to oxygen. Aluminum oxide Al2O3 is a dielectric

material with dielectric constant 9 ε at 25ºC [9]. The press contact could therefore form a .1 0

capacitor in series with the sensor capacitor, Fig. 2.8.

Another factor which influences the capacitance readout is the parallel capacitor, Cp. The

parallel capacitor could be due to several sources, such as electronic devices, measurement setups and wires for circuit connection. With a capacitor Cp in parallel with the mechanical

capacitor CM, the capacitance shifts by a constant, C =C_M +C_p, and the voltage applied on

the sensor is the same with additional parallel capacitor. Comparing to the serial capacitor, the parallel capacitor is of minor importance since serial capacitor changes the shape of the curve of the C-V measurement whereas the parallel capacitance affects the measurement by adding an offset.

Lower electrode connection

Press contact beneath Si plate

Upper electrode connection

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Figure 2.8: Side view of sensor capacitor and position of the suspected serial capacitor.

3.6 Bent Plate

Besides extra capacitors in the system, it is found out that the mechanical sensor CM is not of

purely parallel plates. It is discovered that the upper plate is bent at the four corners from the interferometer measurement, Fig. 2.9.

Figure 2.9: White light interferometer measurement shows the bent degree of the upper plate. The central part is higher than the positions at the four corners.

The possible reasons for the bending of the plate might be stress and strain from type of the Si wafer type used. The plate was made of SOI (silicon on insulator) wafer, where the different lattice constants can give deformation when two materials are bonded. Moreover, the holder placed on the upper plate can also lead to some asymmetrical factors for the sensor’ s plate.

To analyze the effect of a bent-plate on the capacitance, a modified model instead of parallel plate capacitor was used. From Wyko measurement, the bent profile along one edge is shown in Fig. 2.9. Instead of using the arc shape bending curve, an asymmetric trapezoid curve without the bottom line was used for the estimation, Fig. 2.10.

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3.6. Bending Plate

Figure 2.10: Modified curve for bent plate. The light color line is the real profile for the bending shape; the dark line is the trapezoid curve for the bending.

It is worth emphasizing that most of the bending is at the four corners of the plate, the central circle and the middle part of plate edge is flat. With the simplified bending profile shown in Fig. 2.10, the upper plate of a bent-plate capacitor model is shown in Fig. 2.11. To calculate the capacitance for this model, the flat part is considered as a parallel plate capacitor whereas integral was used to calculate the capacitance for the four bent parts of the plate [10]. Thus, the total capacitance for the model is:

plate Bent plate Parallel total C C C = _{_} + _{_} _{( 2.15 )} δ ε − = 0 _ ' d A C_Parallel _plate ( 2.16 )

∑ ∫∫

= = 4 1 _ ₍ _, ₎ i i i i plate Bent _z _x _y dy dx C ε ( 2.17 )

where A' is the flat area, z is the distance at each point to the lower plate and the bent plate

capacitance is the sum of the four corners. Since z is different at every point on the plane, z is a function of x and y.

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Figure 2.11: Schematic 3D plot of the modified bent-plate model. (a) Vertical view from above. (b) Side view.

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3.6. Bending Plate

The calculation of bent plate is shown in Fig. 2.12. Voltages at 10V, 13V, 16V and 19V were chosen for the analysis. Since the voltage is the readout from the whole system, serial and parallel capacitors were also taken into consideration for the bent plate model with Cs 15pF

and Cp 1.1 pF. The deformation degree of the bending does not change as the voltage varies.

Also, it is discovered that the central part of the plate is arched up as the corners are bent down. Thus, the resulting capacitance is not as high as expected. Compensation mechanism exists and does not result in prominent values for the capacitance. Besides the plate bending, the springs are also bent along the longitudinal direction. However, due to limited time, there was no further investigation of how the bent springs influence the capacitance performance.

Figure 2.12: Calculation of bent plate model in comparison with experimental data and theoretical modeling.

3.7 Analytical Model for Nanoindenter Sensor

In this section, a model of the electrostatic behavior of the sensor with all factors taken into consideration will be presented. Establishing a model for the sensor is like investigating a black box, Fig. 2.13. The box cannot be opened to give any clues of the components inside. The models are the capacitance and voltage readouts, which are the result of all the

components inside the black box. Only the displacement, measured by Wyko NI1000, could be specified to the mechanical sensor CM.

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Figure 2.13: Schematic sketch of the sensor model. C and V are the measurements done on the system.

From section 2.4 and section 2.5, the capacitance of a systems with both serial and parallel capacitors can be expressed as _P

S M S M _C C C C C C + +

= , where C_Mindicates the mechanical capacitance – sensor’ s capacitance; C is the serial capacitance and _S C_Pis the parallel

capacitance. As for the voltage, since parallel capacitor does not divide the applied voltage as serial capacitor does, from Eq. 2.10, the total voltage for the system can still be expressed as

M S S V d C d C C V × − − + = ) 1 ( ) 1 ( 0 0 0 δ δ

, where C0 is the initial capacitance without any applied voltage.

Use ) ( 0 0 δ εε − = d A C_M and 2 0 ) ( 2 _δ _δ ε ⋅ − = d A k

VM in the above expressions, C and V can be

rewritten as: P S S C C d A C d A C + + − × − = ) ( ) ( 0 0 0 0 δ εε δ εε ( 1.18 ) 2 0 0 0 0 ) ( 2 ) 1 ( ) 1 ( δ δ ε δ δ − ⋅ × − − + = d A k d C d C C V S S ( 2.19 )

Higher total voltage is required with the serial capacitor in the system. Since the voltage is distributed on both the CS and CM, V is defined as the total applied voltage and VM is the

voltage drop on the mechanical capacitor.

To plot the C-V relation, the capacitance and the voltage can be view as functions of δ,

) (δ

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3.7. Analytical Model for Nanoindenter Sensor

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Chapter 4 Experimental Methods

4.1 Introduction

For the reliability and accuracy of the measurement, two different methods were utilized to measure the relations between capacitance and voltage. One way was to use a commercial chip, AD7746 [11, 12] to measure the capacitance while an external DC bias was applied over the sensor from a power supply unit. The other measurement method was to use a LCR meter, HP 4284A [13], to apply voltage on sensor and simultaneously measure the capacitance. Moreover, white light interferometer, Wyko NT1100 [14], was used to directly measure the displacement while applying a voltage and measuring the capacitance.

4.2 C-V Measurements

To use IC chip AD7746 in combination with an external applied DC bias, the circuit used in a setup show in Fig. 3.1. AD 7746 applies an AC square wave voltage and a DC constant voltage 2.5V to the sensor [12], Fig. 3.2. This preloaded DC voltage gives an offset voltage

5 . 2

− V for the voltage supplied by PSU. The frequency of the square wave is 32 kHz and the excitation voltage 2.5V. The sensor capacitor, marked as CS, was placed in series with a

capacitor CB. CB should have capacitance far exceeds CS in order to give low impedance in the

circuit. According to the formula of impedance [15]:

S fC Z π 2 1 = _{( 3.1 )}

The sensor capacitor gives resistance around 1MΩ whereas CB, which is 100nF here, gives

around 50Ω. One end of capacitor electrode is powered by the PSU with a resistor in parallel to the ground; the other electrode is connected to the USB socket of computer. A big

resistance with respect to the sensor capacitor, R, should also be used in the circuit to avoid leakage current. Moreover, according to the datasheet for AD7746 [12], parasitic resistance more than 30MΩ should be used to get leakage current small enough (i.e. I < 150nA). The supplied voltage was read from the PSU and the capacitance was read out from an evaluation software program for the AD7746.

Different voltages were applied from the power supply unit in the range of 0~25V. At the same time, the capacitances of the sensors were measured with the AD7746. 10 sensors were chosen to repeat this test to obtain general characteristics of the sensor performances. Among the 10 sensors, 4 of them are of spring type I, one turn design, and the rest sensors are type II, two turns design.

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4.2. C-V Measurement

Figure 3.1: Circuit design to test AD7746.

Figure 3.1: Voltage supply from AD7746. A square wave with frequency 32 kHz in combination with a constant voltage 2.5V were supplied together.

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Chapter 4. Micromechanical Test

Figure 3.2: Photograph of the experimental setup. (a) Experimental set up for testing with IC chip AD7746. (b) Photograph of IC chip AD7746 evaluation board.

The second way of testing the C-V relation was to use a LCR meter, HP 4284A. No

additional circuit was needed to be constructed for the testing. The DC voltage from the LCR meter is applied to the sensor directly by two probes in contact with two electrodes on the sensor. The capacitance output was read out directly from the screen on the LCR meter. The HP 4284A efficiently gives the C-V curve compared to AD7746. In the circuit design for AD7746, a long RC recovery time around 20 seconds prolongs the measurement period. Also, HP’ s 4284A LCR meter provides more choices for testing e.g. the dependence of the amplitude and the frequency of the excitation voltage on the capacitance. On the other hand, AD7746 has a much smaller volume as compared to the LCR meter, which is the most dominant advantage and the reason to be chosen as one device in the feedback loop design.

Figure 3.3: Experimental set up for testing with LCR meter HP 4284A.

4.3 Optical Surface Profile

The capacitive sensor is actuated by the electrostatic force. For 1-DOF model of the parallel plate capacitor, the gap distance and electrode displacement is of substantial importance for the resulting capacitance. Optical surface profiler Wyko NT1100 is a convenient way to profile the sensor surface at different applied voltages [16]. From surface profile

measurements, the sensor plate movements d∆ can be extracted. The focus of lens should be adjusted to get circular fringes on the plate; and as for data analysis, sample tilting should be taken into consideration.

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4.3. Optical Surface Profile

Figure 3.4: Optical image for the upper electrode of sensor capacitor. Corner 1 is fixed and independent of applied voltage. Oppositely, corner 2 is sustained by the connected spring and

drops down as the applied voltage increases.

By the white light interferometer, there is no direct way to determine the distance between two electrodes under different voltages. One alternative is to measure the upper electrode’ s displacements instead. A specified corner was chosen out from the four corners, the white light interferometer was used to make a scan of the corner at different voltages. A point on a fixed corner 1 was chosen and compared to another point on the movable electrode 2, and the two points were used to measure the difference in distance differences. The d was obtained 0

by breaking a sensor, measuring the spring thickness and subtracting this from the profile meter measurements from the spring down to the Al electrode. The displacements, d∆ , due to different voltages come from subtraction of the difference in displacement with applied voltage minus distance difference without voltage.

The method to extract d is demonstrated here. The optical profile Fig. 3.5 gives the total ₀

distance from upper electrode down to the bottom. This distance includes gap distance and thickness of spring. Then from photos taken by microscopy, the thickness of the springs was also known. As a result, the original gap separation could easily be obtained.

Figure 3.5: Wyko 1100 optical image to measured . (a) The arrow indicates one ditch for ₀ depth profile. (b) The depth profile for the ditch. It indicates that the distance from electrode

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Chapter 4. Micromechanical Test

Figure 3.6: Microscope photo for the side view of the spring. These springs were picked up from broken sensors. Estimation of spring side thickness is around 14.4_µm.

In order to measure the spring constant, k, tests were done to measure the displacement with a known mass applied. The spring constant could then be calculated using Hooke’ s law. However, due to large bead cross-section area and no suitable mass alternatives found, the idea of using optical profiler to get spring constant was discarded.

4.4 Tilting Effect and Surface Roughness

The reason which supports the method to take only one corner for displacement measurement is that assuming the plate does not tilt and that, the whole plate moves simultaneously and uniformly, meaning that displacement at one corner could be generalized to the whole plate.

Figure 3.7: Two corners at diagonal relative positions were selected for tilting test.

To verify this, one sensor with one turn of spring as seen in Fig. 3.7 was chosen for the measurement, the two corners are at relatively diagonal positions. Comparing the capacitance calculated from the displacement at each corner, it is shown that the capacitance correlated to each other. Therefore, this demonstrates that it is feasible to choose only one corner for analysis. Moreover, this definitely saves time in data analysis.

2

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4.4. Tilting Effect and Surface Roughness

Figure 3.8: Experimental result for tilting effect. The dotted line is the measurement from IC chip AD7746. ∆ comes from calculation of displacement at corner 1 and □ comes from

calculation of displacement at corner 2. Wyko measurements at two corners were photographed while measuring the capacitance with chip AD7746.

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Chapter 5 Experimental Results

5.1 Capacitive Behavior

To ensure the capacitive characteristics of the MEMS sensor, the impedance Z of the sensor was measured using the LCR meter. Impedance Z is the total opposition a circuit or device offers when an alternating current of certain frequency flows through the circuit. Z contains a real and an imaginary part, which could be expressed by impedance and reactance in polar form [17], Z = z∠θ , Fig 4.1 Using LCR meter to measure the impedance and the angle of the sensor, Fig. 4.2, and the phase measurement show a clear capacitive behavior for the frequencies above 10 kHz. [15]. However, 100 kHz had an unexpected affect on the measurement; thus, the measurement was done using 1 MHz.

Figure 4.1: Definition of impedance. (a) Voltage, current and impedance. (b) Vector representation of impedance.

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5.1. Capacitive Behavior

Figure 4.2: The impedance Z and phase shift θ measured by LCR meter under different frequencies and excitation voltage amplitude. (a) Plot of impedance Z with applied voltages

(b) Plot of degree _θ with applied voltage. .

5.2 Optical Profiler Measurement

Displacement-capacitance and displacement-voltage measurements were done by using white light interferometer Wyko NT1100. The experimental results together with theoretical

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Chapter 5. Experimental Results

Figure 4.3: Displacement-Capacitance relation for type I (one turn) spring and type II (two-turns spring). The measured data is from LCR meter.

Figure 4.4: Displacement-Voltage relation for type I (one turn) spring and type II (two-turns spring). The measured data is from LCR meter.

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5.2. Optical Profiler Measurement

Neglecting the fringe effect, the theoretical fitting for the displacement-capacitance measurement shown in Fig. 4.3 is

_PI SI SI PI SI I SI I C C C C C d A C d A C + + − ×× × × × − × × × × = + + − × − = − − − − − − δ δ δ ε δ ε 6 12 12 6 12 12 0 0 10 8 . 1 10 769600 10 854 . 8 1.8 10 10 769600 10 854 . 8 for type I ( 4.5 ) _PII SII SII PII SII II SII II C C C C C d A C d A C + + − ×× × × × − × × × × = + + − × − = − − − − − − δ δ δ ε δ ε 6 12 12 6 12 12 0 0 10 8 . 1 10 699200 10 854 . 8 1.8 10 10 699200 10 854 . 8 for type II ( 4.6 )

where C is 15 pF, _SI C_PIis 0.8 pF, C is 9.3 pF and _SII C_PII1.1 pF. The modeling fitting of displacement-voltage relations shown in Fig. 4.4 is

2 6 12 12 6 6 0 ) 10 8 . 1 ( 10 769600 10 854 . 8 49 . 999 2 ) 10 8 . 1 1 ( ) 10 8 . 1 1 ( δ δ δ δ − × ⋅ × × × × × × − × − + = − − − − − SI SI I C C C V for type I ( 4.8 ) 2 6 12 12 6 6 0 ) 10 8 . 1 ( 10 699200 10 854 . 8 1 . 428 2 ) 10 8 . 1 1 ( ) 10 8 . 1 1 ( δ δ δ δ − × ⋅ × × × × × × − × − + = − − − − − SII SII II C C C V for type II ( 4.9 )

where C0I and C0II are the initial capacitances without any applied voltages for type I and type

II sensor.

To make a comparison, capacitance-voltage measurement with modeling of the parallel-plate capacitor excluding serial and parallel capacitors are shown in Fig. 4.5.

Figure 4.5: Fitting without serial and parallel capacitors. The left one is type I sensor, the right one is type II sensor.

In Fig. 4.5, there were obvious discrepancies between the theoretical fitting and the measurement data for both AD7746 chip and LCR meter. On the contrast, if combining Fig.

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4.3 and Fig. 4.4, the modeling fits well to the C-V measurement if serial and parallel capacitors are taken into consideration, Fig. 4.6.

Figure 4.6: C-V characteristics for type I (one turn, stiff) spring and type II (two turns spring, soft). The measured data is from LCR meter.

5.3 Nanoindenter Feedback Loop

Different masses were applied with a pre-loading voltage. The original purpose was to construct a feedback loop of indentation. In our design of the nanoindenter, one problem is that the probe is pushed back during indentation due to the pressed springs recovering force. At larger forces the probe can move out of the imaged area, which makes the analysis incomplete. The idea behind the feedback loop was that during indentation, the capacitance increases because the two plates become closer; after a decrease of the voltage, the plates were released and the capacitance went back, which could make elastic force small and keep the nanoindenter always under the microscopy focus area.

In the preliminary test, small beads with a known mass were mounted on the sensor holder to simulate applied load during indentation [3], Fig. 4.7. From this preliminary test, maximum workload and the corresponding tuning voltage range could be extracted.

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5.3. Nanoindenter Feedback Loop Selected mass of beads (mg) Load force (µN) 16.35 160.23 12.62 123.68 7.05 69.09 4.06 39.79 2.02 19.79 0.85 8.33

Figure 4.7: (a) Schematic plot of the nanoindenter force-sensor with an added mass. (b)

Table of selected mass of beads and the corresponding load force.

Fig. 4.8 shows the C-V measurement of a type I, stiff spring sensor with small bead 16.29 mg and an initial actuated voltage 15V. The capacitance is measured by AD7746 with conversion time 62.0 ms /16.1 Hz and excitation voltage at VDD/2 level, VDD = 5V. When

comparing the capacitance readout with mass applied and without mass, it shows that the capacitance increases with 0.2 pF when a mass of 16.29 mg is applied. The increased

capacitance implies that the two electrodes are pressed closer together due to the mass. Now with applied voltage and extra load due to the mass, the force exerting on this system could be expressed as: mg d AV k + − = ₂ 0 2 ) ( 2 δ ε δ ( 4.10 )

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Figure 4.8: C-V measurement with and without applied mass. The curve shape with applied

mass is quite similar to the other one without mass.

By measuring C-V with mass applied to the system, it demonstrates the possibility to construct feedback loop mechanism for the nanoindenter sensor. Based on the measurement presented in Fig. 4.8, a manual loop was executed and satisfying result was obtained. The schematic demonstration of manual feedback loop is shown in Fig. 4.9.

Figure 4.9: Manual feedback loop based on measurement in Fig. 4.8. (a) Initial voltage is

15V on the sensor and the capacitance is 4.15pF. (b) Add a mass with 16.29mg, the capacitance increased to 4.38pF. (c) Turn down voltage from 15V to 10V, capacitance drop

back to the initial value.

The bead mass put on the sensor holder is used to simulate applied load on capacitive sensor when the tip is indenting sample, Fig. 1.5. Fig. 4.9(b) characterizes compressed plates as in Fig. 1.5(c). And Fig. 4.9(c) gives the ideas for the voltage needs to be turned down to keep electrodes distance constancy as in Fig. 1.5(d).

Repeating this measurement for different initial voltages, the voltage is needed to

compensate for the load is shown in Fig. 4.10. It shows that higher initial voltage gives larger forces range whereas lower initial voltage decreases the forces range.

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Chapter 6 Conclusion

6.1 Summary

In this thesis work, the performance of an in situ nanoindentation sensor combined with IC chip AD7746 has been investigated. To test the possibility and feasibility of the feedback loop for the sensor, C-V measurement was done as preliminary test. Several unexpected results were measured, like offset voltage, higher snap-in voltage and higher capacitance readout. To explain these unexpected phenomena by a parallel-plate capacitor model, the simple model has been improved and modified. Serial capacitor, parallel capacitor and bending plate were parameters that were added to the model. With those parameters the model could be

completed. To establish the model additional displacement measurements were done by using white light interferometer.

The feedback loop which was the final goal of the project has been tested using manual feedback. Small beads with known mass were used to replace the role of real load, and the manual feedback loop was successfully established. With current sensor design, the feedback loop works well if the applied load is less than 200 µN. The original plan of developing an

automatic feedback loop for the sensor was postponed for several reasons, like the big RC constant results in a long response time, the uncertainty about the serial capacitance and designing new software program interface. Hence, the construction of feedback loop will wait until a new design of nanoindenter sensor is performed.

6.2 Recommended Future Work

According to the basic investigation of nanoindenter capacitive sensor, some work remains before producing the new generation of nanoindentation sensor. Unavoidably, some

mysterious phenomena were found and will remain as new tasks for further studies. These include different offset voltages for different spring type sensor, control over the serial capacitance, different curve shape of the measurements of LCR and AD7746, the bending degree of plates and the precise value of spring constant.

For the next generation nanoindenter sensor, the following items should be considered:

• First, during the design and manufacturing process, the existence of serial capacitor

should be taken into account. Some alternative such as discarding the press contact and using other ways to connect electrodes might be possible.

• Second, a modified design of the sensor electrode might be needed to achieve an

efficient, reactive feedback loop. The existing circuit design gives the reaction time around 20~30 seconds, which are too long for an efficient feedback loop.

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Chapter 6. Conclusion

• Third, the feedback loop which has been tested so far can achieve maximum load

around 200 µN. However, for the actual application it is preferred to have forces up to

1000 µN. Therefore, a new investigation of the spring design is recommended.

• Moreover, it is recommended to investigate the bending plate further. Several related

factors like wafer manufacturing, thickness of sensor plate design and plate shape could be further considered before designing. Besides, it is recommended to do simulation for the bending plate model. It will be more valid and convinced if there are simulation results in comparison with the analytical model presented in this work.

• Finally, it is required to develop a program and new interface for the controlling of

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Acknowledgement

Acknowledgement

First and foremost, my thanks go to my two supervisors, Alexandra Nafari and Johan

Angenete. I would not make anything without their generous help. Moreover, I would like to appreciate them for giving me the chance to do this project in Nanofactory Instruments AB. And thanks for reading and revising my report patiently, carefully and giving me excellent and practical suggestions. Deep and sincere appreciation to Alexandra, for her patience and willingness to teach me, take me to try many new things and give me many opportunities. By working with her, I leaned many useful and interesting new skills.

Secondly, I am grateful to all my colleagues in Nanofactory Instruments AB (alphabetical order: Andrey Danilov, Ann-Jeanet Jörgensen, Björn Ahlgren, Christelè Grimaud, Dan Olofsson, Jens Dahlström, Klas Nordström, Ludvig de Knoop, Mikael Johansson, Mikael von Dorrien, Oleg Lourie, Paul Bengtsson). They are friendly and willing to give me a hand when I need help. Klas is especially thanked for his help with building up the electronic circuits for AD7746 testing, and I sincerely appreciate his patience with teaching and discussing with me the fundamental knowledge of electronics. I would like to mention Gittan here, too. She always brings happiness and laughs wherever she is present, and this makes the working environment more joyful and enjoyable.

Two other people who can not be missed here are Professor Peter Enoksson at the BioNanoSystem Laboratory, Chalmers and Sjoerd Haasl at Imego. Thanks for providing valuable ideas for result discussion and pointing out direction for further investigation. And these help us to make this project a satisfying work.

Finally, I am obliged to my family, the teachers and friends I have met in Linköping and Göteborg. Thanks for encouraging and supporting me to do my thesis work in Nanofactory Instrument AB and to pursue my studies in Sweden.

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Bibliography

Bibliography

[1] R.P. Feynman, “There’ s Plenty of Room at the Bottom” in Miniaturization, pp. 282-296,

Reinhold Publishing, New York, 1961

[2] Dynamics and Nonlinearities of the Electro-Mechanical Coupling in Inertial MEMS, Luis

Alexandre Rocha, PhD thesis, Delft University

[3] MEMS Sensor for In Situ TEM Nanoindentation, Alexandra Nafari, Licentiate thesis,

Chalmers University of Technology, 2007

[4] Nanofactory Instruments AB, www.nanofactory.com

[5] Handbook of Sensors and Actuators, Micro Mechanical Transducers, Pressure Sensors,

Accelerometers and Gyroscopes, M,-H. Bao, Elsevier, 2004

[6] Simulation of Microelectromechanical Systems, K. Fedder, PhD thesis, University of

California at Berkeley, (1994)

[7] Electrical Breakdown Phenomena for Devices with Micron Separations, Ching-Heng

Chen, J Andrew Yeh and Pei-Jen Wang, Journal of Micromechanics and

Microengineering, 2006

[8] Electrostatic Micromechanical Actuator with Extended Range of Travel, Edward K. Chan,

and Robert W. Dutton, Fellow, IEEE [9] http://www.accuratus.com/alumox.html

[10] Fundamentals of Engineering Electromagnetics, David K. Cheng, Addison Wesley (1993)

[11] Analog Devices, www.analog.com/en/

[12] Datasheet for Analog Devices AD7746

[13] http://www.testwall.com/datasheets/HP-4284A.pdf

[14] Veeco, www.veeco.com

[15] Introduction to Electric Circuits, Richard C. Dorf, James A. Svoboda, Wiley

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Bibliography

[17] http://www.murata.com/cap/measure.pdf

[18] Datasheet for LCR meter HP 4284A

[19] Mastering MATLAB 7, Duane Hanselman, Bruce Littlefield, PEARSON Prentice Hall

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Appendix A

Appendix

Appendix A -- Analytical Spring Constants

Serpentine flexure was adopted for the sensor spring design. The snake-like meandering of spring segments gives the name serpentine. Meanders are of length a and width b. For each spring, one end is a guided-end and the other one is a fixed-end, Fig. A1. This boundary conditions lead to the fact that the spring motion is limited to the preferred direction. Fig. A.2 shows the free-body diagram for serpentine spring with n meanders. The longitudinal segments are called span beams whereas the horizontal ones are defined as the connector beams, Fig. A.1. Besides, the connector beams are indexed from i=1 to n and the span beams are indexed from j=1 to n-1.

Figure A.1: Serpentine springs schematic.

Necessary terms are defined first and later will be used to calculate the spring constant. Consider one guided-end beam having length L, width w, and thickness t. If force is applied on the beam, the beam is bending with bending moment of inertia. The bending moment of inertia about the z-axis is defined asI . For the rectangular beam cross-section [5], z

∫ ∫

− − = = /2_/₂ 2 / 2 / 3 2 12 t t w w z tw dxdz x I ( A.2 ) Similarly,

∫ ∫

− − = = /_/2₂ 2 / 2 / 3 2 12 w w t t x w t dzdx z I _{( A.3 )}

With torsion, the torsion modulus G is related to Young’ s modulus E and Poisson’ s ratio υ

) 1 ( 2 ₊ν = E G ( A.4 )

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Appendix A

Also, the torsion constant for a beam of rectangular cross-section is             − =

∑

∞ = iodd i t w i i w t w t J , 1 5 5 3 2 tanh 1 192 1 3 1 π π ( A.5 )

The z-direction spring constant for the flexure is z z z F k = _δ . For n even,         − + + + − + = 3 2 2 2 2 3 2 , ) 3 2 ( 3 ) ( 12 b S S S n b S S ab S S a S S b S bn a S S S n b S a S a S S S S S S k gb ga ea gb ga gb eb ga eb ea ga eb ea ea gb ga eb gb ga eb ea beam z _{( A.6 )}

whereSea ≡EIx,a_,Seb ≡EIx,b_,S ≡ga GJa_{, and}S ≡gb GJb_{. For n odd,}

                − + + + − + + + + + + + − + + + + − = ) 3 ( ) 2 ( 2 ) 4 ) 3 5 ( 2 ( ) 4 ) 3 (( ) ) ( ( ) ) 1 ( ( 12 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 3 2 3 2 4 2 2 2 , a S b S b S S n b S S ab S S a S S b S S n b S S ab S S S b a S S S S a S S b S n b S S a S S S S b a S S n b S S ab S S S S a S S a S S an S n b S S S S S k eb ga ga ea gb ga gb eb ga eb ga eb gb ga gb ga eb gb eb ga eb ga eb ea ga ea gb ga eb ea ga eb ga ea gb ga eb ea gb eb ga eb eb ga gb ga eb ea beam z ( A.7 )

For type I spring, n=3, a=40µm, b=340µm, w=30µm, and t=14µm. Therefore, we

have -21 xa =6.86 10 I × , -21 xb =6.86 10 I × , -9 ea =1.13 10 S × , -9 eb =1.13 10 S × , -9 ga = 1.19 10 S × , -9 gb =1.19 10 S × , and -20 b a=J 1.94 10

J = × . Similarly, for type II spring, all parameters are the same except n=4, b=330µm.

Since there are 8 springs connected to the upper plate, it is equivalent to 8 springs connected in parallel, which results in the spring constantk_z =8×k_z_,_beam. Finally, the spring constant for type I is 999.5 N/m and it is 428.1 N/m for type II.

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Appendix A

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Appendix B

Appendix B -- AD7746 & LCR Meter

AD7746 is a 24-bit, capacitance-to-digital converter with temperature sensor manufactured by company Analog Devices [10]. The capacitance input range is ±4 pF and by using the on-chip program, up to 17 pF capacitance input could be adopted by the device.

The core structure of AD7746 is a converter made by a second order modulator and a third order digital filter. For capacitive input, it functions as a CDC whereas for voltage input or for the voltage from a temperature sensor, it works as an ADC.

Fig. B.1 shows the simplified CDC diagram. The input of the measured capacitance is connected to one Σ-∆ modulator and a square wave excitation source. During the conversion, the modulator samples the charge flaw through Cx continuously. Afterwards, the signals from

the modulator were processed by the digital filter to streams of 0s and 1s. Finally, after scaling and calibration, final results come out at the serial interface.

It is worth noticing that since AD7746 is designed for floating capacitive sensors, none of the measured capacitor Cx plates could be grounded.

Figure B.1: CDC Simplified block diagram.

Two possible capacitance inputs could be used for AD7746, one is single-ended capacitive input, and the other one is the differential capacitive input. In this thesis work, single-ended capacitive input was applied for all the measurements.

For single-ended mode, the allowed input range for CDC is from 0 pF to 4 pF, Fig. B.2. Further, with the programmable CAPDAC, input range could shift up to 21 pF. Fig. B.2 shows how to span a ±4 pF range CDC to measure capacitance between 0 pF to 8 pF and fig. B.3 shows capacitance between 13 pF to 21 pF measured with a programmable CAPDAC.

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Appendix B

Figure B.3: Shift the input range up to 21 pF.

The CDC architecture used in the AD7746 measures the capacitance Cx connected

between the EXC pin and the CIN pin.

Figure B.4: Σ-∆ CDC architecture.

The basic loop for measuring an unknown capacitor is shown in Fig. B.5. A reference voltage is applied on CREF. The charge signals are transmitted to the comparator which

compares to the signals of charge from CSENSOR. The feedback loop is supposed to work as the

following descriptions: the excitation voltage for the CSENSOR generates a signal and sends it

to the integrator; meanwhile, VREF also generate a signal and send it to the integrator. At the

comparator, these two signals are compared and the feedback loop will execute some procedures like charging (by VREF (+)) or discharging (by VREF (-)) CREF so that at the end

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Appendix B

Figure B.5: Measurement circuit.

HP 4284 A LCR meter is one of the most common used LCR meter, the widest application for LCR meter is to measure capacitance and dissipation factor of capacitor.

The basic principle lies behind LCR meter is the “automatic balancing bridge method” [16], Fig. B.6. The name LCR meter implies it can be used to measure the impedance of inductors, capacitors and resistors and other components.

Figure B.6: Principle diagram of Automatic Balancing Bridge.

To measure the capacitance, two modes can be chosen from which depends on if the circuit is serial equivalent or parallel equivalent [16].

According to Eq. 3.1, small capacitance gives high impedance, which therefore gives more prominent parallel resistance compare to the serial capacitance, fig. B.7 (a). This effect leads to the possibility to ignore the effect of serial capacitance in the circuit, thus small capacitor gives parallel capacitor equivalent circuit. Conversely, if the capacitance is large (low impedance), then Rs has relatively more significance than Rp, so the series circuit mode

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Appendix B

Figure B.7: Capacitance measurement circuit mode. (a) Model to use for small capacitance. (b) Model to use for large capacitance.

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Appendix C

Appendix C -- Spring Design

The detailed design of sensors spring and the size parameters are presented here. Type I, stiff spring:

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Appendix C

Electrostatic Feedback for Mems Sensor : Development of in situ TEM instrumentation

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