Thesis Winter Master

Mechanical Design and Modeling of MEMS Thermal Actuators for RF Applications by

Dong Yan

A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Applied Science in Mechanical Engineering

Waterloo, Ontario, 2002

c °Dong Yan, 2002

I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research.

Dong Yan

I authorize the University of Waterloo to reproduce this thesis by photocopying or other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research.

Dong Yan

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The University of Waterloo requires the signatures of all persons using or photocopying this thesis. Please sign below, and give address and date.

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Acknowledgements

First of all, I would like to sincerely thank my supervisors, Dr. Amir Khajepour and Dr. Raafat Mansour, for all they have done for me. Their support, knowledge, advice, patience and troubleshooting skills made my research achievement possible. I also would like to thank my friends and colleagues. In alphabetic order, they are Saeed Behzadipour, David Gairns, Arash Narimani, Tong Qu, Neil Sarkar, Aden Seaman, Yu shen, Ehsan Toyserkani, Wilson R. Wang, Huizhong Yang. Their friendship and support made my life more colorful and enjoyable. The financial support of this project was provided by Natural Sciences and Engineering Research Council of Canada (NSERC) and COM DEV International Ltd. Without their continuous support, this project would not have been possible. Finally, I would like to express my deepest appreciation to my family. Their endless support and encouragement made all of this possible.

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Abstract Micro electro mechanical system (MEMS) technology has shown its bright future in many different fields, especially in space and radio frequency (RF) systems. By using MEMS technology, we can greatly shrink the cost and the footprint of RF circuits since all the off-chip components such as inductors and capacitors can be fabricated and integrated into a whole single chip at one time. Our research is directed by the purpose of developing more powerful RF components. This thesis describes an analytical model of a two-hot-arm horizontal thermal actuator at the beginning. The experimental results are provided to prove the accuracy of the analytical model. It then documents the design and model of a bidirectional vertical thermal actuator. This new novel vertical thermal actuator has the ability to bend up and down without any modification, so it is supposed to have twice the amount of deflection than the traditional vertical thermal R ° actuator. The numerical simulation is done by using commercial software Coventorware . It shows a good agreement with the analytical result. At the end, this thesis documents a new design of multiport switch with a latching mechanism and an improvement of tunable capacitor by using bidirectional vertical thermal actuators.

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Contents 1 Introduction

1

1.1

Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3

Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2 Background

8

2.1

Introduction to MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

MEMS actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3

2.4

8

2.2.1

Electrostatic actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2

Thermal actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.3

Other actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Micromachining techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1

Bulk micromachining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2

Wafer bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.3

LIGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.4

Surface micromachining . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.5

Flip chip technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Micromachining foundry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Two-hot-Arm Horizontal Thermal Actuator

25

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2

Electrothermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1

Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 vi

3.2.2 3.3

Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Mechanical analysis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.1

Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.2

Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4

Fabrication process and experiments . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Bidirectional Vertical Thermal Actuators

49

4.1

Mechanical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2

Electrothermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3

4.4

4.2.1

Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.2

Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Mechanical analysis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3.1

Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3.2

Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 RF Applications of Horizontal and Vertical Thermal Actuators

69

5.1

Multiport switch with a latching mechanism . . . . . . . . . . . . . . . . . . . . . 69

5.2

Tunable capacitor with U-shaped vertical thermal actuators . . . . . . . . . . . . 73

5.3

Fabrication and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6 Conclusions

76

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List of Tables 2.1

MUMPs process layers and their Properties . . . . . . . . . . . . . . . . . . . . . 23

3.1

Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2

Geometrical data of the two-hot-arm thermal acutator . . . . . . . . . . . . . . . 33

4.1

Geometrical data of the U-shaped vertical thermal acutator . . . . . . . . . . . . 58

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List of Figures 2-1 The schematic view of MEMS chip [1] . . . . . . . . . . . . . . . . . . . . .

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2-2 The schematic diagram of electrostatic microactuator . . . . . . . . . . . 11 2-3 (a) Comb-drive electrostatic microactuator. [2] (b) electrostatic micromotor [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2-4 The schematic diagram of thermal pneumatic microactuator . . . . . . . 13 2-5 The thermal bimetallic microactuator with the cantilever prototype . . 13 2-6 Various Bulk-micromachining Structures[3] . . . . . . . . . . . . . . . . . . 15 2-7 the schematic diagram of LIGA process [3] . . . . . . . . . . . . . . . . . . 17 2-8 Processing steps of typical surface micromachining [3]. . . . . . . . . . . 18 2-9 The schematic diagram of flip chip process [4] . . . . . . . . . . . . . . . . 21 2-10 Cross section of MEMS motor fabricated by MUMPs [5] . . . . . . . . . 22 2-11 Cross section of MEMS motor after releasing process [5] . . . . . . . . . 24 3-1 A traditional thermal actuator (one hot arm) . . . . . . . . . . . . . . . . 26 3-2 Schematic diagram of two-hot-arm thermal actuator . . . . . . . . . . . . 26 3-3 (a) Schematic top view of two-hot arm thermal actuator. (b) Simplified one dimensional coordinate system. . . . . . . . . . . . . . . . . . . . . 27 3-4 The schematic cross section of the actuator for thermal analysis . . . . 28 3-5 The schematic diagram of boundary conditions . . . . . . . . . . . . . . . 31 3-6 The analytical result of temperature distribution along the outer and inner hot arms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3-7 The numerical result of temperatue distribution of the two-hot arm thermal actuator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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3-8 Maximum temperature as a function of input voltage: Comparison between analytical and simulation results. . . . . . . . . . . . . . . . . . . 35 3-9 (a) The plane frame structure simplified for the thermal actuator with six redundants. (b) The bending moment of the outer hot arm due to the virtual force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3-10 (a) The bending moment diagram of a unit force in the deflection direction (b) The bending moment diagram of a unit force in the force direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3-11 Deflection of the actuator tip as a function of input voltage . . . . . . . 41 3-12 Numerical result of the deflection of two-hot-arm thermal actuator with 10v input voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3-13 Deflection meter coupled to a two-hot-arm thermal actuator . . . . . . 42 3-14 Overview of the whole chip after HF release. . . . . . . . . . . . . . . . . . 43 3-15 Experiment equipment for measuring the deflection of thermal actuators 44 3-16 Comparison of experimental result with the analytical and numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3-17 The touching of the outer and inner hot arms at high actuating voltage 45 3-18 A curve found in the inner hot arm as seen in SEM . . . . . . . . . . . . 46 3-19 Two modes of the traditional thermal actuator operation [6]. . . . . . . 47 3-20 Back bending of the two-hot-arm thermal actuator . . . . . . . . . . . . . 47 3-21 Over etching of the teeth of the deflection meter. . . . . . . . . . . . . . . 48 4-1 3D schematic view of a vertical thermal actuator showing a cross section through the hot and cold arm.[7] . . . . . . . . . . . . . . . . . . . . . 50 4-2 3D View of the U-shaped vertical thermal actuator . . . . . . . . . . . . 51 4-3 2D schematic top view of the U-shape VTA . . . . . . . . . . . . . . . . . 52 4-4 Simplified one dimensional coordinate system . . . . . . . . . . . . . . . . 53 4-5 Schematic cross section of the VTA for thermal analysis . . . . . . . . . 53 4-6 3D schematic diagram of the element 3 with the cross section . . . . . . 55 4-7 (a) The boundary conditions of temperature continuity. (b) The boundary conditions of the rate of the heat conduction . . . . . . . . . . . . . . 56 x

4-8 Temperature distribution along the top layer of VTA . . . . . . . . . . . 59 4-9 Numerical result of temperature distribution of the U-shaped VTA R ° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 using Coventorware 4-10 Comparison of the maximum temperature as a function of input voltage. 60 4-11 (a) The schematic 3-D view of U-shaped VTA, (b) Four bar linkage representing for the U-shaped VTA. . . . . . . . . . . . . . . . . . . . . . . 62 4-12 (a) The hinged rigid frame for mechanical analysis, (b) schematic of the spring coefficient analysis in y direction.

(c) schematic of the

deflection of the U-shape VTA. . . . . . . . . . . . . . . . . . . . . . . . . . 63 4-13 (a)The bending moment of the top layer long beam due to the virtual force, (b) The bending moment of the top layer long beam due to the thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4-14 The hinged rigid frame with three deflection directions . . . . . . . . . . 65 4-15 (a) The deflection without torsional springs. (b) the deflection with two torsional springs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4-16 Deflection of the tip of the U-shaped vertical thermal actuator as a function of input voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5-1 (a) Schematic of latching mechanism in 3D view. (b) Detail of the latching mechanism.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5-2 (a) Top view of the multiport switch. (b) Closed-up of the multiport switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5-3 Top view of the tunable capacitor with U-shaped vertical thermal actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5-4 Schematic diagram of S-shaped connection and detail of the connection. 75

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Chapter 1

Introduction 1.1

Motivation

The greatest promise of microelectromechanical systems (MEMS) lies in the ability to produce mechanical motion on a small scale. Such devices are typically low power and fast, taking advantage of such microscale phenomena as strong electrostatic forces and rapid thermal responses. MEMS-based sensors have been widely deployed and commercialized. MEMS technologies also show prospective applications in optics, transportation aerospace, robotics, chemical analysis systems, biotechnologies, medical engineering and microscopy using scanned micro probes [8]. The explosive growth of data traffic such as the internet has produced a pressing need for large capacity communication network. Satellites and radio frequency (RF) systems are the important components for the communication network. The emergence of on-chip, discrete RF MEMS has attached the attention of the wireless industry that is interested in smart phones, Bluetooth and so on. MEMS-based RF systems may play a significant role in making such products possible. By using MEMS-based RF components, the footprint of RF circuits can be greatly shrunk by including all the off-chip components such as inductors and capacitors into on-chip components. At the same time, the performance can also be increased by reducing signal delay time and noise effects through the applications of on-chip components. These outstanding advantages and promising applications of MEMS based RF components become a driving motive force for many MEMS designers, including the author of this thesis, to concentrate their research efforts on designing novel RF MEMS devices. However one of 1

the fundamental problems that most of MEMS designers have to face is the limitation of the access to fabrication foundries. Although more and more clean rooms have been founded with the financial support of government and industries, there is still a solid community of MEMS researchers who do not have their own clean room. Fortunately, those MEMS researchers who do not have their own clean room still can manage to do their research with the facilities of a number of commercially available fabrication foundries. Cost and time are other issues for most MEMS researchers. Modeling MEMS devices is one solution to these issues. Before any MEMS design is submitted fabrication, MEMS researchers should be able to grasp the properties of the MEMS designs as much as possible through modeling. Accurate models of MEMS devices also can release MEMS researchers’ work on device level design and allow them to focus on system level design. In this thesis, research effort is directed at these two motivations: the excellent properties of MEMS based RF components and the crucial need for the accurate modeling of MEMS devices.

1.2

Literature review

The first impressive review of the applications of silicon as mechanical material, more than electronic material, was published by Kurt Petersen in 1982 [9]. Almost at the same time, Howe [10] first proved the evolution of a very useful method to build micromechanical elements using technologies that were developed first to build microelectronic devices for the integrated circuits in seminal work done in 1982. R. T. Howe demonstrated techniques to fabricate microbeams from polycrystalline silicon (polysilicon) films [10]. With the encouragement of this demonstration, Howe built the first prototype polysilicon MEMS, a chemical vapor sensor which was a fully integrated micromechanical and microelectronic system [11]. With the development of the micromachining techniques, many complex devices have been produced and some of them are already commercialized. An impressive example of a commercial MEMS that makes use of surface micromachining to build a fully integrated accelerometer is the AD-XL50 microaccelerometer produced by Analog Devices Inc. for use in automobile airbag deployment systems [12]. The impact of MEMS is very wide and deep. The feasibility of MEMS has been proven

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in several markets including the automotive industry. MEMS technology has also received the attention of the wireless industry because of its advantages such as low cost, higher performance, reduced size and weight, and increased reliability. Therefore, a tremendous research effort has focused on the development of MEMS based components in the wireless and microwave technology area. The tunable capacitor (or variable capacitor) is one of the most important and active branches in the area of applying MEMS technology to passive and active components, such as inductors, switches and filters. According to the actuating mechanism, a tunable capacitor can be categorized into two types: electrostatic and electro-thermal. In the category of electrostatic actuating mechanisms, tunable capacitors take two forms: parallel plate and interdigitated (or comb-drive). In the parallel plate approach, the top plate is suspended in a certain distance from the bottom plate by suspension springs, and this distance is used to vary in response to the electrostatic force between the plates induced by an applied voltage. Young, et al [13] reported a tunable capacitor designed for monolithic low-noise voltagecontrolled oscillators (VCOS) . In this work, the new tunable capacitor consists of a thin sheet of aluminum suspended in air approximately 1.5 µm above the substrate. A DC voltage results in an electrostatic force pulling the movable plate closer to the substrate, hence increasing the capacitance. Theoretically, a tuning range of up to 50% can be achieved. The required tuning voltage depends on the suspension dimension. Experimental work has also been done and the result shows that the tuning range is 16%. The conclusion of this work was also highlighted that the aluminum micromachined tunable capacitors constitute an attractive alternative to conventional varactor diodes as the tuning element in VCOS for personal communication devices because this technology requires no changes of the underlying IC process. In order to improve the tuning range of parallel plate tunable capacitors, Aleksander Dec and Ken Suyama have documented two new tunable capacitors in [14], and [15]. In [14], Dec et al presented two new tunable capacitors with two and three plates respectively. Polysilicon was chosen as the structural material for tunable capacitors due to its good mechanical properties. Several tunable capacitors have been fabricated by the standard polysilicon surface micromachining process, which features three layers of polysilicon and one gold layer. For the two plate tunable capacitor, the fixed plate was anchored under the suspended plate; while with the three plate tunable capacitor, the suspended plate is placed in the middle of the three plates. The

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measurements of the tuning range of the two and three plates tunable capacitors are 1.5:1 and 1.87:1, respectively. These two designs have greatly increased the tuning range of the tunable capacitor with a slight modification of the fabrication process. Another new tunable capacitor with one suspended top plate and two fixed bottom plates has been proposed by Jun Zou et al [16]. One of the two fixed plates and the top plate form a variable capacitor, where as the other fixed plate and the top plate are used to provide electrostatic actuation for capacitance tuning. The controllable tuning range of 68% has been achieved experimentally. Its fabrication process is also completely compatible with the existing standard IC fabrication technology. Instead of polysilicon and aluminum, other materials such as the dielectric material [17] can be used. Instead of the parallel plate style tunable capacitor, J. Jason Yao et al have designed, fabricated and experientially tested an interdigitated “comb” structure tunable capacitor [17], [18]. With the special fabrication process, the continuous and controllable tuning range is up to 300%. A tunable capacitor can also be built using an electro-thermal actuating mechanism. Compared to electrostatic, tunable capacitors actuated by thermal actuators have several advantages [19]: • Avoiding the static charges collecting on the plates • Improvement in the reliability of tuning • Approximately linear capacitance tuning • Lower driving voltages A flexible integration of MEMS tunable capacitors can also be obtained by using flip-chip transfer technology. After flip chip transformation, the low resistivity silicon substrate, which has high loss at high frequencies, can be removed to improve the performance of the tunable capacitor. The tunable capacitor with an electro-thermal actuator has some disadvantages such as lower tuning and more space requirements. A series mounted MEMS tunable capacitor with an electro-thermal actuator was reported by Zhiping Feng et al [19]. The electro-thermal actuator has been used to drive the top plate of the tunable capacitor to move vertically (the vertical direction is defined as the direction perpendicular to the substrate). The MEMS structure was mounted on the alumina substrate 4

by using flip chip technology. The tuning range of this type capacitor was reported to be 2:1. In [20], Huey D. Wu et al have presented another tunable capacitor with a thermal actuator array that can be actuated horizontally (the horizontal direction is defined as the direction parallel to the substrate). Experiments have shown two interesting observations. The first is the range of the capacitance change, which achieved a very impressive 2.6 pF. The corresponding gap variation should be from 2 to 0.2 µm. The second observation is the excellent repeatability and resolution of the capacitance-vs-voltage relationship. Small voltage changes such as 0.1 Volt result in visible capacitance variations. These two inspiring observations obtained more researchers’ attention. Kevin F. Harsh et al improved the tunable capacitor by replacing the thermal actuator array with vertical thermal actuators that have the motion perpendicular to the substrate [4]. The advantages of the vertical thermal actuator are the larger deflection in the direction perpendicular to the substrate and more robust for flip-chip transfer process. The capacitor can be tuned from approximately 0.5 to 3.5 pF by using the control voltage less than 1 V. Obviously, the performance of a thermal actuator becomes a key factor for the performance of a tunable capacitor Compared with widely-used electrostatic forces, thermal expansion can provide larger forces and it is also easier to control. However a single-material actuator based solely on the thermal expansion of a beam would have a small deflection relative to the size of the actuator. Differential expansion of a laminate made of two materials of unequal thermal expansion coefficients, the bimetallic or bimorph, [21] can be used to amplify deflection. Horizontal thermal actuators, one of the most famous thermal actuators designed by John H. Comtois and Victor M. Bright, takes advantage of the shape to create a “bimetallic” effect using a single material [22]. The current passes through all the structure when the thermal actuator is activated. Internal Joule heating causes elastic structures to expand and generate deflection when the structures are mechanically constrained. Such actuators were also reported in [6], [23], [24]. Vertical thermal actuators were also mentioned in [22]. The actuation theory of a vertical thermal actuator is similar to that of a horizontal actuator. The only difference is that the current passes through two layers in the case of the vertical thermal actuator instead of one layer in horizontal actuator. The structures are mechanically constrained in two layers, not in one

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layer like the horizontal thermal actuator. So the different thermal expansion of the structures generates the vertical motion out of the plane. Based on the same idea, some modifications of the vertical thermal actuator have been well documented in [25], [26], [4]. Modeling of the thermal actuator began with the horizontal thermal actuator in [23]. Finite element method also has been employed to analysis the horizontal thermal actuator in [23], [27]. The analytical model of the thermal actuator was presented by Qing-An Huang and Neville Ka Shek Lee in [28] , [24]. In the electro thermal analysis, they simplified the thermal analysis of the horizontal thermal actuator as one dimensional problem. Then, force method and virtual work have been used to solve thermal mechanical problem. The analytical result is in good agreement with the experimental results.

1.3

Thesis overview

The objective of this thesis consists of two main parts: the analysis of a two-hot arm horizontal and vertical thermal actuator; and an improved design of a tunable capacitor and multiport switch with latching mechanism for radio frequency (RF) applications. Chapter 1 briefly clarifies the motivation of this thesis work and takes a look at the previous research in the area of tunable capacitor and thermal actuator. The definition of MEMS is given in Chapter 2. Chapter 2 also explains and compares different MEMS actuators, followed by a discussion of the basic fabrication techniques and their limitations, which are the constrains for the design and analysis of the MEMS devices. Multi Users MEMS Process (MUMPs) is highlighted in Chapter 2 because all of the devices in this thesis are fabricated using MUMPs. Chapter 3 documents the analytical solution of the two-hot arm horizontal thermal actuator. Numerical and analytical results are also provided for comparisons. In Chapter 4, a new and novel vertical thermal actuator is designed and modeled. The difference of the new vertical thermal actuator from the traditional vertical thermal actuator is that the new vertical thermal actuator can be bent in two directions, up and down. This allows the actuator to have twice the deflection compared to traditional vertical actuators. By applying a similar approach, the analytical solution to the vertical thermal actuator is also obtained. The analytical results are

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also in good agreement with the numerical results. Based on the analytical modeling of the two types of thermal actuators, two RF components, a tunable capacitor and a multi-port switch are designed in Chapter 5. The latching mechanism is also explained and applied to this type of switch. Chapter 6 concludes the thesis. The key findings are highlighted and recommendations for the future work in this area are presented.

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Chapter 2

Background 2.1

Introduction to MEMS

With the advent of integrated circuit (IC) fabrication technology in the 1960s, human being’s ability to make physically small objects received a big progress. Since the circuits still perform the same function when they are scaled down by factors, competition occurred to develop ways of integrating more and more circuits on a semiconductor wafer. From the economic side, that is beneficial since the greater the number of circuits, the greater the profits. Such an exemplary success in mass production as appeared in IC industry has been achieved, and researchers are motivated to apply the concepts of integrated electronics manufacturing to mechanics, optics and fluidics with the hope of acquiring the same improvements in performance and cost effectiveness experienced by the semiconductor industry. That resulted in the advent of MEMS technologies MEMS is the acronym for Microelectromechanical Systems. In Europe, it is also called Microsystems. By now, there is still no generally accepted definition for MEMS. Some researchers depict it as the integration of miniaturized sensors, actuators and signal processing units, enabling the whole system to sense, decide and react [3]. Other MEMS engineers consider a typical MEMS device as [29] : • A device that consists of a micromachine and microelectronics, where the micromachines are controlled by microelectronics. Quite often, microsensors are involved in the control

8

system by providing signals to the microelectronics. • A device that is fabricated using micromaching technology and an integrated circuit (IC) process, i.e., technologies of batch fabrication. • A device that is integratedly born, without individual assembly steps for the main parts of the device except for the steps required for packaging. More generally speaking, MEMS is simultaneously a toolbox, a physical product and a methodology all in one [30]. As the name implies, “Micro” establishes the size definition, “Electro” intimates that either electricity or electronics is involved and “mechanical” infers that some moving parts should be included. From the physical point view, MEMS is usually the integration of mechanical elements and electronics on a common silicon wafer using microfabrication technologies. The electronics can be fabricated by IC process sequence (e.g., CMOS) and the mechanical elements are constructed by micromachining methods that are compatible with the IC fabrication process. Figure 2-1 depicts MEMS characteristics. The sensors and

Mechanical Elements

Electronics Elements

Figure 2-1: The schematic view of MEMS chip [1] actuators can be made of mechanical elements, and signal processing and control units can be built by using electronics circuits. So, the whole system can be integrated on a single chip without any extra assembly process. The motivation for integrating the whole system on a single chip is miniaturization and parallel processing which leads to inexpensive fabrication in large quantities. It also has the ability to make devices with the functions that cannot be realized with traditional technologies.

9

In the beginning of 1990s, MEMS emerged with the development of IC fabrication processes, in which sensors, actuators and control functions are cofabricated in silicon [31]. With the strong financial support from both governments and industries, MEMS research has achieved remarkable progress. MEMS technology has proven its outstanding and revolutionary capability in many different fields. There are numerous MEMS applications that have been commercialized such as microaccelerometers, microsensors, inkjet printer head, micromirrors for projection, etc. In addition to these less-integrated MEMS devices, more complicated MEMS applications also have been proposed and demonstrated for their concepts and possibilities in such varied fields as biomedical, chemical analysis, microfluidics, data storage, display, optics wireless communications etc. [32], [33]. With more and more energy and effort injected, some new branches of MEMS technologies have appeared such as microoptoelectromechanical systems (MOEMS) and micrototal analysis systems (µTAS) because of their potential applications’ market. MEMS technologies do face a lot of challenges. First of all, from the design point view, MEMS computer aided design (CAD) software packages are still very time consuming and not powerful enough to include all the real factors that affect the operation of MEMS devices at one time. The complexity of MEMS design is also a big issue for MEMS designers. Typical MEMS devices, even simple ones, manipulate energy in several physics domains. That requires that the MEMS designer must understand and find ways to control complex interactions between these domains. Secondly, in the fabrication side view, the cost issue for a state-of-the-art silicon foundry is also a barrier most MEMS designers have to face. High initial investment limits the speed of the MEMS development. Packaging can also affect the performance of MEMS devices and becomes one of the most fundamental problems in MEMS research. Due to the diversity of MEMS devices, each new MEMS device almost needs a totally new and particular packaging method.

2.2

MEMS actuators

A microactuator is the key device for the MEMS to perform physical functions. They are maybe required to drive the resonator to oscillate at their resonant frequencies. They could be needed to produce the mechanical output based on the particular microsystems: they maybe drive

10

micromirrors as a scanner or a switch; they also could actuate micropumps for microfluidic systems. Because of the scaling consideration, the electromagnetic force that is most commonly used in macro actuators is not the only driving force for microactuators [32].With the efforts of researchers, more and more different actuation principles, such as electrostatic force, thermal expansion, piezoelectric force, and shape memory alloys, have been used to design various structures for specific applications. This results in the fact that more and more different, powerful and fancy microactuators have been designed, fabricated, and applied [34]. A brief introduction is given to the microactuators according to their different actuation principles.

2.2.1

Electrostatic actuators

For a simple parallel-plate style electrostatic microactuator, the electrostatic force is created by applying the voltage across the two plates. The schematic diagram of this kind of electrostatic microactuator is shown in Figure 2-2. Usually the two plates are separate by dielectric material

+ + + + + + +

V - - - - - - - -

Figure 2-2: The schematic diagram of electrostatic microactuator such as air. The force generated by applying a voltage can be given by F =

V 2 ∂U 2∂d

where F is the electrostatic force, V is the applying voltage, d is the distance between the two plates, U is the energy stored in the two-plate capacitor, which can be obtained by

CV 2 2 ,

and

C is the capacitance. The electrostatic microactuator is one of the most popular microactuators in MEMS applications. The well-known electrostatic microactuators include comb-drive microactuators [35],

11

and wobble micromotors [36]. Figure 2-3 shows scanning electron microscope (SEM) pictures of these two electrostatic microactuators.

(b)

(a)

Figure 2-3: (a) Comb-drive electrostatic microactuator. [2] (b) electrostatic micromotor [2] From the fabrication point of view, the electrostatic microactuator can be easily integrated on a chip because all fabrication processes are compatible with traditional IC fabrication. Since there is no current consumption during actuation, the electrostatic microactuator consumes no power. But in order to have a large deflection or force, high actuating voltage is needed. Also, hysteresis makes the electrostatic microactuator hard to control.

2.2.2

Thermal actuators

Thermal actuation has been extensively employed in MEMS. It includes a broad spectrum of principles such as thermal pneumatic, shape memory alloy (SMA) effect, bimetal effect, mechanical thermal expansion, etc. [31]. The thermal pneumatic microactuator uses thermal expansion of a gas or liquid or the phase change between liquid and gas to create the actuation. As shown in Figure 2-4, a thermal pneumatic actuator is made of a cavity that contains a volume of fluid with a thin membrane as one wall. Current passed through a heating resistor causes the liquid in the cavity to expand and deform the membrane. Shape memory alloy effect occurs in some alloys in which a reversible thermal mechanical transformation of the atomic structure of the metal happens at a certain temperature. At low temperature, the SMA is kept at the desired deformed shape. When the temperature rises above a threshold value, the deformed SMA is transformed back to the original shape. A

12

Liquid

Heat element

Cavity

Figure 2-4: The schematic diagram of thermal pneumatic microactuator thermal bimetallic microactuator consists of two different materials that are layered together. Figure 2-5 shows a cantilever bimetallic structure. When it is heated, a deflection is generated by the different thermal expansion between the two materials. The more different the two materials’ thermal expansion coefficients, the more deflection is generated. The principle of the Metal layer

Elastic layer

Figure 2-5: The thermal bimetallic microactuator with the cantilever prototype mechanical thermal expansion microactuator is similar to that of the bimetallic microactuator. The only difference is that the mechanical thermal expansion microactuators are made of the same material. The operation procedure of mechanical thermal expansion microactuators will be explained in detail in Chapter 3 and 4. Thermal actuators can generate relatively large force and displacement at low actuating voltage. The deflection can linearly increase as the control voltage is increased within a large 13

range. Mechanical thermal expansion actuator and bimetallic actuator also can be integrated in a chip easily. However the high power consumption and low switching frequency are concerns for applications of thermal actuators.

2.2.3

Other actuators

Other actuators such as magnetic actuators and piezoelectric actuators have also been developed for some special applications [37], [38]. Microactuators are often fabricated by electroplating techniques, using nickel or its compositions. Since nickel is a ferromagnetic material, it can be used in actuators by using the electromagnetic effect. The principle of the piezoelectric actuator is based on the inverse piezoelectric effect. When a voltage is applied to an asymmetric crystal lattice, the material will be deformed in a certain direction. Although these two actuators can provide large forces, the fabrication process needs to be further developed.

2.3

Micromachining techniques

The motivation for micromachining MEMS devices is the same as for integrated circuits: microfabrication allows miniaturization and parallel processing which leads to inexpensive fabrication in large quantities. This can be used to make cheap products, large arrays, integrated systems and devices with the functions that cannot be realized with traditional technologies. Micromachining is the set of design and fabrication tools that precisely machine and form structures and elements at a scale well below the limits of human perceptive capability−the microscale. Micromachining is the underlying foundation of MEMS fabrication, and a key factor for MEMS processes. In general, micromachining is such a process that selectively etches away parts of the silicon wafer or adds new structural layers to form the mechanical and electromechanical devices. The well-established integrated circuit (IC) industry played an important role in fostering an environment suitable for the development and growth of micromachining technologies. Many tools and processes used in the design and micromachining of MEMS products are borrowed from the IC technology. Bulk and surface micromachining are two basic and major microma-

14

chining techniques. Wafer bonding can be used as the post process of bulk micromachining. LIGA (lithographe, galvanoformung, abformung) has been used in high-aspect ratio applications. In some special applications, the substrate is required to have some particular properties which silicon does not have. The flip chip technique is applied to solve this problem. The goal of this section is to briefly introduce these basic micromachining techniques.

2.3.1

Bulk micromachining

The bulk micromachining technique is one of the most popular micromachining techniques. The term bulkmicromachining comes from the fact that this type of micromachining is used to realize micromechanical structures within the bulk of a single crystal silicon wafer by selectively removing (‘etching’) wafer material. Bulk micromachining allows selective removal of significant amounts of silicon from a substrate to form three dimensional mechanical structures such as membranes, trench holes and so on (Figure 2-6). The crystal orientation of the wafer plays a

Figure 2-6: Various Bulk-micromachining Structures[3] decisive role. Different etchants such as solutions of potassium hydroxide (KOH), hydrazinewater have different etching rates in different crystal orientations of silicon [9], [39]. A high aspect ratio can also be reached for micromechanical components that can be formed directly

15

from the silicon wafer. Although bulk micromachining is a mature technique, it has some fundamental limitations. For instance, the wafer’s crystallographic planes determine the maximum obtainable aspect ratios. The higher aspect ratios can requires larger sizes as compared with other micromachining techniques. Also, it is difficult to get complex structures from bulk micromachining. One approach to solve this problem is the wafer bonding technique.

2.3.2

Wafer bonding

Bulk micromachining has the limitation in forming complex three dimensional microstructures in a monolithic format. One of the solutions is through the separate fabrication of the various elements of a complex system followed by subsequently assembling them. Wafer-to-wafer bonding is a technique that enables virtually seamless integration of multiple wafers. Wafer bonding for MEMS can be categorized into three major types: anodic bonding, intermediatelayer bonding-assisted bonding and direct bonding [31]. Anodic bonding is usually established between a sodium glass and silicon for MEMS. A voltage is applied between the glass and silicon, and at the same time, the heater also provides the bonding temperature around 180~500 0 C. During the bonding process, a new strong and hermetic chemical bond is formed between the glass and silicon. Intermediate layer assisted bonding requires an intermediate layer that can be metal, polymer, solders, glass, etc., to fulfill the bonding between wafers [40]. Direct bonding is also called silicon fusion bonding, which is used for silicon wafer to silicon wafer bonding. This type of bonding is based on the chemical reaction between OH-groups present at the surface of native silicon or grown oxides covering the wafers [41].

2.3.3

LIGA

With the development of the MEMS technologies, complex microstructures that are thick and three dimensional are required. Therefore, research and effort of micromachining techniques are directed towards achieving high aspect ratio and three dimensional devices. LIGA process is one of those micromachining techniques. LIGA is an acronym for lithography, electroforming and micromolding (in German, litho16

graphe, galvanoformung, abformung). The LIGA process is a technique for fabrication of three-dimensional microstructures with high aspect ratios having heights of several hundred micrometers, which is not possible with silicon-based micromachining techniques. With the LIGA process it is possible to make more complex microstructures and to work in the third dimension. Different plastics, metal ceramics or combinations of these can be used in connection with the LIGA process in order to produce difficult and complex structures. A schematic diagram of the LIGA process is shown in Figure2-7.

Figure 2-7: the schematic diagram of LIGA process [3]

2.3.4

Surface micromachining

Unlike bulk micromachining, surface micromachining does not remove material from the bulk silicon, but constructs structures on the surface of the silicon wafer by adding (“depositing”) thin films. A thin film is deposited wherever either an open area or a free-standing mechanical structure is desired, is called a sacrificial layer. The thin film out of which the free-standing structure is made, is called the structure layer. Finally the given mechanical structure is defined through removing the sacrificial layer and releasing the structure layer (Figure 2-8). Surface micromachining requires a compatible set of structural materials, sacrificial materials and chemical ethants. First of all, these materials have to be suitable for the application. Then, for the structure materials, they must have good mechanical properties such as high yield 17

Figure 2-8: Processing steps of typical surface micromachining [3].

18

and fracture stress, minimal creep and fatigue, also good wear resistance. The sacrificial materials also need good mechanical properties in order to prevent the devices from the fabrication process. The etchants have to have excellent etch selectivity, which means they have to etch the sacrificial materials quickly without affecting the structure materials. The dimensions of surface micromachined structures can be several orders of magnitude smaller than bulk micromachined structures. The surface micromachined devices are also very easy to integrate in IC circuits since the IC circuits are also made of the silicon wafer. As its name implies, surface micromachined devices are usually planar structures. The assembly process has to be added to build three dimensional devices.

2.3.5

Flip chip technique

Traditionally, flip chip technology is defined as mounting the chip to a substrate with any kind of interconnect materials and methods (e.g., fluxless solder bumps, tape-automated bonding (TAB), wire interconnects, conductive polymers, anisotropic conductive adhesives, metallurgy bumps, compliant bumps, and pressure contacts), as long as the chip surface (active area) is facing the substrate [42]. Flip chip components are predominantly semiconductor devices; however, with the development of flip chip technology, MEMS devices are also beginning to be used in flip chip form. The boom in flip chip technologies results not only from flip chip’s advantages in size, performance, flexibility, reliability and cost over other technologies, but also from the widening availability of flip chip materials, equipment and devices. Using flip chip technologies in MEMS devices, performances can be greatly improved because of the following advantages: • Smallest size: eliminating the packages and bond wires reduces the required area. • Highest electrical performance: eliminating bond wires reduces the delaying inductance and capacitance of the connection. (The inductance of a single solder bump is less than 0.05nH, compared to 1nH for a 125-um-long and 25-um-diameter wire [30]) • Greatest I/O density: unlike wire bonding which requires that bond pads are positioned on the periphery of the die to avoid crossing wires, flip chip allows the placement of bond pads over the entire die. 19

• Most rugged: flip chips are mechanically the most rugged interconnection method because they are solid little blocks of cured epoxy when completed with an adhesive underfill. Besides these general properties, flip chip technologies are attractive to the MEMS industry because of their abilities to integrate a system on a chip through packaging a number of different dies on a single substrate. One of the most attractive features of any MEMS fabrication service is the number of structural layers available to MEMS designers. Most MEMS fabrication processes have a limited number of structure layers because of time and cost issues. The more structure layers the process has, the longer time and more expensive the process needs. One of the most popular MEMS commercial foundries, Muti-User MEMS Processes (MUMPs), is only a threelayer surface micromachining polysilicon process [5]. It is the bottleneck for MEMS designers to design more complex structures. As one solution, flip chip technologies can give designers more room and more releasable layers to construct their designs. Flip chip technologies also can transfer MEMS devices to other substrates. This technique can be used to produce highly advanced micromechanical systems that are better suited to radio frequency (RF), microwave, or optical applications where specific material properties or additional structural layers are fatal [4]. Figure 2-9 illustrates the flip chip technique.The process starts with an unreleased MEMS device; gold transfer bumps are placed on all the transfer pads and one anchor pad. The transfer pads are only connected to the host substrate with the sacrificial SiO2 layer. When the SiO2 layer is dissolved in hydrofluoric acid (HF), the transfer pads and thus the MEMS devices are completely disconnected from the host substrate. Because of permanent connection to the host substrate, the anchor not only prevents the substrate from contacting the device after release, but also suspends the substrate to act as a shield during the release and drying process. Before bonding the MEMS devices to other substrates, the gold bumps on the MEMS host substrate are pressed against a smooth glass substrate. This pressing step is required to flatten any trailing wires from the top of the bump left by the wire-bonding machine. In addition, pressing the bumps provides better planarity across the bumps during the actual bonding. Then the entire structure is flip chip bonded to a target substrate. The silicon substrate is anchored at an anchor bump. Once released, the substrate can be removed sagely by using clamps to break the anchor without damage to the device. After bonding and releasing, the flip chip devices are rinsed in methanol to displace the HF in order to prevent HF further etching from within 20

Figure 2-9: The schematic diagram of flip chip process [4] the devices. After several minutes in a methanol rinse, the devices are super-critically dried in a special drying chamber that uses liquid CO2 to displace the methanol. Without this step, the evaporating methanol would pull devices downward into contact with the substrate and destroy the devices. After these steps, the MEMS device is transferred to another substrate successfully.

2.4

Micromachining foundry

The Multi-user MEMS processes or MUMPs is a three-layer polysilicon surface micromachining process derived from work performed at the Berkeley Sensors and Actuators Center (BSAC) at the University of California in the late 80’s and early 90’s. It is a commercial program that provides the international industrial, governmental and academic communities with costeffective, proof-of concept surface micromachining fabrication [5]. This process has the general features of a standard surface micromachining process as follows: • Polysilicon is used as the structure material, 21

• Deposited silicon oxide is used as the sacrificial layer, • Silicon nitride is used as electrical isolation between the polysilicon and the substrate, • Metal (usually gold) is the top layer of the device and can be used as conductive layer. Figure 2-10 shows the cross section of an electrostatic motor fabricated by the MUMPs process. This device includes all the layers that are available in the MUMPs process. In order

Figure 2-10: Cross section of MEMS motor fabricated by MUMPs [5] to make the process as general as possible, MUMPs process defines all the layers’ thickness and their functions. All MEMS designers have to follow these definitions and design rules. These definitions and design rules limit the designers to design more complex devices, but they make it possible for many different designs to be put on a single silicon wafer in one single fabrication process. Also, the standardization of the fabrication process reduces the fabrication cost and lets more and more designers submit their designs. In this thesis, all the actuators are designed by the following MUMPs design rules. Table 2.1 shows the main limitations of MUMPs process and a brief introduction of each layer’s function. The MUMPs process begins with 100 mm n-type silicon wafers of 1-2 Ω-cm resistivity. In order to prevent or reduce charge feed through to the substrate from electrostatic devices on the surface, these wafers are highly doped with phosphorus. Next, a 600 nm silicon nitride layer is deposited on the wafers as an electrical isolation layer. A 500 nm polysilicon film-Poly 0 is deposited right after this step. The poly 0 is the only layer that can not be released in the MUMPs process, so it is typically used as a ground plane or for routing purposes. Poly 0 is then patterned by photolithography, a process that includes the coating of the wafers with 22

Material Layer Silicon Nitride Poly0 First oxide First oxide Poly1 Second oxide Second oxide Poly2 Metal

Table 2.1: MUMPs process layers and their Properties Thickness Lithography level name Function 0.6 µm Insulator 0.5 µm Poly0 and hole0 Conductive layer 2.0 µm Dimple Release friction 2.0 µm Anchor1 fix poly1 on substrate 2.0 µm Poly1 and hole1 Structure layer 0.75 µm Poly1-poly2-via Connection with poly1 and poly2 0.75 µm Anchor2 fix poly1 on substrate 1.5 µm Poly2 and hole2 Structure layer 0.5 µm Metal and metal hole Conductive layer

photoresist, exposure of the photoresist with the appropriate mask and developing the exposed photoresist to create the desired etch mask for subsequent pattern transfer into the underlying layer. After the photolithography process, the poly 0 layer is etched in a special system. A 2.0 µm phosphosilicate glass (PSG) sacrificial layer is then deposited and annealed. The layer of PSG, known as First Oxide, will be removed at the end of the whole MUMPs process to free the first mechanical layer of polysilicon. This sacrificial layer can be patterned by photolithography with masks such as Dimple and Anchor 1. After patterning first oxide, the first structural layer of polysilicon (Poly 1) is deposited at a thickness of 2.0 µm. The polysilicon is lithographically patterned using a mask designed to form the first structural layer Poly 1. After Poly 1 is etched, a second PSG layer (Second Oxide) is deposited and annealed. The second oxide can be patterned by two different etch masks : Poly 1_Poly 2_VIA and Anchor 2, with different objectives. The Poly 1_Poly 2_VIA level provides the etch holes in the second oxide down to the Poly 1 layer in order to make mechanical and electrical connections between Poly 1 and Poly 2 layers. The second structural layer, Poly 2, is then deposited with 1.5 µm thickness. As Poly 1 patterned, Poly 2 structural layer is patterned by the second designed mask Poly 2. The Poly 1 and Poly 2 layers are the mechanical structural layers in MUMPs process because they both can be released by etching the first oxide and second oxide at the end of the process. A 0.5 µm metal layer is the final deposited layer in the MUMPs process. It provides for probing, bonding, electrical routing and highly reflective mirror surfaces. The metal layer is lithographically patterned by the mask named metal. The release process can be done by MEMS

23

designers in their own facility. The process of releasing chips is performed in the following steps. First chips are immersed in acetone for 3 minutes, and then in De-ionized (DI) water for 30 seconds. These two steps can strip photoresist off. After that, chips are put in the 49% HF etchant for 1.5-2 minutes to etch oxide away. This is followed by several minutes in DI water and then alcohol for 2 minutes to reduce friction followed by at least 10 minutes in an oven at 1100 C. Figure 2-11 shows the device after sacrificial oxide release.

Figure 2-11: Cross section of MEMS motor after releasing process [5]

24

Chapter 3

Two-hot-Arm Horizontal Thermal Actuator In this chapter, modeling of a two-hot-arm horizontal thermal actuator is documented. Finite element analysis and experiment results are also provided.

3.1

Introduction

A typical thermal actuator is shown in Figure 3-1. In the thermal actuator, the hot arm is usually thinner than the cold arm, so the electrical resistance of the hot arm becomes higher than the cold arm. When an electric current passes through the cold and hot arms, the heat generated in the hot arm is much more than that of the cold arm. It causes that the temperature of the hot arm to become much higher than the cold arm. Since the cold and hot arms are made of the same material and same thermal expansion coefficient, the temperature difference causes the hot arm to expand more than the cold arm. This results in the rotation of the actuator. Although traditional thermal actuators can generate much larger deflection than electrostatic actuators without the need of a high actuating voltage, there are still some limitations in traditional thermal actuators. Ideally, the flexure is expected to be as thin as possible. When the flexure becomes thinner, more deflection of the thermal actuator tip can be generated by the different thermal expansion between hot and cold arms. But, if the flexure is thinner than the hot arm, the temperature of the flexure could be higher than that of the hot arm which 25

anchor

cold arm

dimple

hot arm

direction of motion

flexture

Figure 3-1: A traditional thermal actuator (one hot arm) might result in over heating. Also, in order to keep it elastically deflecting, the flexure should be long enough. However, if the flexure is too long, the deflection of the thermal actuator tip will be reduced. Since the current passes through the flexure and the cold arm, the resistance of the flexure and cold arm also contributes to the actuator’s overall resistance. The power consumed in the flexure and cold arm does not contribute to the desired movement of the thermal actuator tip. Only power dissipated in the hot arm is directly transferred into the intended movement of the thermal actuator tip. Since the resistance of flexure and cold arm is comparable with the hot arm, the efficiency issue of electrical power consumption should be concerned. Some efforts have been directed at resolving these limitations of traditional thermal actuators and improving their efficiency. David M. Burns and Victor M. Bright designed a new thermal actuator which has two hot arms [43]. The two-hot arm thermal actuator is shown in Figure3-2. In this new thermal actuator, the electric current only passes through the outer and

outer hot arm

flexure

dimple

cold arm

inner hot arm

anchor

Figure 3-2: Schematic diagram of two-hot-arm thermal actuator inner hot arms. This avoids the cold arm and flexure to being part of the electric circuit. It dramatically increases the efficiency since all the power consumed in the actuator contributes to the deflection of the thermal actuator tip. The flexure can also be thinner than the hot arm because no current passes through the flexure. Obviously, the new two-hot arm thermal actuator has improved the limitations of the tra26

ditional one. As mentioned before, thermal actuators have been widely used in many MEMS applications; in order to reduce the design circle and simplify MEMS design work, modeling of this new two-hot arm thermal actuator is discussed in the following sections.

3.2 3.2.1

Electrothermal analysis Analytical solution

A diagram of the two-hot arm thermal actuator is shown in Figure 3-3 (a). The two-hot arm thermal actuator is usually fabricated by surface micromachining. The size of the cross section of the actuator is much smaller than the actuator length. So the electrothermal analysis of the two-hot arm actuator is generally simplified as a one dimensional problem [28]. The twohot arm thermal actuator shown in Figure 3-2 can be treated as two line shape microbeams connected in series. Figure 3-3 (b) shows the coordinate system for thermal analysis. Since the

Lg

Wh

Wc

Wf Lf

Lc L3 L2 L1

(a)

x=0

x=L1

x=L1+Lg

x=L1+Lg+L2

(b)

Figure 3-3: (a) Schematic top view of two-hot arm thermal actuator. (b) Simplified one dimensional coordinate system. current only passes through the outer and inner hot arms, the coordinate does not include the cold arm and flexure.

27

There are three mechanisms of heat flow: conduction, convection and radiation. Conduction is the transport of energy from high temperature to low temperature region. Convection is the heat transfer between the air and the solid interface when there is a temperature difference. Radiation is the energy emitted from a body due to its temperature [44]. According to the finite element analysis [23], heat dissipation through radiation to ambient can be neglected in comparison with heat losses through conduction to the anchor substrate which is considered as a heat sink, and heat losses through air to the substrate due to convection. As shown in Figure 3-4, the heat flow equation is derived by examining a differential element of the microbeam of thickness tsi , width wh , and length dx [28]. When the heat flow is under steady-state conditions,

wh

PolySi Air Si3N4

X

t si ta tn

X+dX text

Si

Figure 3-4: The schematic cross section of the actuator for thermal analysis resistive heating power generated in the element is equal to the heat conduction and convection out of the element ·

dT −kp wt dx

¸

·

dT + J ρwtdx = −kp wt dx x 2

¸

x+dx

+

Sdxw(T − Ts ) RT

(3.1)

where T and Ts are the beam and substrate temperatures, respectively; kp is the thermal conductivity of polysilicon, J is the current density, ρ is the resistivity of polysilicon, and S is the shape factor which accounts for the impact of the shape of the element on heat conduction to the substrate [45]. This geometric factor represents the ratio of heat loss from the sides and bottom of the beam to the heat loss from the bottom of the beam only. RT is the thermal resistance between the polysilicon microbeam and the substrate if the microbeam is wide enough 28

[28]. The thermal resistance, RT , is given by: ta tn + kv kn

RT =

(3.2)

where ta and tn are the thickness of air above the nitride and the thickness of nitride on the substrate, respectively, and kv and kn are the thermal conductivity of air and nitride, respectively. The shape factor, S , is given by [45] S=

tsi ta (2 + 1) + 1 wh Tsi

(3.3)

where tsi is the thickness of the polysilicon and wh is the width of the hot arm. Usually, the resistivity ρ is related to the temperature of the polysilicon. The resistivity can be assumed here to have a linear temperature coefficient, ξ , so the resistivity becomes a function of temperature ρ = ρ0 [1 + ξ(T − Ts )]

(3.4)

where ρ0 is the resistivity of polysilicon at room temperature. The current density can be written as J=

V ρL

(3.5)

where V is the voltage applied to the outer and inner hot arm, L is the length of the polysilicon that current passes through. After taking the limit as dx → 0 in Equation (3.1) and simplifying the results, the following equation is produced d2 T S(T − Ts ) J 2 ρ − = dx2 kp RT t kp

(3.6)

Substituting Equations (3.5) and (3.4) into Equation (3.6), the final equation for the thermal model is found to be d2 T V2 1 S(T − Ts ) − = 2 2 dx kp RT t L ρ0 kp 1 + ξ(T − Ts )

(3.7)

In the following we linearize Equation (3.7) and derive its analytical solution. In Equation (3.7), the second term of the right hand side is nonlinear. After using the Taylor series expansion and

29

dropping all therms except the first two, Equation (3.7) becomes d2 T V2 S(T − Ts ) − = [1 − ξ(T − Ts )] dx2 kp RT t L2 ρ0 kp In order to simplify the above equation, some variables have been changed and the above equation is rewritten as: d2 T = A2 Tθ − B dx2

(3.8)

where Tθ = T − Ts B= A2 =

V2 L2 ρ0 kp

S + Bξ kp RT t

Solving Equation (3.8) and applying the solution to the outer and inner hot arms, the temperature distribution of the outer and inner hot arms is obtained. Equation (3.9) is the temperature distribution of the outer hot arm and Equation (3.10) is the inner hot arm temperature distribution T1 = Ts +

B1 + C1 eA1 x + C2 e−A1 x A21

(3.9)

T2 = Ts +

B2 + C3 eA2 x + C4 e−A2 x A22

(3.10)

where Ci (i = 1 to 4) are some constants to be obtained. B1 and A1 are the same as B and A, respectively, except that L is replaced by L1 , V is replaced by V1 and w is replaced by wh . B2 and A2 are also the same as B and A, respectively, except that L is replaced by L2 , V is replaced by V2 and w is replaced by wh . V1 and V2 are the voltages across the outer hot arm and inner hot arm, respectively. They can be given by V1 =

V (L1 + Lg ) L1 + L2 + Lg

V2 =

V L2 L1 + L2 + Lg

Figure 3-5 shows the boundary conditions that are needed to solve constants Ci . The qi 30

q1 q2

Tm q3

Ts

Figure 3-5: The schematic diagram of boundary conditions (i = 1 to 3 ) are the rates of heat conduction, Tm is the temperature of the joint between the outer and inner hot arms. The anchor pads can be assumed to have the same temperature as the substrate. According to the continuity of the temperature and rate of heat conduction, five boundary conditions are obtained for Equations (3.9) and (3.10). They can be written in matrix form as: A×C =B

(3.11)

where 

     A=    

1

1

0

0

0

0

0

1

1

0

eA1 (L1 +Lg )

e−A1 (L1 +Lg )

0

0

−1

0

0

eA2 L2

e−A2 L2

−1

A1 eA1 (L1 +Lg ) −A1 e−A1 (L1 +Lg ) A2 eA2 L2 −A2 eA2 L2 −R_cold 

1 −B A21

   − B2  A22   B =  −Ts − B12 A1   2  −Ts − B A22  −Ts R_cold

31

           

          



c1

   c2   C =  c3    c4  Tm

          

and R_cold is the thermal resistance of the cold arm of the thermal actuator. It can be calculated by R_cold =

π h 2wh ln w wc

Equation (3.11) is written in matrix format so that the thermal problem can be solved in the same way. For the given process parameters such as ρ0 and ξ, material properties parameters and drive voltage, the temperature distribution along the outer and inner hot arm can be obtained from Equations (3.9) to (3.11).

3.2.2

Simulation results

To simulate the temperature distribution of the two-hot arm thermal actuator, the parameters in [28] and [5] have been used. All the parameters are listed in Tables 3.1 and 3.2. Table 3.1: Material Material Properties Young’s modulus E Poisson’s ratio v Thermal expansion coefficient K Thermal conductivity of polysilicon kp Thermal conductivity of air kv Thermal conductivity of nitride kn Resistivity of polysilicon ρ0

Properties Value 162 × 109 0.22 4.7 × 10−6 41 × 10−6 0.026 × 10−6 2.25 × 10−6 20

Unit Pa C −1 W · µm−1 · C −1 W · µm−1 · C −1 W · µm−1 · C −1 Ω · µm

R °

The analytical result is calculated by Matlab . Figure 3-6 shows the temperature distribution along the outer and inner hot arms for the specified input voltage. From the figure, the maximum temperature appearing in the middle of the outer hot arm is clearly shown. At the middle of the inner hot arm, the temperature is a little bit lower than the maximum temperature because the length of the outer hot arm is longer than that of the inner hot arm, which means the resistance of the outer hot arm is bigger than that of the inner hot arm. Since the outer hot 32

Table 3.2: Geometrical data of the two-hot-arm thermal acutator Geometrical data Value Unit The length of the outer hot arm L1 252 µm The length of the inner hot arm L2 220 µm The length of the cold arm Lc 162 µm The length of the flexure Lf 38 µm The length of the gap Lg 2 µm The thickness of polysilicon tsi 2 µm The thickness of air ta 2 µm The thickness of nitride tn 0.6 µm

550 Vb=5v

Temperature (K)

500

450

400

350

300

0

50

100

150

200

250

300

350

400

450

500

Position of outer and inner hot arm (µ m)

Figure 3-6: The analytical result of temperature distribution along the outer and inner hot arms

33

and inner hot arms are both connected to the anchor, the temperature at those points are equal to the substrate temperature T s. At the joint point between the outer hot arm and inner hot arm, the temperature has a great jump. This is because the cold arm is also connected at that point. The cold arm becomes a heat sink and brings the temperature down. The numerical R °

result is generated by a commercial software Coventorware

MemETherm solver. This solver

can compute the thermal field and the electrical potential resulting from an imposed voltage or current flow through a resistive material. In this simulation, three different physical domain boundary conditions, electrical, thermal and mechanical, are applied. In the electrical boundary condition, the actuating voltage is applied across the outer and inner hot arms. All of the three anchors are set to the substrate temperature for the thermal boundary conditions since they are connected to the substrate. For the mechanical boundary conditions, these three anchors are also fixed in all directions. The simulation result is shown in Figure 3-7. Obviously, the

Figure 3-7: The numerical result of temperatue distribution of the two-hot arm thermal actuator. analytical results of the temperature distribution for the two-hot arm thermal actuator have good agreement with the numerical simulation results. The error of the maximum temperature between them is less than 10%. In Figure 3-7, the temperature of the cold arm is almost the same as the substrate temperature, which agrees with the physical meaning. The maximum temperature as a function of the input voltage is shown in Figure 3-8. It clearly shows that the maximum temperature increases with the input voltage and the analytical result interpreted 34

R °

here is in good agreement with the numerical result obtained from Coventorware .

Max temperature vs Voltage 1300 Analytical results Simulation results

1200 1100

Maximum Temperature (C)

1000

900 800 700 600 500

400 300

0

1

2

3

4

5

6

7

8

9

10

Voltage (V)

Figure 3-8: Maximum temperature as a function of input voltage: Comparison between analytical and simulation results.

3.3 3.3.1

Mechanical analysis Analytical solution

As the operating principle of the two-hot arm thermal actuator explained before, it is essential to know the linear thermal expansion of the outer and inner hot arms in order to find the mechanical deflection of the actuator. The temperature distribution of the outer and inner hot arms has been obtained from Equations (3.9) and (3.10), respectively. Based on that, the linear thermal expansion of the outer hot arm ∆L1 , inner hot arm ∆L2 and the gap ∆Lg can be given by: ∆L1 = α

Z

0

L1

(T1 − Ts )dx = α(

B1 C1 A1 L1 C1 C2 −A1 L1 C2 L1 + e − − e + ) A1 A1 A1 A1 A21

35

(3.12)

Z

L2

B2 C3 A2 L2 C3 C4 −A2 L2 C4 L2 + e − − e + ) 2 A2 A2 A2 A2 A2 0 · ¸ Z L1 +Lg B1 C1 A1 L1 C2 −A1 L1 A1 Lg ∆Lg = α (T1 − Ts )dx = α L + ( e − e )(e − 1) g A1 A1 A21 L1 ∆L2 = α

(T2 − Ts )dx = α(

(3.13)

(3.14)

where α is the thermal expansion coefficient of the polysilicon. The structure of the two-hot arm thermal actuator shown in Figure 3-2 is similar to a plane-frame structure with three fixed bases for elastic structure engineering. Deflection analysis of such structures has been well documented in [46]. Deflection analysis of the one-hot arm has also been done by using the force method [24]. The force method is applied to analyze the bending moment of the actuator due to the thermal expansion. The two-hot arm thermal actuator is a statically indeterminate structure with the degree of the indeterminacy of 6. Each constraint can be released and replaced by two forces and one moment in the directions of Xi (i = 1 to 6). The six redundants are shown in Figure 3-9 (a). Following the force method [46], the six redundants Xi (i = 1 to

X3 X2

X6 X1

X5 X4

(a)

L1 P=1 (b)

Figure 3-9: (a) The plane frame structure simplified for the thermal actuator with six redundants. (b) The bending moment of the outer hot arm due to the virtual force

36

6) can be obtained by solving a set of simultaneous equations:              

f11 f12 f13 f14 f15 f16



  f21 f22 f23 f24 f25 f26     f31 f32 f33 f34 f35 f36      f41 f42 f43 f44 f45 f46     f51 f52 f53 f54 f55 f56   f61 f62 f63 f64 f65 f66

X1





∆Lg

    X2   ∆L1 − ∆L2     X3   0 =    X4  ∆Lg      X5  ∆L1   X6 0

             

(3.15)

where each item of the right hand side of Equation (3.15) represents the displacement of Xi in their own direction. For example, ∆Lg is the displacement of the force X1 in the X1 direction. fij represents the flexibility coefficient which is defined as the deflection at i direction due to the unit force acting in the j direction. It can be found by diagram product of the bending moments due to respective six unit redundants, Xi (i = 1 to 6 ). f11 is shown as an example to calculate those coefficients. As we mentioned, the subscript of each flexibility coefficient includes two directions: the deflection direction and the force direction. The first step to calculate the flexibility coefficient is to draw the bending moment diagrams caused by two unit forces acting at these two directions, respectively. Figure 3-10 shows the bending moment diagrams. For the flexibility coefficient f11 , the deflection and force directions are the same, so the bending moment diagrams of these two unit forces are also similar to each other in the figure. After the bending moment diagrams are drawn, each element’s bending moment is calculated, i.e. each hatched area in Figure 3-10 (a). For element 1, the hatched area is 12 L22 . Then, we need to find the bending moment with regards to each hatched center point in Figure 3-10 (b). For element 1, it is 23 L2 . Finally, for each element, we should multiply these two items together, and sum all the elements together to get the flexibility coefficient f11 f11 =

1 L32 L3 + L22 Lg + 1 + L22 L1 − L21 L2 ) ( EIh 3 3

37

(3.16)

(1)

X1

(a)

(1)

X1

(b)

Figure 3-10: (a) The bending moment diagram of a unit force in the deflection direction (b) The bending moment diagram of a unit force in the force direction. The following equations give the other flexibility coefficients’ expression: f21 = −

1 (2L1 L2 Lg + L2 L2g − L21 Lg ) 2EIh

f31 = − f41 =

1 (L1 L2 + L2 Lg + L22 − L21 ) 2EIh

1 (2L31 − L21 L2 + 2L2 Lg L3 + 2L2 L1 L3 − L21 L3 ) 2EIh f51 =

1 (2L21 Lg − 4L1 L2 Lg − 3L2g L2 ) 2EIh

f61 = −

1 (2L1 L2 + 2L2 Lg − L21 ) 2EIh f12 = f21

f22 = f32 =

¢ 1 ¡ 3L1 L2g + L3g 3EIh ¢ 1 ¡ 2L1 Lg + L2g 2EIh 38

f42 =

¢ 1 ¡ 2L3 L1 Lg − L2g L2 − L21 Lg 2EIh f52 = f62 =

2L1 L2g EIh

¢ 1 ¡ 2L1 Lg + L2g 2EIh

f13 = f31 ; f23 = f32 f33 = f43 =

1 (L1 + L2 + Lg ) EIh

1 (L2 − L1 L3 − L3 Lg ) 2EIh 1

f53 =

1 (3L2g + 4L1 Lg ) 2EIh

f63 =

1 (L1 + Lg ) EIh

f14 = f41 ; f24 = f42 ; f34 = f43 f44 =

L3f 3EIf

+

Lc (L3 + Lf )(2L3c + 6Lc Lf L3 ) 1 + (6L23 Lg + L31 + 3L1 L23 − 3L3 L21 ) 2 2EIc (3Lc + 6Lc Lf ) 3EIh f54 = −

f64 = −

L2f 2EIf

−

1 (2L1 Lg L3 + 2L2g L3 − L21 Lg ) EIh

Lc (L3 + Lf ) 1 − (4L3 Lg − L21 + 2L1 L3 ) 2EIc 2EIh

f15 = f51 ; f25 = f52 ; f35 = f53 ; f45 = f54 ; f55 = f65 =

4L2g L1 8L3g + EIh 3EIh

1 (2Lg L1 + 2L2g ) EIh

f16 = f61 ; f26 = f62 ; f36 = f63 ; f46 = f64 ; f56 = f65 f66 =

Lf 1 Lc (L1 + 2Lg ) + + EIh EIf EIc

(3.17)

In the above equations, E is the Young’s modulus of polysilicon, Ih , Ic and If are the moment of inertia for the hot arm, cold arm and the flexure, respectively. Once the six redundants are obtained, the deflection of the actuator tip can be calculated by the virtual work method [46]. 39

A virtual force P is applied to the free end of the actuator normal to the hot arm. The bending moment of the outer hot arm due to the virtual force is shown in Figure 3-9 (b). The bending moment due to the virtual force as a function of the position of the outer hot arm is given by M = (L1 − x)P

(3.18)

The bending moment of the outer hot arm due to the thermal expansion, i.e. the moment of the outer hot arm due to the six redundants, can be represented as

M=

2 X

Mi

(3.19)

i=1

M1 = X1 x + X1 (L2 − L1 ) − X2 Lg − X3 M2 = X4 x + X4 (L3 − L1 ) − 2X5 Lg − X6 where M1 is the bending moment of the outer hot arm caused by the redundants X1 , X2 and X3 , and M2 is the bending moment of the outer hot arm caused by the redundants X4 , X5 and X6 . M is the total bending moment of the outer hot arm caused by the thermal expansion. According to the method of virtual work [46], the deflection in the free end of the actuator can be written as u=

Z

L1

MM 1 Ma L31 L1 Ma − Mb 2 + L1 + L21 Mb ) dx = (− EIh EIh 3 2

(3.20)

where Ma and Mb are the variables that can be explained by the following equations:

3.3.2

Ma = X1 + X4

(3.21)

Mb = X1 (L2 − L1 ) − X2 Lg − X3 + X4 (L3 − L1 ) − 2X5 Lg − X6

(3.22)

Simulation results

R ° The mechanical analysis is simulated by Coventorware with MemETherm solver. The ana-

lytical and numerical solutions of the deflection as a function of the input voltage are shown in

40

Figure 4-12. It is clear that good agreement is achieved. One thing that should be highlighted

12

Analitical Results Simulation Results

10

Displacement ( µ m)

8

6

4

2

0

1

2

3

4

5

Voltage (v)

6

7

8

9

Figure 3-11: Deflection of the actuator tip as a function of input voltage here is when the input voltage is increased, the analytical results cannot accurately predict the numerical results anymore. The reason is that at high working voltage, the temperature of the actuator becomes extremely high and nonlinear effects become more important. The first two terms of the Taylor series of the nonlinear part in Equation (3.7) is not accurate enough to represent the whole nonlinear part. It should be also noted that at that high working voltage, the temperature of the actuator is almost equal to the melting point of the material, and therefore the operating voltage of the thermal actuator is usually much lower than that voltage. Furthermore, the inner and outer hot arms may touch each other [43] at high actuating voltage due to large deflection as seen in Figure 3-12. At 10v, the two-hot arm thermal actuator has more than 10 µm deflection and the touching between the outer and inner hot arms is found in the box shown in the figure.

41

Figure 3-12: Numerical result of the deflection of two-hot-arm thermal actuator with 10v input voltage

3.4

Fabrication process and experiments

The two-hot arm thermal actuator presented here has been fabricated using the 44th production run of the Multi-User MEMS Processes (MUMPs). The whole thermal actuator is constructed out of one polysilicon layer, here polysilicon-1 layer is used. In order to reduce the friction effect, dimples are used on the cold arm to reduce the amount of polysilicon in direct contact with the silicon nitride layer. A deflection meter is also placed in front of the tip of the two-hot arm thermal actuator to make it easy to measure the deflection (Figure 3-13). After the chips

Dimple

Deflection Meter

Figure 3-13: Deflection meter coupled to a two-hot-arm thermal actuator arrived, HF release process was done to release thermal actuators out of the substrate. This process was proceeded in the clean room of the University of Waterloo. Figure 3-14 shows the scanning electron micrograph (SEM) of the whole chip. 42

Figure 3-14: Overview of the whole chip after HF release.

43

In this experiment, a power supply with at least 15V (DC) tuning range was needed to provide the actuating voltage. Two DC probes were employed to add the actuating voltage on the thermal actuators. In order to capture the deflection of the thermal actuator at each actuating voltage, a CCD camera was installed on the top of the probe station. When the power supply was tuned from 2 volts to 11 volts, the camera was used to record pictures of the deflection of the actuators at each voltage. The exact deflection of the thermal actuator at any actuating voltage was then obtained by enlarging the picture at the deflection zone. A SEM of deflection meter is also provided to compare with these pictures in order to increase the accuracy. Figure 3-15 shows the experimental equipment.

Figure 3-15: Experiment equipment for measuring the deflection of thermal actuators The experimental data is plotted in Figure 3-16 . Comparing with the analytical and numerical results, a good agreement is achieved.

3.5

Discussion

In Figure 3-12, the simulation results show that the outer and inner hot arms could touch each other at high actuating voltage. This phenomenon has been seen during the experiments. 44

14 analitical result test simulation

12

Deflection um

10

8

6

4

2

0

1

2

3

4

5

6 Voltage

7

8

9

10

11

Figure 3-16: Comparison of experimental result with the analytical and numerical results Figure 3-17 shows the touching of the outer and inner hot arms when the actuator is subjected 9.0v voltage. Another interesting phenomenon that was observed in the experiments was that

Figure 3-17: The touching of the outer and inner hot arms at high actuating voltage the touching of the two hot arms occured, the thermal actuator was not able to move back to its original place even without any actuating voltage. When the voltage was applied again, the thermal actuator moved to the same distance as before. After zooming at the middle of the two hot arms, a curve was found in the inner hot arm (Figure 3-18 ). This curve could be the reason for the fact that the thermal actuator had undergone plastic deformation. As a result, the inner hot arm becomes shorter and draws the thermal actuator to move down a little bit 45

Figure 3-18: A curve found in the inner hot arm as seen in SEM as seen in the tests. A traditional thermal actuator can operate in two modes [6]. Figure 3-19 shows both modes of operation for the actuator. In the basic mode, the thermal actuator is operated as described before. The back-bent mode occurs after the driving current is increased above the level required for the maximum deflection resulted in a reshaping of the hot arm. After reshaping, the hot arm is shorter than its original length and therefore the thermal actuator moves to a negative position. A back-bent thermal actuator still can be used as a traditional thermal actuator except the zero-deflection position has been shifted. For the two-hot arm thermal actuator, back bending is also found in the experiments, when we applied 11v voltage and removed the voltage after a few seconds. Figure 3-20 shows the back bending of the two-hot arm thermal actuator. At high actuating voltage, two different phenomena are found: the touching of the two hot arms and back bending. Both of them are not desirable for most thermal actuator applications. One of these two problems’ solutions is to create an accurate model. According to the model, we should keep the thermal actuator’s working voltages far away from those “dangerous” voltages. Fabrication tolerance also should be concerned. For example, when we do the HF release, the time we put the chips in the HF etchant can affect the final geometry of thermal actuators dramatically. Further experiments are needed to be proceed to achieve average fabrication 46

Figure 3-19: Two modes of the traditional thermal actuator operation [6].

Figure 3-20: Back bending of the two-hot-arm thermal actuator

47

tolerance. Figure 3-21 shows the over etching during the HF releasing process. The teeth of the deflection meter should be rectangular, but they become rounded after etching.

Over etching

Figure 3-21: Over etching of the teeth of the deflection meter.

48

Chapter 4

Bidirectional Vertical Thermal Actuators In this chapter, a novel bidirectional vertical thermal actuator is designed. Thermal analysis and mechanical analysis are presented. The numerical simulation results obtained from R ° Coventorware are also provided to compare with the analytical results. Good agreement is achieved.

4.1

Mechanical design

The horizontal thermal actuator discussed in the previous chapter was operated by different thermal expansions between the hot and cold arms. The same hot and cold arms structure can also be used to create a vertical thermal actuator that can have the motion perpendicular to the substrate. One version of a vertical thermal actuator is shown in Figure 4-1 [22]. In the traditional vertical thermal actuators, the hot arm is above the cold arm and is separated by an air gap. At one end, the arms are connected together with a via, while at the other end, they are anchored separately on the substrate. The flexure connects the cold arm to the anchor to finish the current pass. The driving current passes through the hot and cold arms and results in the generation of thermal energy. Similarly, as the horizontal thermal actuator, the hot arm is thinner than the cold arm, so the hot arm has a higher electrical resistance and thermal resistance. The hot arm thus has a larger thermal expansion than the cold arm. As the hot 49

via

hot arm cold arm gap

flexure

anchor

Figure 4-1: 3D schematic view of a vertical thermal actuator showing a cross section through the hot and cold arm.[7] arm expands, it drives the tip of the vertical actuator downward towards the substrate. The traditional vertical thermal actuator can also be designed for upward motion, however, both motions cannot be achieved by one actuator. Obviously, the traditional vertical thermal actuators have the same limitations as those of the traditional horizontal thermal actuators. Theoretically speaking, the thinner the flexure, the larger the deflection of the tip of the vertical thermal actuator. But the flexure cannot be thinner that the hot arm, otherwise the temperature of the flexure is higher than that of the hot arm. Also, the power consumed by the cold arm has no contribution to the deflection of the tip of the actuator. In this work, research has been directed towards improving the traditional vertical thermal actuator shown in Figure 4-1, and it has resulted in a novel Ushape bidirectional vertical thermal actuator depicted in Figure 4-2. This new vertical thermal actuator (VTA) can either bend upward or downward without any modification. The bending direction of the new VTA depends on where the voltage is applied. When the voltage is applied across anchors 1 and 2 in Figure 4-2, the current only goes through the top layer, and it expands due to the increase of its temperature. Thus, the

50

anchor 3 anchor 1 flexure top layer

via

anchor 4 bottom layer anchor 2

Figure 4-2: 3D View of the U-shaped vertical thermal actuator actuator’s tip is deflected downward to the substrate. For deflecting the actuator upward, the voltage is simply switched from anchors 1 and 2 to anchors 3 and 4. The U-shape VTA is more electrically efficient than the traditional actuator since no electrical power is wasted in the cold arm when the U-shape vertical actuator is operated. This bidirectional motion indicates that the new vertical thermal actuator has almost twice amount of displacement compared to the conventional VTA at the same size. In the following sections, electro-thermal and mechanical analysis of the U-shape vertical thermal actuator are presented. Simulation results are also provided with which the design process could be simplified significantly

4.2 4.2.1

Electrothermal analysis Analytical solution

A schematic top view diagram of the U-shape VTA is shown in Figure 4-3. Since the U-shape VTA is fabricated by using surface micromachining, the electro-thermal analysis of the U-shape VTA can be simplified as one dimensional heat transfer problem similar to the thermal analysis of the two-hot arm thermal actuator. As mentioned in the above section, when the U-shape VTA is operated, the current only passes through one layer of the actuator. In the following analysis, the current is assumed to pass through the top layer of the actuator. The actuator 51

Wb2 Wb1 Lb2

Lb1

Le

W2 W1 L1 L2

Figure 4-3: 2D schematic top view of the U-shape VTA shown in Figure 4-2 can be seen as several microbeams connected in series. The coordinate system for the thermal analysis is shown in Figure 4-4. In this coordinate system, there are five microbeams connected to each other. The two short and long bars of the microbeams have the same dimensions. In order to simply the analysis, the two short bars are numbered as element 1, the two long beams are named as element 2, and the connection between two long beams is shown as element 3. The thermal analysis of the U-shape VTA is similar to the thermal analysis of the two-hot arm thermal actuator. Only the heat loss through conduction and convection is concerned, and the heat that is dissipated through radiation to the ambient is neglected based on the previous finite element analysis [23]. As seen in Chapter 3, the heat flow equation can be derived from a differential element of the microbeam shown in Figure 4-5. Under steady-state conditions, ohmic power generated in the element is equal to heat conduction and convection out of the element

·

dT −kp wt dx

¸

·

dT + J ρwtdx = −kp wt dx x 2

¸

x+dx

+

Sw(T − Ts )dx RT

(4.1)

The definitions of parameters in Equation (4.1) are similar to those in Equation (3.1). Using

52

element 1

element 2

X=Lb1

element 3

X=Lb1+L1

X=Lb1+ 2L1+Le

X=Lb1+ L1+Le

X=2Lb1+ 2L1+Le

Figure 4-4: Simplified one dimensional coordinate system

PolySi2 Air PolySi1 X

t p2 Lg tp1 tv tn

X+dX

Air Si3N4

text

Si

Figure 4-5: Schematic cross section of the VTA for thermal analysis

53

the same procedure used in Section 3.2.1, the general solution to the temperature distribution of each element of the U-shape VTA can be written as: T = Ts +

B + C1 eAx + C2 e−Ax A2

where Ci (i = 1 to 6 ) are the constants to be obtained. For simplification, A and B are employed to represent two long terms during solving Equation (4.1). The subscript is assigned to them for different elements in the following. For element 1, the temperature distribution is B1 + C1 eA1 x + C2 e−A1 x A21

T1 = Ts +

(4.2)

where B1 = A21 =

Vb12 L2b1 ρ0 kp

Sb1 + B1 ξ kp RT 1 tp2

V Lb1 2 (Lb1 + L1 ) + Le ¸ · 2 (Lg + tp1 + tv ) +1 +1 tp2

Vb1 = Sb1 =

tp2 wb1

RT 1 =

tv + Lg tp1 tn + + kv kn kp

and Vb1 is the potential acted on element 1; Sb1 is the shape factor of element 1. For element 2, the temperature distribution is similar to element 1 except that Lb1 is replaced by L1 , and wb1 is replaced by w1 , that is T2 = Ts +

B2 + C3 eA2 x + C4 e−A2 x A22

where B2 = A21 =

Vb22 L21 ρ0 kp

S1 + B2 ξ kp RT 1 tp2

54

(4.3)

Vb2 = Sb2 =

V L1 2 (Lb1 + L1 ) + Le

¸ · tp2 2 (Lg + tp1 + tv ) +1 +1 w1 tp2

Element 3 is the connection between the top layer and the bottom layer, the cross section of element 3 is not rectangular like elements 1 and 2. Figure 4-6 shows the 3-D view of the cross section of element 3. For element 3, under steady state, the heat flow Equation (4.1) takes the

top layer

via

current

Ac bottom layer

Figure 4-6: 3D schematic diagram of the element 3 with the cross section form kp Av

d2 T Se w2 (T − Ts ) = − J 2 ρAc 2 dx RT 2

(4.4)

where Av is the sum of the cross sections of the top layer, via, and bottom layer of the element 3, Ac is the cross section of the top layer in element 3, and Se is the shape factor for element 3. Solving Equation (4.4), the temperature distribution of element 3 can be obtained as T3 = Ts +

B3 + C5 eA3 x + C6 e−A3 x A23

where B3 = Vb3 =

Vb32 Ac L2e ρ0 kp Av

V Le 2 (Lb1 + L1 ) + Le 55

(4.5)

Se w2 + B3 ξ kp RT 2 Av · ¸ tp1 2tv +1 +1 Se = w2 tp1 A23 =

RT 2 =

tv tn + kv kn

In order to solve for constants ci (i = 1 to 6 ) in Equations (4.2), (4.3), and (4.5), at least six boundary conditions are needed. Figure 4-7 (a) shows the boundary conditions that represent Ts

Tm2

Tm1

Tm1

Tm2 (a)

Ts q1 q2

q3

(b)

Figure 4-7: (a) The boundary conditions of temperature continuity. (b) The boundary conditions of the rate of the heat conduction the continuity of temperature from one element to another. Since the U-shape VTA is symmetrical, the temperature distribution of the actuator also should be symmetrical. Therefore, the temperatures of both ends of element 3 are equal to Tm2 , and the two joints between elements 1 and 2 are equal to Tm1 . Figure 4-7 (b) shows the boundary conditions of the rate of the heat flow. Substituting all the boundary conditions into Equations (4.2), (4.3) and (4.5), the 56

following equations are obtained AC = B

(4.6)

where 

1 1 0 0 0 0 0   AL  e 1 b1 e−A1 Lb1 0 0 0 0 0    0 0 1 1 0 0 −1    e−A2 L1 0 0 0 0 0 eA2 L1  A=  0 0 0 0 1 1 0    0 0 0 0 0 eA3 Le e−A3 Le    A2 0 0 0  A1 eA1 Lb1 −A1 e−A1 Lb1 −A2  0 0 λeA2 L1 −λe−A2 L1 eA3 L1 −e−A3 L1 0 

          B=         

1 −B A2 1

−Ts −

B1 A21

−Ts −

B2 A22

−Ts −

B2 A22

−Ts −

B3 A23

−Ts −

B3 A23

0 −RTs kp w2 tp1 A3



          C=         



C1   C2    C3    C4    C5    C6     Tm1   Tm2

57

                    

0 0 0 −1 −1 −1 0 −R kp w2 tp1 A3

                    

Here λ is equal to w1 tp2 A2 Áw2 tp1 A3 , R is the thermal resistance of the bottom layer of the U-shape vertical thermal actuator, and it is calculated by

R=

1 A2 KA L1 Lb1

A1 L1

+

A2 Lb1

(4.7)

where A1 and A2 are the cross section area of the long bar and short bar, respectively. Solving Equation (4.6) and substituting the given process parameters to Equations (4.2), (4.3) and (4.5), the temperature distribution of the U-shape VTA can be obtained.

4.2.2

Simulation results

In the simulation of the temperature distribution of the U-shape VTA, all the material parameters are the same as those used in Chapter 3. The geometrical data are listed in Table 4.1.

Table 4.1: Geometrical data of the U-shaped vertical thermal acutator Geometrical data Value Unit The length of the long beam of the top layer L1 177 µm The length of the long beam of the bottom layer L2 217 µm The length of the short bar of the top layer Lb1 50 µm The length of the short bar of the bottom layer Lb2 60 µm The width of the long beam of the top layer w1 10 µm The width of the long beam of the bottom layer w2 18 µm The width of the short bar of the top layer wb1 13 µm The width of the short bar of the bottom layer wb2 15 µm The length of the connection between two long beams Le 38 µm The gap between the top layer and the bottom layer 0.75 µm The thickness of the top layer Tp2 1.5 µm The thickness of the bottom layer Tp1 2.0 µm The thickness of air Tv 2 µm The thickness of nitride Tn 0.6 µm Figure 4-8 shows the temperature distribution of the U-shaped vertical thermal actuator. The input voltage is 5V, and the other parameters are listed in Tables 4.1 and 3.1. Since the U-shaped vertical thermal actuator is symmetrical about its center line, the temperature distribution also should be symmetrical about its center line. The above analytical results show that characteristic. The maximum temperature appears in element 2 rather than element 3 58

700

Vb = 5v 650

600

element 1

element 2

Temperature

550 element 3 500

450

400

350

300

0

50

100

150

200

250

300

350

400

450

500

Top layer position of vertical actuator

Figure 4-8: Temperature distribution along the top layer of VTA because element 3 is the connection between the top and bottom layers. The bottom layer becomes a heat sink which reduces element 3 temperature. Also, the cross section of element 3 is bigger than that of element 2 (Figure 4-6), hence element 3 has a bigger thermal capacitance compared to element 2. Figure 4-9 shows the numerical simulation of the same actuator using Coventorware software. In this simulation, three different physical domain boundary conditions, electrical, thermal and mechanical, are applied. In the electrical boundary condition, the actuating voltage is added across anchors 1 and 2 in Figure 4-2. All of the four anchors are set to the substrate temperature for the thermal boundary condition since they are connected to the substrate. For the mechanical boundary conditions, these four anchors are also fixed in all directions. The simulation results are shown in Figure 4-9. The temperature distribution is in good agreement with the analytical results. The maximum temperature as a function of the input voltage is also provided in Figure 4-10. Like the two-hot arm thermal actuator and for the same reason, the analytical results are in better agreement with the numerical results at low voltage. However, the difference at high input voltages is acceptable.

59

Figure 4-9: Numerical result of temperature distribution of the U-shaped VTA using R ° Coventorware

1100 Analytical results Simulation results

1000

Maximum Temperature (K)

900

800

700

600

500

400

300

0

1

2

3

4

5

6

7

Voltage (V)

Figure 4-10: Comparison of the maximum temperature as a function of input voltage.

60

4.3 4.3.1

Mechanical analysis Analytical solution

The linear thermal expansions of the top and bottom layers are the essential inputs for the mechanical analysis of the U-shape vertical thermal actuator. Based on Equation (4.3), the thermal expansion of the top layer can be obtained from ∆L1 = α

Z

0

L1

(T − Ts )dx = α

·

¸ B2 C3 A2 L1 C4 −A2 L1 L + (e − 1) − (e − 1) 1 A2 A2 A22

(4.8)

where the parameters’ definitions are similar as those in section 3.3.1. Here, the thermal expansions of elements 1 and 3 of the top layer are neglected in comparison with the thermal expansion of element 2. From Figure 4-9, it is clear that the temperature of the bottom layer is also increased. Since, no current passes through the bottom layer, the temperature distribution along the bottom layer is a simple linear heat conduction problem. The thermal expansion of the bottom layer can be calculated by ∆L2 = α

Z

0

L2

1 (T − Ts )dx = α (Tm2 − Ts ) L2 2

(4.9)

where Tm2 is the tip temperature of the bottom layer as shown in Figure 4-7 (a). Since the U-shape VTA is symmetrical, it can be simplified to that shown in Figure 4-11a. In this section, it is intended to convert the continuous model shown in Figure 4-11a to a lumped model four-bar linkage shown in Figure 4-11 (b). In this model, element 1 (short bar) is treated as a torsional spring, because when the tip of the U-shape vertical thermal actuator is bent upward or downward, element 2 (long beam) rotates about element 1 (short bar). The deflection of the VTA can be calculated by the following steps. First, the deflection of the structure shown in Figure 4-12 (a) can be obtained by using the same method used in Section 3.3.1. After that, the spring coefficient KT of the structure in the y direction at the tip of the actuator can be found (Figure 4-12 (b)). Then, the whole structure in Figure 4-11 (b) can be redrawn as the one in Figure 4-12 (c). In Section 3.3.1, the fixed base of the plane rigid frame was represented by three force components. But here, the base of the plane rigid frame shown in Figure 4-11 (b) is hinged 61

top layer

bottom layer

via

cross section (a)

Kb1

Kb2

(b)

Figure 4-11: (a) The schematic 3-D view of U-shaped VTA, (b) Four bar linkage representing for the U-shaped VTA. and therefore two force components can be used when the hinged base is released (Figure 4-12 (a)). The two force components (X1 and X2 ) can be calculated by solving Equation (4.10):  

f11 f12 f21 f22

 

X1 X2





=

∆L1 − ∆L2 0

 

(4.10)

where fij represents the flexibility coefficients, and they all can be obtained by f11 =

L2 Lg L2 L1 L32 L31 + 2 + 2 − 3EI2 EIg EI1 3EI1

f21 =

L21 Lg L2 Lg L1 2L2g L2 − − 2EI1 EI1 3EIg f12 = f21 f22 =

L3g L2g L1 + 3EIg EI1

where E is the Young’s modulus of polysilicon, I1 , I2 and Ig are the moment of inertia for the 62

KT

X2

X1

(a)

(b)

Deflection u

y

KT Kb1

Kb2 (c)

y

Figure 4-12: (a) The hinged rigid frame for mechanical analysis, (b) schematic of the spring coefficient analysis in y direction. (c) schematic of the deflection of the U-shape VTA.

63

top and bottom layer long beams and the via, respectively. Once the two force components are achieved, the deflection of the end of the rigid frame without torsional spring (Figure 4-12 (a)) can still be calculated by using the virtual work method. The bending moment of the top layer long beam due to the virtual force is shown in Figure 4-13 (a).The bending moment due to the

L1

P=1

(a) X2Lg

X1(L2-L1)-X2Lg

(b)

Figure 4-13: (a)The bending moment of the top layer long beam due to the virtual force, (b) The bending moment of the top layer long beam due to the thermal expansion virtual force as a function of the position of the top layer long beam is given by M = L1 − x The bending moment due to the thermal expansion is shown in Figure 4-13 (b). It can be obtained by M = X1 x + X1 (L2 − L1 ) − X2 Lg According to the virtual work method, the deflection of the hinged rigid frame without the torsional springs (Figure 4-12 (a) ) can be found as 1 u= EI1

Z

0

L1

M M dx =

1 1 1 1 (− X1 L31 + X1 L21 L2 − X2 L21 Lg EI1 3 2 2

(4.11)

In order to find the stiffness coefficient KT in Figure 4-12 (b), three deflections are assigned 64

to the hinged rigid frame structure (Figure 4-14).By using the force method, the stiffness matrix

V3

V2

V1

Figure 4-14: The hinged rigid frame with three deflection directions of the structure in Figure 4-14 can be obtained 

k11 k12 k13

   k21 k22 k23  k31 k32 k33



∆1





F1



          ∆2  =  F2      ∆3 F3

(4.12)

where kij is the stiffness coefficient. The definition of a stiffness coefficient is analogous to the definition of the flexibility coefficient: a typical coefficient kij represents the force at i due to a unit displacement applied at j [46, lea]. ∆i is the deflection in i direction and Fi is the force at i direction. The stiffness coefficient kij can be given by k11 =

3EI2 3EI1 + L32 L31

k21 =

3EI2 L22

k31 =

3EI1 L21

k12 = k21 k22 =

3EI2 4EIg + L2 Lg 65

k32 =

3EIg Lg

k13 = k31 k23 = k32 k33 =

3EI1 4EIg + L1 Lg

Let F2 and F3 equal to zero, the stiffness coefficient in the direction of V1 can be found from equation 4.12. KT = k11 +

k23 k31 − k33 k21 k32 k21 − k22 k31 k12 + k13 k22 k33 − k23 k32 k22 k33 − k23 k32

(4.13)

where KT is the stiffness coefficient of the hinged frame in the direction of V1 . Figure 4-15 shows the steps of how to find the final deflection of the U-shape vertical thermal actuator. In Figure 4-15 (a), the thermal expansion can generate the deflection u at the tip of the actuator, it can be treated as an equivalent force F acting at the tip and generates the same deflection. Hence, the value of force F is uKT . When the two torsional springs are added to the structure shown in Figure 4-15 (b), the final deflection of the U-shape vertical thermal actuator can be obtained from uf =

KT KT +

Kb1 L21

+

Kb2 L22

u

(4.14)

where Kb1 and Kb2 are the torsional spring coefficients of the top and bottom layer short bars, respectively.

4.3.2

Simulation results

R ° The deflection as a function of the input voltage is simulated by Coventorware with MemETherm

solver. The analytical solution is also provided which is in a good agreement with the simulation results ( Figure 4-16).

66

KT

u

(a)

Kb1

1

uf 2

Kb2 (b)

Figure 4-15: (a) The deflection without torsional springs. (b) the deflection with two torsional springs

67

7 Analytical results Simulation results 6

Displacement ( µ m)

5

4

3

2

1

0

0

1

2

3

4

5

6

7

Voltage (V)

Figure 4-16: Deflection of the tip of the U-shaped vertical thermal actuator as a function of input voltage

4.4

Conclusion

The lumped model developed in this chapter for the mechanical deflection of VTA does not need prior experiments for tuning the model as opposed to the model in [47]. The simulation R ° results obtained from Coventorware have a good agreement with the analytical results. The U-shape VTA presented here has been fabricated by using the 46th production run of MUMPs. The top layer is fabricated by using poly2 and the bottom layer is constructed out of poly1. The four anchors are made of the stack of the poly0, poly1, poly2 and gold layers. Here, the gold is used to reduce the contact resistance when we use probes to apply a voltage on the VTA. In order to measure the vertical deflection of VTA, an optical measuring system has to be developed. The other way to measure the vertical deflection of VTA is to measure other properties that can represent the deflection of VTA. For example, the capacitance of a tunable capacitor can be used for deflection measurement. Further Experiments will require special equipment which will be prepared in the future.

68

Chapter 5

RF Applications of Horizontal and Vertical Thermal Actuators In this chapter, a new multiport switch with a latching mechanism is designed. An improvement is proposed to increase the tuning range of a tunable capacitor by using bidirectional vertical thermal actuators.

5.1

Multiport switch with a latching mechanism

MEMS technology has proven its ability in the application of wireless communication, especially in the RF field. Many single-pole-single-throw (SPST) RF MEMS switches have been designed, fabricated and modeled. Some companies also have commercialized SPST RF switches based on MEMS technology. However, multiport switches (N-pole-N-throw, NPNT ) are still under investigation. The new design of a MEMS switch with a latching mechanism is presented here. This novel design can be used to build multiport switches or a switch matrix. The new multiport switch consists of a horizontal thermal actuator, which has been well documented in Chapter 3, as the actuation part, and electrostatic actuating cantilevers as the switching part. The switching part also could be the U-shape vertical thermal actuator, which depends on the application and the requirements for the multiport switch. For a low speed switch and large switching distance, the U-shape vertical thermal actuator is a good choice. 69

A general latching mechanism structure is shown in Figure 5-1 (a). It includes two horizontal thermal actuators and one bidirectional vertical thermal actuator. The actuating sequence is as follows: first the horizontal thermal actuators are actuated. When plate A is moved away from plate B, the vertical actuator is activated, it brings plate B downward to the substrate. Then, the horizontal thermal actuators are released, they bring plate A back to the original position. After that, the vertical actuator is also released. Because plate A is brought back first and blocks the way of plate B, it cannot go back to its original position any more. Before actuation, plate A was under plate B, after actuation, plate A is above plate B, so two different states of plate B are generated, which can be treated as the switch’s two states: “on” and “off”, respectively. A closed view of the latching mechanism is shown in Figure 5-1 (b). The white arrows show the moving direction of the two plates. The three dimensional structure of the multiport switch is shown in Figure 5-2. This structure is similar to the one shown in Figure 5-1. Electrostatic cantilever beam actuators have been used instead of the vertical thermal actuators as the switching part in order to increase the switching speed. Some holes are also considered on the cantilever beam. These holes can decrease the damping effect when the switch is activated at high speed. Meanwhile, these holes can also reduce the stiffness of cantilevers, which means less electrostatic actuating force, i.e. less input voltage is required to actuate the switch. The purpose of putting holes on the plate is analogous to the purpose of putting holes on the cantilever beams. The actuating sequence is similar to the above explanation of the latching mechanism structure. Each cantilever beam can carry one RF signal. Any of the cantilever beams can be the signal input port and the others are signal output ports. For example, if the signal input port is cantilever beam A, and the signal is to be sent out through cantilever beam B, cantilever beams A and B should be actuated together, and cantilever beam C should be left quiescent. So, cantilever beams A and B will be changed from one state to another together and connected through the substrate. The most important advantage of this type multiport switch is that there is no power consumption in the quiescent state. The number of the ports the switch can have depends on the properties of the horizontal thermal actuators and the working frequency. Obviously, the more ports the switch has, the larger the force the horizontal thermal actuator needs to move

70

Vertical thermal actuator Horizontal thermal actuator

(a)

B A

(b)

Figure 5-1: (a) Schematic of latching mechanism in 3D view. latching mechanism.

71

(b) Detail of the

A

B

C

Electrostatic cantilever actuator

Horizontal thermal actuator array (a)

(b)

Figure 5-2: (a) Top view of the multiport switch. (b) Closed-up of the multiport switch.

72

the plate. If the distance of the two cantilever beams is too small, the signals will “talk” to each other (cross talk) at high frequency, which affects the property of the multiport switch. This compromise has to be made.

5.2

Tunable capacitor with U-shaped vertical thermal actuators

The tunable capacitor has been introduced in Chapter 1. Its advantages attract many researchers’ attention. The tunable capacitor with vertical thermal actuators documented in [4] has shown the tuning range up to the factor of seven. In Chapter 4, the U-shape vertical thermal actuator was designed, modeled and simulated. The results showed the ability of this type thermal actuator to have larger deflection than the traditional vertical thermal actuators. So the tuning range of the tunable capacitor can be greatly increased by replacing the traditional vertical thermal actuator with the U-shape vertical thermal actuator. Figure 5-3 shows an overview of the new tunable capacitor with the U-shape vertical thermal actuator.

RF singal line DC power line U-shape thermal actuator

Figure 5-3: Top view of the tunable capacitor with U-shaped vertical thermal actuators With the increase of the deflection of the vertical thermal actuator, the connection between the actuator and the capacitor plate has to be redesigned. Ideally, the connection should have a

73

small stiffness in the horizontal direction and a large stiffness in the vertical direction. The small stiffness in the horizontal direction allows the vertical thermal actuators to lift the capacitor plate easily. The large stiffness in the vertical direction can keep the capacitor plate in the same plane with the vertical thermal actuator. Based on these requirements, a new design is shown in Figure 5-4. A S-shaped spring connection is employed here. Obviously, the stiffness of the S-shaped spring in the horizontal direction is very soft. One special structure is also built to make the stiffness of the S-shaped spring in vertical direction larger. The cross section of this structure is zoomed in Figure 5-4. When the U-shape vertical thermal actuator is bent up, the connection between the tip of the U-shape vertical thermal actuator and the S-shaped spring is bent down because of the weight of the capacitor plate. But after a certain bending degree, the two separated poly1 parts of the U-shape vertical thermal actuator and the S-shaped spring will touch each other, it absorbs most further bending moment and makes the stiffness of the S-shaped spring stronger in the vertical direction.

5.3

Fabrication and future work

The multiport switch with a latching mechanism and the tunable capacitor with vertical thermal actuators has been fabricated using the 46th production run of MUMPs. All the pads are not anchored on the silicon substrate. And they are covered by gold in order to transfer devices to the other substrate. The purpose of transferring devices to another substrate is to reduce the effect of the silicon substrate on the RF properties of devices because silicon is conductive material and lossy for RF signal. A flip chip bonding machine is needed to transfer devices to another substrate. A vacuum environment is also required to test devices’ RF properties. The required flip chip bonding machine is not available yet and Designing a vacuum chamber for RF properties tests is also under the way. All of these work will be done in my PhD program and experimental results will be provided in future work

74

A

A

U-shape vertical thermal actuator

S-shape spring connection poly2

poly1

Figure 5-4: Schematic diagram of S-shaped connection and detail of the connection.

75

Chapter 6

Conclusions In this thesis, a two-hot-arm horizontal thermal actuator model was documented in Chapter 3. Some special phenomena, such as back bending, were found during the experiments. In Chapter 4, a bidirectional vertical thermal actuator was designed, modeled and simulated. Chapter 5 discussed applications of these two types of thermal actuators. A multiport switch with a latching mechanism was developed for RF applications by using thermal actuators. An improvement of the tunable capacitor was also proposed by employing the novel bidirectional vertical thermal actuator. The traditional and well-known one-hot-arm horizontal thermal actuator has been well documented in many previous published works. Because of its numerous advantages, such as large displacement, low actuating voltage, and so on, many research effort focuses on this area, which results in the arising of the two-hot-arm horizontal thermal actuator with larger deflection and more cost-efficient power consumption. According to the best knowledge of the author, modeling of two-hot-arm horizontal thermal actuator is first reported here. The numerical simulation and test results were also provided to corroborate the modeling. Comparing with the analytical results, a good agreement was achieved. In the experiments, we also found the fact that the inner and outer hot arm would touch each other at large deflections. At large deflections, the temperature was also high enough to make structure material-polysilicon to become soft. therefore, keeping the actuating voltage less than 8V was suggested here based on the geometry data provided in Chapter 3. Back bending was also reported in the test results at one-hot-arm thermal actuators, here it was found in the experiments of two-hot-arm 76

thermal actuator. When increasing the driven current and time above a certain level, back bending occurred. During this process, the inner and outer hot arm deforms. After removing the current, both of hot arms were shorter than their original length due to plastic deformation. Based on the strategy of the two-hot-arm horizontal thermal actuator, A U-shape vertical thermal actuator was designed. This novel actuator had the ability to move bidirectionally without any remodification, which indicated twice deflection of the traditional vertical thermal actuators. A new lumped model method was employed to calculate the deflection of the novel R ° bidirectional thermal actuator. Simulation results using Coventorware were provided to show the accuracy of the analytical results. By applying two-hot-arm thermal actuators and bidirectional vertical thermal actuators, a multiport switch with a latching mechanism, and an improved tunable capacitor were designed. A multiport switch is a key device for a communication network. Some multiport switches with electrostatic actuators need voltage supply when they stay at “on” state. The new multiport switch with a latching mechanism do not need any power supply for maintaining its on or off status. The latching mechanism keeps the switch in the desired state. A tunable capacitor is an important component for a system with a tuning capability. The tuning range of a tunable capacitor is a significant property. By using new bidirectional vertical thermal actuators, the tuning range of a tunable capacitor can be greatly increased. In order to measure the deflection of the new vertical thermal actuator, some future work is needed. Because of the fabrication limitation, vertical thermal actuators should be transferred to another substrate in order to test the ability of bidirectional motion. An optical system is also needed to measure the vertical deflection. For capturing the RF properties of multiport switches and tunable capacitors they also need to be transferred to another substrate. All the device transformation can be done by using flip chip technologies.

77

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