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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Microsystem and Nanotechnology Series
- Sprache: Englisch
Mechanics of Microsystems
Alberto Corigliano, Raffaele Ardito, Claudia Comi, Attilio Frangi, Aldo Ghisi and Stefano Mariani, Politecnico di Milano, Italy
A mechanical approach to microsystems, covering fundamental concepts including MEMS design, modelling and reliability
Mechanics of Microsystems takes a mechanical approach to microsystems and covers fundamental concepts including MEMS design, modelling and reliability. The book examines the mechanical behaviour of microsystems from a ‘design for reliability’ point of view and includes examples of applications in industry.
Mechanics of Microsystems is divided into two main parts. The first part recalls basic knowledge related to the microsystems behaviour and offers an overview on microsystems and fundamental design and modelling tools from a mechanical point of view, together with many practical examples of real microsystems. The second part covers the mechanical characterization of materials at the micro-scale and considers the most important reliability issues (fracture, fatigue, stiction, damping phenomena, etc) which are fundamental to fabricate a real working device.
Key features:
- Provides an overview of MEMS, with special focus on mechanical-based Microsystems and reliability issues.
- Includes examples of applications in industry.
- Accompanied by a website hosting supplementary material.
The book provides essential reading for researchers and practitioners working with MEMS, as well as graduate students in mechanical, materials and electrical engineering.
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Seitenzahl: 726
Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Copyright
Dedication
Series Preface
Preface
Acknowledgements
Notation
About the Companion Website
Chapter 1: Introduction
1.1 Microsystems
1.2 Microsystems Fabrication
1.3 Mechanics in Microsystems
1.4 Book Contents
References
Part I: Fundamentals
Chapter 2: Fundamentals of Mechanics and Coupled Problems
2.1 Introduction
2.2 Kinematics and Dynamics of Material Points and Rigid Bodies
2.3 Solid Mechanics
2.4 Fluid Mechanics
2.5 Electrostatics and Electromechanics
2.6 Piezoelectric Materials in Microsystems
2.7 Heat Conduction and Thermomechanics
References
Chapter 3: Modelling of Linear and Nonlinear Mechanical Response
3.1 Introduction
3.2 Fundamental Principles
3.3 Approximation Techniques and Weighted Residuals Approach
3.4 Exact and Approximate Solutions for Dynamic Problems
3.5 Example of Application: Bistable Elements
References
Part II: Devices
Chapter 4: Accelerometers
4.1 Introduction
4.2 Capacitive Accelerometers
4.3 Resonant Accelerometers
4.4 Examples
4.5 Design Problems and Reliability Issues
References
Chapter 5: Coriolis-Based Gyroscopes
5.1 Introduction
5.2 Basic Working Principle
5.3 Lumped-Mass Gyroscopes
5.4 Disc and Ring Gyroscopes
5.5 Design Problems and Reliability Issues
References
Chapter 6: Resonators
6.1 Introduction
6.2 Electrostatically Actuated Resonators
6.3 Piezoelectric Resonators
6.4 Nonlinearity Issues
References
Chapter 7: Micromirrors and Parametric Resonance
7.1 Introduction
7.2 Electrostatic Resonant Micromirror
References
Chapter 8: Vibrating Lorentz Force Magnetometers
8.1 Introduction
8.2 Vibrating Lorentz Force Magnetometers
8.3 Topology or Geometry Optimization
References
Chapter 9: Mechanical Energy Harvesters
9.1 Introduction
9.2 Inertial Energy Harvesters
9.3 Frequency Upconversion and Bistability
9.4 Fluid–Structure Interaction Energy Harvesters
References
Chapter 10: Micropumps
10.1 Introduction
10.2 Modelling Issues for Diaphragm Micropumps
10.3 Modelling of Electrostatic Actuator
10.4 Multiphysics Model of an Electrostatic Micropump
10.5 Piezoelectric Micropumps
References
Part III: Reliability and Dissipative Phenomena
Chapter 11: Mechanical Characterization at the Microscale
11.1 Introduction
11.2 Mechanical Characterization of Polysilicon as a Structural Material for Microsystems
11.3 Weibull Approach
11.4 On-Chip Testing Methodology for Experimental Determination of Elastic Stiffness and Nominal Strength
References
Chapter 12: Fracture and Fatigue in Microsystems
12.1 Introduction
12.2 Fracture Mechanics: An Overview
12.3 MEMS Failure Modes due to Cracking
12.4 Fatigue in Microsystems
References
Chapter 13: Accidental Drop Impact
13.1 Introduction
13.2 Single-Degree-of-Freedom Response to Drops
13.3 Estimation of the Acceleration Peak Induced by an Accidental Drop
13.4 A Multiscale Approach to Drop Impact Events
13.5 Results: Drop-Induced Failure of Inertial MEMS
References
Chapter 14: Fabrication-Induced Residual Stresses and Relevant Failures
14.1 Main Sources of Residual Stresses in Microsystems
14.2 The Stoney Formula and its Modifications
14.3 Experimental Methods for the Evaluation of Residual Stresses
14.4 Delamination, Buckling and Cracks in Thin Films due to Residual Stresses
References
Chapter 15: Damping in Microsystems
15.1 Introduction
15.2 Gas Damping in the Continuum Regime with Slip Boundary Conditions
15.3 Gas Damping in the Rarefied Regime
15.4 Gas Damping in the Free-Molecule Regime
15.5 Solid Damping: Thermoelasticity
15.6 Solid Damping: Anchor Losses
15.7 Solid Damping: Additional unknown Sources – Surface Losses
References
Chapter 16: Surface Interactions
16.1 Introduction
16.2 Spontaneous Adhesion or Stiction
16.3 Adhesion Sources
16.4 Experimental Characterization
16.5 Modelling and Simulation
16.6 Recent Advances
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 Typical commercial microsystem: a nine-axis accelerometer, gyroscope, magnetometer.
Figure 1.2 16 nine-axis MEMS superposed on a 1 euro cent coin.
Figure 1.3 Lithographic process for MEMS.
Figure 1.4 Patterned wafer.
Figure 1.5 Single die and cross-sectional view. IC, integrated circuit.
Chapter 2: Fundamentals of Mechanics and Coupled Problems
Figure 2.1 Reference system.
Figure 2.2 Two reference systems.
Figure 2.3 Linear elastic spring.
Figure 2.4 Weight force.
Figure 2.5 Viscous force.
Figure 2.6 One-degree-of-freedom oscillator.
Figure 2.7 Damped oscillation of a one-dof system.
Figure 2.8 One-dof oscillator: amplitude as a function of the ratio between the frequency of the external force and the frequency of the oscillator for varying damping factors.
Figure 2.9 One-dof oscillator: phase as a function of the ratio between the frequency of the external force and the frequency of the oscillator for varying damping factors.
Figure 2.10 Rigid body.
Figure 2.11 Euler angles.
Figure 2.12 Deformable body.
Figure 2.13 Infinitesimal volume with stress tensor components.
Figure 2.14 Infinitesimal volume with principal stress tensor components.
Figure 2.15 Tensile test on material specimen.
Figure 2.16 Typical experimental responses of materials under a uniaxial tensile test: (a) ductile; (b) brittle.
Figure 2.17 Geometry of a beam.
Figure 2.18 Deformed beam.
Figure 2.19 Infinitesimal element of an Euler–Bernoulli beam.
Figure 2.20 Beam under torsion.
Figure 2.21 Clamped beam subject to a distributed axial force.
Figure 2.22 Clamped beam subject to a concentrated shear force at the free end.
Figure 2.23 Doubly clamped beam subject to imposed displacement at one end.
Figure 2.24 Doubly clamped beam subject to an imposed rotation at one end.
Figure 2.25 Three-folded beam.
Figure 2.26 Two electric charges in empty space.
Figure 2.27 Parallel-plate capacitor.
Figure 2.28 Comb-finger capacitor.
Figure 2.29 Parallel-plate capacitor connected with an elastic spring.
Figure 2.30 Parallel-plate capacitor connected with an elastic spring: equilibrium of forces.
Figure 2.31 Parallel-plate capacitor connected with an elastic spring: voltage–displacement plot.
Figure 2.32 General scheme for a coupled electromechanical problem.
Figure 2.33 Piezoelectric modes.
Figure 2.34 Solid subject to thermal boundary conditions.
Chapter 3: Modelling of Linear and Nonlinear Mechanical Response
Figure 3.1 Electrostatically actuated resonator.
Figure 3.2 Vibrating beam and free body diagram.
Figure 3.3 Forced frequency response of nonlinear resonator normalized dynamic amplification factor versus normalized frequency.
Figure 3.4 Forced frequency response of nonlinear resonator for increasing excitation load. Amplitude in [µm].
Figure 3.5 SEM of a MEMS shock sensor based on bistable beams.
Figure 3.6 Simplified scheme: rigid shuttle and bistable element. The coordinate system is attached to the anchors; denotes the shuttle position.
Figure 3.7 Close-up of bistable element in two stable configurations before and after actuation.
Figure 3.8 Simulated midspan deflection for two different values of (see Equation 3.56) just below and above the snap-through threshold. Design input frequency Hz.
Figure 3.9 Cumulative probability of rupture versus maximum acceleration.
Chapter 4: Accelerometers
Figure 4.1 1D capacitive accelerometer.
Figure 4.2 Folded spring of in-plane accelerometer.
Figure 4.3 Parallel-plate sensing.
Figure 4.4 Torsional spring of an out-of-plane accelerometer.
Figure 4.5 Capacitive sensing in an out-of-plane accelerometer.
Figure 4.6 (a) Accelerometer with resonating proof mass. (b) Accelerometer with resonating beam device coupled to proof mass.
Figure 4.7 Function of resonant accelerometer.
Figure 4.8 Uniaxial accelerometer with resonant beam.
Figure 4.9 Resonant accelerometer with a change of momentum of inertia.
Figure 4.10 (a) Resonant accelerometer with a resonating beam; (b) forces acting when an external acceleration is applied.
Figure 4.11 Resonant accelerometer proposed by Aikele
et al.
(2001). Reproduced with permission of Elsevier.
Figure 4.12 Three-axis capacitive accelerometer.
Figure 4.13 SEM of three-axis capacitive accelerometer.
Figure 4.14 Eigenmodes and eigenfrequencies: (a) torsional mode; (b, c) translational modes.
Figure 4.15 Capacitance variation for different external acceleration components.
Figure 4.16 (a) SEM of -axis accelerometer with two torsional resonators A and B; (b) side view of electrostatically actuated accelerometer, inclined due to external acceleration.
Figure 4.17 (a) Resonant accelerometer. (b) Effect of external acceleration .
Figure 4.18 SEM of resonant accelerometer.
Figure 4.19 (a) Normalized output spectrum of the oscillating circuit for a single resonating beam evaluated for four different applied accelerations, . (b) Variation of the peak frequency difference between the resonators as a function of the external acceleration in the range of for three different devices. corresponds to the peak frequency difference at .
Chapter 5: Coriolis-Based Gyroscopes
Figure 5.1 Roll, pitch and yaw, components of angular velocity.
Figure 5.2 Reference frame –– attached to MEMS containing a proof mass and inertial reference frame ––.
Figure 5.3 Coriolis vibratory yaw rate gyroscope.
Figure 5.4 Driving and sensing mode resonance frequencies: (a) separated; (b) matched.
Figure 5.5 Symmetric, decoupled yaw gyroscope, as proposed by Alper and Akin (2004). Reproduced with the permission of Elsevier.
Figure 5.6 Dual-mass tuning-fork yaw gyroscope.
Figure 5.7 Three-axis heart-beating gyroscope: (a) scheme of sensing modes for roll, pitch and yaw as a consequence of an
expansion
; (b) drive mode.
Figure 5.8 SEM of integrated structure for resonant microgyroscope and accelerometer.
Source
: Zega
et al
. (2014), Figure 5. Published under the Open Journal Systems 2.4.8.1, freely distributed by the Public Knowledge Project under the GNU General Public License. http://www.gruppofrattura.it/pdf/rivista/numero29/numero_29_art_29.pdf. CC-BY 4.0.
Figure 5.9 Plan view of the structure of Figure 5.8, for detection of acceleration and angular velocity.
Figure 5.10 (a) Detection of yaw angular velocity ; (b) detection of linear acceleration .
Figure 5.11 (a) Detection of pitch angular velocity ; (b) detection of linear acceleration .
Figure 5.12 Ring resonator gyroscope: (a) shape of two orthogonal modes, with separation; (b) shape of two orthogonal modes, with separation.
Figure 5.13 Disc resonator gyroscope: (a) SEM of disc resonator gyroscope and drawing of disc resonator gyroscope shape, with inset SEM of rings; (b) orthogonal elliptical mode shapes, with contours of displacement.
Source
: Nitzan
et al
. (2015), Figure 1. Licensed under a Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0/.
Chapter 6: Resonators
Figure 6.1 Classification of MEMS resonators based on mode of vibration: (i) flexural mode resonators, (ii) contour mode or Lamb-wave resonators, (iii) thickness-extensional mode resonators and (iv) shear mode resonators.
Figure 6.2 Flexural mode MEMS resonators: (a) clamped–clamped in-plane resonator; (b) clamped–clamped out-of-plane resonator.
Figure 6.3 Double-ended tuning-fork resonator.
Figure 6.4 Extensional bulk acoustic wave resonator: (a) geometry; (b) resonant mode.
Figure 6.5 Wine glass disc resonator: (a) geometry; (b) resonant mode.
Figure 6.6 Contour mode resonators: (a) simple scheme; (b) multiscaled subresonators.
Figure 6.7 Frequency response of nonlinear resonator for different values of electrostatic nonlinear stiffness .
Figure 6.8 Torsional resonator: (a) SEM of polysilicon resonator fabricated through ThELMA surface micromachining process developed by STMicroelectronics; (b) comparison between experimental data (continuous lines) and numerical predictions (dotted lines) for and = 45, 65, 85, 105 and 150 mV – only the backward frequency sweeps are reported for sake of clarity.
Chapter 7: Micromirrors and Parametric Resonance
Figure 7.1 Resonant micromirror: SEM of device and layout.
Figure 7.2 Geometrical model of one complete series of interdigitated fingers.
Figure 7.3 Input voltage: square wave at 5300 Hz, 150 V.
Figure 7.4 Power spectrum for the square wave of Figure 7.3.
Figure 7.5 Sinusoidal excitation at 5 kHz, V; experimental upward and downward sweeps (discrete symbols) and numerical continuation (continuous line).
Figure 7.6 Electrostatic torque and derivative of electrostatic torque for one set of comb fingers with respect to torsional angle .
Figure 7.7 Set-up for dynamic characterization of the mirror.
Figure 7.8 Square wave excitation at 2 kHz, V; experimental downward sweep (discrete symbols) and numerical continuation (continuous line).
Figure 7.9 Square wave excitation at 5 kHz, V; experimental upward and downward sweeps (discrete symbols) and numerical continuation (continuous line).
Figure 7.10 Square wave excitation at 10 kHz, V; experimental downward sweep (discrete symbols) and numerical continuation (continuous line).
Chapter 8: Vibrating Lorentz Force Magnetometers
Figure 8.1 -axis parallel-plate MEMS magnetometer. The suspended mass is subject to a Lorentz force in the presence of a magnetic field; the corresponding displacement can be sensed through the pair of differential capacitors.
Figure 8.2 Simple -axis magnetometer. Each spring is long, while the dimension in the orthogonal direction is .
Figure 8.3 Magnetometers featuring a current flowing through the clamped–clamped beam, with motion sensed via optimized stators having a comb-shaped configuration (left) or a block-shaped configuration (right).
Figure 8.4 Optimized magnetometers made using a doubly clamped resonant shuttle beam and four different types of stator.
Figure 8.5 SEM of the resonating structure of a -axis Lorentz force magnetometer.
Figure 8.6 Objective function and lines representing its intersections with the bounds on the resonance frequency: (left) and ; (right) and .
Figure 8.7 Example of the path followed by the solution provided by the CONLIN minimizer ( and ).
Figure 8.8 SEM of resonating double-ended tuning-fork structure of a -axis Lorentz force magnetometer, with reference dimensions (in micrometres).
Chapter 9: Mechanical Energy Harvesters
Figure 9.1 SEM of piezoelectric generator proposed by Jeon
et al.
(2005). The comb-finger electrodes are viewable on the top of three layered piezoelectric cantilevers with different materials used to control the initial curvature.
Figure 9.2 Stretching nonlinear harvester, as proposed by Hajati and Kim (2011), Gafforelli
et al.
(2013) and Gafforelli
et al.
(2014).
Figure 9.3 Cantilever beam used as energy harvester: the tip mass is shown, along with a magnified view of the layered cross-section.
Figure 9.4 Normalized frequency response function for displacement and voltage for a cantilever harvester with and .
Figure 9.5 (a) Normalized frequency response function for harvested power for a cantilever beam with and . (b) Optimal normalized power versus excitation frequency for different levels of mechanical damping ().
Figure 9.6 Operating principle of the magnetic frequency upconversion device proposed by Procopio
et al.
(2014). Left: plan view showing central low-frequency oscillator and four high-frequency piezoelectric cantilevers. Top right: cross-section; magnetic interaction allows the cantilever to bend. Bottom right: alternative scheme for the supporting springs.
Figure 9.7 Piezoelectric beam subject to the effects of a fluid flow.
Figure 9.8 Frequency response function of harvested power due to vortex-induced vibration, corresponding to optimal electric resistance: (a) the fluid is air; (b) the fluid is water.
Chapter 10: Micropumps
Figure 10.1 Device functioning over a pumping cycle: (a) rest position; (b) filling phase; (c) fluid discharge.
Figure 10.2 Actuator under analysis: the light grey circular plate is the diaphragm of the pumping chamber, which is actuated by the black electrode.
Figure 10.3 Nondimensional midpoint displacement versus load parameter: comparison between the solution of the one-degree-of-freedom model and more refined numerical procedures. DDBC, displacement-dependent boundary conditions; FDM, finite difference method; FEM, finite element method.
Figure 10.4 Parametric analysis of a micropump: variation of ideal stroke volume with respect to diaphragm thickness and capacitor gap .
Figure 10.5 Parametric analysis of micropump: variation of pull-in voltage with respect to diaphragm thickness and capacitor gap .
Figure 10.6 Scheme adopted for computation of elastic restoring energy after adhesion of microplate on substrate.
Figure 10.7 Flow rate of electrostatic micropump computed by means of the dynamic fully coupled electro-fluid-mechanical model: (a) effect of capacitor gap; (b) effect of membrane thickness.
Figure 10.8 Efficiency index of electrostatic micropump computed using the dynamic fully coupled electro-fluid-mechanical model: (a) effect of capacitor gap; (b) effect of membrane thickness.
Figure 10.9 Piezoelectric diaphragm micropump.
Figure 10.10 Parametric analysis of piezoelectric micropump: maximum displacement and stroke volume are plotted with respect to the radius of the piezoelectric layer.
Figure 10.11 Comparison between electrostatic and piezoelectric actuation: (a) actuation voltage versus stroke volume; (b) electric power versus stroke volume.
Figure 10.12 Flow rate for piezoelectric micropump, for actuation voltage equal to 60 V.
Chapter 11: Mechanical Characterization at the Microscale
Figure 11.1 On-chip in-plane bending test.
Source
: Reproduced with permission of STMicroelectronics.
Figure 11.2 Two beams with different volumes subject to axial loading.
Figure 11.3 Weibull plots for two beams with different volumes subject to axial loading.
Figure 11.4 Two beams with equal volumes subject to different loading conditions.
Figure 11.5 Weibull plots for two beams with equal volumes subject to different loading conditions.
Figure 11.6 Rotational electrostatic actuator for on-chip bending tests: (top) general view; (bottom) detail of the bending specimens.
Figure 11.7 Data reduction procedure applied to rotational electrostatic actuator: (a) experimental capacitance versus voltage; (b) rotation versus measured capacitance; (c) torque versus applied voltage.
Figure 11.8 Rotational electrostatic actuator. Experimental torque versus rotation plots.
Figure 11.9 Rotational actuator for the in-plane bending test: distribution of Young's modulus.
Figure 11.10 Rotational actuator for in-plane bending tests – Weibull cumulative probability densities: (a) equivalent Weibull plot for a uniaxial, unit volume specimen; (b) experimental data obtained from 50 tests on the rotational structure, = 2.89 GPa.
Figure 11.11 Parallel-plate actuator for out-of-plane bending tests: (a) general view; (b) detail of one of the two specimens.
Figure 11.12 Parallel-plate actuator for out-of-plane bending tests: experimental distribution of Young's modulus.
Figure 11.13 Parallel-plate actuator for out-of-plane bending tests – Weibull cumulative probability densities: (a) equivalent Weibull plot for a uniaxial, unit volume specimen; (b) experimental data obtained from 21 tests on the parallel-plate structure, = 3.03 GPa.
Figure 11.14 Electrothermomechanical actuator for on-chip tensile tests. On the right: the zoomed images of the capacitor's gap varying with the applied voltage.
Figure 11.15 Electrothermomechanical actuator for on-chip tensile tests: broken specimen.
Figure 11.16 Electrothermomechanical actuator for on-chip tensile test: example of experimental displacement versus voltage plot.
Figure 11.17 Electrothermomechanical actuator for on-chip tensile tests: count of specimen ruptures in 38 on-chip tests versus rupture stress.
Figure 11.18 Electrothermomechanical actuator for on-chip tensile tests: Weibull plot of rupture stresses.
Figure 11.19 Test structure for thick polysilicon: top view of structure and enlargement to show specimen.
Figure 11.20 Test structure for thick polysilicon film: the frame is cross-hatched; the anchor points are shown in black; the six suspension springs are shown in grey.
Figure 11.21 Test structure for thick polysilicon: deformed shape of the specimen and contour plot of principal tensile stress of the notched zone.
Figure 11.22 Test structure for thick polysilicon: capacitance variation versus applied voltage.
Figure 11.23 Test structure for thick polysilicon: force versus displacement.
Figure 11.24 Test structure for thick polysilicon: Weibull plot of experimental data (asterisks) and interpolating Weibull cumulative distribution (dashed line).
Figure 11.25 Test structure for thick polysilicon: Optical micrographs of broken specimens.
Chapter 12: Fracture and Fatigue in Microsystems
Figure 12.1 SEM showing popcorn cracking and delamination induced by humidity testing of a device.
Figure 12.2 Scanning acoustic micrographs of two failed devices due to popcorn effect.
Figure 12.3 SEM showing preferential crack orientations in single-crystal silicon.
Figure 12.4 Effect of loading condition on cracking in single-crystal silicon.
Figure 12.5 Orientation dependence of the fracture toughness of single-crystal silicon for (from top to bottom) crystallographic planes parallel to the , and directions.
Figure 12.6 SEM showing secondary cracking at a polysilicon grain boundary (indicated by the black arrow in the picture).
Figure 12.7 SEM of transgranular-dominated cracking in polysilicon.
Figure 12.8 SEM of uniaxial, on-chip testing structures for polysilicon films.
Figure 12.9 Failure of polysilicon obtained through on-chip testing, and relevant numerical prediction based on a cohesive approach.
Figure 12.10 (a) Common terms used in mechanical fatigue; (b) – (Wöhler) curve; (c) Paris' law representation.
Figure 12.11 Cumulative fracture probability as a function of relative humidity (RH) at different stress level for polysilicon membranes with thickness equal to (left) nm and (right) nm.
Figure 12.12 - plots including ramping-stress test results to evaluate initial fracture strength: (a) 250 nm thick polysilicon membrane; (b) 500 nm thick polysilicon membrane.
Figure 12.13 On-chip fatigue testing device. A, mass; B, comb drive; C, comb fingers; D, notch.
Figure 12.14 On-chip fatigue testing device (see also Langfelder
et al
. (2009) and Corigliano
et al
. (2011)).
Figure 12.15 Off-chip fatigue testing device.
Chapter 13: Accidental Drop Impact
Figure 13.1 One-degree-of-freedom model of a falling microsystem.
Figure 13.2 Half-sine acceleration (left) and uniaxial wave propagation problem for a two material-geometry domain (right).
Figure 13.3 Failure of a suspension spring of a MEMS accelerometer.
Figure 13.4 Reference device (uniaxial accelerometer): (a) mould-free package; (b) uncapped die; (c) movable MEMS structure.
Figure 13.5 Grain morphologies for varying representative volume element size, (average grain size ): (a) ; (b) ; (c) ; (d) .
Figure 13.6 Effect of tilting on the stress envelope in the suspension springs.
Figure 13.7 MEMS accelerometer; the enlarged panel shows the region prone to failure as studied in the micromechanical analysis.
Figure 13.8 Example of crack propagation, up to percolation, in the most stressed region of the polysilicon film.
Figure 13.9 Statistical forecasts of microcracking pattern at failure. Top row: drop case A; bottom row: drop case B. Left column: perfect grain boundary case; right column: defective grain boundary case.
Figure 13.10 (a) 3D Voronoi tessellation of the most stressed polysilicon region; (b) longitudinal stress (in MegaPascals) and crack pattern under tensile loading directed along the -direction; (c) example of discretization; (d) spatial decomposition in six domains.
Figure 13.11 Package drop, bottom orientation: time evolution of the displacement at plate corners relative to die or cap surfaces.
Figure 13.12 Comparison between stress envelopes in the suspension springs, as induced by die and package drops: (a) top drop; (b) bottom drop.
Chapter 14: Fabrication-Induced Residual Stresses and Relevant Failures
Figure 14.1 Axisymmetric reference system frame adopted for a thin film on a thick substrate.
Figure 14.2 Axisymmetric reference system frame adopted for a thin film on a thick substrate.
Figure 14.3 The continuous (dashed) line represents the locus of points where the Stoney formula (14.11) overestimates (underestimates) the curvature by 10%, taking into account the actual thickness ratio .
Figure 14.4 Continuous lines represent, under the constant-curvature hypothesis, the linear relationship between normalized mismatch strain or normalized curvature and the nonlinear law by Equation 14.19. Dashed lines are the results of nonlinear finite analyses accounting for nonconstant curvature along the radial distance on the substrate.
Figure 14.5 Experimental determination of crystallographic spacing (eventually modified by a residual stress) through interferometric measurement of the Bragg angle, .
Figure 14.6 Laser scanning method.
Figure 14.7 Multibeam inspector for residual stress determination.
Figure 14.8 2D interpretation of the bulge test.
Figure 14.9 Delamination front in thin film with equi-biaxial residual stress field.
Figure 14.10 Tangential () and normal () interface stresses for an interior crack.
Figure 14.11 Tangential () and normal () interface stresses for an edge crack.
Figure 14.12 Average of the residual in-plane stress (see Equation 14.46) between edges of film strips.
Figure 14.13 Buckling-induced delamination due to a residual stress in a thin film.
Figure 14.14 Advancing crack into a thin film due to residual stresses.
Chapter 15: Damping in Microsystems
Figure 15.1 Comb-finger device: quality factor versus pressure down to near vacuum.
Figure 15.2 Biaxial accelerometer.
Figure 15.3 Single unit used for simplified squeeze and Couette analysis: geometry and finest mesh.
Figure 15.4 Comb-finger resonator: 3D view and 2D layout.
Figure 15.5 Comb-finger resonator: detail of the finest mesh adopted for the boundary element method approach.
Figure 15.6 Boundary element method results with slip boundary conditions (BC): comparison with experiments. Viscous force exerted on the shuttle for a unit velocity.
Figure 15.7 Single unit used to analyse the structure.
Figure 15.8 Biaxial accelerometer: comparison between experimental and numerical forces [N] for the finest mesh M5.
Figure 15.9 Damping force between two parallel identical rectangular plates at K; mbar; gap ; longer side of the plates . Comparison between the coefficients predicted by the integral equation approach, the model of Veijola
et al
. (1995) and the model of Bao
et al
. (2002).
Figure 15.10 Out-of-plane rotational resonator: detail of the perforated mass.
Figure 15.11 Physical bounding surfaces of a fluid elementary cell: (a) 3D view; (b) in-plane dimensions.
Figure 15.12 Damping coefficients: comparison of experiments and simulations in the free-molecule regime.
Figure 15.13 SEM of comb-finger structures.
Figure 15.14 Typical comb-finger structures. The shaded portion is enlarged on the right with indications of typical dimensions after production.
Figure 15.15 Comb-finger device 13. Quality factor versus pressure: zoom in the linear region.
Figure 15.16 Numerical and experimental data for the comb-finger devices at mbar.
Figure 15.17 Quality factor of single-crystal resonant beams versus beam length, thickness : numerical results, Zener's formula and experimental results. , with thermoelastic damping, EF, finite element method; exp, experimental.
Figure 15.18 Doubly clamped beam.
Figure 15.19 Functions , and .
Figure 15.20 Beam on a semi-infinite substrate: geometry and example perfectly matched layers. PML, perfectly matched layer.
Figure 15.21 SEMs of aluminium nitride contour mode resonators: (a) 220 MHz; (b) 370 MHz; (c) 1.05 GHz. IDT, interdigitated.
Figure 15.22 Geometric model and detail of a typical mesh.
Figure 15.23 220 MHz devices, . Numerically predicted (circles) for varying anchor width versus experimental data. Bars denote average experimental data with superposed standard deviations.
Figure 15.24 for and .
Figure 15.25 Experimental results compared with classical thermoelastic approach, for beam resonators with small thickness . , with thermoelastic damping, exp, experimental.
Figure 15.26 1.05 GHz devices, . Numerically predicted (circles) for varying anchor width versus experimental data at 10 K.
Chapter 16: Surface Interactions
Figure 16.1 Meniscus between spherical asperity and flat surface.
Figure 16.2 Longitudinal cross-section of doubly clamped beam adhering to its substrate.
Figure 16.3 Comparisons of theoretical and experimental results for circular plates sticking to the substrate in their central part.
Figure 16.4 Longitudinal cross-section of cantilever beam, as considered in the Sandia experimental set-up.
Figure 16.5 Interferogram of detached lengths versus relative humidity (RH), after 40 h exposure.
Figure 16.6 Adhesion energy as a function of relative humidity (RH). Data from De Boer
et al
. (1999).
Figure 16.7 Experimental set-up proposed by the Virginia group.
Figure 16.8 Experimental load–displacement curve for the indentation point: cyclic behaviour.
Figure 16.9 Micrograph of a structure tested by the ETH group.
Figure 16.10 Results of experimental tests after application of the Weibull approach.
Figure 16.11 Theoretical (left) and experimental (right) plots of current versus applied voltage during a pull-in–pull-off test.
Figure 16.12 Cross-section of stuck–unstuck device proposed by Ardito
et al
. (2013) to study adhesion energy by means of electrostatic actuation and capacitive read-out.
Figure 16.13 Typical layout for evaluation of sidewall adhesion force.
Figure 16.14 Device for inline monitoring of sidewall adhesion force, proposed by the group at the Politecnico di Milano.
Figure 16.15 Lennard-Jones potential for contacting molecules.
Figure 16.16 Contact between rough surfaces: equivalence between original situation (a) and simplified model (b) in the GW approach; and represent the rms roughness of the original surfaces.
Figure 16.17 Specific adhesion energy versus relative humidity for wet stiction. Experimental results are from De Boer
et al
. (1999), ‘new model’ refers to results of Hariri, Zu and Ben Mrad (2007). Results of Van Spengen, Puers and De Wolf (2002) are also reported.
Figure 16.18 Finite element model for typical artificially generated rough surface.
Figure 16.19 Comparison of numerical results with the experimental results of DelRio
et al
. (2005), for the specific case of perfectly dry conditions (van der Waals forces only).
Figure 16.20 Detailed view of numerically generated rough surface. The same length scale is adopted for both in-plane and out-of-plane dimensions.
Figure 16.21 Adhesion energy versus relative humidity (RH) for a surface of roughness 2 nm rms: comparison of experimental data from De Boer (2007) and numerical outcomes. M1, model 1; StdAp, standard approximation.
Figure 16.22 Adhesion energy vs. relative humidity (RH): comparison of experimental data, from DelRio
et al
. (2007), and numerical outcomes. vdW, van der Waals.
List of Tables
Chapter 2: Fundamentals of Mechanics and Coupled Problems
Table 2.1 Piezoelectric material parameters. F/m
Chapter 3: Modelling of Linear and Nonlinear Mechanical Response
Table 3.1 Eigenfrequencies and eigenfunctions of a single-span beam
Table 3.2 Coefficients and in Equation 3.40 for single-span beams with different boundary conditions
Chapter 8: Vibrating Lorentz Force Magnetometers
Table 8.1 Parameters of the designed magnetometers (theoretical resonance frequency kHz)
Table 8.2 Values of for the different stator configurations
Table 8.3 Device parameters
Chapter 9: Mechanical Energy Harvesters
Table 9.1 Example of standard and effective piezoelectric properties for uniaxial stress ( F/m)
Chapter 13: Accidental Drop Impact
Table 13.1 Definition of the problem depending on characteristic times
Chapter 15: Damping in Microsystems
Table 15.1 Comparison of experimental results with numerically computed damping forces (for unit velocity) at ambient pressure: contribution from different parts of the rotor and global results
Table 15.2 Forces [N] acting on the a cross-section of the shuttle of unit depth
Table 15.3 Mesh M3: number of iterations and CPU time
Table 15.4 Comb-finger structures: nominal gap ; overlap between stator and shuttle fingers ; nominal resonating frequency ; number of shuttle fingers
Table 15.5 Thermal and effective mechanical properties of monocrystalline silicon
Table 15.6 Quality factors for 1.05 GHz resonators
The Wiley Microsystem and Nanotechnology Series
Series Editors-Ronald Pethig and Horacio Espinosa
Mechanics of Microsystems
Corigliano, Ardito, Comi, Frangi, Ghisi, and Mariani, December 2017
Advanced Computational Nanomechanics
Silvestre, February 2016
Micro-Cutting: Fundamentals and Applications
Cheng and Huo, August 2013
Nanoimprint Technology: Nanotransfer for Thermoplastic and Photocurable Polymers
Taniguchi, Ito, Mizuno, and Saito, August 2013
Nano and Cell Mechanics: Fundamentals and Frontiers
Espinosa and Bao, January 2013
Digital Holography for MEMS and Microsystem Metrology
Asundi, July 2011
Multiscale Analysis of Deformation and Failure of Materials
Fan, December 2010
Fluid Properties at Nano/Meso Scale: A Numerical Treatment
Dyson, Ransing, Williams, and Williams, September 2008
Introduction to Microsystem Technology: A Guide for Students
Gerlach and Dötzel, March 2008
AC Electrokinetics: Colloids and Nanoparticles
Morgan and Green, January 2003
Microfluidic Technology and Applications
Koch, Evans, and Brunnschweiler, November 2000
Mechanics of Microsystems
Alberto Corigliano, Raffaele Ardito, Claudia Comi, Attilio Frangi, Aldo Ghisi, and Stefano Mariani
Politecnico di Milano Italy
This edition first published 2018
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Library of Congress Cataloging-in-Publication Data
Name: Corigliano, Alberto, author.
Title: Mechanics of microsystems / by Alberto Corigliano, Dr. Raffaele Ardito, Dr. Claudia Comi, Dr. Attilio Frangi, Dr. Aldo Ghisi, Dr. Stefano Mariani.
Description: Hoboken : Wiley, [2018] | Series: The Wiley microsystem and nanotechnology series ; 7646 | Includes bibliographical references and index. |
Identifiers: LCCN 2017033389 (print) | LCCN 2017052694 (ebook) | ISBN 9781119053804 (ePDF) | ISBN 9781119053811 (ePUB) | ISBN 9781119053835 (cloth)
Subjects: LCSH: Microelectromechanical systems.
Classification: LCC TK7875 (ebook) | LCC TK7875 .C665 2018 (print) | DDC 621.381-dc23
LC record available at https://lccn.loc.gov/2017033389
Cover Design: Wiley
Cover Images: (First 3 images) Courtesy of Alberto Corigliano;(Abstract) © LuxEterna/Gettyimages; (Large image) Courtesy of Alberto Corigliano;(Lower left corner) © Fuse/Gettyimages
To our families
Series Preface
The Microsystem and Nanotechnology book series provides a thorough contextual summary of the current methods used in micro- and nano-technology research and how these advances are influencing many scientific fields of study and practical application. Readers of these books are guided to learn the fundamental principles necessary for the topic while finding many examples that are representative of the application of these fundamental principles. This approach ensures that the books are appropriate for readers with varied backgrounds and useful for self-study or as classroom materials.
Micro- and nano-scale systems, fabrication techniques, and metrology methods are the basis for many modern technologies. Several books in this series, including Introduction to Microsystem Technology by Gerlach and Dotzel, Microfluidic Technology and Applications edited by Koch, Evans, and Brunnschweiler, and Fluid Properties at Nano/Meso Scale by Dyson, Ransing, P. Williams and R. Williams, provide a resource for building a scientific understanding of the field. Multiscale modeling, an important aspect of microsystem design, is extensively reviewed in Multiscale Analysis of Deformation and Failure of Materials by Jinghong Fan. Emergent nanofabrication techniques are presented in Nanoimprint Technology: Nanotransfer for Thermoplastic and Photocurable Polymer by Jan Taniguchi. Modern topics in mechanics are covered in Nano and Cell Mechanics: Fundamentals and Frontiers edited by Espinosa and Bao. Specific implementations and applications are presented in AC Electrokinetics: Colloids and Nanoparticles by Morgan and Green, and Digital Holography for MEMS and Microsystem Metrology edited by Asundi.
This book, by A. Corigliano, R. Ardito, C. Comi, A. Frangi, A. Ghisi, and S. Mariani, presents in-depth mechanics analyses and powerful numerical modeling strategies particularly useful to the field of microsystems. Topics such as mechanical characterization at the microscale, fracture and fatigue of microsystems, intrinsic and extrinsic dissipative mechanisms, and surface interactions are treated in a unique perspective and depth not found in other MEMS books. Given the focus and depth of the topics covered, the reader will find this book complementary to classic books in MEMS such as Fundamentals of Microfabrication, by M. Madou, and Microsystem Design, by S. Senturia.
The book starts by covering the fundamentals needed to design and anlayze microsystems. An extensive chapter is dedicated to the analytical and numerical treatment of linear and nonlinear mechanics, which is essential to understand design principles exploiting geometric and electrostatic stiffness variations in various sensing modalities.
The authors have made numerous and unique contributions to the field by working closely with STS engineers on microsystems, which designs were translated into commercial products. Hence the book contains many examples of novel microsystems, e.g., three-axis resonant accelerometers with optimized performance and integration. In addition to accelerometers, the book also discusses Coriolis-based gyroscopes and vibrating Lorentz force magnetometers. As such, the reader will find in one book all the knowledge needed to gain insight into the use of microsystems in inertial measurement unites typically found in modern cell phones, unmanned or remotely operated vehicles, space satellites, and civil and military aviation. Other applications include the use of piezoelectric materials in resonators and energy harvesters.
The pedagogic treatment given by the authors makes this book suitable for inclusion in undergraduate and graduate courses in engineering. Students who are familiar with undergraduate dynamics, strength of materials, and electricity and magnetisms, should be able to grasp the majority of the book content. Some chapters may require background in continuum mechanics and finite element modeling to take full advantage of their contents. The book as a whole should be considered as recommended reading for researchers across a wide range of disciplines including materials science, mechanical engineering, electrical engineering, and applied physics.
Horacio Espinosa Series co-editor
Preface
This book originated from the experience that our research group, working on the mechanics of solids and structures, had the opportunity of accumulating in the fascinating field of microsystems.
Microsystems are multidisciplinary devices that are creating new opportunities in many markets, such as the consumer sector and the automotive industry, and are now undergoing a great expansion, owing to the emerging Internet of Things.
When one looks inside these very small machines, one soon realizes that, in addition to many fundamental electronic components and read-out circuits, in many cases their core is based on mechanics and related complex interactions in other physical domains.
Another thing that newcomers to the microsystem world very quickly learn is that microsystems design is related to the whole process of fabrication, with related high technology processes, up to the final packaging and assembly, and to many reliability issues that can arise along the long journey from the initial idea to the final product. Design for reliability is a necessity if one is to create successful commercial products.
Mechanics can greatly help in understanding the basic working principles of microsystems, in proposing new designs and in understanding many reliability issues. To put it briefly: good mechanics is of paramount importance for good microsystems.
The purpose of this book is precisely to give researchers, students and designers a mechanical perspective of the world of microsystems and to focus on those mechanically related aspects that, in our view, are most important for the study and design of microsystems. Therefore, this is not a book about the whole world of microsystems; many important features of microsystem research and design are not dealt with here, such as microfabrication technologies, electronics and control theory.
The book is divided into three main parts.
The first part, ‘Fundamentals’, gives the reader fundamental knowledge for understanding the microsystems world; it contains notions that are traditionally given in various disciplines, such as solid and structural mechanics, fluid mechanics, electrostatics, thermal analysis and a first introduction to typical coupled and nonlinear problems encountered in microsystems.
The second part, ‘Devices’, contains examples of typical microsystems interpreted from the point of view of mechanics. Important inertia devices such as accelerometers and gyroscopes are discussed, together with other less common but important devices like micropumps and energy harvesters.
The third part, ‘Reliability and dissipative phenomena’ has the purpose of illustrating, in some detail, fundamental reliability issues in microsystems: fracture and fatigue, accidental drops, residual stresses, damping phenomena and stiction.
In our opinion, this book could be used in various ways. It can be a useful reference for microsystems researchers and designers looking for precise information on many mechanical issues in microsystems and for help in understanding and modelling some reliability issues. It can be used in graduate courses, either as an introduction to the mechanics of microsystems (Parts One and Two), or in more advanced courses (Parts Two and Three).
Milano, March 2017
Alberto CoriglianoRaffaele ArditoClaudia ComiAttilio FrangiAldo GhisiStefano Mariani
Acknowledgements
Our group started working in the world of microsystems thanks to a collaboration with STMicroelectronics in 2002; the experience accumulated over the last 15 years would not have been possible without the intense academia–industry collaborations that consolidated during these years. A special acknowledgement goes to the whole MEMS group of STMicroelectronics, which includes mechanical and electronic designers and experts in fabrication processes.
Another key ingredient behind our expertise in microsystems is the active collaboration with other research groups on the Politecnico di Milano, working at the Departments of Electronics, Materials, Mechanics and Mathematics. We are perfectly aware that without close multidisciplinary collaborations, many features of microsystems are simply intractable and therefore we would like to acknowledge the importance of their contribution behind many of the results discussed in this book.
Many results and experiences described in this book are also based on the work of many young collaborators, post-docs, Ph.D. and M.S. students; to them our thanks for their fundamental contribution and for giving us the opportunity of introducing them to the strange and fascinating world of microsystems.
Notation
Latin symbols
crack length
unknown variables in the method of weighted residuals
acceleration
cross-sectional area of beam
body force
beam width; magnetic field intensity
damping coefficient
specific heat
distance vector between two origins; material compliance matrix
C
concentrated couple in a beam
capacitance
material stiffness matrix
electric displacement
Young's modulus
electric field
frequency
surface force
electrostatic force
viscous force
concentrated force
elastic force
acceleration due to gravity
initial gap in a capacitor
energy release rate
critical energy release rate
convection constant; function in Weibull approach
beam height
,
,
unit vectors of Cartesian axes
moment of inertia of beam
geometrical torsional stiffness of beam
stiffness of linear elastic spring; thermal conductivity
electrostatic stiffness
mode I stress intensity factor
mode II stress intensity factor
mode III stress intensity factor
material fracture toughness in mode I
stiffness matrix
length of beam; length of other device
length of fracture process zone
length of beam
Lagrangian functional
angular momentum with respect to point
point mass; Weibull material parameter
bending moment in a beam
torsional moment in a beam
mass matrix
axially distributed load in a beam
axial force in a beam
origin of a reference system
hydrostatic part of a stress tensor or distributed load in a beam orthogonal to beam axis; gas pressure
external power
probability of failure in Weibull approach
internal power
assigned axial load in a beam
electric charge; flow rate
electric charge contained in a volume
heat flux
internal source of thermal power per unit volume
linear momentum
radial coordinate in linear elastic fracture mechanics
R
error; residual in the method of weighted residuals
stress ratio in fatigue
out-of-plane beam thickness
deviatoric stress
surface in a capacitor
action functional
time; thickness
temperature
kinetic energy
displacement function
approximating function in the method of weighted residuals
displacement vector
displacement amplitude
displacement function; stroke volume
velocity vector
weight functions in the method of weighted residuals
shear force in a beam
work of nonconservative forces
,
,
Cartesian axes
position vector
time-dependent amplitude of free vibration of beam
Greek symbols
coefficient of thermal expansion
parameter in Weibull approach
boundary of a deformable body
film fracture energy
free boundary of a deformable body
constrained boundary of a deformable body
displacement jump across a crack
permittivity of free space
relative permittivity
column matrix of strains
axial deformation of beam
angle of torsional rotation per unit length in a beam; angle of rotation in a rotational microactuator
Euler angle; circumferential coordinate in linear elastic fracture mechanics
first Lamé constant
second Lamé constant
dynamic viscosity
Poisson's ratio
kinematic viscosity
nondimensional constant for damping
total potential energy
mass density per unit volume
electric charge density per unit length
electric charge density per unit surface area
electric charge density per unit volume
,
,
incident, reflected, transmitted stress in impacts
nominal stress in Weibull approach
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Chapter 1Introduction
The purpose of this first chapter is to give, in a brief and simple way, preliminary information on what are currently termed microsystems, how they are fabricated and the role of mechanics in their design and overall behaviour.
This preliminary information helps in understanding the purpose, organization and limitations of this book. At the end of this introductory chapter, a short description of the contents of each chapter is given.
1.1 Microsystems
It is usually recognized that the history of microsystems started with the talk given by Feynman on December 1959 (Feynman, 1960) and with the creation of the resonant gate transistor (Nathanson et al., 1967).
After a period in which microsystems were the subject of intense research activity in academic laboratories, the MEMS industry started with a large number of spin-offs and small and medium enterprises. More recently MEMS production expanded, mainly thanks to the wide diffusion of inertial MEMS (microaccelerometers and microgyroscopes) in consumer market products.
The ‘more than Moore’ trend driven by MEMS was able to compensate a partial saturation of ICT product growth and opened new possibilities for distributed sensing and monitoring. Nowadays, the new popular phrases ‘Internet of Things’ and ‘Internet of Everything’ are paradigms of an increasingly connected world in which many kinds of information can be automatically transmitted by everyday life smart products such as phones, tablets, watches, glasses and cars.
We are now in a ‘more than MEMS’ era in which, after a first phase mainly driven by microsystem miniaturization, augmented capabilities are added to microsystems; for example, multiaxis sensor units, which combine accelerometers, gyroscopes, pressure and magnetic field sensors. In the near future, we will witness a new phase, in which microsystems inserted in wireless sensor networks will have extra abilities and performances, such as energy autonomy and high reliability, even in extremely aggressive environments.
A first glance at microsystems can be obtained examining the popular acronym (MEMS) which stands for micro electro mechanical system.
Micro means that we are speaking of small devices, in which the single smallest dimension can also be at the submicrometre scale. A complete MEMS containing mechanical and electronic parts can be of the order of millimetres. These dimensions tell us that we are not yet in the field of the nanoscopic world, but that we are very near to it. Some phenomena, e.g. interaction forces between surfaces almost in contact, must in fact be studied and modelled taking into account the nanoscale.
To have an immediate feeling of the microsystems' dimensions, let us observe Figure 1.1, which shows schematically a commercial product. The fully packaged device has dimensions 3.5 mm 3 mm 1 mm; it has, therefore, a volume of 10.5 mm. Inside the device there are three sensors: a three-axis accelerometer, a three-axis gyroscope and a three-axis magnetometer. This is why the device is called a nine-axis module.
Figure 1.1 Typical commercial microsystem: a nine-axis accelerometer, gyroscope, magnetometer.
If we now make the exercise of superposing the device of Figure 1.1 on a 1 euro cent coin, we realize that more than 16 nine-axis MEMS can be arranged on its surface, as shown in Figure 1.2. This gives the impressive result that on a surface equivalent to 1 euro cent, one can, in principle have, sensing signals!
Figure 1.2 16 nine-axis MEMS superposed on a 1 euro cent coin.
This remark gives a clear idea of the potentialities behind the microsystems technology; these small machines can really be placed everywhere!
Electro means that inside these small devices there are electric and electronic components; these are needed to create connections between the MEMS and the external world, to transform physical information (inertia forces, pressure, …) in electric signals and also to activate movements inside the device. In addition to the electronic components needed to make the MEMS core work, it is always necessary to add read-out electronic circuits. In Figure 1.1, electric and electronic components are represented by the small wires that connect various components and by the thin lower plate that represents the application-specific integrated circuit for read-out control. Definitely, electronics form a very important part of every microsystem.
Mechanical means that microsystems, in addition to the fact that they are very small and contain electronic components, have some portion of their architecture that works thanks to mechanical principles. For instance, inside the MEMS there can be very small beams or plates that are loaded by inertia forces caused by the overall acceleration of the device and that can be considered as structural components exactly in the same way as beams and plates are structural components of large structures, such as the buildings in which we all live. In addition to this immediate evidence of mechanics in microsystems, there are many other implications, as briefly discussed in Section 1.3.
System means that the microdevices are not simple; they must be interpreted as complex systems combining various components: the electric and electronic parts, the mechanical parts, and possibly other parts, such as optical components. Moreover, they may be produced by means of complex fabrication processes and complex integration of different portions.
1.2 Microsystems Fabrication
The fabrication of microsystems is a complex process that was mainly adapted from those used in the fabrication of integrated circuits. Here, only a few concepts are given with reference to one of the possible fabrication processes; for a full understanding of microsystems fabrication processes, the reader must consult specialized textbooks, e.g. Madou (2002).
The starting point for current microsystems is a wafer of monocrystalline silicon, which is used as a support on top of which various materials can be subsequently deposited by means of various techniques. The wafer is a flat disc very similar to those used in CDs for music or data storage.
Microsystems industries with high volume production currently use 8 inch wafers, i.e. discs with a diameter of 20.32 cm.
Various materials are added on top of the wafer, such as metals or other kinds of silicon, e.g. polycrystalline silicon. Each added layer has a pre-specified thickness and role in the design and fabrication of the device.
Beside the stratification, or deposition, of various materials, microsystems fabrication has another recurrent and fundamental step, which is the selective elimination of portions of one or more deposited layers. This is the so-called lithography process, which means writing on stone (lithos = stone, in Greek).
Lithography is used in the production of electronic circuits and is conceptually similar to artistic lithography, in which drawings are chemically engraved on stone surfaces.
During a lithographic phase, a thin film, called resist, is first exposed to light only on some portions of the surface, depending on the pattern or drawings
