MEMS Sensors and Transducers Part 1 PDF

MEMS –Module 2 Topics Thermal sensors and actuators Electrostatic sensors and actuators Piezoelectric sensors and actuators Magnetic sensors  Types of Beams a) A fixed-free cantilever parallel to the plane of the substrate, with the free tip capable of moving in a direction...

MEMS –Module 2 Topics Thermal sensors and actuators Electrostatic sensors and actuators Piezoelectric sensors and actuators Magnetic sensors  Types of Beams a) A fixed-free cantilever parallel to the plane of the substrate, with the free tip capable of moving in a direction normal to the substrate. Lateral, in-plane movement of the free end would encounter much significant resistance. b) A fixed-fixed beam (bridge) parallel to the substrate plane. c) There are actually two ways to classify this beam. It can be considered a fixed-fixed cantilever parallel to the substrate plane with a thick and stiff part in the middle. Alternatively, this beam can also be considered as two fixed-guided beams jointed in parallel to support a rigid part. d) A fixed-free cantilever with the free end capable of movement perpendicular to the substrate. Its behavior is similar to that of (a). e) A fixed-free cantilever with the free end capable of movement within the substrate plane. With its thickness greater than its width, the movement of the free end in a direction perpendicular to the substrate plane would encounter much greater resistance.  Types of Beams f) A fixed-fixed beam (bridge). g) A fixed-free cantilever carrying a stiff object at the end. The stiff object does not undergo flexural bending due to increased thickness. h) This beam is very similar to case (c) except for the fabrication method. i) A fixed-free cantilever with folded length. It consists of several fixed-free beam segments connected in series. The free end of the folded cantilever is capable of movement in a direction parallel to the substrate surface. Movement of the free end perpendicular to the substrate would encounter much greater resistance. j) Two fixed-free cantilever connected in parallel. The combined spring is stiffer than any single arm. k) Four fixed-guided beam connect to a rigid shuttle, which is allowed to move in the substrate plane but with restricted out-of-plane translational movement. The most commonly encountered beam structures in MEMS are double-clamped suspension structures and single-clamped cantilevers. Thermal Sensors & Actuators  Thermal Energy (Heat) can cause physical changes to materials such as:  Thermal expansion/contraction (size)  Electrical resistance  Optical radiation emission (light)  Phase change (fluid-gas)  MEMS devices can transduce thermal energy to create:  Microactuators:  Thermal bimorph  Fluid dispensors  Micro-sensors:  Thermal bimorph  Micro thermocouples  Thermo resistive sensors Example of Ink Jet Thermal Actuator  Inkjet printers operate on the ‘Phase change’ aspect of micro-thermal actuation.  When current is applied to the polysilicon strip, ohmic heating occurs.  This causes local heating of fluid adjacent to the heater, causing a phase change of the ink from fluid to gas. Video on a thermal Inkjet printer Example of Electro-Thermal Actuator  Electro-Thermal ‘bimorph’ Actuators operate on the principle of ‘Differential Thermal Expansion’ to produce motion.  Example of Electro-Thermal Actuator  Operational details of electro-thermal actuator:  The different areas, given the constant current, i, causes a different amount of heating in each area.  This in turn causes a different amount of thermal expansion, which can be utilized to produce motion of the tip.  This lateral motion can be harnessed to do useful work. Basics of Heat Transfer  There are four modes of heat transfer 1. Thermal conduction: transfer of heat through a solid media in the presence of a temperature gradient Basics of Heat Transfer  There are four modes of heat transfer 2. Natural thermal convection: transfer of heat from a surface into a stationary body of fluid Basics of Heat Transfer  There are four modes of heat transfer 3. Forced thermal convection:flow of heat from a surface into a moving fluid Basics of Heat Transfer  There are four modes of heat transfer 4. Radiation: -loss of heat via electromagnetic radiation through air or vacuum from a surface Example of Heat Transfer: Boiling Pot of Water  Thermal Conduction  For the boiling pot example, the ‘overall’ driving force is: Tcoil – Troom  In order to determine how all the heat moves, from the coil into the room air, we can create an equivalent ‘thermal circuit’  The ‘thermal circuit’ represents the heat flow in the system, and is analogous to an ‘electric circuit’  Consider the heat transfer through solid bodies (i.e. thermal conduction) in greater detail, with the diagram:  Here we have:  Using the electrical analogy, we can define thermal resistance as:  Therefore Energy Storage  The relationship between stored thermal energy (Q) and temperature change is 𝑄 = 𝑠ℎ. 𝑚. ∆𝑇 = 𝐶𝑡ℎ. ∆𝑇 Where sh (J/KgK) is the specific Heat, which is the amount of heat per mass required to raise the temperature of an object by one degree Celsius or Kelvin. Cth is called the heat capacity, which is the equivalent od electrical capacitance in a thermal electrical analogy  The general expression of the time constant associated with heating or cooling of microstructure is 𝜏 = 𝑅𝑡ℎ𝐶𝑡ℎ = 𝑅𝑡ℎ. 𝑠ℎ. 𝑚 Example: Thermal Resistance of a Suspended Bridge Comparison of Thermal Actuation and Electrostatic Actuation Electrostatic actuation Thermal actuation  Power: low power due to  Relatively high power: due to voltage operation. current operation.  Response speed: high speed.  Lower response speed due to thermal time constant  Construction and fabrication: (dissipation and thermal relatively simple charging)  Range of motion: for parallel  Constructionand fabrication: plate capacitor, range of more complex due to material motion relatively small compatibility considerations.  Range of motion: relatively large.  Micro Ciliary Motion System - biomimetic micro motion system  Biomimetic ciliary transport system  utilizing large number of distributed actuators to achieve macroscopic motion Thermal Couples - Seebeck Effect  Thermal electric effect refers to the generation of electrical potential when a temperature differential exist across a piece of material. At the high temperature end, more electron will be excited into the conduction band and starts diffusion into the colder region.  The Seebeck effect (nameed after Seebeck), is commonly characterized by the Seeback coefficient which is expressed in the following form, for a single piece of metal: V   T  A working thermal couple with two different Seeback coefficients develop a voltage difference when subject to a temperature change of T. High T ΔV Low ab  a b T V  (a b )T Electrostatic Sensors and Actuators  Sensing  capacitance between moving and fixed plates change as  distance and position is changed  media is replaced  Actuation  electrostatic force (attraction) between moving and fixed plates as a voltage is applied between them.  Two major configurations Interdigitated finger configuration  parallel plate capacitor (out of plane)  interdigitated fingers - IDT (in plane) A d Parallel plate configuration  Examples  Parallel Plate Capacitor  Comb Drive Capacitor  Parallel Plate Capacitor A d Q C V Fringe electric field (ignored in first order analysis) E  Q / A Q A C  Q d d A  Equations without considering fringe electric field.  A note on fringe electric field: The fringe field is frequently ignored in first-order analysis. It is nonetheless important. Its effect can be captured accurately in finite element simulation tools. Forces of Capacitor Actuators 1 1Q 2  Stored energy U  CV 2  2 2 C  Force is derivative of energy with U 1 C 2 F   V respect to pertinent dimensional d 2 d variable  Plug in the expression for Q A C  capacitor Q d d A 1  We arrive at the expression for U   A 1 CV 2 F  V 2  force d 2d 2 2 d Merits and demerits of capacitor actuators Merits Demerits  Nearly universal sensing and  Force and distance inversely scaled actuation; no need for special - to obtain larger force, the materials. distance must be small.  Low power. Actuation driven by  In some applications, vulnerable to voltage, not current. particles as the spacing is small - needs packaging.  High speed. Use charging and discharging, therefore realizing full  Vulnerable to sticking phenomenon mechanical response speed due to molecular forces.  Occasionally, sacrificial release. Efficient and clean removal of sacrificial materials. Capacitive Accelerometer  Proof mass area 1x0.6 mm2, and 5 m thick.  Net capacitance 150fF  External IC signal processing circuits Example video Example video – working of accelerometer Example video – airbag crash test Equilibrium Position of Electrostatic Devices  Consider the following parallel plate capacitor system:  We can describe the mechanical force as:  We can describe the electrical force as: * Note, that C is also a function of d  Equilibrium Position of Electrostatic Devices  From the diagram, let:  Therefore, the expression for the electrostatic force becomes:  To find an expression for the equilibrium position, (x0+x) we must equate: Fm=Fe  So we have the expression as  Which yields the quadratic equation, *Note, this equation yields two solutions Graphical analysis of equilibrium position  A plot of the mechanical force and electrical force shows: If the right-hand plate moves closer to the fixed one, the magnitude of mechanical force increases linearly. If a constant voltage, V1, is applied in between two plates, the electric force changes as a function of distance. The closer the two plates, the large the force. X0 Equilibrium position - The linear mechanical function intersects with the electrical function at two points. - Note: Only the solution closest to the starting position (right side) is realizable. Concept of ‘Pull-in’ Voltage  As we increase voltage, the previous graph will change as follows: (Fig 4.5) Concept of ‘Pull-in’ Voltage  Eventually, we reach a ‘Critical Point’ voltage where there is only one solution, where the mechanical force is equal to the electricalforce  This is called ‘Pull-in’ voltage  Consider the consequences of applying a voltage higher than the ‘Pull-in’ voltage.  To conclude: Electrostatic devices should be designed or operated such that the applied voltage remains below the ‘Pull-in’ voltage to avoid ‘snap-in’.  ‘Snap-in’ may damage the mechanism or cause burn-out due to contact under high applied voltage. Mathematical Determination of Pull-in Voltage Step 1 - Defining Electrical Force Constant  Let’s define the tangent of the electric force term. It is called electrical force constant, Ke. F CV 2 ke  x ke  d2  When voltage is below the pull-in voltage, the magnitude of Ke and Km are not equal at equilibrium  Review of Equations Related To Parallel Plate E 1 A 2 1 CV 2  The electrostatic force is F  V  d 2 d2 2 d 1 A 2 A V 2 V2  The electric force constant is Ke   (2) V  C 3 2 2 d d d d2 Mathematical Determination of Pull-in Voltage Step 2 - Pull-in Condition  At the pull-in voltage, there is only one intersection between |Fe| and |Fm| curves.  At the intersection, the gradient are the same, i.e. the two curves intersect with same tangent. ke  k m  This is on top of the condition that the magnitude of Fm and Fe are equal. 2  2k x(x  x ) 2  2k x(x  x )  Force balance yields V  m 0 ฀m 0 Eq.(*) A C CV 2  Plug in expression of V2 into the expression for Ke, ke  d2  we get CV 2  2k x ke   ฀ m (x  x0 ) (x  xo ) 2  This yield the position for the pull-in condition, x=-x0/3. Irrespective of the magnitude of km. Mathematical Determination of Pull-in Voltage Step 3 - Pull-in Voltage Calculation  Plug in the position of pull-in into Eq. * on previous page, we get the voltage at pull-in as 2 4x02 V p  km 9C  At pull in, C=1.5 Co A (2 /3)d  Thus, 2x0 km Vp . 3 1.5C0 Piezoelectric effect – Definition  Direct Piezo Effect a mechanical stress on a material produces an electrical polarization  Inverse Piezo Effect  an applied electric field in a material produces dimensional changes and stresses within a material.  In general, both piezoelectricity and inverse piezoelectricity are denoted piezoelectric effects. Origin of Phenomena of Piezoelectric Effect  The microscopic origin of piezoelectricity is the displacement of ionic charges within a crystal. Symmetric (centrosymmetric) lattice structure does not produce piezoelectricity when deformed.  Asymmetric lattice structures will create an electric potential when deformed Origin of Phenomena of Piezoelectric Effect  Piezoelectric effects are strongly dependent on the crystal orientation w.r.t. the strain/electric field.  In most cases, one particular orientation exhibits the strongest piezoelectric effect.  The direction of positive polarization is customarily parallel with the z axis (i.e. the Poling axis is parallel to the z-axis)  The standard piezoelectric notation used is such that the x, y and z axes correspond to subscripts 1, 2, and 3, respectively. Origin of Phenomena of Piezoelectric Effect  Therefore, if the electric field is applied parallel with the z-axis it is applied in ‘direction 3’.  Note: The resulting strain generated due to an electric field in direction 3, is parallel with the x-axis (direction 1).  Conversely, if a strain is applied in direction 1, the generated electric field will occur parallel to direction 3. Governing Equations of Piezoelectric Effect  The direct effect of piezoelectricity can be described by the general equation: Where D  dT  E D: Electrical Polarization T: Applied Mechanical Stress d: Piezoelectric Coefficient Matrix T  ε: Electrical Permittivity Matrix T2  1 E: Electrical Field  D1  d 11 d12 d13 d14 d15 d16    11 12  13  E1  D 2  d d d d d d  T3       E     21 26   4  23  2  d  T     22 23 24 25 21 22  D  d d d d d E   3   31 32 33 34 35 36  T5   31 32 33  3    T6  The direct effect of piezoelectricity can be simplified down to the equation, in the absence of an external electric field (i.e. E=0). D=dT Governing Equations of Piezoelectric Effect  The inverse effect of piezoelectricity can be described by the general equation: Where s - Strain Vector s  ST  dE S - Compliance Matrix T - Stress Vector (N/m2) d - Piezoelectric Coefficient Matrix E - Electric Field Vector (V/m) S11  d11 d31  s 1  s S12 S13 S14 S15 S16 T1  d 21 S S S S S S T  d d d   2  S 21 26  2   12 32     22 S T  22 23 24 25 s  S S S S d d E d 33   1  s 4   S 3 31 32 33 34 35 S T    d 36 3 13 23     41 S S S S 46  4  d d 34  E 2  s 5  S 42 43 44 S 45 S T  d  14 d 24  E 3  S S S d 35        51 52 53 54 55 56 5 15 25 S66    s 6   S 61 S 62 S63 S64 S65 T6  d16 d 26 d 36  The inverse effect of piezoelectricity can be simplified to the expression, if there is no additional mechanical stress present (i.e. T=0). Where strain is related the electric field by: S=dE Governing Equations of Piezoelectric Effect  The units of the piezoelectric constant, dij, are the units of electric displacement over the unit of the stress. Therefore:  FV  [d ] [D]  [ ][E]  m m  Columb   33 [T ] [T ] N N m2  Therefore the piezoelectric constant is a good way to measure the intensity of the piezoelectric effect, since we can think of it in terms of Columbs generated, per Newton applied. Commonly Used Piezoelectric Materials  Si is symmetric and does not exhibit piezoelectricity.  (Si: positive charge; bond electrons: negative change)  GaAs lattice is not symmetric and exhibits piezoelectricity.  (However, GaAs has poor piezoelectric material properties) Commonly Used Piezoelectric Materials  ZnO  sputtered thin film  d33=246 pC/N  Lead zirconate titanate (PZT)  ceramic bulk, or sputtering thin film  d33=110 pC/N  Quartz  bulk single crystal  d33=2.33 pC/N Diagram of a ‘Sputtering System’ for  Polyvinylidene fluoride (PVDF) depositing piezoelectric materials onto wafers,  polymer  d33=1.59 pC/N. Commonly Used Piezoelectric Materials Material Relative permitivity Young’s Density Coupling Curie temperature (oC) (dielectric constant) modulus (kg/m3) factor (k) (GPa) ZnO 8.5 210 5600 0.075 ** PZT-4 1300-1475 48-135 7500 0.6 365 (PbZrTiO3) PZT-5A 1730 48-135 7750 0.66 365 (PbZrTiO3) Quartz 4.52 107 2650 0.09 ** (SiO2) Lithium tantalate 41 233 7640 0.51 350 (LiTaO3) Lithium niobate 44 245 4640 ** ** (LiNbO3) PVDF 13 3 1880 0.2 80 Issues with Piezoelectric Materials  Curie temperature  temperature above which the piezoelectric property will be lost.  Material purity  the piezoelectric constant is sensitive to the composition of the material and can be damaged by defects.  Frequency response  most materials have sufficient leakage and cannot “hold” a DC force. The DC response is therefore not superior but can be improved by materials deposition/preparation conditions.  Bulk vs thin film  bulk materials are easy to form but can not integrate with MEMS or IC easily. Thin film materials are not as thick and overall displacement is limited.  Poling  establishment of preferred sensing direction  application of electric field for long period of time after material is formed Example of Piezoelectric Cantilever Beam  Bi-Layer Bending Configuration: 1  2 slong (t p  te )( Ap E p Ae Ee )  r 4(E p I p  Ee I e )( A p E p  Ae Ee )  ( A p E p Ae Ee )(t p  t e ) 2 Where: Ap and Ae are the cross-section areas of the piezoelectric and the elastic layer, Ep and Ee are the Young’s modulus of the piezoelectric and the elastic layer, and tp and te are the thickness of the piezoelectric and the elastic layer  Example of Piezoelectric Cantilever Beam Cr/Au Si3N4 3 ZnO 1 Si3N4 Cr  Example 2  A patch of ZnO thin film is located near the base of a cantilever beam, as shown in the diagram below. The ZnO film is vertically sandwiched between two conducting films. The length of the entire beam is l. It consists of two segments – A and B. Segment A is overlapped with the piezoelectric material while segment B is not. The length of segments A and B are lA and lB, respectively. If the device is used as a force sensor, find the relationship between applied force F and the induced voltage. MASS UIUC Example 2 T1  T2   D1  d11 d12 d13 d14 d15 d16  T  11 12 13  E1  D2  d d d d d d   3      E    23     21 26   4   2    22 25 21 22 d   E  23 24 D  d d d d d T  3   31 32 33 34 35 36  T5   31 32 33  3    T6   0 0 0 0 11.34 0 d   0 0 0 11.34 0 0 pC / N    5.43  5.43 11.37 0 0 0     Solution The c-axis (axis 3) of deposited ZnO is generally normal to the front surface of the substrate it is deposited on, in this case the beam. A transverse force would produce a longitudinal tensile stress in the piezoelectric element (along axis 1), which in turn produces an electric field and output voltage along the c-axis. The shear stress components due to the force is ignored. The stress along the length of the piezoresistor is actually not uniform and changes with position. For simplicity, we assume the longitudinal stress is constant and equals the maximum stress value at the base. The maximum stress induced along the longitudinal direction of the cantilever is given by. The stress component is parallel to axis 1.  1,max  Mt /(2I ) Flt beam / 2I beam According to Equation 2, the output electric polarization in the direction of axis 3 is. The overall output voltage is then D d31 1,max 3. with Tpiezo being the thickness of the piezoelectric stack. VEt D3t piezo Fltbeamt piezo   3 piezo  2I beam Example 3  For the same cantilever as in Example 2, derive the vertical displacement at the end of the beam if it was used as an actuator. The applied voltage is V3.  Example 3  V3 Under the applied voltage, the electrical field in axis 3 is E3  t piezo The applied electric field creates a longitudinal strain along axis 1, with the magnitude given by Equation 5 as S1  E3 d31 Segment A is curved into an arc. The radius of the curvature r due to applied voltage can be found from Equation 13. The displacement at the end of segment A,  (x  lA ) , can be found by following similar procedure used in Example 1. The angular displacement at the end of the piezoelectric patch is (x  l A )  l A r The segment B does not curl and remains straight. The vertical displacement at the end of the beam is  (x  l)   (x  l A )  lB sin(x  l A ) Example 4  A ZnO thin film actuator on a cantilever is biased by co-planar electrodes. The geometry of beams and piezoelectric patches is identical as in Example 2. Find the output voltage under the applied force. If the structure is used as an actuator, what are the stress components when a voltage is applied across the electrodes? Example 4 The applied force generates two stress components – normal stress T1 and shear stress T5. The output electric field is related to the stresses according to the formula for direct effect of piezoelectricity T1     D  d d 12 d13 d14 d15 d16  T2      E  D 1   d 11 T  d  3    11 12 13 1 d d d d    E   2   21 23  2  d  T4     E 22 23 24 25 26 21 22 D  d d d d d   3   31 32 33 34 35 36  5  31 32 33  3  T  T6  Because no external field is applied, the terms E1, E2, and E3 on the righthand side of the above equation are zero. The formula can be simplified T1  to the form  0   D1   0 0 0 0 11.34 0 0   D    0 0 0 11.34 0 0 1012  2     D   5.43  5.43 11.37 0 0 0  0   3   T    5 0  Therefore, The output voltage is related to the polarization in axis-1, D3 5.43 10 12  T1 D1  11.34 10 12  T5 D1 V1   lA   Example 4 Let’s find the output stress when the device is used as an actuator. Suppose a voltage V is applied across the longitudinal direction. Here we assume the spacing between the two electrode is lA, hence the magnitude of the electric field is V E1  l A The applied electric field creates a longitudinal strain along axis 1. The strain is found by s1  s11 s12 s13 s14 s15 s16 T1   d11 d 21 d31  s  s s s s s s T  d d d   2  s 21 26  2   12 32    E1 22 25 22 s T  23 24 s  s s s s d d  d 33   s 4    s 3 31 32 33 34 35 s T    d 36 3 13 23  E2     41 s s s s 46  4  d   d 34 E 42 43 44 45  14 24 s5  s s s s s s T  d d d 35  3     51 52 53 54 55 56  5  15 25  s66     s6   s 61 s62 s63 s64 s65 T6  d16 d 26 d 36  Since no external stresses are applied, we set T1 through T6 zero. The simplified formula for strain is  s1   0 0  5.43  0  s   0 0  5.43   0   2   E    s 3   0 0 11.37  1   0       0 1012      No longitudinal strain components are s  0  11.34 0  0 generated in this manner.  4   0   s    11.34 0 0  S5    5   0 0 0  s 0    6         Example 5  Derive the expression for the end displacement of piezoelectric transducer configured similarly as Example 4, with the difference that the electrodes are used to pole the ZnO material. In other words, axis-3 is now forced to lie in the longitudinal direction of the beam length. A voltage V is applied across two electrodes.  Example 5 V The electric field in the longitudinal axis is E3  l A The applied field induced a longitudinal strain (S3) according to  s1   0 0  5.43     ss 2   00 0  5.43 0 11.37  0       0  1012 3 s4   0 11.34 0     E3   11.34 s 5  0 0  s6   0 0 0       or s3  d33 E3 We should use s3 to replace slong in Equation 8. The subsequent analysis is similar to the one performed for Example 3. Magnetic Sensing and Actuation  Magnetic fields and forces can be used to actuate micro-scale devices, or be used to create novel micro-sensors. Magnetism Due to Moving Charge  A current-carrying conductor such as a wire, will induce a magnetic field around it, as follows:  Where: H is the ‘magnetic field intensity’.  Note: You can use the ‘right hand rule’ to determine the orientation of the magnetic field around the conductor. Magnetism Due to Magnetic Materials  Magnetic fields also arise in permanent ferromagnets, also known as “hard” magnets.  Any piece of magnetic material is comprised of many ‘magnetic dipoles’:  For magnetic materials in a natural or raw state, these magnetic dipoles may be unaligned:  Therefore, there is little or ‘no net’ magnetic field Magnetism Due to Magnetic Materials  Creation of permanent magnets: 1. An appropriate hard-magnetic material is elevated to a high temperature, and subjected to a very strong external magnetic field. 2. Due to the elevated temperature, the magnetic dipoles move easily, and align approximately with the magnetic field. 3. The temperature is then reduced, and the magnetic dipoles become “frozen” in their aligned positions. The external magnetic field is removed, leaving the ‘magnetized’ material. 4. The dipoles remain aligned to a high degree at all times, thereby creating a permanent magnetic field.  In “soft magnets” the dipoles are normally un-aligned, and must be driven into alignment by an external magnetic field H, to induce a further magnetic field by the soft magnet. Magnetism Due to Magnetic Materials  The “magnetic field density”, B, inside a piece of magnetic material is measured in units of:  The “magnetic field density” is also known as the ‘magnetic induction’ or the ‘magnetic flux density’. Difference Between B and H Fields  H is defined as the “magnetic field intensity” and describes a magnetic field in space, which is measured in units of:  The relationship between B and H is presented as: Difference Between B and H Fields  Lets define B ‘more generally’ as: the “magnetic field density” within any material or within any medium.  In this sense, either B or H can be used to describe any magnetic field.  ** Even if the B field is in air, or in empty space.**  Where as B is ‘related to the medium properties’, while H is not. Magnetization Hysteresis Curve Lorentz Force  The ‘Lorentz Force’ arises as a charged body moves through a magnetic field, and is governed by: Where: F - Force Matrix q - total charge of body v - Velocity Matrix of body B - Magnetic Field Matrix  This equation can be simplified for a one-dimensional case, as: where - Angle between B Field and v Magnetic Dipoles in Magnetic Fields  The operation of a compass is well known.  The needle, which can be considered as a magnetic dipole, is held in an almost frictionless way.  When the needle starts at some arbitrary position, a magnetic torque will be developed, such that the needle will align itself with the Earth’s magnetic field. Magnetic Dipoles in Magnetic Fields  External magnetic fields can be classified into two main categories:  Uniform magnetic fields  Non-uniform magnetic fields  The effect of these fields on permanent ‘hard magnets’ is intuitive, in that they behave much the same way as a compass needle.  The effect of these fields on ‘soft magnetic’ materials, is interesting, in that these materials often exhibit ‘shape anisotropy’.  This means that ‘soft magnetic’ materials, when subjected to a magnetic field, will tend to develop a magnetic moment M, based on their shape, rather than the orientation of the field.  Practically, ‘soft magnets’ will develop a moment M, on their longitudinal axis, irrespective of of the direction of the induction field. Fabrication of Magnetic MEMS  To make magnetic micro-devices, appropriate thin-film process technologies are required.  One of the important processes for depositing magnetic materials is electroplating, as shown below: Fabrication of Micro-inductors  Micro-inductors represent a class of ‘passive devices’ that are of great interest.  They have application to a wide area of microelectronic and MEMS applications, including inductors, communications coils (RF or other), transformers, and magnetic actuators.  Presently, micro-inductors are fabricated as ‘spirals’ or ‘square spirals’ in 2-D layouts, as shown below: 2D Spiral Micro-inductors  2-D micro-inductors, such as the one shown in Fig. 8.9(a) are simple to fabricate. However, they are not too effective due to their spiral shape, and the relatively low magnetic permeability of air or free space.  To improve their performance in creating a strong magnetic field, the magnetic cores have been fabricated at their center, as shown below:  However, the resulting improvements are marginal. 2D Spiral Micro-inductors  An even bigger problem with ‘in-plane’ micro-inductors is their poor efficiency, or ‘quality factor’ since they are fabricated inplane with the substrate.  By being in-plane with the substrate, the magnetic flux must pass through the silicon substrate, which is conductive, yet has a high resistance. Eddy currents will form in the substrate, and degrade the performance of the device. 3D Micro-inductors  In order to avoid the problems with 2D in-plane micro-inductors, researchers are attempting to construct 3D micro-inductors with magnetic cores, and without cores.  The primary motivation is to minimize the amount of magnetic flux that must pass through the substrate. Monolithic Fabrication of 3D Micro- inductors  The micro-inductors shown below are fabricated using surface micromachining, or similar thin-film fabrication technologies. References 1. Foundation of MEMS, Chang Liu, Second edition, Pearson 2. http://home.sogang.ac.kr/sites/memslab/%EC%9E%90%EB%A3%8C%EC%8B%A4/ Lists/b49/Attachments/5/04Electrostatic-SenAct_44.ppt 3. https://www.engr.uvic.ca/~mech466/MECH466-Lecture-6.pdf 4. MECH 466-Microelectromechanical Systems, Lecture 11: Piezoelectric Sensors & Actuators 5. Micromachined Piezoelectric Devices, Chang Liu Micro Actuators, Sensors, Systems Group University of Illinois at Urbana-Champaign