ENG/PHYS3320 Microsystems Technology Chapter 3 Mechanical Microsystems

Transcription

1 ENG/PHYS3320 Microsystems Technology Chapter 3 Mechanical Microsystems ENG/PHYS3320: R.I. Hornsey Mech: 1

2 Mechanical transducers Mechanical transducers are probably the most important branch of the non-standard microsystems as opposed to electrical, light, temperature, which can be measured with normal IC technology While the basic principles of mechanical transduction are well established from mechanics and civil engineering, their adaptation to microsystems has required new approaches to fabrication and design In this section, we are interested in direct transduction i.e. the direct transduction from the mechanical to electrical domains, and vice versa ENG/PHYS3320: R.I. Hornsey Mech: 2

3 This is in contrast to tandem transduction, where there is an intermediate conversion stage e.g. a tachometer: a magnet is attached to the rotating shaft, a sensor (e.g. reed relay, Hall sensor) detects the magnetic pulses as the shaft turns, and outputs an electrical signal i.e. mechanical Æ magnetic Æ electrical this is a common means to avoid mechanical contact with the transducer In this chapter, we will look at: transduction categories mechanical principles transduction mechanisms mechanical properties of silicon ENG/PHYS3320: R.I. Hornsey Mech: 3

4 Then we will discuss some examples of sensors in particular, accelerometers and actuators electrostatic (motor, comb drive, micromirror) ENG/PHYS3320: R.I. Hornsey Mech: 4

5 Transduction techniques Mechanical effects are broadly classified into two categories static and dynamic From the transducer point of view, the difference is that the magnitudes are important for static signals while the frequency is relevant to dynamic signals Based on these, there are essentially three ways of achieving mechanical sensing: detection of stress (forces) detection of deformation (e.g. bending) detection of resonant frequency ENG/PHYS3320: R.I. Hornsey Mech: 5

6 Stress piezoresistance piezoelectric capacitance Deformation tunnel current optical interference Resonance frequency Actuation mechanisms also include the above, but often the desired effect is real motion so other techniques (e.g. electrostatic) are used sensors frequently do not need the additional complexity of rotation/translation (although turbine-like flow sensors have been made) ENG/PHYS3320: R.I. Hornsey Mech: 6

7 Before examining these mechanisms in more detail, we will first review basic mechanics mechanics of materials structural mechanics ENG/PHYS3320: R.I. Hornsey Mech: 7

8 Mechanics of materials Fundamental to discussions of mechanical effects are stress and strain two terms which have precise meanings, but which are often misused Stress is what occurs when a force is applied to a surface the average stress is the force per unit area (for engineering stress, the original area is used) s = F/A so the units of s are N/m 2 = Pascals (Pa) conventionally, tensile stress is positive and compressive stress is negative ENG/PHYS3320: R.I. Hornsey Mech: 8

9 F D A F L o L 0 + DL Forces that act perpendicularly to the surface are axial, or normal so it is important to note that force and stress are vector quantities ENG/PHYS3320: R.I. Hornsey Mech: 9

10 Strain is effectively the result of stress, and refers to the extension/contraction of the material: strain = fractional change in length e = DL/L 0 this is only valid within the elastic limit of the material i.e. strain returns to zero when the stress is removed Within the elastic limit, the material follows Hooke s Law deformation is linearly proportional to load which means that strain is proportional to stress The constant of proportionality is known as Young s Modulus, or Elastic Modulus so E = s/e (the units are still N/m 2 ) ENG/PHYS3320: R.I. Hornsey Mech: 10

11 e creep slope -1 = E E Si = 190 GPa, E quartz = 73GPa plastic deformation yield stress higher values of E mean a material that is more stiff s ENG/PHYS3320: R.I. Hornsey Mech: 11

12 Above the yield stress, the material deforms plastically, and the strain will not return to zero after the stress is removed yield stress 7 GPa for Si (2.1 GPa for steel) the extreme of this is creep, where the strain keeps increasing, even at a constant stress (analogous to electric breakdown) eventually the material will break completely at its ultimate stress If a material deforms significantly before breaking (i.e. s ultimate > s yield ), it is referred to as ductile (e.g. most metals) for silicon, s ultimate s yield, and the material is referred to as brittle ENG/PHYS3320: R.I. Hornsey Mech: 12

13 Even if all stresses are below the yield limit, failure can still occur due to repeated cycling of the stress known as fatigue an effect which was demonstrated dramatically in early jet airplane crashes ENG/PHYS3320: R.I. Hornsey Mech: 13

14 Shear stress In contrast to axial stress (normal to surface), shear stress acts parallel to surfaces tan -1 g DX Area, A F L now, shear stress, t = F/A and shear strain is the angular displacement, g = DX/L, in radians Now shear modulus = shear stress/shear strain: G = t/g (F/A)/(DX/L) ENG/PHYS3320: R.I. Hornsey Mech: 14

15 Young s modulus for Si The previous mechanical properties were derived effectively for polycrystalline (i.e. normal) metals crystalline silicon requires some special treatment In the same way that anisotropic etching highlighted different crystal planes, the mechanical properties also vary with crystal direction Since s = Ee in each direction, we have in general a matrix equation ENG/PHYS3320: R.I. Hornsey Mech: 15

16 È Í Í Í Í Í Í Í Î s 1 s 2 s 3 s 4 s 5 s 6 È c 11 c 12 c È Í Í Í c 21 c 22 c Í Í c 31 c 32 c Í = Í c Í Í Í Í c 55 0 Í Í Î c Í 66 Î e 1 e 2 e 3 e 4 e 5 e 6 where s 1, s 2, and s 3 are normal stresses, and s 4, s 5, and s 6 are shear stresses such a matrix of a physical property (usually directiondependent) is known as a tensor ENG/PHYS3320: R.I. Hornsey Mech: 16

17 By symmetry, some of the coefficients are equal for Si: c 11 = GPa, c 12 = 63.9 GPa, and c 44 = 79.6GPa hence, there is a factor of ~2 difference in stiffness between the [100] and [111] directions, which makes the mechanical behaviour of Si complex È Í Í Í Í Í Í Í Î s 1 s 2 s 3 s 4 s 5 s 6 x s 1 z s 5 s 5 s 3 s 4 s 4 s 2 s 6 s 6 y È c 11 c 12 c È Í Í Í c 12 c 11 c Í Í c = 12 c 12 c Í Í c Í Í Í Í c 44 0 Í Í Î c Í 44 Î e 1 e 2 e 3 e 4 e 5 e 6 ENG/PHYS3320: R.I. Hornsey Mech: 17

18 Poisson s ratio Axial strain describes how the material deforms under axial stress, in the direction of the stress In general, however, the material will also deform in the perpendicular direction a material under tension will get longer, and also typically narrower a material under compression typically gets both shorter and fatter In such cases, there are two strains, axial and transverse: e a = DL/L 0, and e t = DD/D 0 where D is shown in the diagram on p.5 under the conditions above, the two strains are of opposite sign (tensile = +ve) ENG/PHYS3320: R.I. Hornsey Mech: 18

19 The ratio of -e t /e a is Poisson s Ratio, n for metals, n 0.3 where n = 0.2 to 0.5 for most materials ENG/PHYS3320: R.I. Hornsey Mech: 19

20 Mechanical equations As we have seen, certain structures are easier to fabricate than others, and are therefore important to understand especially beams and diaphragms (membranes) In microstructures, these are usually assumed to have a rectangular cross section and to undergo deflection or torsion Such structures allow motion, without requiring bearings, sliding, etc. Loading for beams is either at a point, or uniformly distributed (e.g. pressure) point load is a force, F, in N uniformly distributed load is r, in N/m ENG/PHYS3320: R.I. Hornsey Mech: 20

21 In the following L is the beam length t is the beam thickness (we assume L» t & w) I is the bending moment of inertia, I = wt 3 /12 (m 4 ), where w is the beam width Note that deflection is proportional to load in all four cases ENG/PHYS3320: R.I. Hornsey Mech: 21

22 Cantilevers y x F y( x) = F ( 16IE 3x2 L - x 3 ) s max = FLt 2I y( x) = rx2 ( 24IE 6L2-4Lx + x 2 ) r s max = rl2 t 4( 2)I ENG/PHYS3320: R.I. Hornsey Mech: 22

23 y F x Built-in beams y( x) = Fx 48IE ( 3Lx - ) 4x2 (for x L/2 from support) s max = FLt 8I y( x) = rx2 ( 24IE L - x ) 2 r s max = rl2 t 12I ENG/PHYS3320: R.I. Hornsey Mech: 23

24 Torsion Torsion occurs when a beam is twisted about its axis Here, the angle of twist, q, is given by q = TL KG where T is the torque (in Nm), G is the shear modulus, and K is a geometry-dependent constant K = ϖr 4 /2 for a circular cross section for a rectangular beam of dimension x 0 by y 0, K = x 0 y Ê Á Ë x Ê 0 1- y 4 0 y Á 4 0 Ë 12x 0 ˆ ˆ ENG/PHYS3320: R.I. Hornsey Mech: 24

25 Membranes A membrane (diaphragm) is a special case of a plate, characterised by having being thinner and by being supported around the edges (e.g. drum) in both membranes and plates, the lengths and widths are comparable (in contrast to a beam) Membranes are typically used in applications, such as pressure sensors, where the pressure is different on the two sides ENG/PHYS3320: R.I. Hornsey Mech: 25

26 Under uniform loading pressure difference, P (in N/m 2 ), the central deflection of a circular membrane (in the absence of built-in stress) is d centre = 3Pr 4 ( 1-u 2 ) 16t 3 E n is Poisson s ratio, r is the radius, and E is Young s modulus the term with n arises because the membrane is deformed in two directions, and the Poisson s ratio relates axial and transverse components typically, membranes are designed to be in tension, to avoid buckling from compressive built-in stress square membranes deform similarly at the centre, but have higher edge stresses and rupture at lower pressures ENG/PHYS3320: R.I. Hornsey Mech: 26

27 Dynamics Many of the mechanical microsystems of interest are designed to operate dynamically i.e. with time-varying forcing functions e.g. resonating beam In such cases, the transient stresses can be significant, and must be considered In general, a mechanical structure consists of a resonant system a mass on a spring and a damping system that causes oscillations to decrease in amplitude as a function of time damping is present and frequently desirable in all practical systems ENG/PHYS3320: R.I. Hornsey Mech: 27

28 damping (coefficient, b) x external force mass, m spring (coefficient, k) The equation for this structure is: m d 2 x dt 2 + b dx dt + kx = F external where m is the mass (kg), b is the damping coefficient (Ns/m), k is the spring constant (N/m), and Fexternal is the driving force (N) ENG/PHYS3320: R.I. Hornsey Mech: 28

29 Expressed in complex terms, the transfer function of this system (force Æ displacement) is 1 H( s) = m s 2 Ê + b ˆ Á s + k Ë m m where s = jw which is a low-pass filter type of response, directly analogous to an LCR circuit, as follows V L R C H( s) = 1 LC s 2 Ê + 1 ˆ Á s + 1 Ë RC LC ENG/PHYS3320: R.I. Hornsey Mech: 29

30 Indeed, SPICE and other circuit models can be used to simulate mechanical structures by using such analogies note: this is really only true for sinusoidal driving signals These equations can be generalised into: H( s) = where w 0 is the resonant (or natural) frequency and Q is the quality factor Q = (energy stored per cycle)/(energy lost per cycle) so a perfectly undamped system oscillates for ever with Q = Q also describes the sharpness of the resonance peak (as a function of frequency) ENG/PHYS3320: R.I. Hornsey Mech: 30 w 0 2 s 2 Ê + w 0 ˆ 2 Á s +w 0 Ë Q

31 In all practical systems, damping results from factors such as aerodynamic (in air) or viscous (liquid) drag hysteresis in the structure (which should be zero if the material is completely elastic) Parameter Mechanical Electrical DC gain Natural frequency Quality factor 1/k (k/m) 1/2 (km/b 2 ) 1/2 1 (1/LC) 1/2 (R 2 C/L) 1/2 ENG/PHYS3320: R.I. Hornsey Mech: 31

32 As a rule of thumb: w < w 0 : gain DC gain w = w 0 : 90 out of phase, gain = Q x DC gain w > w 0 : gain falls at 40dB/decade, phase Æ 180 note that, at resonance, the maximum stress is also Q times the maximum static stress ENG/PHYS3320: R.I. Hornsey Mech: 32

33 Fundamental effects - mech. sensors There are essentially only four basic effects that can be used to measure mechanical effects by micro-sensors (see table on p.211 of Kovacs): piezoresistance piezoelectric effect (not Si) capacitance electrostatic measure of separation tunnel current quantum-mechanical measure of separation Of these, only piezoresistance and capacitance are readily applicable to silicon ENG/PHYS3320: R.I. Hornsey Mech: 33

34 Kovacs p.211 Piezoelectric materials which generate a voltage in response to a stress can be deposited as an additional layer typical materials are ZnO, quartz, BaTiO3 however, piezoelectric materials generate a voltage, not a current, making DC readout very difficult piezoelectric materials often also generate a voltage in response to heat, which is disadvantageous in a sensor ENG/PHYS3320: R.I. Hornsey Mech: 34

35 Sensor based on tunnel currents are very sensitive, due to the exponential dependence of current on separation but they are also susceptible to contamination and hence drift characteristics vary with time Below, we will look at the basic mechanisms of piezoresistance and capacitance sensing along with the example of an accelerometer in each technology ENG/PHYS3320: R.I. Hornsey Mech: 35

36 Piezoresistance Piezoresistance describes the change of a materials resistance with applied stress it is the basis of many strain(!) gauges, often made from metal films in a plastic film the effect was discovered in 1856 by Lord Kelvin (aka W. Thomson) While metals show a relatively small change of resistance, semiconductors by happy circumstances display a stronger effect the sensitivity is expressed as the gauge factor GF = (relative resistance change)/(strain): GF = DR R DL L = DR er ENG/PHYS3320: R.I. Hornsey Mech: 36

37 Type of strain gauge metal foil thin film metal semiconductor semiconductor diffusion Gauge factor 1 5 ~ So it is possible to make integrated strain gauges from diffused Si, poly, or metal ENG/PHYS3320: R.I. Hornsey Mech: 37

38 Piezoresistance in metals In a metal, the change of resistance is essentially due to the geometry change of the metal under stress: metal film substrate or film D length: L area: A = D 2 The resistance is rl/a, where r is the resistivity ENG/PHYS3320: R.I. Hornsey Mech: 38

39 Differentiating both sides: (dr/r) = (dr/r) + (dl/l) - (da/a) we assume that r is stress-independent for a metal and we note that Poisson s ratio, n = -e D /e L hence n = - (dd/d)/(dl/l) because, under axial stress, both the width and thickness of the metal change, we find (da/a) = 2(dD/D), assuming a square cross section so now (dr/r) = (dl/l)(1 + 2n) So finally, the gauge factor is 1+ 2n With n 0.2, GF 1.4, which is relatively small because this effect is entirely due to geometrical changes, it is sometimes called the geometrical piezoresistance effect ENG/PHYS3320: R.I. Hornsey Mech: 39

40 By contrast, some semiconductors including Si really do change resistivity in response to stress the reasons for this are a little involved but we will cover the gist of the effect in a few slides ENG/PHYS3320: R.I. Hornsey Mech: 40

41 Piezoresistance in n-type Si The band structure of silicon is such that electrical conduction in the six orthogonal directions is performed by distinct groups of electrons the bandgap is the same (at 1.1eV) regardless of direction one gap, many valley model In Si under no stress, each of these 6 valleys is equally populated with electrons however, mobility (µ), and resistivity (r = 1/nqµ) are directiondependent (i.e. tensors) The energy valleys arise because of the atomic spacing in the crystal lattice. So when stress is applied, the symmetric picture above gets distorted ENG/PHYS3320: R.I. Hornsey Mech: 41

42 For example, if n-type Si is compressed along the [100] direction the valley energy in that direction gets lowered while the energy of the [010] and [001] valleys are raised hence, electrons move to the lower energy, increasing n However the mobility in the [100] direction decreases (essentially because the density of atoms in that direction is now larger) So the overall effect is that resistivity increases with compressive stress Since the resultant strain is negative (compressive), and the the resistivity change is positive, the gauge factor is negative ENG/PHYS3320: R.I. Hornsey Mech: 42

43 Because the valley lowering redistributes essentially a fixed number of electrons, and the magnitude of the effect depends on the fraction of the electrons that are redistributed weakly doped materials have higher gauge factors than heavily doped and temperature change has a higher influence on lower doped materials ENG/PHYS3320: R.I. Hornsey Mech: 43

44 Piezoresistance in p-type Si Experimentally, p-type Si shows higher piezoresistance gauge factors than n-type Si For reasons we will not go into, there are two effective masses for holes and positive (tensile) stress causes a redistribution of the available holes from light to heavy masses and the resistivity increases the effect is most pronounced in the [111] direction The gauge factor for p-type is therefore positive and temperature/doping affects are similar to n-type ENG/PHYS3320: R.I. Hornsey Mech: 44

45 Summary for Si Doping/direction Resistivity (Ωcm) GF p [111] p [110] p [100] n [111] n [110] n [100] ENG/PHYS3320: R.I. Hornsey Mech: 45

46 Accelerometers Accelerometers are used in may applications: automotive (airbags) vibration/short detection & control navigation medical (heart monitoring) A range of applications is given in the table on the following page The general idea is to measure acceleration by detecting either displacement or force exerted on a proof mass ENG/PHYS3320: R.I. Hornsey Mech: 46

47 damper proof mass spring frame motion limiter some damping must be included to control the frequency response In this example, the acceleration of the system is determined by measuring the force exerted by the spring on the proof mass F = ma = kx rel where x rel is the displacement of the proof mass (m) relative to the frame (not of the frame itself) ENG/PHYS3320: R.I. Hornsey Mech: 47

48 The damper is to provide a force proportional to the relative velocity of the mass, v rel so F damper = bv rel = b(dx rel /dt) Now, the overall force balance equation is F = m(d 2 x/dt 2 ) = kx rel + b(dx rel /dt) From before, w 0 = (k/m) 1/2 and Q = (mk/b 2 ) 1/2 Critical damping occurs when Q = 0.5 causing oscillations to die away in half a period which is the ideal configuration In practice, the spring constant is controlled by adjusting the stiffness of a beam that supports the proof mass and the damping is achieved by constricting the flow of air around the mass ENG/PHYS3320: R.I. Hornsey Mech: 48

49 Strain gauge accelerometers The basic structure of the strain gauge accelerometer is straightforward p + piezoresistor proof mass bulk micromachined beam A relatively large proof mass is supported on a thin micromachined beam with a piezoresistor diffused into the beam at the point of highest stress (at the root of the beam) ENG/PHYS3320: R.I. Hornsey Mech: 49

50 Typical performance figures are: w 0 Parameter Minimum detectable acceleration Maximum detectable acceleration Sensitivity Value 0.001g (g = 9.8 m/s 2 ) ± 200g 50µV/(g.VDD) 2330 Hz Although there is no intrinsic reason why such structures cannot be integrated with CMOS electronics the need for precise control of the gaps has required doublesided processing and yield issues hinder a fully integrated design ENG/PHYS3320: R.I. Hornsey Mech: 50

51 from Kovacs ENG/PHYS3320: R.I. Hornsey Mech: 51

52 Piezoresistive sensors are typically read out using a Wheatstone bridge: if all 4 resistances are the same, Vout = 0 this is designed so that all resistors have the same temperature dependence the output voltage changes when the piezoresistor responds to bending of the Si beam piezoresistor on accelerometer V V out similar resistors on substrate ENG/PHYS3320: R.I. Hornsey Mech: 52

53 from Kovacs ENG/PHYS3320: R.I. Hornsey Mech: 53

54 Capacitive accelerometer The general principle of capacitive sensing is simple, but can be implemented in a number of ways The most obvious is just to move one plate of the capacitor here, the capacitance varies non-linearly with displacement but if the device just acts as a trigger (as opposed to measuring the value of acceleration) that is not necessarily a problem proof mass C µ 1/d ENG/PHYS3320: R.I. Hornsey Mech: 54

55 A better way, however, is to use a capacitive divider: proof mass V out this provides a differential output when the mass moves, one capacitor increases, while the other decreases if anti-phase signals are applied as shown above, the Vout = 0 if the mass is central Vout 0 once the mass moves ENG/PHYS3320: R.I. Hornsey Mech: 55

56 Assuming parallel-plate capacitors, we can determine the expected change of capacitance initially, each capacitance is equal, C 0 = ea/d = k/d when the central plate is disturbed, the capacitances C 1 and C 2 are no longer equal C 1 = k/(d + Dd) = C 0 [d/(d + Dd)] similarly C 2 = C 0 [d/(d - Dd)] C 0 C 0 C 1 C 2 d d d+dd d-dd ENG/PHYS3320: R.I. Hornsey Mech: 56

57 After simplification DC = C 2 - C 1 DC = 2dDD d 2 - DD 2 C 0 ª 2 DD d C 0 where we have ignored Dd 2 terms so, for small displacements, DC µ Dd Capacitive sensors can be readily fabricated using surface micromachining techniques which makes them more suitable for integrated microsystems We will look at two commercial implementations of capacitive accelerometers both based on the differential technique above ENG/PHYS3320: R.I. Hornsey Mech: 57

58 Asymmetric torsion plate In this design, a single pedestal is used to support an asymmetric plate (mass) that is free to rotate: Silicon Designs Inc. readout ASIC 2 sensors ENG/PHYS3320: R.I. Hornsey Mech: 58

59 When the sensor experiences acceleration perpendicular to the chip surface the mass twists on its torsion bars so the gap on the heavy side gets smaller, while that on the light side gets bigger (for upwards motion) so the mass forms the central plate of the capacitive divider ENG/PHYS3320: R.I. Hornsey Mech: 59

60 The plate is made from 5-10µm nickel, typically 1000µm x 600µm, and 5µm above the surface the nickel is electroplated on top of a sacrificial layer Each of the two capacitors is ~150pF and the torsion bar is 8µm wide, by 100µm long by 5µm thick for a 25g airbag accelerometer ENG/PHYS3320: R.I. Hornsey Mech: 60

61 Force-balanced accelerometer Here we will look at the famous Analog Devices ADXL50 accelerometer chip the first mass produced micromachined accelerometer ENG/PHYS3320: R.I. Hornsey Mech: 61

62 The proof mass is 2µm thick polysilicon separated from the substrate by ~1µm released from the substrate by a sacrificial oxide The idea of the force-balance approach is that a feedback signal is used, via actuation, to maintain the position of the proof mass so the strength of the feedback signal needed to keep the mass in a fixed location (in opposition to the acceleration force) is a measure of the acceleration ENG/PHYS3320: R.I. Hornsey Mech: 62

63 zero acceleration applied acceleration centre plate beam fixed plates anchor points The comb structure of the sensor operates in the differential capacitance mode discussed above from before, DC 2(Dd/d)C 0, so the sensitivity is increased for a larger C 0, hence the multitude of capacitor plates used in the ADXL-50 the two fixed plates are held at 0.2V and 3.4V, while the proof mass is held at 1.8V ENG/PHYS3320: R.I. Hornsey Mech: 63

64 As the sensor detects a movement of the proof mass, the beam voltage is adjusted to keep the centre plate equispaced between the fixed plates the mass moves by a maximum of 10nm! the advantage is that the sensor does not have to cope with large excursions of the mass, so gaps can be kept small to increase C0, and hence a high sensitivity The system diagram (taken from the ADXL-50 data sheet) is: ENG/PHYS3320: R.I. Hornsey Mech: 64

65 Performance figures are: maximum acceleration sensitivity bandwidth ± 50 g ~40mV/g 1kHz Other versions of this sensor have now been developed with, for example, support arms of different stiffnesses ENG/PHYS3320: R.I. Hornsey Mech: 65

66 Pressure sensors Accelerometers are, of course, only one example of mechanical micro-sensors a whole range is described in the Kovacs text also relevant are gyroscopes, for measuring rotation angle or rate (see IEEE Spectrum magazine, July 1998, p.66 for a good article) Note that the main differences between a pressure sensor and a microphone are: sensitivity, DC response (not needed for microphone) and high frequency response The most noteworthy of these are pressure sensors they are similar to the piezoresistive accelerometers, but employ a membrane instead of a cantilever a typical structure is shown below ENG/PHYS3320: R.I. Hornsey Mech: 66

67 piezoresistor micromachined Si bonded glass substrate ENG/PHYS3320: R.I. Hornsey Mech: 67

68 Pressure sensors come in four basic types: these sealed sensors are known as aneroid because they are not referenced to air P input1 P input1 vacuum ambient Absolute Gauge P input1 P input1 P reference P input2 Sealed gauge Differential ENG/PHYS3320: R.I. Hornsey Mech: 68

69 Mechanical actuators Integrated mechanical actuation mechanisms are very limited by far the most common is electrostatic actuation thermal actuation is also possible on-chip externally actuated structures include magnetically driven motors, pneumatic and hydraulically actuated devices see Kovacs pp for comparisons of actuation mechanisms (next page) Moreover, the geometry of such structures is essentially planar although hinged structures can form vertical mirrors etc. (e.g. Sandia example) ENG/PHYS3320: R.I. Hornsey Mech: 69

70 All of which leaves us with two main families of on-chip electrostatic actuators linear comb drives rotary micromotors So we will discuss these, as well as some examples of thermal actuation ENG/PHYS3320: R.I. Hornsey Mech: 70

71 Electrostatic actuation Electrostatic actuation is typically impossible to treat analytically the systems are non-linear geometries are complex edge effects, corners, fringing fields, etc. must be included and so numerical methods are important However, the basic principle is straightforward Considering a simple parallel plate capacitor, we can calculate the force between the plates: we know that energy = force x distance and the energy stored in a capacitor is CV 2 /2 so F = de/dx = (V 2 /2) dc/dx ENG/PHYS3320: R.I. Hornsey Mech: 71

72 from Kovacs ENG/PHYS3320: R.I. Hornsey Mech: 72

73 from Kovacs ENG/PHYS3320: R.I. Hornsey Mech: 73

74 but C = ea/x, so Ê F = eav 2 ˆ Á d Ê 1 Á ˆ = eav 2 Ë 2 dx Ë x 2x 2 where e = e 0 e r this force pulls the plates of the capacitor together The non-linearity of force with plate separation, even for this simple case, is of great practical importance it means that, even with a constant voltage, the attractive force increases quadratically as the distance decreases i.e. as the structure moves this makes it very difficult to control the motion continuously, and tends to lead to a bistable operation (deflected or undeflected) ENG/PHYS3320: R.I. Hornsey Mech: 74

75 We can extend this simple example to that of an electrostatically deflected cantilever here, the additional complexity arises because the plate separation is not uniform here, we need to determine the tip deflection as a function of the applied voltage q(x) dx x t d T V spacer d L The approach is to determine the tip deflection for a point load and then to integrate along the beam to account for the distributed electrostatic loading ENG/PHYS3320: R.I. Hornsey Mech: 75

76 The deflection under the load is (from p.22) ( dd) T = Qx2 where Q is the force at that point, I is the moment of inertia, and E is Young s modulus, and other symbols are defined in the diagram above Q is given as follows ( ) 6IE 3L - x Q = e Ê 0 V ˆ Á ( w.dx) 2 Ë d - d( x) where the area, A = wdx TTo find the total tip deflection, we integrate dd along the beam: 2 ENG/PHYS3320: R.I. Hornsey Mech: 76

77 unfortunately, to solve this equation, we need to assume a form for the deflection we then work back to get the deflection so we assume a normalised parabolic deflection which gives: e 0 wl 4 V 2 2IEd 3 = d T V 2 we 0 12IE d x ( 3L - x)x 2 dx d - d x [ ( )] 2 where D = d T /d is the normalised deflection L Ú 0 Ê ( ) = Á x Ë L È 2 Í Î 3 1- D 2 ˆ d T 4D 2 ( ) - atanh D D ENG/PHYS3320: R.I. Hornsey Mech: 77 - ( ) ln 1- D 3D

78 The curve of this function is normalised load, F unstable normalised deflection, D ENG/PHYS3320: R.I. Hornsey Mech: 78

79 Beyond the threshold voltage the beam continues deflecting spontaneously until it contacts the substrate V th ª 18IEd3 5WL 4 e 0 Note that many microfabricated cantilever beams consist of several layers of materials usually chosen so that built-in stresses cancel, leading to an initially straight beam In this case, the IE term in the above equations must be an effective value experimentally, a good approximation for a beam of two layers was found to be ENG/PHYS3320: R.I. Hornsey Mech: 79

80 Ê Ê ( IE) eff = wt 1 3 ˆ Á Á Á Ë 12 Á Ë t 2 t 1 + E 1 t 1 E 2 t 2 1+ E 1t 1 E 2 t 2 where subscripts 1 refer to the lower layer in the beam, and 2 to the upper layer ˆ ENG/PHYS3320: R.I. Hornsey Mech: 80

81 Micromirrors Micromirrors, used in reflective projection displays Texas Instruments, which has commercialised the technology, calls them digital light processors Seoul National University ENG/PHYS3320: R.I. Hornsey Mech: 81

82 There are a number of designs, but the principle is common a reflective plate is suspended above the substrate on hinges that allow rotation electrodes on the substrate are used to attract one corner of the mirror, so it can be tilted This is different to the cantilever, since we will assumed that the mirror plate is rigid and just rotates electrode ENG/PHYS3320: R.I. Hornsey Mech: 82

83 Early versions of the micromirror used torsion bars to support the corners of the mirror support hinge electrode but these take up area that could be used for the mirrored surface so now supports under the mirror are now used as seen by the dimple in the centre of each mirror in the photo above Despite the assumption of the rigid plate, the expressions for deflection, and the instability are broadly similar to the cantilever ENG/PHYS3320: R.I. Hornsey Mech: 83

84 Sandia labs ENG/PHYS3320: R.I. Hornsey Mech: 84

85 Electrostatic comb dives The electrostatic stabilisation of the ADXL-50 accelerometer is similar to a comb drive The concept of a comb drive is to use electrostatic attraction between the plates of an interdigitated capacitor to provide linear motion e.g. Sandia comb drive, where the linear motion is converted to rotary motion by a crank ENG/PHYS3320: R.I. Hornsey Mech: 85

86 ENG/PHYS3320: R.I. Hornsey Mech: 86

87 The general operation is simple: flexible support undercut, movable beam motion anchor undercut, anchored beams The structure is symmetrical perpendicular to the motion ( Ø), so that forces in this direction cancel ENG/PHYS3320: R.I. Hornsey Mech: 87

88 However, it is clear that the parallel plate capacitance which is supposed to provide the force (see bottom left of diagram above) is really quite small (e.g. see photo) Bosch ENG/PHYS3320: R.I. Hornsey Mech: 88

89 So what provides the force? fringing fields between the ends of the arms and the neighbouring fixed arms Fringing fields also have the unfortunate additional effect of pulling the the structure upwards, out of the plane this is because the effective dielectric constants above and below the beam are different ENG/PHYS3320: R.I. Hornsey Mech: 89

90 air above, and substrate below this can be reduced by adding appropriate ground-plane electrodes Such devices are usually fabricated by a sacrificial layer technique and are therefore amenable to CMOS compatibility They also have the advantage of not having surfaces that move against each other hence, no wear or stiction problems ENG/PHYS3320: R.I. Hornsey Mech: 90

91 However, comb drives give only linear motion for rotary motion, we need a micromotor which does have rubbing surfaces Sandia ENG/PHYS3320: R.I. Hornsey Mech: 91

92 Electrostatic motor Regular motors employ magnetic coupling between the stator and the rotor However, sufficiently large magnetic fields cannot be developed on-chip and would likely be in the wrong direction anyway So rotary motion is achieved electrostatically although external magnetic fields have been coupled into microscopic nickel rotors The basic mechanism is the same as for the comb drive, but a hub is required to achieve the rotary motion ENG/PHYS3320: R.I. Hornsey Mech: 92

93 hub stator rotor The number of stator arms primarily affects the operating voltage voltages are typically in the V range speeds of 300,000 revolutions per minute (rpm) are possible with micromotors (compare with 3000 rpm for a cruising car) lifetimes of millions of revolutions have been measured Tima ENG/PHYS3320: R.I. Hornsey Mech: 93

94 ENG/PHYS3320: R.I. Hornsey Mech: 94 Sandia

95 Fabrication A basic process flow for a rotating micromachine is shown on the next page Important features are that: the hub is self-aligned to the rotor (the separation is defined by the oxide thickness) the contact area between the rotor and the substrate is reduced by using a rim near the hub The process for a practical micromotor needs rather thicker layers that those in standard CMOS and usually needs several poly-si layers ENG/PHYS3320: R.I. Hornsey Mech: 95

96 TEOS is a CVD oxide layer Sandia s SUMMIT process Cross section through a gear in Sandia s SUMMIT process (using focused ion beam) ENG/PHYS3320: R.I. Hornsey Mech: 96

97 from Kovacs ENG/PHYS3320: R.I. Hornsey Mech: 97

98 from Kovacs ENG/PHYS3320: R.I. Hornsey Mech: 98

99 One of the principal failure mechanisms of these machines is wear between the hub and the gear the microscopic mechanism of such wear and what materials are most resistant is the subject of current research it appears that reducing play between hub and gear in both vertical and lateral directions is key A major issue in micromachines is friction the need for a substantially higher force to get the motor moving than to keep it moving sometimes to the point where it is hard to prevent destruction of the device before it works which results in higher voltage requirements ENG/PHYS3320: R.I. Hornsey Mech: 99

100 Wobble motors Although it play at the hub is usually bad, wobble motors exploit excessive play to reduce friction ideally, this eliminates sliding friction entirely, as the rotor rolls around the hub it also leads to a gearing reduction because the rotor rotates by less that one revolution for every cycle of the drive frequency n = r b /d, where n is f drive /f rotation, r b is the hub (bearing) radius, and d is the gap between hub and rotor ENG/PHYS3320: R.I. Hornsey Mech: 100

101 Other methods for tackling the wear issue include hub designs which result in smaller play than simple designs and to reduce vertical forces (see comb drives) which result in additional friction ENG/PHYS3320: R.I. Hornsey Mech: 101

102 Low voltage operation Reduced operating voltage is another area of research one method being developed in Sandia is to cause the rotor to pass between stator layers In this way, there is more interaction between the rotor and the stator but fewer vertical fringing effects, because the rotor is shielded to some extent from the substrate rotor stator rotor stator 1 stator 2 cross section ENG/PHYS3320: R.I. Hornsey Mech: 102

103 Thermal actuation The third major category of actuation for integrated MEMS (=imems) is thermal activation for macroscopic structures, thermal effects are usually too slow to be useful however, on the microscopic scale, thermal actuation is practical Heaters are relatively easy to realise on-chip, simply by resistive heating of polysilicon layers One of the most common ways to derive motion from heating arises from differential expansion of solids leading to bimorph thermal actuators here, the gold layer expands more than the epitaxial silicon layer, and deflection is downwards ENG/PHYS3320: R.I. Hornsey Mech: 103

104 electrodeposited gold deflection SiN polysilicon heater SiN p + silicon substrate Large-scale examples of bimorphs are common e.g. bimetallic strip used in thermostats and car indicator flashers Bimorph actuators have the advantage of being almost linear (heater power Æ deflection) and relative ruggedness disadvantages (compared to electrostatic) are high power, low bandwidth and complex construction ENG/PHYS3320: R.I. Hornsey Mech: 104

105 Shape memory alloys Another class of thermal actuator are known collectively as shape memory alloys (SMAs) These metals, once mechanically deformed at low temperature, can return to their original shape (typically by contraction) when they are heated the process is reversible although there will likely be hysteresis in the stresstemperature characteristics The SMA is deformed mechanically by a bias force which is subsequently overcome when the material is heated ENG/PHYS3320: R.I. Hornsey Mech: 105

106 A common alloy is titanium/nickel ( nitinol ) also Au/Cu and In/Ti and they can be heated by passing a current through them Such structures can provide large stresses (>200 MPa) and long lifetimes (provided strain < 2%) but their power efficiency is only ~3% and the manufacture of the alloys requires careful control of composition moreover, annealing temperatures can be too high for CMOS compatibility SMAs operate due to temperature dependent phase changes i.e. changing the crystal structure, and hence the density while the alloy composition remains unchanged ENG/PHYS3320: R.I. Hornsey Mech: 106

107 Summary Integrated mechanical transducers have only relatively recently been possible and the range of new applications has prompted a rapid increase in research and development of such devices including now commercialised sensors It is widely believed that imems will come to be a large market as some of the production-scale fabrication and lifetime issues are resolved In contrast, optical transducers have been known for many years in various forms However, practical integrated optical microsystems are also surprisingly recent innovations as we shall see in the next chapter ENG/PHYS3320: R.I. Hornsey Mech: 107