SENSOR DEVICES MECHANICAL SENSORS

SENSOR DEVICES MECHANICAL SENSORS

OUTLINE 4 Mechanical Sensors Introduction General mechanical properties Piezoresistivity Piezoresistive sensors Capacitive sensors Applications

INTRODUCTION MECHANICAL SEMICONDUCTOR SENSORS Combine electronic properties of semiconductorswith its excellent mechanical properties mechanical properties TWO MAJOR CLASSES OF MECHANICAL SENSORS Piezorestistive sensors (material property p in silicon) Capacitive sensors (relative motion of electrodes) APPLICATIONS Pressure sensors Accelerometer Flow sensors Piezo = squeeze or press

INTRODUCTION Piezoresistive sensing applications Load cell Accelerometer Pressure sensor

General mechanical properties Hooke's law: σ = Eε Stress: σ = F Area, [N/m 2 ] Strain: ε =ΔLL Young's module: E, [N/m 2 =Pa], Volumetric change: ΔV V ΔL L 2ΔL l L = ( 1 2ν ) ΔL L Poisson's ratio: ν = ΔL l ΔL = -ε l ε, l =lateral Silicon: E Si 190 GPa, ν Si 0.28

General mechanical properties Brittle Fracture x Ductile Silicon Linear elasticity until fracture No plastic deformation Excellent for sensor applications Metals Linear elastic behaviour for small strain only Strength Yield strength = tensile stress where plastic deformation starts (non-reversible) Tensile strength = maximum tensile stress before facture

General mechanical properties

General mechanical properties Stress in thin film R Stress in thin film cause a curvature of the sample, which can be measured using a laser system 1 Δs = 61 ν R ET Δ s =σt = surface stress [N/m] unstressed ( ) 2 stressed R= radius E= Young s module in substrate T= substrate thickness t = thin film thickness v = Poisson s ratio in substrate

General mechanical properties p Cantilever beams Max deflection Max longitudinal stress Resonant frequency Square membranes Max deflection Max longitudinal and transverse stress Resonant frequency

General mechanical properties Cantilever beam with uniform distributed load (P=F/Δx) P[N/m] 4 Beam equation: EI d w(x) = P dx 4 Beam stifness: EI = Eat 3 12 I = at 3 12 (2nd moment of inertia) L t a Deflection: w(x) = ( ) P 2 2 2 24EI x2 6L 2 4Lx+ x 2 Max stress SENSOR: P = at ρ acceleration Δ P= atρ g measurand w(l) = PL4 8EI Surface stress: σ (x)=- te d 2 w(x) 2 dx 2 Max stress: σ (0) = PL2 t = 3PL2 4I at 2

General mechanical properties Cantilever beam point load at the end L Q [N] a 2 Qx Defelction: wx ( ) = 3L x 6EI 3 QL wl ( ) = 2EI QLt 6QL Max stress: σ (0) = = 2 I at ( ) t 2 Max stress SENSOR: Q = mass acceleration Resonant frequency: F t E t Eta = 0.161 = 0.161 L ρ L ML 0 2 Quasi-static static sensing f measure < F 0

General mechanical properties SQUARE MEMBRANES (UNIFORM LOAD) P [N/m^2] E, ρ, ν a t Plate equation: D 4 w(x, y) = P Et 3 Membrane stiffness: D = 12 1 ν 2 ( ) Max deflection: w 00126 Pa4 max = 0.001265 D Max longitud. stress: σ Pa2 l = 0.3081 t 2 Max transverse stress: σ t νσ l Resonant frequency: F 0 =1.654 12D ρta 4

Piezoresistivity L R = ρ 2 a Resistivity change in semiconductor: ρ = ρ( σ) Resistivity change due to mechanical stress L piezoresistive effect R( σ) = R+ ρσ 2 Large resistivity change a Dependence on Δ RR = ( ρ ρ ) σ Doping (n- or p-type, doping concentration) πσ Temperature Direction of force and direction of current flow = π Eε (anisotropic effect) ΔR R 100ε Resistivity change in metal strain gauge mainly due to geometric effect F L L R = ρ 2 L+ΔL a a F a+δa

Piezoresistivity Longitudinal and transverse piezoresistance coefficients Force σ l Current flow V Longitudinal stress: ΔR/R = π l σ l π l = longitudinal piezoresistance coefficient Force Force σ t Current flow Force V Transverse stress: ΔR/R = π t σ t π t = transverse piezoresistance coefficient Stress: σ=force/area E = j ρ j i ij j ρ = π σ ij k l ijkl kl In general we have both longitudinal and transverse stresses: ΔR/R = π t σ t + π l σ l

PIEZORESISTIVITY Piezoresistance coefficients in p-type silicon [10-11 /Pa] 100 plane Upper half Longitudinal coefficient π l Lower half Transverse coefficient π t In sensor application the π should be as large as possible, i.e. resistors along <110> direction ( ) π 1 l = π 2 + π + π π 1 t = π 2 + π π 11 12 44 ( ) 11 12 44

PIEZORESISTIVITY Resistors along <110> direction in (100) wafers (common for bulk micromachining) ( ) ( ) π l = 1 2 π 11 + π 12 + π 44 π = 1 π + π π t 11 12 2 44 ΔR R = π l σ l + π t σ t π 44 2 (σ l σ t ) <110> ΔR π π E R 44 2 σ 44 Eε 100ε 2

Piezoresistive Sensors Piezoresitive pressure sensor Membrane fabrication Anisotropic etch Piezoresistor fabrication doped d area or deposited polysilicon resistor on an insulator (SiO 2 or Si 3 N 4 ) Piezoresistor position at the edges of the membrane where the stress is maximal

Piezoresistive Sensors Piezoresistive accelerometer The piezoresistor must be places where the stress is maximal To increase the sensitivity an inertial mass is included

Piezoresistivity R= ρ L w t π( NT, ) = π0pnt (, ) π 0 = low-doped room-temerature value

Piezoresistiv Sensor Wheatstone Bridge Configuration R1 and R3 under lateral stress ΔR and decrease R π 44 2 σ R2 and R4 under longitudinal stress and increase ΔR R π 44 2 σ R 1 = R 3 = R Δ R R2 = R4 = R+ΔR Δ R π = 44 ( σ l σ t) R 2 Δ R π 44 Vm = Vb = Vb σ l σ t R 2 ( )

Piezoresistive Sensors Pressuresensitivity for constantv b : S v = ΔVV b ΔP [mv/v-bar] = ΔRR ΔP = 1 2ΔP π 44 ( σ σ l t ) Pressure sensitivity for constant I b : ΔV I b S i = [mv/ma-bar] ΔP = ΔR = 1 Rπ 44 ΔP 2ΔP ( σ σ l t )

Piezoresistive Sensors Offset voltage Symmetrical mismatch of the resistors, caused by difference in layout (parallel and perpendicular to the edges of the membrane) R 1 = R 3 = R R 2 = R 4 = R+ r r V o =V b 2R+ r V r 1 O = o = = V b 2R+ r 1+ 2R r Offset also caused by residual stress on resistors - pre-stress due to passivation layers and packaging

Piezoresistive Sensors Temperature coefficient of offset O 2Rr r R = T + r R ( 2Rπ r ) 2 If resistors have equal temperature coefficients r R O =, = 0 r R T However, temperature dependence of pre-stress might be significant.

Piezoresistive Sensors Temperature coefficient of sensitivity Constant bridge voltage S π 44 (σ l σ t ) Temperature coefficient for π 44 can be high for p type silicon Constant bridge current S π 44 R(σ l σ t ) - +

Piezoresistive Sensors

Capacitive Sensors Capacitor two electrodes separated by a dielectric Electronic should be close to the sensor, minimising the stray capacitance Δd<< d result in High sensitivity means Large area S and a small distance d Advantage with capacitive sensors no direct sensitivity to temperature

Capacitive Sensors a) Pressure sensor b) Accelerometer c)? θ

Comparison of different technologies

Applications Symmetric capacitive accelerometer with low thermal sensitivity In some cases the movabel electrode must be damped to avoid serious oscillations. A small cavity with a viscous liquid or gas can fulfil the requirements

Flow sensors (gas) With no flow the two sensors display the same temperature With gas flow the first sensor is cooled, while the second is heated up by the gas

Some examples, Bulk micro-machinedmachined piezoresistive sensor Laboratory for Electron Devices Ljubljana SLOVENIA

EXERCISES 1) 2) 3)

EXERCISES 4) Force Q between two parallel Force Q between two parallel plates of area A, separation d and applied voltage V

EXERCISES ANSWER: 1) Wmax=1.17µm, σl=12.3 MPa, σt=3.45 MPa 2) σmax= 4.3*10 7 Pa, a=150 µm 3) fo= 4.39 khz 4) V=9.6V