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Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig” målebro Rotasjon til 110 akser Overgang til ”forenklede” koeffisienter Følsomheten til en ”vanlig” sensor X-ducer Virkemåte Transformasjon av stresset Følsomheten til en Motorola MAP sensor Electronics and Cybernetics 1 Piezoresistive pressure sensors Electronics and Cybernetics 2 Modellering av trykkmembran u ( x, y , z ) ( )( u ) 2u 0 3 D kontiniumsmekanikk 1mm*1mm*20µm ~1018atomer (masser og fjærer) w( x, y) 2 D Plateligning w ( r) 3 16 p 1 E t 3 2 a2 r22 stress Electronics and Cybernetics 3 Stress (σxx) i trykkmembranen x Electronics and Cybernetics 4 Isotrop resistivitet d 1 J E E V d V Electronics and Cybernetics 8 Anisotrop resistivitet J E Electronics and Cybernetics 9 The resistivity changes with the mechanical stress E - electric field, three components j - current density, three components 0 – homogeneous resistivity, unstressed silicon V1 V2 When mechanical stress is applied, the resistivity changes depending on the stress in different directions and the piezo E1 coefficients d1 d 6 d5 j1 j1 E j d d d j 0 2 0 6 2 4 2 2 d5 d 4 d 3 j3 E3 j3 Electronics and Cybernetics 10 Silicon: Three independent piezoresistive coefficients Example of piezoresistive coefficients: doping: p-type sheet resistivity: 7.8 cm value of 11= 6.6 10-11 Pa-1 value of 12=-1.1 10-11 Pa-1 value of 44= 138 10-11 Pa-1 Equations 18.3, 18.4, 18.5 in Senturia d1 d 6 d5 j1 E1 j1 E j d d d j 0 2 0 6 2 4 2 2 d5 d 4 d 3 j3 E3 j3 d1 11 12 12 0 0 0 d 11 12 0 0 0 2 12 d 3 12 12 11 0 0 0 0 0 44 0 0 d 4 0 d 5 0 0 0 0 44 0 d 6 0 0 0 0 0 44 Electronics and Cybernetics x y z yx zx xy 11 Forenklet beskrivelse Hvis det er “bestemt” hvilken retning vi vil legge motstandene i, ønsker vi et enklere uttrykke J t l Transverse and longitudinal coefficients R l l t t R The resistor axis is defined according to the direction of the current through the resistor Electronics and Cybernetics 12 Rotasjon Stress er opplinjert etter sidekantene som er (110) Piezokoeffisientene er relatert til (100) akser Kan rotere piezo koeffisientene Electronics and Cybernetics 13 Resistors along <110> direction in (100) wafers Much used direction for piezoresistors, bulk micromachining Pre-calculated longitudinal and transverse piezo-coefficients positive: tensile stress negative: compressible stress positive: increased resistivity with tensile stress negative: decreased resistivity with tensile stress l 1/ 2( 11 12 44 ) t 1/ 2( 11 12 44 ) Electronics and Cybernetics 14 Båndstruktur og resistivitet Stor forskjell på n- og p- type silisium Electronics and Cybernetics 15 ”Doping” av Al Electronics and Cybernetics 16 p-type Si l 1 / 2( 11 12 44 ) t 1 / 2( 11 12 44 ) R 44 ( l t ) R 2 Electronics and Cybernetics 17 Piezoresistor placed normal to diaphragm edge Apply pressure from above Diaphragm bends down Piezoresistor is stretched longitudinally l is positive, tensile stress Rough argument for mechanical stress in transversal direction: stress must avoid contraction: t= l Transverse stress is tensile/positive Change in resistance: R l l t t R R1 / R1 ( l t ) l (t is negative) Resistance increases p-type piezoresistor along <100> direction in (100) wafer Electronics and Cybernetics 18 Piezoresistor placed parallel to diaphragm edge Apply pressure from above Diaphragm bends down Piezoresistor is stretched transversally t is positive Rough argument for mechanical stress in longitudinal direction: stress must avoid contraction: l= t Tensile, positive stress in longitudinal dir. Change in resistance: R2 / R2 ( t l ) t p-type piezoresistor along <100> direction in (100) wafer (t is negative) Resistance decreases Electronics and Cybernetics 19 Wheatstone bridge circuit R2 R3 V0 Vs R2 R1 R3 R4 R1 R1 R R2 R2 R R3 R3 R R4 R4 R R V0 Vs R Electronics and Cybernetics 20 Electronics (Chapter 14.1 - 14.4) Doped resistors Define a p-type circuit in a n-type wafer n-type wafer must be at positive potential relative to the p-type circuit n p +V- Reverse biased diode no current between circuit and wafer/substrate Alternative methods: •SOI •Surface micromachining Electronics and Cybernetics 21 Motstandsposisjon og lednigsføring Electronics and Cybernetics 22 Forventet følsomhet V 44 L 0.9 0.8 1 0.3 P Vs 2 H 2 Pi44 2 1mm 1 mV 0.9 0.8 ( 1 0.23) 0.3 0.287 2 V kPa 20m Electronics and Cybernetics 23 X-ducer • Resistor langs 100 akse • Har allerede piezo koeffisientene i dette aksesystemet [100]=1 wR V1 E1d1 J1LR V2 E2 d 2 44 12 J1wR LR Electronics and Cybernetics V2 w 44 12 R V1 LR 24 Men vi må rotere stresset 100 Electronics and Cybernetics 25 Forventet følsomhet Electronics and Cybernetics 26 Re-design Electronics and Cybernetics 27 Dependence of piezoresistivity on doping Electronics and Cybernetics 28 Pressure Measurement in Medicine Example: Hydrocephalus abnormal accumulation of brain fluid increased brain pressure occurs in approximately one out of 500 births treated by implantation of a shunt system Electronics and Cybernetics 29 Complex requirements for the measurement system Small dimensions Effective pressure transmission No wires through the skin No batteries Material acceptable for MRI scans Electronics and Cybernetics 30 The sensor Piezoresistive Surface micro machined Wheatstone bridge two piezoresistors on diaphragm two on substrate for temperature reasons Absolute pressure sensor Electronics and Cybernetics 31 Sensor design Electronics and Cybernetics 32 Sensor design (polySi) (Al) polySi SiO2 Si3N4 (not to scale) Electronics and Cybernetics 33 Polysilicon Silicon exists in any of three forms: monocrystalline silicon poly crystalline silicon, also called polysilicon or poly-Si amorphous The extent of regular structure varies from amorphous silicon, where the atoms do not even have their nearest neighbors in definite positions, to monocrystalline silicon with atoms organized in a perfect periodic structure. Electronics and Cybernetics 34 Piezoresistivity in polysilicon The piezoresistive coefficients loose sensitivity to crystalline direction Average over all orientations Gauge factor of 20 – 40, about one fifth of the gauge factor of monocrystalline silicon Gauge factor up to 70% of monosilicon has been reported The structure; i.e. the grain size and the texture (preferred orientation of the crystallites) is decisive for the piezoresistivity The longitudinal gauge factor is always larger than the transverse one Electronics and Cybernetics 35 Functionality & sensitivity Electronics and Cybernetics 36