Piezoresistive pressure sensors. Electronics and Cybernetics 1
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1 Piezoresistive pressure sensors Electronics an Cybernetics
2 Two sensing principles Piezoresistive measure mechanical stress in ope resistor-area iaphragm pressure sensor bening beam ue to volume forces (e.g. acceleration) en force (e.g. protein attache) capacitive measure eflection (istance to other capacitor plate) iaphragm pressure sensor bening beam ue to volume forces (e.g. acceleration) en force (e.g. protein attache) Electronics an Cybernetics
3 Piezoresistive sensing applications Veieceller Akselerometer Trykksensorer Electronics an Cybernetics
4 Electronics an Cybernetics elation between stress an strain in a coorinate system with axes equivalent to the axes of the unit cell xy zx yz z y x xy zx yx z y x C C C C C C C C C C C C F x = E x D hooke s law
5 Electronics an Cybernetics 5 Small eflections Beam equation, plate equation Beam equation: Plate equation: Fin isplacement an stress q x w EI F p ), ( ) ( y x q y w y x w x w D
6 General: Finite Element Analysis Solve Navier s equation (partial ifferential equation) ( ) ( u) u Divie omain into elements Approximation of function (solution to partial ifferential equation) over omain Simple function over each element (linear, parabolic) Connect elements at noes Electronics an Cybernetics 6
7 Example: beam with en loa Electronics an Cybernetics 7
8 esistor change in metal strain gauges Mainly ue to change of resistor FOM (geometric effect) L L+L F a a = L/a a+a = + L/L+ a/a a/a =-L/L =. / L/L / Electronics an Cybernetics 8
9 For silicon: large ESISTIVITY change with stress (not mainly a geometric resistor-change factor) Metal: Silicon: - + / / 9 Electronics an Cybernetics 9
10 Electronics (Chapter. -.) Dope 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 everse biase ioe no current between circuit an wafer/substrate +Vn p Electronics an Cybernetics
11 Electronics an Cybernetics The resistivity changes with the mechanical stress E - electric fiel, three components - current ensity, three components homogeneous resistivity, unstresse silicon When mechanical stress is applie, the resistivity changes epening on the stress in ifferent irections an the piezo coefficients E E E V V
12 Electronics an Cybernetics Silicon: Three inepenent piezoresistive coefficients Example of piezoresistive coefficients: oping: p-type sheet resistivity: 7.8 cm value of = Pa - value of =-. - Pa - value of = 8 - Pa - Equations 8., 8., 8.5 in Senturia xy zx yx z y x E E E
13 Depenence of piezoresistivity on oping Electronics an Cybernetics
14 Long, narrow resistors Pre-calculate piezocoefficients that enables the esigner to calculate the resistivity change for a long, narrow resistor Often given for a resistor that is place in the <> irection Transverse an longituinal coefficients l l t t Electronics an Cybernetics
15 esistors in <> irection Much use irection for piezoresistors, bulk micromachining Pre-calculate longituinal an transverse piezo-coefficients positive: tensile stress negative: compressible stress positive: increase resistivity with tensile stress negative: ecrease resistivity with tensile stress / ( l t / ( ( l ) t ) ) p-type silicon: ominates Electronics an Cybernetics 5
16 Beam accelerometer Long resistors in <> irection Piezoresistance coefficients Electronics an Cybernetics 6
17 Cantilever with piezoresistors length m with m thickness 5 m point loa at free en p-type piezoresistor length m with m epth. m / = l l =. Electronics an Cybernetics 7
18 Placement of piezoresistors on iaphragm Over/uner konfigurason er ikke praktisk i silisium. Men vi kan snu retningen på motstanene Electronics an Cybernetics 8
19 Stress level at point in structure: Mises yiel criterion mieses / Electronics an Cybernetics 9
20 x, normal stress on x=const. planes Electronics an Cybernetics
21 y, normal stress on y=const. planes Electronics an Cybernetics
22 Piezoresistor place normal to iaphragm ege Apply pressure from above Diaphragm bens own Piezoresistor is stretche longituinally l is positive, tensile stress ough argument for mechanical stress in transversal irection: stress must avoi contraction: t = l Transverse stress is tensile/positive Change in resistance: l / l ( t is negative) esistance increases l t t ( ) t l Electronics an Cybernetics
23 Piezoresistor place parallel to iaphragm ege Apply pressure from above Diaphragm bens own Piezoresistor is stretche transversally t is positive ough argument for mechanical stress in longituinal irection: stress must avoi contraction: l = t Tensile, positive stress in longituinal ir. Change in resistance: / t ( t is negative) esistance ecreases ( ) l t Electronics an Cybernetics
24 Membrane pressure sensor Electronics an Cybernetics
25 Electronics an Cybernetics 5 Wheatstone brige circuit <> irection V V V V s s t l compressible stress negative, tensile stress positive,
26 Electronics an Cybernetics 6 Averaging over stress an oping variations Senturia 8..5 z z z L W z l l o e, ) ( ) ( E E E
27 Motorola MAP sensor Electronics an Cybernetics 7
28 Electronics an Cybernetics 8 Potential across piezoresistor Electric fiel in transverse irection E E E
29 Coventor tutorials-choose one In files mems_analy.pf an mems_supp.pf ( version) In files MEMS Design an Analysis Tutorials vol + (5 version) Mirror esign (electrostatic forces) Beam simulation analysis (pull-in) Moal an harmonic analysis (resonant frequencies, moal shapes) Temperature analysis (temperature istribution, ifferent coefficients) MemHenry (magnetic sensor) MemPackage (thermal an mechanical effects) MemPZ (piezoresistors) MemETherm (Joule heating, thermal expansion) AutoSpring (Extract spring constants) MemDamping (Squeeze film, slie amping) MemTrans (Transient analysis) Electronics an Cybernetics 9
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