1. Electronics and Cybernetics 1 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

2. Electronics and Cybernetics 2 Piezoresistive pressure sensors

3. Electronics and Cybernetics 3 Modellering av trykkmembran 1mm*1mm*20µm ~10 18 atomer (masser og fjærer) 3 D kontiniumsmekanikk 2 D Plateligning eksakt variasjonsprinsipp stress FEM modellering

4. Electronics and Cybernetics 4 Stress ( σ xx ) i trykkmembranen x

5. Electronics and Cybernetics 5 Piezoresistive sensing applications Load cell Accelerometer Pressure sensor

6. Electronics and Cybernetics 6 Resistor change in metal strain gauges Mainly due to change of resistor FORM (geometric effect) a a L R 0 =  L/a 2 a+  a L+  L  a/a =-  L/L =0.3

7. Electronics and Cybernetics 7 For silicon: large RESISTIVITY change with stress (not mainly a geometric resistor-change factor)  R/R  2  Metal:  R/R  90  Silicon:

8. Electronics and Cybernetics 8 Isotrop resistivitet Vd

9. Electronics and Cybernetics 9 Anisotrop resistivitet

10. Electronics and Cybernetics 10 The resistivity changes with the mechanical stress E - electric field, three components j - current density, three components  0 – homogeneous resistivity, unstressed silicon When mechanical stress is applied, the resistivity changes depending on the stress in different directions and the piezo coefficients V1V2

11. Electronics and Cybernetics 11 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

12. Electronics and Cybernetics 12 Forenklet beskrivelse Hvis det er “bestemt” hvilken retning vi vil legge motstandene i, ønsker vi et enklere uttrykke Transverse and longitudinal coefficients The resistor axis is defined according to the direction of the current through the resistor l t J

13. Electronics and Cybernetics 13 Rotasjon Stress er opplinjert etter sidekantene som er (110) Piezokoeffisientene er relatert til (100) akser Kan rotere piezo koeffisientene

14. Electronics and Cybernetics 14 Resistors along 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

15. Electronics and Cybernetics 15 Båndstruktur og resistivitet Stor forskjell på n- og p- type silisium

16. Electronics and Cybernetics 16 ”Doping” av Al

17. Electronics and Cybernetics 17 p-type Si

18. Electronics and Cybernetics 18 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: (  t is negative) Resistance increases p-type piezoresistor along direction in (100) wafer

19. Electronics and Cybernetics 19 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: (  t is negative) Resistance decreases p-type piezoresistor along direction in (100) wafer

20. Electronics and Cybernetics 20 Wheatstone bridge circuit

21. Electronics and Cybernetics 21 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 Reverse biased diode  no current between circuit and wafer/substrate +V- np Alternative methods: SOI Surface micromachining

22. Electronics and Cybernetics 22 Motstandsposisjon og lednigsføring

23. Electronics and Cybernetics 23 Forventet følsomhet

24. Electronics and Cybernetics 24 X-ducer [100]=1 Resistor langs 100 akse Har allerede piezo koeffisientene i dette aksesystemet LRLR wRwR

25. Electronics and Cybernetics 25 Men vi må rotere stresset 100

26. Electronics and Cybernetics 26 Forventet følsomhet

27. Electronics and Cybernetics 27 Re-design

28. Electronics and Cybernetics 28 Dependence of piezoresistivity on doping

29. Electronics and Cybernetics 29 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

30. Electronics and Cybernetics 30 Complex requirements for the measurement system Small dimensions Effective pressure transmission No wires through the skin No batteries Material acceptable for MRI scans

31. Electronics and Cybernetics 31 The sensor Piezoresistive Surface micro machined Wheatstone bridge two piezoresistors on diaphragm two on substrate for temperature reasons Absolute pressure sensor

32. Electronics and Cybernetics 32 Sensor design

33. Electronics and Cybernetics 33 Sensor design Si 3 N 4 SiO 2 polySi (Al) (polySi) (not to scale)

34. Electronics and Cybernetics 34 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.

35. Electronics and Cybernetics 35 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

36. Electronics and Cybernetics 36 Functionality & sensitivity