Denne forelesningen

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. Piezoresistive pressure sensors

3. 3 D kontiniumsmekanikk 2 D Plateligning eksakt FEM modellering variasjonsprinsipp stress Modellering av trykkmembran 1mm*1mm*20µm ~1018atomer (masser og fjærer)

4. Stress (σxx) i trykkmembranen x

5. Isotrop resistivitet d V

6. Anisotrop resistivitet

7. V1 V2 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

8. 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

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

10. Rotasjon • Stress er opplinjert etter sidekantene som er (110) • Piezokoeffisientene er relatert til (100) akser • Kan rotere piezo koeffisientene

11. 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

12. Båndstruktur og resistivitet Stor forskjell på n- og p- type silisium

13. ”Doping” av Al

14. p-type Si

15. 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 <100> direction in (100) wafer

16. 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 <100> direction in (100) wafer

17. Wheatstone bridge circuit

18. n p +V- 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 • Alternative methods: • SOI • Surface micromachining

19. Motstandsposisjon og lednigsføring

20. Forventet følsomhet

21. X-ducer • Resistor langs 100 akse • Har allerede piezo koeffisientene i dette aksesystemet [100]=1 wR LR

22. Men vi må rotere stresset 100

23. Forventet følsomhet

24. Re-design

25. Dependence of piezoresistivity on doping

26. Pressure Measurement in MedicineExample: Hydrocephalus • abnormal accumulation of brain fluid • increased brain pressure • occurs in approximately one out of 500 births • treated by implantation of a shunt system

27. Complex requirements for the measurement system • Small dimensions • Effective pressure transmission • No wires through the skin • No batteries • Material acceptable for MRI scans

28. The sensor • Piezoresistive • Surface micro machined • Wheatstone bridge • two piezoresistors on diaphragm • two on substrate for temperature reasons • Absolute pressure sensor

29. Sensor design

30. Sensor design (polySi) (Al) polySi SiO2 Si3N4 (not to scale)

31. 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.

32. 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

33. Functionality & sensitivity