Piezoresistive Sensors

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Piezoresistive Sensors. EE485A Lecture Oct. 6, 2009. Piezoresistivity. Resistivity dependent on strain True for most semiconductors, including Si Also used to describe metal resistors where resistance change is geometry-driven (strain gauges)

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## Piezoresistive Sensors

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### Piezoresistive Sensors

EE485A Lecture

Oct. 6, 2009

Piezoresistivity
• Resistivity dependent on strain
• True for most semiconductors, including Si
• Also used to describe metal resistors where resistance change is geometry-driven (strain gauges)
• Characterized by Gauge Factor, G (s = strain, R = resistance)
• Longitudinal and transverse strains often present at same time and could have different gauge factors. General expression for resistance change:
Exercise
• A silicon resistor has resistivity 11.7 W-cm, and dimensions given by L = 20 um, W = 1 um, t = 0.5 um. Its longitudinal gauge factor is given by 120.6
• What is the resistance value for the resistor at rest?
• What is the resistance change when the resistor undergoes a strain of 0.1%?
Piezoresistive Materials
• Metal strain gauges typically exhibit gauge factors in range of 0.8 to 3
• G for single crystal silicon is orientation dependent and doping dependent but can range from 1 to 150.
• G for polycrystalline silicon is not orientation dependent (and much smaller than for SCS), but is still doping dependent.
• Peaks at -24 for n-type silicon doped to 3 x 1019 cm-3
• Peaks at 30 for p-type silicon doped to 1019 cm-3
Stress in Flexural Cantilevers

A

B

E

Fixed End

C

Free End

t

D

W

L

Under Longitudinal Stress:

A

B

E

C

F

D

Same strain seen at all points so piezoresistor location doesn’t matter

s = F/A = F/(Wt)

s = s/E

Stress in Flexural Cantilevers, cont.

F

Under Transverse Stress:

A

B

E

C

D

Maximum tensile stress (and strain) occur at points A, B, C. Compressive stress/strain occurs at D. E would be a poor choice for piezoresistor location)

smax = FLt/(2I)

s = FLt/(2EI)

Effective designs

Ineffective designs

Exercise

Ftransverse

• A silicon resistor is located at the base of a cantilever with resistivity 11.7 W-cm, and dimensions given by L = 100 um, W = 1 um, t = 0.5 um, and the material has a gauge factor given by 120.6 (same as previous example). The cantilever dimensions are given by length = 200 um, W = 20 um and t = 5 um. If a longitudinal force of 100 uN is applied to the end of the beam, what will be the resistance change?
• Repeat if the force is transverse (applied at the tip)

Flongitudinal

Translating resistance change into voltage
• Simple voltage divider:
• Wheatstone bridge:
• Compared in homework
Stress in membranes
• Maximum stress occurs at edges
• Maximum stress of opposite sign occurs at center
• For governing equations see sect. 6.3 in text
• Typical piezoresistor configuration for pressure sensor:
Case Studies
• See pp. 224-239 in text
• Class exercise