文档介绍：Lecture 7 Case studies
清華大學材料科學與工程系
廖建能教授
1
NTHU, Chien-Neng Liao
Pressure sensing (diaphragm)
Stress (strain) voltage (piezoelectric)
optical detection (Moiré pattern)
tunneling current detection
capacitance change
resistance change (piezoresistive)
vacuum
P
Pref
P
Absolute pressure
Differential pressure
2
NTHU, Chien-Neng Liao
Piezoresistivity
Mechanical strain affect the energy band gap, and hence carrier conc. and resistivity
Piezoresitive coefficient:
The piezoresistive effect is linear when small strain is assumed
E: electric field
J: current density
re: resistivity tensor
s: stress
P: piezoresistive tensor
3
NTHU, Chien-Neng Liao
Longitudinal and transverse piezoresistivity
If a relatively long, relatively narrow resistor is defined in a planar structure
l: longitudinal t: transverse
(l1,m1,n1) : direction cosines between the longitudinal resistor direction and the axes
(l2,m2,n2) : direction cosines between the transverse resistor direction and the axes
4
NTHU, Chien-Neng Liao
Longitudinal and transverse piezoresistivity
If a piezoresistor is fabricated along [110] directions in a (100) Si wafer
(l2,m2,n2) =
(l1,m1,n1) =
l: longitudinal
t: transverse
5
NTHU, Chien-Neng Liao
Piezoresistive coefficients of Si
pij is a weak function of doping level when n<1019 cm-3
pij decrease markedly with doping levels at high doping
pij decrease with increasing temperature, (dpij /dT) decrease at high doping level
Type
Resistivity
p11
p12
p44
Units
W-cm
10-11 Pa-1
10-11 Pa-1
10-11 Pa-1
n-type
-
-
p-type
-
Lightly-doped Si has high sensitivity and temp dependence.
For a wide operation temperature range, heavily doped Si is selected at the expense of sensitivity
6
NTHU, Chien-Neng Liao
Structural example
Two bulk micromachined piezoresistors oriented along [110] directions
n-type : pl= - , pt= - ; p-type : pl= , pt= - 10-11 Pa-1
Bridge-type senso