A High Sensitive Piezoresistive Sensor for Stress
Measurements in Packaged Semiconductor Die
Ahsan Mian, Jeffrey C. Suhling, and Richard C. Jaeger
Abstract----- The authors have developed new two-
dimensional piezoresistive stress sensors that replace
conventional serpentine resistor rosettes. These sensors
are named van der Pauw (VDP) sensors as they are
based upon four-terminal van der Pauw type resistance
measurements. The resistance of such a sensor is size
independent, and hence can be made as small as
lithographically possible to capture stresses in critical
areas on the surface of a packaged semiconductor die. It
was predicted theoretically that the VDP sensor should
exhibit a greater than three times improvement in
sensitivity relative to resistor sensor rosettes. Then the
response of actual VDP structures fabricated on (111)
silicon surface was characterized under uniaxial load
using four-point-bending tests. These experimental
results confirm that the VDP stress sensitivities are more
than three times higher than those of their corresponding
resistor sensor counterparts.
I
.
I
NTRODUCTION
For many years, resistive stress sensors have been used
successfully to measure die stresses in a wide range of
packaging applications [1-2]. However, resistor sensors
possess several drawbacks. Diffused and implanted resistors
have high temperature sensitivity relative to the stress
response, and great care must be exercised to achieve
accurate measurement of stress. Resistors are often designed
with relatively large meandering patterns to increase the
total resistance, but they then suffer from transverse
sensitivity which is difficult to estimate due to the lateral
diffusion that occurs during the fabrication process.
Transverse sensitivity can be minimized by interconnecting
resistor legs with metal links, but these require additional
contacts that further increase the resistor size.
In a paper published recently [3],
the authors have fully
developed the theory for a new piezoresistive stress sensor
termed the van der Pauw (VDP) sensor that is designed to
replace conventional serpentine resistor sensors. The sensor
utilizes the technique of measuring “resistances” based on
the theoretical developments of van der Pauw. When used
as stress sensors, VDP devices have the potential to reduce
some of the error sources in resistor-based sensors. As will
be demonstrated, they offer a greater than thee times
increase in sensitivity compared to that of resistors, and
therefore they also exhibit a corresponding reduction in
A. Mian is with the Dept. of Mechanical and Industrial Eng., Montana
State University, Bozeman, Montana 59717 (
amian@me.montana.edu
)
J. C. Suhling is with the Dept. of Mechanical Eng., Auburn University,
Auburn, Alabama 36849
R. C. Jaeger is with the Dept. of Electrical and Computer Eng., Auburn
University, Auburn, Alabama 36849
sensitivity to thermal errors. The classical VDP structure
itself requires only one square of material plus room for four
contacts. Thus, these sensors have the potential to be made
small enough to capture localized stress variations without
any loss of sensitivity. The VDP characteristics are size
independent and do not have the transverse sensitivity issue.
In contrast, it is the distributed nature of the VDP structure
that leads to the enhanced sensitivity.
In this work, the sensitivity of the VDP sensor is first
predicted theoretically. Then, VDP and resistor sensors
fabricated on (111) silicon surfaces are characterized using
uniaxial stress, and the predicted enhancement of the
sensitivity of the sensors is experimentally demonstrated.
II.
V
DP
S
ENSOR
P
IEZORESISTIVE
T
HEORY
The van der Pauw sensor has four electrical contacts A,
B, C, and D located at the four corners of the sample as
shown in Fig. 1. The “resistance” R
AB,CD
of the sample is the
potential difference V
D
-V
C
between contacts D and C per
unit current through contacts A and B. A similar resistance
R
BC,DA
can be defined in an analogous manner. The
orientation
φ of the sensor indicates the angle between the
1
x
′
- axis and the line connecting points A and B. Also, a
simplified notation is introduced for the resistance of the
oriented VDP sensor:
AB
C
D
CD
AB
I
V
V
R
R
/
)
(
,
−
=
=
φ
(1)
Note that a given VDP structure as shown in Fig. 1 can be
used to measure both
φ
R
and
90
+
φ
R
.
A local coordinate system has also been considered
denoted by the
1
x
′′ -
2
x
′′ axes that are directed along the edges
of the VDP sensor. As developed in [3], the sensor
resistance change equations for such sensors fabricated on
(111) silicon surfaces are given as
′
−
+
′
−
−
′
−
=
∆
−
∆
23
22
1
1
11
2
1
90
90
0
0
)
(
2
4
)
(
)
(
16
.
3
3
2
σ
σ
σ
n
n
B
B
B
B
B
B
R
R
R
R
(2)
[
]
12
2
1
13
2
1
45
45
45
45
)
(
2
)
(
2
4
16
.
3
σ
σ
′
−
+
′
−
=
∆
−
∆
−
−
B
B
B
B
R
R
R
R
(3)
The normalized resistance change is defined by
0
0
/
)
(
/
φ
φ
σ
φ
φ
φ
R
R
R
R
R
−
=
∆
(4)
where
σ
φ
R
is the resistance measured for the stressed VDP,
and
0
φ
R
is the reference resistance measured for the
“unstressed” sensor.
In order to verify the theory, we focus on the uniaxial
stress case where
σ
σ
=
′
11
is applied in
1
x
′
direction, and all
other stress components are assumed to be zero. For this
case, the difference between the normalized resistance
19
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