Results
Create a mirrored dataset to visualize a cross section of the device.
Datasets
1
In the Results toolbar click More Datasets
and choose Mirror 3D
.
2
In the Settings window for Mirror 3D locate the Data section. From the Dataset list, choose Study 2/Solution 2.
3
Leave the plane as the default y-z plane.
Displacement (solid) 1
1
In the Model Builder window, under Results right-click Displacement (solid)
and choose Duplicate
.
2
In the Settings window for 3D Plot Group locate the Data section. From the Dataset list, choose Mirror 3D 1.
3
Click the Plot button
.
Notice that the entire structure now has nonzero movements at room temperature, as a result of thermal stress.
Now look at the effect of the thermal stress on the response of the sensor.
Add an additional global node to the previously defined plot. This separate node can point to a different dataset, creating a plot of the displacement of the thermally stressed device alongside the unstressed plot.
Diaphragm Displacement vs Pressure
1
In the Model Builder window, under Results > Diaphragm Displacement vs Pressure
right-click Global 1
and choose Duplicate
.
2
In the Settings window for Global locate the Data section. From the Dataset list, choose Study 2/Solution 2.
3
Locate the y-Axis Data section. In the table, enter the following settings for the first row and remove the 2nd row (aveop1):
Expression
Unit
Description
intop1(w)
um
Maximum Displacement with Package Stress
4
Click the Plot button
.
The maximum displacement of the membrane is now nonzero at zero applied pressure, as a result of the packaging stress. The gradient of the displacement-pressure line has also changed.
Model Capacitance vs Pressure
Now add the thermally stressed results to the Capacitance vs Pressure plot.
1
Click on the Model Capacitance vs Pressure node
. On the Model Capacitance vs Pressure toolbar click Global
.
2
In the Settings window for Global locate the Data section. From the Dataset list, choose Study 2/Solution 2.
3
Click Replace Expression
in the upper-right corner of the y-Axis Data section. From the menu, navigate to Component 1 > Electrostatics > Terminals > es.C11 - Maxwell capacitance - F; then double click to select the item.
4
Locate the y-Axis Data section. In the table, modify the first row to match the following settings (Note the unit is changed to pF to match the previous Global plot):
Expression
Unit
Description
es.C11
pF
Capacitance with Package Stress
5
Click the Plot button
.
The packaging stress causes a significant change in the response of the device. At zero applied pressure the sensitivity of the COMSOL Multiphysics model has increased to 10
×
10
-6
pF/Pa (40
×
10
-6
pF/Pa for the entire device). Compare to the unstressed value of 7.3e-6 pF/Pa (29
×
10
-6
pF/Pa for the entire device). The effect is even more pronounced at a pressure of 20 kPa, where the model that includes thermal stresses shows a pressure sensitivity of 25
×
10
-6
pF/Pa (100 pF/Pa for the entire device), compared to the unstressed pressure sensitivity of 14
×
10
-6
pF/Pa (sensor output 57 pF/Pa).
It may be possible to calibrate the device to remove the effect of the packaging strains. However, the addition of the thermal stresses to the system has created an additional issue, since the response of the sensor has now become temperature dependent - due to the temperature sensitivity of the thermal strains. This effect is assessed in the final study.
and choose Mirror 3D 
.
and choose Duplicate 
.
.
right-click Global 1 
and choose Duplicate 
.
.
. On the Model Capacitance vs Pressure toolbar click Global 
.
in the upper-right corner of the y-Axis Data section. From the menu, navigate to Component 1 > Electrostatics > Terminals > es.C11 - Maxwell capacitance - F; then double click to select the item.
.