MEMS Pressure Sensor Drift Due to Hygroscopic Swelling

For their integration in microelectronic circuits, MEMS and other devices are often overmolded with an epoxy mold compound (EMC) to protect the devices and their interconnects with the board. The epoxy polymers used for such applications are subject to moisture absorption and hygroscopic swelling, which can lead to delamination between the EMC and the board or to incorrect behavior of MEMS components. This example studies how the moisture absorption of an EMC affects the response of a MEMS pressure sensor over a one-year time period.

Model Definition

Figure 1: Component geometry.

It is sufficient to model a quarter of the whole structure due to the symmetry (Figure 1). The geometry is composed of:

•

An FR4 board, on which the die is glued.

•

The pressure sensor die made of:

A silicon component with a processed membrane. The membrane is modeled with a shell interface. The strain on the membrane surface is used to measure the pressure.

A silica glass capping

•

An EMC that covers the die and a large part of the board.

When external pressure is applied on the bottom face of the membrane, the membrane deforms, and the strain is measured by means of a Wheatstone bridge made of piezoresistors. The measure of strain on the X- and Y-axes makes it possible to calculate the pressure. The membrane is modeled with a shell interface that is connected to the silicon domains via a shell-solid connection.

The moisture transport in the EMC is governed by the diffusion equation:

The moisture diffusion coefficient is temperature dependent:

Here U is the activation energy and k is the Boltzmann’s constant. For a typical EMC, D0 = 7.35·10-6 m2/s, U = 0.43 eV, and the diffusion coefficient at 25°C is approximately 4·10−13 m2/s.

The boundary conditions on the exterior faces of the EMC should be a flux of moisture concentration. However, given the long simulation time (one year) a concentration constraint can be assumed. The concentration applied on the boundaries is the saturation concentration of the material at a given temperature and humidity conditions:

where S is the solubility on the water in the material a given condition, Psat is the vapor saturation pressure of water, and

is the relative humidity. The product of solubility and saturation pressure is supposed to be temperature-independent, thus the saturation concentration in the material depends only on the relative humidity. At 60% humidity, the saturation concentration is 140 mol/m3.

The initial moisture concentration after molding is set to 40 mol/m3. This value can be also taken as reference for hygroscopic swelling because all the stresses are assumed relaxed just after molding.

In order to avoid problems that can be caused by the discontinuity of concentration at initial state, the concentration boundary condition is applied smoothly, and a boundary layer type mesh is used near those boundaries (Figure 2).

Figure 2: Mesh of the device.

As hygroscopic swelling induces a unidirectional dependence between concentration and mechanics, the concentration is calculated in a first time-dependent study, and then the structural domains are computed in a stationary study. This sequential approach reduces the computation time compared to a single solution including all physical interfaces.

Results and Discussion

The moisture diffuses progressively in the EMC. After 6 days, the moisture has already partially reached the top face of the die (Figure 3).

Figure 4 shows that the concentration at the die location starts to increase after 2 days until approximately 100 days. This is confirmed by the mass uptake shown in Figure 5, where the maximum value is reached after the same period of time.

Figure 3: Moisture concentration in the EMC after 6 days.

Figure 4: Moisture concentration at die location over time.

Figure 5: Total mass uptake in the EMC.

The progressive moisture diffusion is also noticed on displacement plots after hygroscopic swelling calculation: the EMC swells only on its boundaries during the first days (Figure 6), and it swells everywhere after one year (Figure 7). During the first time, the expansion on the exterior boundaries implies a stretching on the membrane and thus an increase of the measured strain. Then, the expansion of the center implies compression on the die and a decrease of the strain along the axes; see Figure 8.

The moisture absorption and hygroscopic swelling have significant effect on the sensor sensibility, which have to be taken in account during the measurements, or when designing the sensor.

Figure 6: Displacement after 6 days.

Figure 7: Displacement after 1 year.

Figure 8: Evolution of measured strain on membrane axes.

Structural_Mechanics_Module/Hygroscopic_Swelling/pressure_sensor_hygroscopic_swelling

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select .

Click .

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
l	20[mm]	0.02 m	length of the device
w	15[mm]	0.015 m	width of the device
l_MC	15[mm]	0.015 m	length of the eopxy mold compound
w_MC	10[mm]	0.01 m	width of the epoxy mold compound
l_die	1.2[mm]	0.0012 m	side length of the pressure sensor
l_memb	700[µm]	7E-4 m	side length of the silicon membrane
l_hole	800[µm]	8E-4 m	side length of the hole in FR4
t_FR4	1[mm]	0.001 m	thickness of the FR4
t_Si	200[µm]	2E-4 m	thickness of the silicon
t_memb	20[µm]	2E-5 m	thickness of the silicon membrane
t_glass	200[µm]	2E-4 m	thickness of the silica glass wafer
t_MC	1.5[mm]	0.0015 m	thickness of the mold compound
cmax	140[mol/m^3]	140 mol/m³	saturated concentration of the mold compound
cini	40[mol/m^3]	40 mol/m³	initial moisture concentration
pext	1[bar]	1E5 Pa	external pressure
t	0[s]	0 s	time used for parametric sweep

Geometry 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

Create a block for the silicon wafer and the glass cap.

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_die/2.

In the text field, type t_Si+t_glass.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	t_Si

Create a block for the EMC.

Block 2 (blk2)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_MC/2.

In the text field, type w_MC/2.

In the text field, type t_MC.

Create a block and substract it to make the cavity in the wafer.

Block 3 (blk3)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_memb/2.

In the text field, type t_Si.

Difference 1 (dif1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select the object only.

Click

Create a block for the board.

Block 4 (blk4)

In the toolbar, click

In the window for , locate the section.

In the text field, type l/2.

In the text field, type w/2.

In the text field, type t_FR4.

Locate the section. In the text field, type -t_FR4.

Create a block and substract it to make a hole in the board.

Block 5 (blk5)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_hole/2.

In the text field, type t_FR4.

Locate the section. In the text field, type -t_FR4.

Difference 2 (dif2)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select the object only.

Click

Create a rectangle in a work plane to build the membrane.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , click

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_memb/2.

Click

In the window, right-click and choose .

Click the

button in the toolbar.

Definitions

Create selections to select domains easily in the following steps.

FR4

In the toolbar, click

In the window for , type FR4 in the text field.

Select Domain 4 only.

Silicon

In the toolbar, click

In the window for , type Silicon in the text field.

Select Domain 3 only.

Glass

In the toolbar, click

In the window for , type Glass in the text field.

Select Domain 1 only.

Mold Compound

In the toolbar, click

In the window for , type Mold Compound in the text field.

Select Domain 2 only.

Membrane

In the toolbar, click

In the window for , type Membrane in the text field.

Locate the section. From the list, choose .

Select Boundary 1 only.

Shell (shell)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click to expand the section. In the z text field, type -1.

Thickness and Offset 1

Set the shell thickness and the offset so that the bottom face is at z = 0, and set the height of evaluation so that the results are calculated on the bottom face.

In the window, under click .

In the window for , locate the section.

In the d text field, type t_memb.

From the list, choose .

In the zreloffset text field, type 1.

Use symmetry on the shell edges. The normal of the symmetry plane is the second axis of the local edge system, which is orthogonal to the edge and to the shell normal.

Symmetry 1

In the toolbar, click

and choose .

Select Edges 1 and 2 only.

Face Load 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the p text field, type -pext.

Solid Mechanics (solid)

First, set the discretization to in in order to fit the discretization of .

In the window, under click .

In the window for , click to expand the section.

From the list, choose .

Fixed Constraint 1

In the toolbar, click

and choose .

Select Boundary 15 only.

Symmetry 1

In the toolbar, click

and choose .

Select Boundaries 2, 3, 5, 6, 9, 13, 24, and 26 only.

Definitions

Create a step function in order to apply the concentration boundary condition progressively.

Step 1 (step1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 0.5.

Click to expand the section. In the text field, type 1.

Click

Transport of Diluted Species (tds)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. Clear the check box.

Click to expand the section. From the list, choose .

Transport Properties 1

In the window, under click .

In the window for , locate the section.

In the Dc text field, type 4e-13[m^2/s].

Initial Values 1

In the window, click .

In the window for , locate the section.

In the c text field, type cini.

Symmetry 1

In the toolbar, click

and choose .

Select Boundaries 5 and 6 only.

Concentration 1

In the toolbar, click

and choose .

Select Boundaries 8, 20, and 29 only.

In the window for , locate the section.

Select the check box.

In the c0,c text field, type cini+(cmax-cini)*step1(t[1/s]/3600).

Multiphysics

Add a multiphysics node to model hygroscopic swelling.

Hygroscopic Swelling 1 (hs1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the cmo,ref text field, type cini.

Connect the shells and solids.

Solid-Thin Structure Connection 1 (sshc1)

In the toolbar, click

and choose .

In the window for , locate the section.

Select the check box.

Locate the section. In the list, select .

Click

Select Boundaries 10 and 23 only.

Definitions

Click the

button in the toolbar.

In the dialog box, in the tree, select the check box for the node .

Click .

Mass Properties 1 (mass1)

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Materials

Add a material for each domain and for the membrane.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

FR4 (Circuit Board) (mat1)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Silicon (mat2)

In the window, click .

In the window for , locate the section.

From the list, choose .

Silicon (membrane)

In the window, under click .

In the window for , type Silicon (membrane) in the text field.

Locate the section. From the list, choose .

From the list, choose .

Silica glass (mat4)

In the window, click .

In the window for , locate the section.

From the list, choose .

Mold Compound

In the window, right-click and choose .

In the window for , type Mold Compound in the text field.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	22[GPa]	Pa	Basic
Poisson’s ratio	nu	0.4	1	Basic
Density	rho	1900	kg/m³	Basic
Coefficient of hygroscopic swelling	beta_h_iso ; beta_hii = beta_h_iso, beta_hij = 0	1.1e-4	m³/kg	Basic