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Heat Transfer in a Surface-Mount Package for a Silicon Chip
Introduction
All integrated circuits — especially high-speed devices — produce heat. In today’s dense electronic system layouts heat sources are many times placed close to heat-sensitive ICs. Designers of printed-circuit boards often need to consider the relative placement of heat-sensitive and heat-producing devices, so that the sensitive ones do not overheat.
One type of heat-generating device is a voltage regulator, which can produce several watts of heat and reach a temperature higher than 70°C. If the board design places such a device close to a surface-mounted package that contains a sensitive silicon chip, the regulator’s heat could cause reliability problems and failure due to overheating.
Figure 1: Layout of the simulated silicon device, its package, and a voltage regulator. The chip and the voltage regulator are connected through a ground plate, a pin, and the interconnect.
This simulation investigates the thermal situation for a silicon chip in a surface-mount package placed on a circuit board close to a hot voltage regulator. The chip is subjected to heat from the regulator and from internally generated heat.
Model Definition
The model is based on a SMD IC and voltage regulator layout as in Figure 1. The silicon chip sits in the center of the package and dissipates its heat to the surrounding environments. The chip also connects to a ground plane through an interconnect and one of the pins. A heat generating voltage regulator is placed on the same ground plane. This means that the voltage regulator may affect the silicon chip by the conducted heat and this may lead to overheating of the chip.
Heat transfers through the mount package to the surroundings through conduction according to:
The heat source, Q, is negligible in the circuit board, pins, and package, while in the chip, this model sets that parameter to a value equivalent to 20 mW. The conductivities of the components are chosen to be similar to:
•
silicon, for the chip
•
aluminum, for the pins
•
FR4, for the PC board
•
copper, for the ground plane and interconnect
•
an arbitrary plastic, for the chip package
Heat dissipates from all air-exposed surfaces through forced heat convection, which is modeled using a heat transfer coefficient, h:
The voltage regulator is simulated by setting a fixed temperature at that surface. The thin conducting layers of the ground plane and interconnect within the package is modeled using a 2D shell approximation, according to:
where ds is the layer’s thickness, and ∇t represents the nabla operator projected onto the direction of the plane. The model uses a Heat Transfer interface to describe the 3D heat transfer as well as the 2D shell heat transfer.
Results and Discussions
Figure 2 illustrates the temperature distribution through the thickness. Being a good conductor, the interconnect delivers heat to the outer edge of the package, which gives the fairly constant temperature distribution around the interconnect.
Figure 2: Slice plot of the temperature through the circuit board, interconnect, chip, and package. The effect of the interconnect is evident by its ability to conduct heat from the chip to the outer parts of the package.
An alternative view is achieved by using the transparency feature in the visualization tools of COMSOL Multiphysics. This results in a transparent 3D view of the temperature distribution, as shown in Figure 3. In that figure you can see the temperature distribution around the chip and along the interconnect.
Figure 3: Boundary plot of the temperature created with the assistance of the transparency tool in COMSOL Multiphysics. This view also gives the temperature distribution on the chip and along the interconnect.
To get a closer look at the stationary temperature of the silicon chip, plot the temperature at the bottom boundary of the chip.
Figure 4: Temperature distribution on the bottom surface of the silicon chip.
The simulation predicts a maximum temperature of the silicon device of 47.6°C. This means that the device does not overheat in the present configuration.
Application Library path: Heat_Transfer_Module/Power_Electronics_and_Electronic_Cooling/surface_mount_package
Notes About the COMSOL Implementation
This tutorial uses the Heat Transfer interface from the Heat Transfer Module and, in particular, its Thin Layer feature. The thin layers of the modeled device are good heat conductor, so the Thin Layer feature is well-adapted for their representation. The two layers that have this definition are:
•
The interconnect between the chip and the grounded pin.
•
The ground plate that is also thermally connected to the temperature constraint coming from the voltage regulator.
While the numerical method considers these two modeling domains as interior boundaries, the model still includes a thickness to take the 3D heat flux into account.
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Heat Transfer > Heat Transfer in Solids (ht).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Stationary.
6
Click  Done.
Geometry 1
The geometry sequence for the model is available in a file. If you want to create it from scratch yourself, you can follow the instructions in the Geometry Modeling Instructions section. Otherwise, insert the geometry sequence as follows:
1
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file surface_mount_package_geom_sequence.mph.
3
In the Geometry toolbar, click  Build All.
4
Click the  Zoom Extents button in the Graphics toolbar.
5
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
You should now see the geometry shown above.
The geometry includes the interconnect between the pin and the chip as well as the ground plate and the temperature surface resulting from the voltage regulator. To see the interconnect and the chip, you need to turn on transparency.
6
Click the  Transparency button in the Graphics toolbar.
7
Click the  Transparency button in the Graphics toolbar again to remove the transparency.
Now, define the domain settings including material properties, element order, heat source, and initial values.
Materials
To define material properties for the model domains, use four predefined materials from the Material Browser and one custom material.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Aluminum.
4
Click the Add to Component button in the window toolbar.
5
In the tree, select Built-in > FR4 (Circuit Board).
6
Click the Add to Component button in the window toolbar.
Materials
Aluminum (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Pins.
FR4 (Circuit Board) (mat2)
1
In the Model Builder window, click FR4 (Circuit Board) (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose PC Board.
Plastic
1
In the Materials toolbar, click  Blank Material.
2
In the Settings window for Material, type Plastic in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Chip Package.
4
In the Model Builder window, expand the Component 1 (comp1) > Materials > Plastic (mat3) node, then click Basic (def).
5
In the Settings window for Basic, locate the Output Properties section.
6
Click  Select Quantity.
7
In the Physical Quantity dialog, type density in the text field.
8
In the tree, select General > Density (kg/m^3).
9
Click OK.
10
In the Settings window for Basic, locate the Output Properties section.
11
Click  Select Quantity.
12
In the Physical Quantity dialog, type heatcapacity in the text field.
13
In the tree, select Transport > Heat capacity at constant pressure (J/(kg*K)).
14
Click OK.
15
In the Settings window for Basic, locate the Output Properties section.
16
Click  Select Quantity.
17
In the Physical Quantity dialog, type thermalconductivity in the text field.
18
In the tree, select Transport > Thermal conductivity (W/(m*K)).
19
Click OK.
20
In the Settings window for Basic, locate the Output Properties section.
21
In the table, enter the following settings:
Property
Variable
Expression
Unit
Size
Density
rho
2700[kg/m^3]
kg/m³
1x1
Heat capacity at constant pressure
Cp
900[J/(kg*K)]
J/(kg·K)
1x1
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
0.2[W/(m*K)]
W/(m·K)
3x3
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in > Silicon.
3
Click the Add to Component button in the window toolbar.
4
In the tree, select Built-in > Copper.
5
Click the Add to Component button in the window toolbar.
6
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Silicon (mat4)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Chip.
Copper (mat5)
1
In the Model Builder window, click Copper (mat5).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Copper Layers.
This completes the materials settings.
Heat Transfer in Solids (ht)
Heat Source 1
1
In the Physics toolbar, click  Domains and choose Heat Source.
2
Select Domain 11 only.
3
In the Settings window for Heat Source, locate the Heat Source section.
4
In the Q0 text field, type 2e8[W/m^3].
This completes the domain settings. Now, set up the boundary conditions.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Exterior Boundaries.
4
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
5
In the h text field, type 50[W/(m^2*K)].
6
In the Text text field, type 30[degC].
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundary 4 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type 50[degC].
Thin Layer 1
1
In the Physics toolbar, click  Boundaries and choose Thin Layer.
2
Select Boundary 7 only.
3
In the Settings window for Thin Layer, locate the Shell Properties section.
4
From the Shell type list, choose Nonlayered shell. Locate the Layer Model section. From the Layer type list, choose Thermally thin approximation.
Thin Layer 2
1
In the Physics toolbar, click  Boundaries and choose Thin Layer.
2
In the Settings window for Thin Layer, locate the Boundary Selection section.
3
From the Selection list, choose Interconnect.
4
Locate the Shell Properties section. From the Shell type list, choose Nonlayered shell. In the Lth text field, type 5e-6[m].
5
Locate the Layer Model section. From the Layer type list, choose Thermally thin approximation.
Mesh 1
Size 1
1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 4 and 7 only.
5
Locate the Element Size section. From the Predefined list, choose Extra fine.
Free Tetrahedral 1
In the Mesh toolbar, click  Free Tetrahedral.
Size
1
In the Model Builder window, click Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Fine.
4
Click  Build All.
The mesh should consist of around 16,500 elements.
Study 1
In the Study toolbar, click  Compute.
Results
By default, you get a 3D plot of temperature. Note that the temperature is displayed in degrees Kelvin, which is the default temperature unit in the SI system.
To get a temperature plot in degrees Celsius, simply set the preferred unit for the temperature results.
Preferred Units 1
1
In the Results toolbar, click  Configurations and choose Preferred Units.
2
In the Settings window for Preferred Units, locate the Units section.
3
Click  Add Physical Quantity.
4
In the Physical Quantity dialog, select General > Temperature (K) in the tree.
5
Click OK.
6
In the Settings window for Preferred Units, locate the Units section.
7
In the table, enter the following settings:
Quantity
Unit
Preferred unit
Temperature
K
°C
8
Click  Apply.
Nonlayered Shell
1
In the Model Builder window, expand the Temperature (ht) node, then click Nonlayered Shell.
2
In the Settings window for Surface Slit, locate the Expression on the Upside section.
3
From the Unit list, choose °C.
4
Locate the Expression on the Downside section. From the Unit list, choose °C.
5
In the Temperature (ht) toolbar, click  Plot.
6
Click the  Go to Default View button in the Graphics toolbar.
To see the chip as well, turn on transparency.
7
Click the  Transparency button in the Graphics toolbar.
Compare the resulting plot to that in Figure 3.
8
Click the  Transparency button in the Graphics toolbar again to remove the transparency.
Result Templates
1
In the Results toolbar, click  Result Templates to open the Result Templates window.
2
Go to the Result Templates window.
Reproduce the temperature multislice plot in Figure 2 by adding a plot from the Result Templates.
3
In the tree, select Study 1/Solution 1 (sol1) > Heat Transfer in Solids > Temperature, Multislice (ht).
4
Click the Add Result Template button in the window toolbar.
5
In the Results toolbar, click  Result Templates to close the Result Templates window.
Results
Multislice 1
1
In the Model Builder window, expand the Temperature, Multislice (ht) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the X-planes subsection. In the Planes text field, type 3.
4
Find the Z-planes subsection. In the Planes text field, type 2.
5
In the Temperature, Multislice (ht) toolbar, click  Plot.
6
Click  Plot.
Compare the result to that in Figure 2.
To visualize the temperature distribution on the silicon chip’s bottom surface, follow the steps given below.
Temperature, Chip Surface
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Temperature, Chip Surface in the Label text field.
3
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
Surface 1
1
In the Temperature, Chip Surface toolbar, click  Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose HeatCameraLight.
Selection 1
1
In the Temperature, Chip Surface toolbar, click  Selection.
2
Select Boundary 195 only.
3
In the Temperature, Chip Surface toolbar, click  Plot.
4
Click the  Zoom Extents button in the Graphics toolbar.
Compare the resulting plot to that in Figure 4.
Geometry Modeling Instructions
If you want to create the geometry yourself, follow these steps.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
PC Board
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, type PC Board in the Label text field.
3
Locate the Size and Shape section. In the Width text field, type 20.
4
In the Depth text field, type 10.
5
Locate the Position section. In the x text field, type -10.
6
In the y text field, type -5.
7
In the z text field, type -1.9.
8
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
Block 2 (blk2)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 9.9.
4
In the Depth text field, type 3.9.
5
In the Height text field, type 0.2.
6
Locate the Position section. From the Base list, choose Center.
Hexahedron 1 (hex1)
1
In the Geometry toolbar, click  More Primitives and choose Hexahedron.
2
In the Settings window for Hexahedron, locate the Vertices section.
3
In row 1, set x to -4.95.
4
In row 2, set x to 4.95.
5
In row 3, set x to 4.95.
6
In row 4, set x to -4.95.
7
In row 5, set x to -4.95.
8
In row 6, set x to 4.95.
9
In row 7, set x to 4.95.
10
In row 8, set x to -4.95.
11
In row 1, set y to -1.95.
12
In row 2, set y to -1.95.
13
In row 3, set y to 1.95.
14
In row 4, set y to 1.95.
15
In row 5, set y to -1.713419348.
16
In row 6, set y to -1.713419348.
17
In row 7, set y to 1.713419348.
18
In row 8, set y to 1.713419348.
19
In row 1, set z to 0.1.
20
In row 2, set z to 0.1.
21
In row 3, set z to 0.1.
22
In row 4, set z to 0.1.
23
In row 5, set z to 0.75.
24
In row 6, set z to 0.75.
25
In row 7, set z to 0.75.
26
In row 8, set z to 0.75.
27
In row 5, set y to -1.72.
28
In row 6, set y to -1.72.
29
In row 7, set y to 1.72.
30
In row 8, set y to 1.72.
Mirror 1 (mir1)
1
In the Geometry toolbar, click  Transforms and choose Mirror.
2
Select the object hex1 only.
3
In the Settings window for Mirror, locate the Input section.
4
Select the Keep input objects checkbox.
Chip Package
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
In the Settings window for Union, type Chip Package in the Label text field.
3
Select the objects blk2, hex1, and mir1 only.
4
Locate the Union section. Clear the Keep interior boundaries checkbox.
5
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
Block 3 (blk3)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 0.4.
4
In the Depth text field, type 0.26.
5
In the Height text field, type 0.2.
6
Locate the Position section. In the x text field, type -4.645.
7
In the y text field, type -2.21.
8
In the z text field, type -0.1.
Revolve 1 (rev1)
1
In the Geometry toolbar, click  Revolve.
2
On the object blk3, select Boundary 3 only.
3
In the Settings window for Revolve, locate the Revolution Angles section.
4
Click the Angles button.
5
In the End angle text field, type 90.
6
Locate the Revolution Axis section. From the Axis type list, choose 3D.
7
Find the Point on the revolution axis subsection. In the y text field, type -2.211.
8
In the z text field, type -0.24.
9
Find the Direction of revolution axis subsection. In the x text field, type 1.
10
In the y text field, type 0.
Extrude 1 (ext1)
1
In the Geometry toolbar, click  Extrude.
2
On the object rev1, select Boundary 2 only.
3
In the Settings window for Extrude, locate the Distances section.
4
In the table, enter the following settings:
Distances (mm)
0.322
Revolve 2 (rev2)
1
In the Geometry toolbar, click  Revolve.
2
On the object ext1, select Boundary 3 only.
3
In the Settings window for Revolve, locate the Revolution Angles section.
4
Click the Angles button.
5
In the End angle text field, type -90.
6
Locate the Revolution Axis section. From the Axis type list, choose 3D.
7
Find the Point on the revolution axis subsection. In the y text field, type -2.69.
8
In the z text field, type -0.561.
9
Find the Direction of revolution axis subsection. In the x text field, type 1.
10
In the y text field, type 0.
Extrude 2 (ext2)
1
In the Geometry toolbar, click  Extrude.
2
On the object rev2, select Boundary 2 only.
3
In the Settings window for Extrude, locate the Distances section.
4
In the table, enter the following settings:
Distances (mm)
0.16
Union 2 (uni2)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
Select the object ext2 only.
3
In the Settings window for Union, locate the Union section.
4
Clear the Keep interior boundaries checkbox.
Array 1 (arr1)
1
In the Geometry toolbar, click  Transforms and choose Array.
2
Select the object uni2 only.
3
In the Settings window for Array, locate the Size section.
4
In the x size text field, type 8.
5
Locate the Displacement section. In the x text field, type 1.27.
6
Locate the Selections of Resulting Entities section. Find the Cumulative selection subsection. Click New.
7
In the New Cumulative Selection dialog, type Pins in the Name text field.
8
Click OK.
Mirror 2 (mir2)
1
In the Geometry toolbar, click  Transforms and choose Mirror.
2
In the Settings window for Mirror, locate the Input section.
3
Select the Keep input objects checkbox.
4
From the Input objects list, choose Pins.
5
Locate the Selections of Resulting Entities section. Find the Cumulative selection subsection. From the Contribute to list, choose Pins.
6
Locate the Normal Vector to Plane of Reflection section. In the y text field, type 1.
7
In the z text field, type 0.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
In the z-coordinate text field, type -0.9.
Work Plane 1 (wp1) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 6.
4
In the Height text field, type 4.
5
Locate the Position section. In the xw text field, type -10.
6
In the yw text field, type -5.
7
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
2
8
Clear the Layers on bottom checkbox.
9
Select the Layers to the left checkbox.
Interconnect
1
In the Model Builder window, under Component 1 (comp1) > Geometry 1 right-click Work Plane 1 (wp1) and choose Work Plane.
2
In the Settings window for Work Plane, type Interconnect in the Label text field.
3
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
Interconnect (wp2) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Interconnect (wp2) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 4.145.
4
In the Height text field, type 2.15.
5
Locate the Position section. In the xw text field, type -4.645.
6
In the yw text field, type -1.95.
Interconnect (wp2) > Rectangle 2 (r2)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 3.745.
4
In the Height text field, type 1.75.
5
Locate the Position section. In the xw text field, type -4.245.
6
In the yw text field, type -1.95.
Interconnect (wp2) > Difference 1 (dif1)
1
In the Work Plane toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object r1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the object r2 only.
Chip
1
In the Model Builder window, under Component 1 (comp1) > Geometry 1 right-click Interconnect (wp2) and choose Block.
2
In the Settings window for Block, type Chip in the Label text field.
3
Locate the Size and Shape section. In the Height text field, type 0.1.
4
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
5
Locate the Position section. From the Base list, choose Center.
Form Union (fin)
1
In the Model Builder window, click Form Union (fin).
2
In the Settings window for Form Union/Assembly, click  Build Selected.
Geometry
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Geometry in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Object.
4
Select the object fin only.
Exterior Boundaries
1
In the Geometry toolbar, click  Selections and choose Adjacent Selection.
2
In the Settings window for Adjacent Selection, type Exterior Boundaries in the Label text field.
3
Locate the Input Entities section. Click  Add.
4
In the Add dialog, select Geometry in the Input selections list.
5
Click OK.
Copper Layers
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, locate the Entities to Select section.
3
From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 7 and 37 only.
5
In the Label text field, type Copper Layers.