Thermo-Mechanical Analysis of a Surface-Mounted Resistor

The drive for miniaturizing electronic devices has resulted in today’s extensive use of surface-mount electronic components. An important aspect in electronics design and the choice of materials is a product’s durability and lifetime. For surface-mount resistors and other components producing heat it is a well-known problem that temperature cycling can lead to cracks propagating through the solder joints, resulting in premature failure (Ref. 1). For electronics in general there is a strong interest in changing the soldering material from lead- or tin-based solder alloys to other mixtures.

The following multiphysics example models the heat transport and structural stresses and deformations resulting from the temperature distribution using the Heat Transfer in Solids and Solid Mechanics interfaces.

This application requires either the Structural Mechanics Module or the MEMS Module.

Model Definition

Figure 1 shows a photograph of a surface-mount resistor together with a diagram of it on a printed circuit board (PCB).

Figure 1: A photo and diagram of a typical surface-mounted resistor soldered to a PCB.

Table 1 shows the dimensions of the resistor and other key components in the model including the PCB.

Table 1: Component Dimensions
Component	Length	Width	Height
Resistor (Alumina)	6 mm	3 mm	0.5 mm
PCB (FR4)	16 mm	8 mm	1.6 mm
Cu pad	2 mm	3 mm	35 μm
Termination (Silver)	0.5 mm	3 mm	25 μm
Stand-off (gap to PCB)	-	-	105 μm

The simulation makes use of the symmetry so that it needs to include only half of the component (Figure 2). The modeling of the PCB is terminated a distance away from the resistor, in order to reduce effects of the boundary conditions.

Figure 2: The simulation models only one half of the resistor.

In operation, the resistor dissipates 0.2 W of power as heat. Conduction to the PCB and convection to the surrounding air provide cooling. In this model, the heat transfer occurs through conduction in the subdomains. The model simplifies the surface cooling and describes it using a heat transfer coefficient, h, in this case set to 10 W/(m2·K); the surrounding air temperature, Tinf, is at 300 K. The resulting heat transfer equation and boundary condition (included in the model using the Heat Transfer interface) are

where k is the thermal conductivity, and Q is the heating power per unit volume of the resistor (equal to 22.2 MW/m3 corresponding to 0.2 W in total).

The model handles thermal expansion using a static structural analysis using the Structural Mechanics interface (a description of the corresponding equations is available in the Structural Mechanics Module User’s Guide). The thermal and mechanical material properties in this model are taken from the material library The data for the solid materials are temperature independent, and the reference values are shown in the table below.

Table 2: Material properties
Material	E (GPa)	ν	α (ppm)	k (W/(m·K))	ρ (kg/m3)	Cp (J/(kg·K))
Silver	83	0.37	18.9	420	10500	230
Alumina	300	0.222	8.0	27	3900	900
Cu	110	0.35	17	400	8700	385
Fr4	22	0.28	18	0.3	1900	1369
60Sn-40Pb	10	0.4	21	50	9000	150

Air has temperature-dependent and pressure-dependent properties in the built-in material library. Because the temperature is a variable of the problem, it is automatically used. The pressure is by default set to 1 atm.

The stresses are zero at room temperature, 293 K. The boundary condition for the Solid Mechanics interface is that the cuts in the PCB do not rotate and have no net force normal to the cut.

Results and Discussion

The isosurfaces in Figure 3 show the temperature distribution at steady state. The highest temperature occurs in the center of the resistor. The circuit board also heats up significantly.

Figure 3: Temperature distribution in the resistor and the circuit board at steady state.

Thermal stresses appear as a result of the temperature increase; they arise from the materials’ different expansion coefficients and from the bending of the PCB. Figure 4 plots the effective stress (von Mises) together with the resulting deformation of the assembly.

Figure 4: The thermally induced distribution of von Mises effective stress together with the deformation (magnified).

The highest stresses seem to occur in the termination material. It is interesting to compare these effective stresses to the yield stress and thereby investigate whether or not the material is irreversibly deformed. In that case the solder is the weak point. Figure 5 the stress in the solder alone.

Figure 5: Close-up of the von Mises effective stresses in the solder joints.

The yield stress for solder is approximately 220 MPa. The highest effective stress appears to be about 60 percent of this value. The structure does not get permanently deformed directly when heated. However, it is possible that the solder displays creep strains over time because of the combination of fairly high stress levels and elevated temperatures.

Notes About the COMSOL Implementation

In this example, the Thermal Stress interface automatically adds and couples the Solid Mechanics interface and the Heat Transfer interface. This is done by the two predefined multiphysics features Thermal Expansion and Temperature Coupling.

Build the geometry as an assembly of the bottom plate and the resistor to make it possible to mesh the parts independently. Use continuity conditions for the temperature and the displacements to connect the top and bottom parts of the geometry.

It is assumed that the temperature gradient in the normal direction on the cuts in the PCB is zero. The mechanical boundary conditions on the cuts must not impose a general state of compressive stress due to thermal expansion. At the same time, the restraint from the part of the PCB that is not modeled means that there is no rotation of the cross section. To obtain this effect, the entire cut must have the same (but unknown) displacement in the direction normal to the cut.

You can achieve this by using the roller constraint at the left cut of the plate that prevents the boundary to move in the direction normal to the cut. For remaining two cuts, introduce two new degrees of freedom (named uface and vface) in the model and prescribe the displacements of the cut faces to them.

You solve the problem sequentially using two stationary study steps. The heat transfer problem is nonlinear because the air has temperature-dependent properties. The structural problem, on the other hand, is linear. For the structural analysis, use a memory-efficient iterative solver to make it possible to solve the problem also on computers with limited memory.

References

1. H. Lu, C. Bailey, M. Dusek, C. Hunt, and J. Nottay, “Modeling the Fatigue Life of Solder Joints of Surface Mount Resistors,” EMAP, 2000.

2. J.M. Coulson and J.F. Richardson, Chemical Engineering, vol. 1, Pergamon Press, appendix, 1990.

Heat_Transfer_Module/Thermal_Stress/surface_resistor

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 .

Global Definitions

Parameters

On the toolbar, click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
T_air	300[K]	300 K	Air temperature
h_air	10[W/(m^2*K)]	10 W/(m²·K)	Heat transfer coefficient
Psource	0.2[W]/2	0.1 W	Heat dissipated by the resistor on the half geometry
p0	1[atm]	1.013E5 Pa	Air pressure
T0	80[degC]	353.2 K	Initial temperature guess