Power Transistor

Transistors are building blocks of electronic appliances, and can be found in radios, computers, and calculators, to name a few. When working with electrical systems you typically have to deal with heat transfer; electric heating is often an unwanted result of current conduction.

This example simulates a system consisting of a small part of a circuit board containing a power transistor and the copper pathways connected to the transistor. The purpose of the simulation is to estimate the operating temperature of the transistor, which can be substantially higher than room temperature due to undesired electric heating.

Transistors are semiconductor devices used to switch or amplify electronic signals. There are different types of transistors, ranging in size depending on how they are packaged. Power transistors carry and dissipate more power and therefore come in larger packages. These packages can be attached to a heat sink for better cooling and to avoid overheating of the system.

The heat sink would then be attached to the transistor via the copper plate located behind the ceramic piece (shown in Figure 1 to the left). While it’s often important to construct a way to cool electronic systems, such as in the case of components in hybrid cars, each system has its own acceptable operating temperature range. What determines the maximum and minimum temperature limits include the semiconductor material properties, the transistor type, the design of the device, and so forth. There is a conventional temperature range, however, which is thought to be between -55 °C and 125 °C.

Model Definition

Figure 1 shows the model geometry used in the simulation. The power transistor is mounted on the circuit board using through-hole technology. The solder in the holes give mechanical support and electronic contact between the copper routes and the transistor pins.

Figure 1: Model geometry and position of transistor chip.

The transistor chip itself is a very thin structure represented by an internal surface in Figure 1. The chip is connected to the pins but this connections are assumed to have negligible effects on heat transfer.

The transistor package front part is made of ceramics while the back part, which could be clamped to a heat sink, is made of copper. The transistor chip and the front part of the package have matching thermal properties. The copper pins are soldered to the circuit board by the solder material 60Sn-40Pb (60 % tin and 40 % lead). The circuit board is made of FR4.

Current conduction and Joule heating take place in the copper routes, in the solders, and in the pins. In these parts, the physics of heat transfer and heat production due to Joule heating are fully coupled to the conduction of electric current. In all other parts of the transistor, only heat transfer and heat production take place.

The transistor chip itself is represented by an internal boundary with an internal production of heat corresponding to 0.9 W. Cooling through convection takes place at all external boundaries with a heat transfer coefficient of 5.0 W/(m2·K). This value of the heat transfer coefficient corresponds to the worst case scenario when the fan is switched off. The ambient temperature is 293.15 K.

Current enters the circuit board at the left vertical boundaries of the copper routes connected to the base, emitter, and collector in Figure 1. The value of the current at the boundary of the route connected to the emitter is 0.12 A. The value of the current at the boundary of the route connected to the collector is 0.11988 A. The difference in absolute current between the emitter and collector currents corresponds to the current at the boundary of the route connected to the base, which is 0.12 mA.

Results and Discussion

Figure 2 below shows the temperature distribution in the device. The maximum temperature is about 354 K or 81 °C. This is well within the acceptable operation temperature range for the transistor, which implies that attaching it to a heat sink is not needed in this case.

Figure 2: Temperature distribution.

Also worth noting is that electric heating, or Joule heating as it is also referred to, hardly influences the temperature of the copper routes at the distance from the transistor modeled above. That’s most likely due to copper’s high conductivity; some of the heat produced in the transistor chip is conducted away from the device via the copper routes. Figure 3 shows the temperature along the copper routes connected to the base and the collector respectively. The current density in the base is 1/1000 of that in the collector but the temperature in the copper routes connected to the base and collector is almost identical.

Figure 3: Temperature along the copper routes connected to the base and collector.

The fact that the Joule heating effect does not increase temperature in the copper routes leads to the conclusion that the higher temperature in these routes is due to coppers high conductivity. The copper routes conduct some of the heat produced in the transistor chip away from this device. The circuit board has a poor thermal conductivity and is therefore not heated to the same extent as the copper routes.

Notes About the COMSOL Implementation

You can find all the material properties for this application in COMSOL’s Material Library. Furthermore, the ready-made physics interface for Joule heating sets up all model formulations that you need for the simulation: Electric Current and Heat Transfer in Solids are added with the corresponding Joule Heating coupling features in the Multiphysics node.

The Joule heating interface is by default available for all materials in the model. However, the circuit board material and the package material do no conduct electric current. For this reason, you have to edit the selection of Electric current physics to remove non-conducting domains. On the circuit board material, only heat transfer physics is calculated. By removing the non-conductive parts of the device to the list of Electric Current physics, Electromagnetic Heat Source and Boundary Electromagnetic Heat Source are automatically not applicable on these domains.

Heat_Transfer_Module/Power_Electronics_and_Electronic_Cooling/power_transistor

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 .

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:

On the toolbar, click .

Browse to the model’s Application Libraries folder and double-click the file power_transistor_geom_sequence.mph.

On the toolbar, click .

Click the button on the toolbar.

You should now see the geometry shown above.

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
j_CE	1e5[A/m^2]	1E5 A/m²	Current density, collector and emitter routes
Q_h	1e5[W/m^2]	1E5 W/m²	Boundary heat source strength
h_coeff	5[W/(m^2*K)]	5 W/(m²·K)	Heat transfer coefficient