Equivalent thermal model of IGBT module and heat dissipation system

As the core components of power electronic devices, how to ensure their reliable operation during design and use has always been the most concerned issue for R&D engineers. In addition to evaluating whether the electrical characteristics of power devices operate within the safe operating area, the thermal characteristics of the devices and systems must be accurately designed to ensure long-term reliable operation of the devices and fully tap the potential of the devices. The thermal design of power devices and the entire system is modeled and analyzed based on the thermal circuit model of the devices and systems. This article provides a basic introduction to the equivalent thermal circuit model of the IGBT module. The methods and ideas described can also be used for the thermal design of other power devices.

There are two physical parameters that characterize thermal properties: thermal resistance R and heat capacitance C. Thermal resistance R reflects the object's resistance to heat conduction, while heat capacitance C is a physical quantity that measures the amount of heat contained in a substance. Generally, materials have both thermal resistance and heat capacitance, and due to the simultaneous effects of thermal resistance and heat capacitance, the transient thermal impedance Zth characteristic is generated.

Generally, there are two equivalent thermal circuit models in the industry to describe the thermal characteristics of power devices: the continuous network model and the local network model , also known as the Cauer model and the Foster model, or simply the T-type model and the π-type model, as shown in Figure 1.

(a) Continuous network thermal circuit model

(Also called Cauer model or T-type model)

(b) Local network thermal circuit model

(Also called Foster model or π-type model)

Figure 1. Schematic diagram of two thermal circuit models

Figure 2. Infineon IGBT module transient thermal impedance curve (based on Foster model, example: FF600R12ME4)

As shown in Figure 1(a), the structure of the Cauer model more realistically reflects the actual physical structure of thermal resistance and heat capacity. If the characteristic parameters of the materials in each layer of the heat dissipation system are known, this model can be established through theoretical calculation formulas. In addition, each layer in the module (from the chip, the chip's welding layer, the insulating substrate, the substrate welding layer, to the bottom plate) has a pair of R/C parameters corresponding to it, so the temperature of each layer of material can be obtained through the nodes in Figure 1(a). However, for actual systems, it is difficult to determine the distribution of heat flow in each layer during heat transfer, so the Cauer model is generally not used in actual modeling.

Unlike the Cauer model, the R/C parameters of the Foster model in Figure 1(b) no longer correspond to the material layers, and the network nodes have no physical meaning. However, the R/C parameters in the model can be easily fitted and extracted from the transient thermal impedance Zth curve obtained from actual measurements. Therefore, the model is often used for actual modeling and simulation calculation of the junction temperature of the chip. The data sheet of the Infineon IGBT module gives the Zthjc curves of the IGBT chip and the anti-parallel diode chip, as well as the fourth-order parameter list based on the Foster model loop (in the form of corresponding combinations of thermal resistance ri and time constant τi). Figure 2 shows the transient thermal impedance curve of the Infineon FF600R12ME4 module.

Given in Figure 2:

The dynamic thermal resistance curve can be expressed as:

If the chip loss P(t) of the IGBT module is known and the base plate temperature of the IGBT module is known during the dynamic temperature rise process, the junction temperature of the IGBT and diode chips can be obtained by the following formula:

So, should the system modeling of IGBT plus heat sink be done using the Cauer model or the Foster model?

Users often want to avoid the cost of measurement and want to use the existing IGBT and heat sink thermal parameters to build a thermal circuit model diagram. Both the Cauer thermal circuit model and the Foster thermal circuit model provide descriptions of the heat transfer process from the IGBT junction to the case and from the heat sink to the surrounding environment. If you want to combine the IGBT and heat sink models together, which model is more suitable?

IGBT and heat sink in Cauer thermal circuit model:

Figure 3. Combined system thermal circuit model - Cauer model

Each part of the Cauer thermal model actually corresponds to each material layer, making the physical meaning of the heat transfer process clear, that is, each material layer transfers heat layer by layer. The heat flow (analogous to the current in the circuit) reaches and heats the heat sink after a period of delay. The Cauer thermal model can be obtained by simulation or by transforming a measured Foster thermal model.

By analyzing the material of each layer of the entire structure and finite element modeling simulation, it is clear that a Cauer model can be established. However, this is only possible if a specific heat sink is included, because the heat sink has a mutually coupled effect on the heat transfer in the IGBT, and therefore also has an impact on the thermal response time and the Rthjc of the IGBT. If the actual heat sink is different from the heat sink used in the simulation, then the actual heat sink cannot be modeled through simulation.

The parameters of the Foster thermal model are generally given in the data sheet because they are based on the results obtained by measurement. The Foster thermal model can be mathematically transformed into a Cauer thermal model, but the result of such a transformation is not unique because there can be many possible R/C combinations, and the R/C values ​​and nodes in the new Cauer thermal model after the transformation have no clear physical meaning. A Cauer thermal model that cannot be matched with other thermal models after the transformation often leads to various errors.

IGBT and heat sink in Foster thermal circuit model:

Figure 4. Combined system thermal circuit model - Foster model

The Foster thermal model of the IGBT given in the data sheet is obtained based on the measurement when a specific heat sink is used for heat dissipation. For air-cooled heat sinks, since the heat flux in the module is widely distributed, a better and lower Rthjc is obtained during measurement. For water-cooled heat sinks, since the heat flux distribution is limited, a relatively higher Rthjc is obtained during measurement. When Infineon describes the module characteristics in the data sheet, it uses the Foster thermal model based on the water-cooled heat sink, that is, it uses a relatively unfavorable heat dissipation working condition to describe the module thermal characteristics. Therefore, using such thermal characteristics for system design has a higher safety factor for the module.

Since the two thermal circuits of the IGBT and the heat sink are connected in series, the power injected into the chip - analogous to the current in Figure 4 - is immediately transmitted to the heat sink without delay. Therefore, in the initial stage, the rise in junction temperature depends on the type of heat sink used, and actually depends on the heat capacity of the heat sink.

However, the time constant of the heat sink in the air-cooled system ranges from tens to hundreds of seconds, which is much larger than the time constant of the IGBT itself, which is about 1 second. In this case, the temperature rise of the heat sink has only a small effect on the IGBT temperature. For the water-cooled system, this effect is large, because the heat capacity of the water-cooled system is relatively low, that is, the time constant is relatively small. Therefore, for "very fast" water-cooled heat sinks, such as systems with direct water cooling of the IGBT substrate, the Zth of the entire system of the IGBT plus the heat sink should be measured.

Since there is a coupled interaction effect on the heat transfer in the module, whether in the Cauer thermal circuit model or the Foster thermal circuit model, as long as the modeling of the IGBT and the heat sink and the measurement of Zth are separated from each other, there may be problems in the connection and use of the IGBT and the heat sink. To overcome this problem, the IGBT module and the heat sink must be thermally modeled as a whole or their transient thermal impedance must be measured. The modeling of a completely problem-free IGBT plus heat sink system can only be obtained by measuring the thermal resistance Zthja, that is, measuring the entire heat flow path from the IGBT junction, thermal conductive glue and heat sink to the environment at the same time. This is to establish the Foster thermal circuit model of the entire system, through which the junction temperature can be accurately calculated.

Generally, radiator manufacturers will provide a first-order thermal equilibrium time, which is 3 times the value. Using a first-order fractional fit, it can be expressed as a formula:

It can be concluded that the calculation formula for the IGBT junction temperature considering the heat sink thermal resistance is:

When the heat balancing time of the heat sink is tens of seconds or even hundreds of seconds, the chip junction temperature Tvj can be calculated without considering the temperature rise of the heat sink, and formula (3) can be used. If the system thermal balancing time is a few seconds, the heat sink temperature rise needs to be considered and can be calculated using formula (5). If a more accurate multi-order thermal resistance model including the contact surface thermal grease is required, the experimental calibration curve Zthja needs to be used to extract the model.