Evaluation of Temperature Curves Regarding Power Module Lifetime

All internal connections of power modules are subject to aging caused by temperature fluctuations. The fatigue of material as well as wear and tear is caused by thermal stress due to the different expansion coefficients of the connected materials. Module lifetime or respectively, the number of possible temperature cycles, declines as a function of the rising junction temperature ΔT_j .

Alterations of power loss below a frequency of some 100 Hz will no longer be smoothed by the transient thermal impedance of the chips and will lead to a minimal temperature fluctuation in the module. At this frequency, however, ΔT is so small that this is counter-balanced by elastic deformations, or the aging effect is so weak that it is unimportant for lifetime evaluations. During normal operation at frequencies of few Hz and especially at duty cycle operation, such as prevailing in traction, lift, and pulse applications, the internal connections in a module will be exposed to temperature cycling, such connections being:

• Bonded connections
• Rear chip soldering
• DBC/base plate soldering
• And substrate lamination (Cu on Al₂O₃ or AlN)

Therefore, it is important for thermal dimensioning to check whether ΔT_j is so high that the projected number of power cycles will not be reached. In this case, the temperature difference

$\Delta T_j = T_{j(max)} -T_{j(min)}$

during the power cycles under analysis constitutes the rating criterion for the power module and not the maximum permissible chip temperature T_j(max).

The correlation between the possible number of power cycles n and the temperature cycling amplitude ΔT_j is determined by many parameters. Corresponding measurements require a lot of time and effort. The first extensive tests in which the dependency of temperature cycling on the mean temperature T_jm was verified were published in the LESIT Study in the late 1990s [1]. With the aid of parameter adjustment for A, α, and the activation energy E_a, the study results with respect to lifetime function can be analytically calculated using the following equation:

$N_f = A \cdot \Delta T_j^{\alpha} \cdot e^{\Big ( \frac{E_a}{k_b \cdot T_{jm}} \Big )}$

Adjusted parameters for the points in Figure 1: A=3.025·10 5 , α = -5,039, E_a =9.891·10 -20 J, k_b – Boltzmann constant, ΔT_j & T_jm [K]

Figure 1. Power cycling curves as established for power modules in dependency of different mean temperatures in the LESIT Study

As Figure 1 demonstrates, the number of possible power cycles for ΔT_j > 30 K declines by a power of ten for every increase in temperature cycling amplitude by 20...30 K. Periodical power cycling within seconds or minutes thus requires temperature cycling amplitudes below 30 K. These curves were established with modules from various manufacturers and represent the past state of the art. Packaging has improved so that present day power semiconductor modules will attain higher power cycling values. These values have been summarized for IGBT modules in two groups in the following illustrations.

Figure 2. Dependency of the power cycling value n as a function of the temperature cycling amplitude ΔT_j and the mean temperature T_jm for all of the IGBT modules that do not use IGBT4 chips (as per 2009); also see the following diagram

Figure 3. Dependency of the power cycling value n for IGBT4 modules as a function of the temperature cycling amplitude Δ T_j and the mean temperature T_jm (date: 2009); right: the necessary
test duration for a cycle time of 30 s

The LESIT curves consider the effect of the mean temperature or respectively, the temperature level where the temperature cycling takes place. Many test results indicate, however, that other parameters, such as pulse duration t on and the current amplitude I_B will influence the test results just as much as packaging parameters such as bond wire thickness and bond wire angle of inclination or chip and solder thicknesses. In [2], an extended model based on the analysis of a great number of tests is shown. Parameters, validity limits, and coefficients are listed in the following table:

$N_f = A \cdot \Delta T_j^{\beta_1} \cdot exp \Big ( \frac {\beta_2}{(T_{j, min} + 273)} \Big ) \cdot t_{on}^{\beta_3} \cdot I_B^{\beta_4} \cdot V_C^{\beta_5} \cdot D^{\beta_6}$

Table 1. Parameters and limits for the calculation of power cycles using the equation above

Example: Let us assume a given number of power cycles N_f and a test duration t_on(test). If a component would be used for a different pulse duration t_{on(application)} in the application, this would equal to

$N_{application} = N_{test} \cdot \Big (\frac {t_{on(application)}}{t_{on(test)}} \Big )^{\beta_3}$

This means, if the application pulse duration is 1/10 of the test pulse duration, the lifetime would roughly triple. This model gives a good impression of the impact of various parameters on power cycling figures, but it is only suitable to a limited extent in order to calculate concrete lifetime values isolated from any other parameter. The reason is physical constraints since not all of the parameters are independent of each other. For example, a small ΔT_j is not possible in the event of high currents and long pulse durations. Or, as assumed for the pulse duration in our example, an identical ΔT would require different current values for different pulse durations t_on.

References:

[1] Held, M.; Jacob, P.; Nicoletti, G.; Scacco, P.; Poech, M.H.: "Fast Power Cycling Test for IGBT Modules in Traction Application", Power Electronics and Drive Systems 1997, Conference Proceedings

[2] Bayerer, R.; Herrmann, T.; Licht, T.; Lutz, J.; Feller, M.: "Model for Power Cycling Lifetime of IGBT Modules – Various Factors Influencing Lifetime", CIPS 2008, Conference Proceedings

For more information, please read:

Heat Transfer in Power Semiconductor Devices

Heat Dissipation and Thermal Resistance in Power Modules

Thermal Equivalent Circuit Diagrams for Junction Temperature Calculations

Failure Mechanisms During Power Cycling

Power Module Junction Temperature Calculation