Power Module Cooling
Theory: thermal resistance of stacked layers
Overview
Our inverter IGBT is running near its temperature limit. Should we switch to a pricier substrate?
Work out the resistance breakdown before deciding. Chip heat flows through many layers — solder, copper, ceramic substrate, baseplate, grease, cold plate — into the coolant. Each has a thermal resistance; the total times the loss is the temperature rise. The effective fix depends entirely on which layer is largest: a better substrate helps little if the coolant side or grease dominates. Also remember heat spreads as it goes down, so lower layers of the same thickness have smaller resistance.
Stack resistance
Each layer's resistance is integrated assuming heat spreads at 45°. $a_0$ is chip width, $w(z)$ the spread width at depth $z$, and $k_i$, $t_i$ each layer's conductivity and thickness.
The coolant side is expressed by the spread area $A$ and an effective coefficient $h_{eff}$ that includes fin effects.
From railways to electric vehicles
IGBTs became practical in the 1980s and spread through railway traction and industrial motor drives as devices switching high currents quickly. Early modules typically used alumina substrates mounted to cold plates with grease. As hybrids and electric vehicles spread in the 2000s, handling large power in small, light inverters brought high-conductivity aluminium nitride and silicon nitride substrates and grease-free direct cooling with baseplates contacting the coolant. Cooling innovations translate directly into higher power density.
Worked example: a 10 mm chip at 100 W
Chip (0.12 mm), solder 0.1 mm, copper 0.3 mm, ceramic, copper 0.3 mm, solder 0.2 mm, 3 mm copper baseplate, 0.1 mm grease (3 W/mK), cold plate (effective 10,000 W/m²K). Direct cooling: no grease, pin fins at effective 30,000 W/m²K. Coolant 65 °C, loss 100 W:
| Configuration | Ceramic | Grease | Coolant side | Total | Junction |
|---|---|---|---|---|---|
| Alumina, indirect | 0.117 | 0.093 | 0.277 | 0.583 K/W | 123 °C |
| AlN, indirect | 0.027 | 0.089 | 0.263 | 0.470 K/W | 112 °C |
| Si₃N₄, indirect | 0.028 | 0.095 | 0.281 | 0.499 K/W | 115 °C |
| Alumina, direct | 0.117 | — | 0.094 | 0.307 K/W | 96 °C |
| AlN, direct | 0.027 | — | 0.089 | 0.208 K/W | 86 °C |
Other layers (chip, solders, coppers, baseplate) total about 0.1 K/W. Alumina (0.38 mm), AlN (0.63 mm) and Si₃N₄ (0.32 mm) are typical thicknesses.
Switching alumina to AlN drops 11 °C, but direct cooling drops 27 °C even with alumina.
Right. The breakdown shows the coolant side and grease making up 60–80% in indirect cooling. With alumina the substrate is about 20%, so changing it has merit, but it's not the largest item. Direct cooling removes the grease and raises coolant-side transfer with pin fins, so it helps a lot. Of course, higher coolant flow or thinner grease are options too. The basic approach is to see which layer is largest in numbers, then pick the most cost-effective fix.
Analysis workflow
- Compute chip losses (conduction and switching) for each operating condition.
- Use a 1D stack model to break down resistance and find the layer to improve.
- Use 3D heat transfer to include thermal coupling between chips and coolant temperature rise.
- Obtain transient thermal impedance and compute junction temperature swings for duty cycles.
- Estimate power-cycling life (e.g. of solder joints) from the temperature swing.
“It ran cool when new”
After a few years in service, an inverter's IGBT ran over 10 °C hotter at the same load. The grease between baseplate and cold plate had been gradually squeezed out (pump-out) by repeated warping from temperature cycling, letting air into the gap; the grease resistance had more than doubled. Switching to a phase-change material and clamping that limited baseplate warp reduced the ageing drift. The resistance breakdown can change over a product's life.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Acting without a breakdown | Low-return spending | Break down resistance |
| Ignoring heat spreading | Lower layers overestimated | Include spreading |
| Assuming ideal grease thickness | Hotter in practice | Use measured thickness and ageing |
| Steady state only | Cycling life missed | Transient thermal impedance |
| Ignoring chip-to-chip coupling | Centre chips hotter | Solve in 3D |
I'd like to learn related topics.
Try the coolant side with the heat sink designer. Related pages include junction temperature, thermal resistance, thermal interface materials, heat sink design and compact thermal models.