What does power module thermal design calculate?

The thermal resistance, layer by layer, as heat from the semiconductor die flows through solder, copper traces, insulating ceramic substrate, baseplate and thermal grease to the heatsink. It checks that peak die temperature stays within limits (about 175 °C for SiC) and evaluates fatigue of each layer, such as solder cracking, under temperature cycling.

Which ceramic substrate should be used?

It's a balance of conductivity and toughness. From a 10 mm die to heatsink, resistance was 0.268 K/W with alumina (0.32 mm), 0.188 K/W with aluminium nitride (0.635 mm) and 0.198 K/W with silicon nitride (0.32 mm). Silicon nitride conducts less than AlN but is tougher and can be thinner, so it's used where thermal cycling is severe.

Which layer has the largest resistance?

Here, the thermal grease: even at 0.1 mm and 3 W/mK it contributes about 0.09 K/W, 30–50% of the total, followed by the alumina substrate at 0.096 K/W. Grease application and thickness variation change temperature a lot, motivating direct-cooled structures and grease-free bonding.

Power Module Packaging Analysis

Category: Electromagnetic Analysis – Power Electronics | Revised 2026-10-01

CAE visualization for power module packaging theory - technical simulation diagram

Theory: a layered heat path

Overview

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Where should I start in estimating power module die temperature?

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Heat from the die escapes through layer after layer to the heatsink: solder under the die, copper traces, insulating ceramic, another copper layer, substrate solder, a thick copper baseplate and thermal grease against the heatsink. Each has thermal resistance; their sum times power gives temperature rise. Heat spreads sideways as it descends, so lower layers have larger areas and less resistance. Start with this 1D stack to see which layers matter, then confirm with 3D thermal analysis.

Layer resistance with heat spreading

$$ R_i = \frac{t_i}{k_i\,a_{i}\,a_{i+1}},\qquad a_{i+1} = a_i + 2t_i\tan 45^\circ,\qquad \Delta T_j = P\sum_i R_i $$

a is the side of the square heat-flow area, starting at the 10 mm die and spreading at 45° through each layer (capped at the 60 mm baseplate). Layer area is the geometric mean of inlet and outlet. Stack: SiC die 0.35 mm (370 W/mK), solder 0.1 mm (50), copper 0.3 mm (390), ceramic, copper 0.3 mm, solder 0.1 mm, copper baseplate 3 mm (390), thermal grease 0.1 mm (3).

Thermal-expansion mismatch

$$ \varepsilon_{mis} = (\alpha_{Cu} - \alpha_{cer})\,\Delta T $$

Coffee Break Trivia

Starting from broken wire bonds

Typical life-limiting failures in power modules are aluminium bond wires on the die lifting off at their roots under temperature cycling, and cracks growing in solder beneath the die and substrate. Both arise from strain repeated at each temperature change due to differing thermal expansion. Reliability was studied in detail from the 1990s for railway and industrial use; with EVs and high-temperature SiC operation, sintered-silver bonding and wire-free structures are spreading.

Worked examples

Example 1: ceramic type and thermal resistance (10 mm die, 200 W)

Layer	Alumina 0.32 mm	AlN 0.635 mm	Si3N4 0.32 mm
SiC die	0.009	0.009	0.009
Die solder	0.017	0.017	0.017
Ceramic	0.096	0.025	0.025
Cu baseplate	0.031	0.029	0.031
Thermal grease	0.092	0.086	0.092
Junction to case	0.176	0.102	0.106
Junction to heatsink	0.268	0.188	0.198
Rise at 200 W	54 K	38 K	40 K

Units K/W (except last row). The two copper layers and substrate solder total about 0.02 K/W and are omitted.

Example 2: copper–ceramic expansion mismatch (100 K)

Ceramic	CTE	Difference from Cu	Mismatch strain
Alumina	7 ppm/K	10 ppm/K	0.10%
AlN	4.5 ppm/K	12.5 ppm/K	0.12%
Si3N4	3 ppm/K	14 ppm/K	0.14%

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Si3N4 has the largest mismatch with copper, so why is it called the most cycling-resistant?

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Because what matters is not only the mismatch strain but whether the ceramic survives it. Thermal cycling concentrates stress at the edges of the copper–ceramic interface, cracking the ceramic or peeling the copper. Silicon nitride's fracture toughness is about twice that of alumina or AlN, so it tolerates thick copper, which also spreads heat and lowers resistance further. AlN conducts well but cracks easily and needs about 0.635 mm thickness; as the table shows, thin Si3N4 matches thick AlN thermally. The other key point is the grease, the largest layer here: better substrates and dies won't cool the die if grease is applied thick, so design must include baseplate warpage and grease thickness control.

Analysis workflow

Estimate each layer's resistance with a 1D stack to find dominant layers.
Confirm multi-die thermal interaction and spreading with 3D analysis.
Derive losses from current waveforms and compute die temperature swings with transient thermal impedance.
Estimate solder and wire life from temperature swing with lifetime models.
Compare with thermocouple, infrared and thermal-transient measurements.

Coffee Break Trivia

“Identical modules ran 10 K apart”

In one system, identical power modules side by side showed die temperatures differing by up to about 10 K. Hand-applied grease varied, exceeding 0.2 mm in places. With grease accounting for over 30% of thermal resistance, doubling its thickness markedly raises temperature. Screen-printing the grease to uniform thickness and setting a tightening sequence that accounts for baseplate warpage reduced the spread to about 2 K.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Ignoring spreading	Lower-layer resistance overestimated	Account for spreading
Omitting grease	Temperature underestimated	Include thickness variation
Steady-state only	Temperature swings missed	Transient impedance
Choosing substrate on conductivity alone	Cracks under cycling	Consider toughness
Ignoring die-to-die coupling	Centre die overheats	Analyse in 3D

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Power Module Packaging Analysis

Theory: a layered heat path

Overview

Layer resistance with heat spreading

Thermal-expansion mismatch

Starting from broken wire bonds

Worked examples

Example 1: ceramic type and thermal resistance (10 mm die, 200 W)

Example 2: copper–ceramic expansion mismatch (100 K)

Analysis workflow

“Identical modules ran 10 K apart”

Common mistakes

Mistakes and fixes

Related Topics

Related Fields