Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Example uncertainty budget for an indirect thermographic measurement die with Tc=90 °C_
| Symbol xi | Unit | Estimate of quantity xi | Standard uncertainty u(xi) | Distribution of probability | Sensitivity coefficient c | Contribution of uncertainty ui(y) |
|---|---|---|---|---|---|---|
| τa | - | 0.9987 | 0.0010 | normal | 0.4488 | 0.0004 |
| Wtot | W/m2 | 0.1554 | 0.0066 | rectangular | 67.7701 | 0.4472 |
| ɛ | - | 0.97 | 0.0086 | rectangular | −7.6450 | −0.0657 |
| Trefl | °C | 30 | 2.8868 | rectangular | 0.0119 | 0.0344 |
| τl | m | 0.95 | 0.0289 | rectangular | −10.3189 | 0.2982 |
| Ta | °C | 26.5 | 4.9000 | rectangular | −0.0151 | −0.0740 |
| Tl | °C | 26.5 | 4.9000 | rectangular | −0.0151 | −0.0740 |
| Tus | °C | 3.25 | 1.88 | normal | 1 | 1.63 |
| Tc | °C | 90 | 3.25 |
Type B uncertainty values for different temperatures Tc ranging from 30 °C to 120 °C_
| No. | Tc [°C] | u(Tc) [°C] |
|---|---|---|
| 1 | 30 | 1.63 |
| 2 | 60 | 2.44 |
| 3 | 90 | 3.25 |
| 4 | 105 | 4.21 |
| 5 | 120 | 5.17 |
Standard uncertainty for the quantity Tc (package temperature)_
| The value of the standard uncertainty | u(Tc) [°C] |
|---|---|
| Law of propagation of uncertainty | 1.63 |
| Monte Carlo method | 1.68 |
The materials used in the developed model, along with their corresponding thermal conductivity coefficients k [13], [14], [15]_
| Internal structure component | Material | k [W/m·K] |
|---|---|---|
| Black part of the case | EME 590 | 0.25 |
| Back part of the case | Copper | 400 |
| Semiconductor element | Silicon carbide | 150 |
| Lead, Internal connections | Copper | 400 |
| Grease | Melamine resin | 0.20 |
Mesh element size and the corresponding duration of the simulation_
| No. | Mesh element edge length [mm] | Simulation time [s] | ΔTcs [s] |
|---|---|---|---|
| 1 | 2.0 | 5 | 0.4 |
| 2 | 1.5 | 10 | 0.2 |
| 3 | 1.0 | 20 | 0.1 |
| 4 | 0.5 | 211 | 0.1 |
| 5 | 0.2 | 1455 | 0.1 |
Expanded uncertainty for the quantity Tdie (die)_
| No. | Tdie [°C] | U(Tdie) [°C] |
|---|---|---|
| 1 | 30 | 5.40 |
| 2 | 90 | 4.78 |
| 3 | 120 | 6.50 |