Understanding the Thermal Time Constants of GaN HEMTs through Model Order Reduction Technique
Abstract
:1. Introduction
2. Extraction of Real Thermal Time Constants with Ritz Model Order Reduction Technique
Finite Element Linear Formulation of the Heat Equation
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- The number n of numerical equations is very large (few 100,000), so it is very difficult to compute all the eigenvalues and the eigenvectors;
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- The second difficulty involves selecting the main eigenvalues;
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- The steady state is not reached if all the eigenvalues are not considered.
3. One Dimensional (1-D) Analysis
3.1. 1-D, Single-Layer Simulation
3.2. One-Dimension, Two-Layers Simulation
4. Two-Dimensional (2-D) Analysis
4.1. 2-D, One-Layer Simulation
4.2. 2-D, Two-Layer Simulation
5. Calibration between Simulation Results and Measurements
6. Conclusions
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- that there are several thermal time constants in a HEMT, even with a 1-D, single layer;
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- the influence of the GaN layer on the thermal time constants;
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- the evolution of the thermal time constants with the dimensions of the devices, and in particular with the gate length, which is one of the key points to address in high-frequency applications.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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ρ (Kg.m−3) | Cp (J. Kg−1. K−1) | K (W.m−1. K−1) | L (m) |
---|---|---|---|
3210 | 665 | 390 | 70 × 10−6 |
Thermal Time Constant (s) | Order Reduction | Ref. [7] |
---|---|---|
τ1 | 1.087 × 10−5 | 1.087 × 10−5 |
τ2 | 1.208 × 10−6 | 1.208 × 10−6 |
τ3 | 4.358 × 10−7 | 4.348 × 10−7 |
τ4 | 2.228 × 10−7 | 2.218 × 10−7 |
τ5 | 1.352 × 10−7 | 1.342 × 10−7 |
Example | α1 (W.m2.J−1) | α2 | L1 (µm) | L2 (µm) |
---|---|---|---|---|
1 | 1.827 10−4 | 6.414 × 10−5 | 70 | 2 |
2 | 1.827 10−4 | 6.414 10−5 | 70 | 8 |
3 | 8.696 10−5 | 6.414 10−5 | 70 | 2 |
Thermal Time Constant (s) | Order Reduction | Equation (14) | Equation (15) |
---|---|---|---|
Example 1 (GaN 2 µm/SiC) | |||
Example 2 (GaN 8 µm /SiC) | |||
Example 3 (GaN 2 µm/Si) | |||
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Jakani, A.; Sommet, R.; Simbélie, F.; Nallatamby, J.-C. Understanding the Thermal Time Constants of GaN HEMTs through Model Order Reduction Technique. Electronics 2021, 10, 3138. https://doi.org/10.3390/electronics10243138
Jakani A, Sommet R, Simbélie F, Nallatamby J-C. Understanding the Thermal Time Constants of GaN HEMTs through Model Order Reduction Technique. Electronics. 2021; 10(24):3138. https://doi.org/10.3390/electronics10243138
Chicago/Turabian StyleJakani, Anass, Raphael Sommet, Frédérique Simbélie, and Jean-Christophe Nallatamby. 2021. "Understanding the Thermal Time Constants of GaN HEMTs through Model Order Reduction Technique" Electronics 10, no. 24: 3138. https://doi.org/10.3390/electronics10243138
APA StyleJakani, A., Sommet, R., Simbélie, F., & Nallatamby, J.-C. (2021). Understanding the Thermal Time Constants of GaN HEMTs through Model Order Reduction Technique. Electronics, 10(24), 3138. https://doi.org/10.3390/electronics10243138