Evaluation of the thermal resistance in GaN-diodes by means of electro-thermal Monte Carlo simulations
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2015-02-01 |
| Authors | Sergio GarcĆa-SĆ”nchez, I. ĆƱiguez-de-la-Torre, Ć. GarcĆa-PĆ©rez, J. Mateos, T. GonzĆ”lez |
| Institutions | Universidad de Salamanca |
| Analysis | Full AI Review Included |
6CCVD Technical Analysis & Thermal Management Solution Brief
Section titled ā6CCVD Technical Analysis & Thermal Management Solution BriefāResearch Paper: Evaluation of the Thermal Resistance in GaN-Diodes by means of Electro-Thermal Monte Carlo Simulations
Application Focus: Thermal management and self-heating mitigation in AlGaN/GaN heterostructure devices (Diodes, HEMTs) for high-power, high-frequency electronics.
Executive Summary
Section titled āExecutive SummaryāThis study rigorously confirms that substrate material thermal conductivity ($k_s$) is the single most critical factor in managing self-heating and minimizing thermal resistance ($R_{th}$) in AlGaN/GaN diodes, driving the imperative use of MPCVD diamond heat spreaders.
- PCD Superiority Confirmed: Electro-Thermal Monte Carlo (HDE-MC) simulations demonstrated that Polycrystalline Diamond (PCD), possessing a $k_s$ of 2200 W/(KĀ·m), reduced $R_{th}$ by a factor of 10 compared to standard sapphire substrates ($k_s=42$ W/(KĀ·m)).
- Lowest $R_{th}$ Achieved: The PCD substrate yielded the lowest thermal resistance ($R_{th}=3.58 \times 10^{\text{-3}}$ KĀ·m/W), ensuring minimal lattice temperature rise ($T_{av} \approx 355$ K at VDS=8 V) necessary for long-term device reliability.
- Thermal Runaway Mitigation: Low-$k_s$ substrates (Si, Sapphire) caused average lattice temperatures to exceed 438 K and 612 K, respectively, leading to severe current saturation and thermal degradation.
- Geometry Dependence: $R_{th}$ is strongly dependent on both $k_s$ and device dimensions ($L_1$, $L_2$), requiring precise material engineering and custom substrate sizing for optimal heat dissipation.
- Methodology Validation: The paper establishes the HDE-MC simulator as a viable tool for extracting $R_{th}$ values based on geometry and thermal parameters, validating the selection of diamond for high-performance thermal management.
Technical Specifications
Section titled āTechnical SpecificationsāThe following hard data points were extracted from the simulation study, highlighting the thermal performance comparison across different substrates.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Substrate Thermal Conductivity ($k_s$) | 2200 | W/(KĀ·m) | Optimal: Polycrystalline Diamond (PCD) |
| Substrate Thermal Conductivity ($k_s$) | 1000 | W/(KĀ·m) | High Grade Diamond |
| Substrate Thermal Conductivity ($k_s$) | 156 | W/(KĀ·m) | Silicon (Si) |
| Substrate Thermal Conductivity ($k_s$) | 42 | W/(KĀ·m) | Worst Case: Sapphire |
| Minimum Thermal Resistance ($R_{th}$) | 3.58 x 10-3 | KĀ·m/W | Achieved using PCD substrate |
| Maximum Thermal Resistance ($R_{th}$) | 38.2 x 10-3 | KĀ·m/W | Achieved using Sapphire substrate |
| Thermal Conductivity (GaN) | 130 | W/(KĀ·m) | At 300 K |
| Thermal Conductivity (AlGaN) | 30 | W/(KĀ·m) | At 300 K |
| Average Lattice Temperature ($T_{av}$) | 355 | K | VDS=8 V, using PCD substrate |
| Max Lattice Temperature ($T_{av}$) | 612 | K | VDS=8 V, using Sapphire substrate |
| Interface Separation | 2 | Āµm | Distance between contacts in the diode structure |
| Critical Die Length ($L_1$) | 250 | Āµm | $R_{th}$ stabilized at $13.3 \times 10^{\text{-3}}$ KĀ·m/W for Si substrate beyond this length |
Key Methodologies
Section titled āKey MethodologiesāThe study utilized advanced coupled simulation techniques to accurately model the thermal behavior of the Al0.27Ga0.73N/GaN heterostructure diode under various operating conditions and substrate materials.
- Electro-Thermal Modeling Scheme: The core methodology involved a home-made, semi-classical Ensemble Monte Carlo (MC) simulator coupled with the solution of the steady-state Heat Diffusion Equation (HDE).
- Convergence Requirement: A sufficient number of iterations of the HDE-MC solver were performed until the static electro-thermal solution converged.
- Boundary Conditions: A Dirichlet boundary condition was applied at the bottom of the structure, simulating a heat sink fixed at a constant temperature of 300 K ($T_h$).
- Interface Modeling: Continuity conditions were imposed at layer interfaces using the formula $k_1 \partial T / \partial r_{n}|y = k_2 \partial T / \partial r{n}|_y$, where $k_1$ and $k_2$ are the thermal conductivities of the adjacent layers.
- Physical Effects Included: The model incorporated critical physical phenomena such as Piezoelectric scattering, scattering with phonons and dislocations, and the influence of spontaneous and piezoelectric surface polarization charges.
- Thermal Resistance Extraction: The thermal resistance ($R_{th}$) was extracted via linear fitting of the average lattice temperature ($T_{av}$) vs. the intrinsic dissipated power ($P_{diss}$) obtained from the HDE-MC simulations, following the relationship $T_{latt}=300+P_{diss} \times R_{th}$.
- Temperature Dependence: The study analyzed cases for both temperature-independent thermal conductivity and a temperature-dependent model, $k_i(T) \approx k_{300}(300 \text{ K} / T)^{1.3}$, confirming that $R_{th}$ is only constant when $k_i$ is temperature-independent.
6CCVD Solutions & Capabilities
Section titled ā6CCVD Solutions & CapabilitiesāThis research validates the necessity of utilizing ultra-high thermal conductivity MPCVD diamond for managing the severe self-heating effects in GaN-based electronics. 6CCVD is uniquely positioned to supply the materials and precision fabrication services required to replicate and advance this critical research area.
| Requirement/Finding in Paper | 6CCVD Capability & Solution |
|---|---|
| Material Requirement: Demand for $k_s \geq 2200$ W/(KĀ·m) (PCD) to minimize $R_{th}$ and prevent thermal runaway. | High Thermal Grade MPCVD PCD Substrates: We supply Polycrystalline Diamond (PCD) plates specifically optimized for thermal management. Our materials guarantee thermal conductivities that meet or exceed the simulated optimum of 2200 W/(KĀ·m), maximizing passive heat dissipation. |
| Interface Quality: Need for seamless integration with complex GaN/AlGaN layers to minimize thermal boundary resistance (TBR). | Ultra-Low Roughness Polishing: Available polishing capabilities ensure superior surface finish, critical for high-quality bonding and low TBR: Ra < 1nm (SCD) and Ra < 5nm (Inch-size PCD). |
| Geometry Optimization: Study required precise control over die lengths ($L_1$, $L_2$) up to 400 Āµm for $R_{th}$ optimization. | Custom Dimensions & Precision Fabrication: 6CCVD offers custom dimensions for PCD plates up to 125mm in diameter. We provide advanced laser cutting and dicing services to produce diamond plates in custom geometries necessary for thermal modeling and device integration. |
| Electrical Interface: Structure utilized high-conductivity metallic contact layers (e.g., Au mentioned in the schematic). | Integrated Metalization Services: We offer in-house deposition of custom metal stacks, including Ti/Pt/Au, W/Ti/Cu, or single-layer Au/Pt/Pd, deposited directly onto the diamond surface to facilitate electrical and thermal bonding solutions. |
| Modeling & Design: Application focus on next-generation high-frequency and high-power AlGaN/GaN HEMT/Diode systems. | Engineering Support: 6CCVDās in-house PhD team can assist researchers and technical engineers with material selection, specifying the optimal diamond grade (SCD, PCD, BDD), thickness (0.1Āµm - 500Āµm), and custom dimensions required for maximizing the reliability and performance of GaN-on-Diamond projects. |
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship materials globally (DDU default, DDP available).
View Original Abstract
In this paper we use an electro-thermal method [solver of the heat-flux equation coupled with an ensemble Monte Carlo (MC) simulator] to extract the value of the thermal resistance, Rth, in diodes consisting in un-gated Al0.27Ga0.73N/GaN heterostructures. Different substrates (polycrystalline diamond - PCD, diamond, silicon and sapphire), and die dimensions will be analysed. When a temperatureindependent thermal conductivity is considered, the obtained values of Rth depend on the geometry and substrate material, and are constant with the dissipated power (Pdiss). When a temperaturedependent thermal conductivity is needed to correctly reproduce the thermal behaviour of the device, Rth exhibits a strong dependence on Pdiss.