Thermal simulation in semiconductor context calculates the temperature distribution across a chip, package, or system by modeling heat generation, conduction, convection, and radiation — enabling engineers to identify hot spots, verify thermal limits, and optimize cooling solutions.
Why Thermal Simulation Matters
- Semiconductor device performance is strongly temperature-dependent:
- Mobility decreases with temperature → slower transistors.
- Leakage current increases exponentially with temperature → more power consumption.
- Reliability degrades at high temperature → electromigration, NBTI, HCI all accelerate.
- Modern chips can dissipate 100–300+ watts across an area of a few hundred mm² — creating temperatures exceeding 100°C at hot spots if not properly managed.
Heat Sources on Chip
- Dynamic Power: $P_{dyn} = \alpha C V^2 f$ — from switching activity. Distributed across active circuit blocks.
- Static Power: Leakage current × supply voltage — increasingly dominant at advanced nodes. Temperature-dependent (creates positive feedback).
- Interconnect Joule Heating: $P = I^2 R$ in metal lines — significant in power grid and high-current signals.
What Gets Simulated
- Die-Level: Temperature map across the chip surface and through the silicon thickness. Identify hot spots in high-activity blocks (CPU cores, memory controllers, I/O).
- Package-Level: Temperature through the package stack — die attach, substrate, heat spreader, TIM (thermal interface material), heat sink.
- System-Level: Airflow through the chassis, heat sink fin design, fan placement.
Simulation Methods
- Finite Element Method (FEM): Most common for solid thermal analysis. Mesh the geometry, solve the heat equation: $
abla \cdot (k
abla T) + q = \rho c_p \frac{\partial T}{\partial t}$.
- Finite Difference Method (FDM): Simpler meshing, faster for regular geometries.
- Compact Thermal Models (CTM): Reduced-order models (thermal RC networks) for quick estimation and system-level analysis.
- CFD (Computational Fluid Dynamics): For convective cooling analysis — airflow patterns, heat sink optimization.
Key Parameters
- Thermal Conductivity ($k$): Silicon: ~150 W/m·K, SiO₂: ~1.4 W/m·K, Cu: ~400 W/m·K. The low conductivity of dielectric layers creates thermal resistance.
- Thermal Resistance ($R_{th}$): Junction-to-case, case-to-ambient — quantifies the thermal path quality.
- Junction Temperature ($T_j$): The maximum allowable temperature — typically 105–125°C for commercial, 150°C+ for automotive.
Electrothermal Coupling
- Temperature affects leakage → leakage affects power → power affects temperature. This positive feedback loop requires iterative electrothermal simulation for accurate results.
Thermal simulation is essential for modern chip design — as power density increases with each technology node, thermal management becomes the primary constraint on performance and reliability.