thermal simulation

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: $\nabla \cdot (k \nabla T) + q = \rho c_p \frac{\partial T}{\partial t}$.
• 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.