Multi-Physics Simulation

Why Simulation is Essential in Semiconductor Manufacturing

Real experiments are expensive, time-consuming, and limited in visibility. Numerical simulation enables us to model complex multi-physics phenomena and uncover the fundamental causes of process behavior.

1/100×
Cost Reduction
10×
Faster Development
Deeper Insights

Why Experiments Alone Aren't Enough

Semiconductor processes involve nanometer-scale phenomena where plasma, heat, chemistry, and mechanics interact simultaneously.

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High Cost

Each wafer costs hundreds to thousands of dollars. Equipment operation, materials, and cleanroom time add up quickly.

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Time Consuming

A single experiment takes hours to days. Result analysis and iteration can extend to weeks or months.

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Limited Visibility

You cannot observe inside the chamber during processing. Only final results are measurable, not the process dynamics.

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Safety Constraints

Toxic gases, high temperatures, and plasma create hazardous conditions that limit experimental flexibility.

Simulation Unlocks New Possibilities

Numerical simulation complements experiments by providing insights that are impossible or impractical to obtain otherwise.

1/100×

Cost Reduction

Run thousands of virtual experiments at a fraction of the cost. No materials wasted, no equipment wear.

10×

Speed Increase

Iterate rapidly through parameter spaces. Find optimal conditions in days instead of months.

Complete Visibility

Visualize every variable in real-time. Understand the physics behind every outcome.

Coupled Phenomena in Semiconductor Processes

Multiple physical phenomena occur simultaneously and interact with each other, requiring integrated simulation approaches.

Plasma Physics

Electron density, ion energy, sheath voltage, RF power coupling, ionization rates

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Heat Transfer

Wafer temperature distribution, plasma heating, radiative cooling, thermal gradients

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Chemical Reactions

Surface reaction kinetics, etch/deposition selectivity, radical generation and transport

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Mechanical Stress

Film stress, thermal expansion mismatch, lattice strain, delamination prediction

Governing Equations

These fundamental equations form the mathematical foundation of semiconductor process simulation.

Boltzmann Transport (Plasma)

∂f/∂t + v·∇f + (F/m)·∇ᵥf = C[f]

Describes the evolution of particle distribution functions in plasma, accounting for collisions and electromagnetic forces.

Navier-Stokes (Flow)

ρ(∂v/∂t + v·∇v) = -∇p + μ∇²v

Governs gas flow dynamics in the chamber, including pressure-driven and viscous effects.

Heat Conduction (Thermal)

ρcₚ∂T/∂t = ∇·(k∇T) + Q

Determines temperature distribution considering conduction, heat sources, and boundary conditions.

Surface Reaction (Etching)

R = k₀·exp(-Eₐ/kT)·Γ·(1-θ)

Arrhenius-type rate equation for surface reactions, dependent on temperature, flux, and surface coverage.

Experience Simulation First-Hand

Simulation doesn't replace experiments—it makes them more efficient. Use simulation to find the direction, then validate with experiments.

Launch Simulator