Multiscale Simulation is the strategy of connecting computational models operating at different length and time scales into a hierarchical chain — passing parameters, rates, and fitted coefficients upward from quantum-mechanical calculations through atomistic models to mesoscale and continuum TCAD simulations — enabling accurate prediction of macroscopic semiconductor device and process behavior from first-principles physics without solving the computationally intractable quantum problem at device scale.

What Is Multiscale Simulation?

No single computational method can bridge the 10-order-of-magnitude gap between quantum mechanical atomic interactions (Angstrom/femtosecond scale) and device-level manufacturing behavior (millimeter/second scale). Multiscale simulation creates a hierarchical bridge:

The Semiconductor Multiscale Hierarchy

Level 1 — Ab Initio / DFT (Ångström / femtosecond): Density Functional Theory solves Schrödinger's equation for electrons using the electron density as the fundamental variable (Kohn-Sham equations). Provides formation energies, migration barriers, and electronic structure for individual defects and dopant-defect pairs with no empirical parameters.

• Output Examples: Boron-interstitial binding energy (0.7 eV), {311} defect formation energy, High-K dielectric band alignment with silicon.

Level 2 — Molecular Dynamics (Nanometer / picosecond): Uses interatomic potentials (fitted to DFT data) to simulate thousands to millions of atoms. Samples the DFT energy landscape statistically to observe thermally activated processes.

• Output Examples: Point defect diffusivity as a function of temperature, amorphization threshold damage density, oxide/silicon interface roughness RMS.

Level 3 — Kinetic Monte Carlo (Tens of nm / microseconds): Uses rates from MD/DFT (Arrhenius parameters) to stochastically simulate defect and dopant evolution over technologically relevant timescales.

• Output Examples: Cluster dissolution time constants, TED enhancement factors as a function of implant damage profile.

Level 4 — Continuum TCAD (Micron to mm / seconds to hours): Solves coupled partial differential equations for dopant concentration fields using effective diffusivities and reaction rates from KMC/MD.

• Output Examples: Final 3D junction depth map, oxide thickness distribution across wafer, full device doping profile.

Level 5 — SPICE / Device Simulation (Device to circuit): Uses TCAD-computed device structures and material parameters to extract electrical characteristics (I-V, C-V) for circuit-level simulation.

Why Multiscale Simulation Matters

• Parameter-Free Process Prediction: Traditional TCAD relies on empirical fitting to experimental data — parameters tuned for existing processes may not extrapolate correctly to new materials, geometries, or process conditions. Multiscale simulation derives TCAD parameters from first principles, enabling predictive simulation of processes before experiments are run.
• New Material Enablement: When semiconductor technology transitions to new channel materials (Ge, InGaAs, GaSb, 2D materials like MoS₂), there is no empirical database of TCAD parameters. Multiscale simulation provides the parameters needed to simulate these new materials from their known atomic structure and bonding.
• Sub-Nanometer Scale Breakdown: At device dimensions below 5 nm, continuum descriptions of dopant distributions (treating implanted atoms as a continuous concentration field) break down — discrete dopant atom statistics dominate. KMC provides the discreteness-preserving bridge to continuum descriptions.
• Self-Heating Analysis: Nanowire FETs have dramatically suppressed thermal conductivity due to phonon confinement. MD phonon simulation provides thermal conductivities as inputs to continuum thermal simulation — essential for reliability analysis of highly scaled devices.
• High-K/Metal Gate Stack Design: The interface between silicon, silicon dioxide, high-K dielectric (HfO₂), and metal gate involves multiple material phases at nanometer scale. DFT and MD provide band alignments, interface state densities, and diffusion barriers that continuum models cannot self-consistently compute.

Tools

• Synopsys Sentaurus Suite: Complete TCAD environment with links to external MD/DFT tools and internal KMC-based diffusion.
• Vienna Ab initio Simulation Package (VASP): The most widely used DFT code for generating multiscale input parameters.
• LAMMPS + Tersoff/Stillinger-Weber: MD simulations that feed defect migration rates to KMC.

Multiscale Simulation is connecting the quantum to the wafer — the computational strategy that translates the first-principles physics of electron-atom interactions through a hierarchy of increasingly coarse-grained models to predict manufacturing-scale process outcomes, enabling semiconductor engineers to design processes from atomic understanding rather than empirical trial and error.