Diffusion Simulation

Diffusion Simulation is the TCAD computational modeling of dopant atom migration through the silicon crystal lattice during thermal processing — predicting the spatial concentration profile, junction depth, and activation state of implanted or deposited dopants (boron, phosphorus, arsenic, antimony) as a function of thermal budget (temperature × time), accounting for the complex interactions between dopants, native defects (vacancies and interstitials), and the crystal microstructure that govern modern transistor doping profiles.

What Is Diffusion Simulation?

Dopant atoms implanted into silicon must be thermally activated (annealed) to move from interstitial positions (between crystal atoms) to substitutional positions (replacing silicon atoms in the lattice) where they contribute electrically. During annealing, dopants inevitably diffuse — spread spatially — which simultaneously activates them and potentially moves them too far from the desired location.

Fick's Laws — The Starting Point

The simplest diffusion model uses Fick's second law:

∂C/∂t = D∇²C

Where C = dopant concentration, D = diffusivity, t = time. This predicts Gaussian profiles from implants — but reality is far more complex.

Physical Mechanisms Beyond Simple Diffusion

Vacancy and Interstitial Mediated Diffusion: Dopants do not diffuse through perfect crystal — they move via lattice defects. The two primary mechanisms:
- Vacancy Mechanism: Dopant hops into adjacent vacancy. Boron diffuses primarily this way under certain conditions.
- Kick-Out Mechanism: Dopant ejects a silicon atom, creating a silicon interstitial, then jumps to the now-vacated lattice site. This is the dominant mechanism for many dopant-interstitial combinations.

Transient Enhanced Diffusion (TED): Ion implantation generates excess silicon interstitials along the damage cascade. These excess interstitials dramatically accelerate dopant diffusion — by 100× or more — during the early stages of annealing before they recombine with vacancies at the surface and bulk. TED is the primary mechanism that limits how shallow source/drain junctions can be made: annealing long enough to activate dopants causes TED to push them deeper than desired.

Dopant-Defect Clustering: At high concentrations, boron forms immobile BnIm clusters that tie up electrically inactive dopant. Phosphorus and arsenic form similar clusters. Accurately modeling cluster formation and dissolution during annealing determines the fraction of dopants that are electrically active versus electrically inactive.

Oxidation-Enhanced/Retarded Diffusion (OED/ORD): Oxidizing silicon injects silicon interstitials into the crystal, which enhance diffusion of interstitial-diffusing species (phosphorus: OED) and retard diffusion of vacancy-diffusing species (antimony: ORD). This creates cross-process coupling — an oxidation step affects diffusion in a subsequent anneal.

Why Diffusion Simulation Matters

- Junction Depth (Xj) Control: The source/drain junction depth must be shallow to suppress short-channel effects (SCEs) that degrade transistor switching behavior. Modern FinFET source/drain junctions require Xj < 10–15 nm — achievable only by using millisecond annealing (laser spike, flash anneal) combined with simulation-guided thermal budget optimization to activate dopants while minimizing TED.
- Short-Channel Effect Prevention: If dopants diffuse under the gate, the channel cannot be fully depleted, causing punchthrough leakage that scales as the square of the diffusion distance. Sub-10 nm gate length transistors require sub-nanometer junction control, which only simulation-guided thermal processing can achieve.
- Halo/Pocket Implant Design: Counter-doped regions under the gate edges (halo implants) control the threshold voltage rolloff. Diffusion simulation predicts how halo profiles broaden during source/drain activation anneals, guiding the implant energy/dose and anneal conditions.
- Retrograde Well Design: Deep well profiles are engineered with multiple-energy implants and diffusion steps. Simulation predicts the as-implanted and post-anneal profiles to ensure the intended vertical doping structure is achieved.

Tools

- Synopsys Sentaurus Process: Full physical diffusion models including TED, clustering, and OED/ORD for all major dopant species.
- Silvaco ATHENA / Victory Process: Comprehensive diffusion simulation with kinetic Monte Carlo coupling for advanced TED modeling.
- FLOOPS (University of Florida): Academic process simulator foundational to the diffusion modeling field.

Diffusion Simulation is tracking the thermal migration of atoms — mathematically modeling how heat causes dopant atoms to redistribute through the silicon lattice via complex defect-mediated mechanisms, enabling engineers to design the precise doping profiles that define transistor electrical characteristics in devices where atomic-scale control of dopant position determines whether a chip meets its specifications.