Computational modeling has become an indispensable tool for understanding and predicting vapor-liquid-solid (VLS) growth dynamics, a widely used technique for synthesizing nanowires and other one-dimensional nanostructures. By leveraging theoretical and numerical approaches, researchers can explore the atomic-scale mechanisms governing nucleation, catalyst behavior, and defect formation, providing insights that complement experimental observations. Three primary computational methods—density functional theory (DFT), phase-field modeling, and kinetic Monte Carlo (kMC) simulations—have emerged as key techniques for studying VLS growth, each offering unique advantages in addressing different aspects of the process.

Density functional theory provides a quantum mechanical framework for investigating the electronic and atomic-scale interactions critical to VLS growth. DFT calculations are particularly useful for studying the energetics of catalyst-substrate interfaces, adsorption dynamics, and the role of impurities. For example, DFT has been employed to analyze the wetting behavior of gold catalysts on silicon substrates, revealing that the interfacial energy between the liquid catalyst droplet and the solid nanowire strongly influences the nucleation site and growth direction. Studies have shown that the contact angle of the catalyst droplet, typically ranging between 90 and 120 degrees for common systems like Au-Si, determines the stability of the growth front. Additionally, DFT can predict the incorporation of dopants and point defects, such as vacancies or antisite defects, by calculating their formation energies under varying growth conditions. These insights help explain experimental observations of unintentional doping or defect clustering in nanowires grown via VLS.

Phase-field modeling offers a mesoscale perspective, bridging the gap between atomic-scale DFT and macroscopic growth phenomena. This approach treats the solid, liquid, and vapor phases as continuous fields, allowing researchers to simulate the evolution of the nanowire morphology and the dynamics of the triple-phase boundary where growth occurs. Phase-field models incorporate thermodynamic and kinetic parameters, such as diffusion coefficients and interfacial energies, to predict growth rates and diameter-dependent effects. For instance, simulations have demonstrated that the Gibbs-Thomson effect, which accounts for curvature-dependent solubility, leads to slower growth rates for thinner nanowires, consistent with experimental measurements. Phase-field methods also capture the instability mechanisms that cause kinking or tapering in nanowires, often linked to fluctuations in catalyst droplet volume or temperature gradients. Validation against in situ TEM observations has confirmed that phase-field simulations can accurately reproduce the transition from steady axial growth to lateral branching under supersaturation variations.

Kinetic Monte Carlo simulations excel at modeling the stochastic nature of atomic attachment and surface diffusion during VLS growth. Unlike DFT or phase-field methods, kMC tracks individual atoms or lattice sites, making it ideal for studying defect formation and growth mode transitions. By incorporating Arrhenius-type rates for surface diffusion, nucleation, and step-flow processes, kMC can predict the emergence of stacking faults, twin boundaries, or polytypism in compound semiconductor nanowires. For example, kMC simulations of III-V nanowire growth have shown that variations in V/III flux ratios can switch the crystal structure between wurtzite and zinc blende phases, matching experimental observations. The method also quantifies the role of catalyst composition, demonstrating that alloying Au with elements like Ga or Sn alters the nucleation barrier and influences nanowire uniformity. Cross-validation with growth experiments has established that kMC reliably predicts the temperature-dependent critical nucleus size, which governs the onset of axial versus radial growth.

A critical aspect of computational modeling is its validation against experimental data, ensuring that theoretical predictions align with real-world observations. For VLS growth, key validation metrics include nanowire diameter distributions, growth rates, and defect densities. Studies comparing DFT-predicted interfacial energies with measured contact angles show agreement within 10-15%, while phase-field simulations of growth kinetics typically match experimental rates within a factor of two. Kinetic Monte Carlo results for defect densities in Si nanowires, for instance, correlate well with TEM-based statistics, particularly for stacking fault probabilities at different growth temperatures. Discrepancies often arise from uncertainties in input parameters, such as surface diffusion barriers or precursor dissociation rates, highlighting the need for iterative refinement between modeling and experiments.

Despite their strengths, each computational method has limitations. DFT’s high computational cost restricts system sizes to a few hundred atoms, making it impractical for modeling large-scale growth phenomena. Phase-field models rely on phenomenological parameters that may not capture atomistic details, while kMC simulations require predefined rate catalogs that may omit rare but critical events. Combining these approaches in multiscale frameworks offers a promising solution, where DFT informs kMC rates, and kMC outputs guide phase-field boundary conditions. Such integrated strategies have successfully predicted complex behaviors like catalyst poisoning or the self-assembly of nanowire heterostructures.

Future advancements in computational modeling of VLS growth will likely focus on improving material-specific parameter databases and incorporating more realistic environmental conditions, such as variable pressure and non-equilibrium precursor fluxes. Coupling these models with in situ characterization data will further enhance predictive accuracy, enabling the rational design of nanowires with tailored properties for applications in electronics, photonics, and energy conversion. By continuing to refine these computational tools, researchers can unlock new levels of control over VLS growth dynamics, paving the way for next-generation nanostructured materials.