Van der Waals Epitaxy: Principles & Advances

• Van der Waals epitaxy is a growth method that deposits crystalline films on atomically flat, chemically inert substrates using weak dispersive interactions.
• It leverages unique kinetic and thermodynamic principles to enable strain-free, high-quality film growth with controlled domain orientation via defect engineering.
• Innovative strategies like interfacial dative bonding and predictive locking indices are expanding applications in optoelectronics, quantum devices, and spintronics.

Van der Waals Epitaxy

Van der Waals (vdW) epitaxy is a heteroepitaxial growth mode in which a crystalline film is deposited on a substrate that presents a chemically inert, atomically flat surface, typically by virtue of its layered or quasi-2D structure. Unlike conventional epitaxy, which enforces strict lattice matching via strong covalent or ionic bonds and often leads to misfit dislocations when mismatch is present, vdW epitaxy leverages weak, non-directional dispersive forces across the interface. This decouples the film from the substrate at the atomic scale, enabling high-quality, often dislocation-free crystalline layers to be grown with substantial lattice and symmetry mismatch. Advanced variants and phenomena—including enhanced vdW epitaxy via interfacial dative bonding, deterministic registry locking by defect engineering, and predictive frameworks for orientation control—are redefining the integration possibilities for thin-film materials and device architectures (Xie et al., 2016, Liang et al., 26 Dec 2025).

1. Fundamental Characteristics and Physical Principles

A defining feature of vdW epitaxy is the suppression of the elastic strain energy term that governs the critical thickness and defect formation in conventional heteroepitaxy. The substrate presents a surface terminated by vdW planes (e.g., graphene, h-BN, mica, topological insulators, 2D chalcogenides) with no dangling bonds, and the overlayer nucleates and crystallizes while “floating” above the substrate, separated by an interlayer gap where only nonlocal dispersive (vdW) interactions operate (Yimam et al., 2023, Lahiji et al., 14 Feb 2025, Pierucci et al., 2018).

Mathematically, the lattice mismatch $\delta$ loses its dominant role:

$$\delta = \frac{a_{\text{film}} - a_{\text{sub}}}{a_{\text{sub}}}$$

but, due to the absence of strong covalent coupling, even $\delta \sim$ 10–20% can be tolerated (Llopez et al., 2024, Claro et al., 20 Nov 2025). Misfit dislocations are not formed; instead, strain can relax via sliding or local in-plane rotations and the growth proceeds strain-free up to large thicknesses, as shown by the negligible out-of-plane strain and the thickness-independent d-spacing in α-MoO$_3$/mica over 2.5–160 nm (Lahiji et al., 14 Feb 2025).

In many systems, domain orientation is set only weakly by the low-energy differences among possible in-plane registries, leading to polycrystalline films with a distribution of rotational domains, unless additional locking mechanisms are engaged (Liang et al., 26 Dec 2025, Mortelmans et al., 2020).

2. Kinetic and Thermodynamic Models of vdW Epitaxy

The absence of strong film–substrate chemical interaction profoundly affects nucleation kinetics, critical nucleus sizes, surface diffusion, and domain morphology (Wang et al., 2015, Llopez et al., 2024):

• Nucleation: Only weak adsorption energies ($E_\text{ad} \sim 0.4–0.8$ eV) result in large critical nucleus sizes and low nucleation densities; nucleation rates $J$ are described by classical nucleation theory:

$J = A\exp(-\Delta G^*/k_BT)$

with increased $\Delta G^*$ due to the weak bonding to the substrate.

• Surface Diffusion and Island Growth: Long adatom diffusion lengths $L_D$ enable adatoms to reach energetically preferred nucleation or step sites, favoring large lateral grains or flakes as demonstrated for WTe$_2$/graphene ($\overline{S} = 110$ nm at low flux) (Llopez et al., 2024).
• Post-nucleation Growth: Lateral versus vertical competition is governed by unique energetics. The vertical nucleation rate is strongly suppressed by the lower sticking probability of adatoms on the newly formed 2D layer compared to the substrate, enabling genuine monolayer or few-layer morphologies, especially for non-layered crystals (Wang et al., 2015).
• Nucleation Control via Defect Engineering: Focused ion-beam irradiation (He$^+$, 30 keV) in SAvdWE can deterministically seed defects as nucleation centers in graphene, enabling controlled spatial placement and orientation of h-BN domains (Heilmann et al., 2020).

Key expressions summarized for typical nucleation kinetics, coverage, and strain are: | Quantity | Formula | Key Parameterization | |------------------|-----------|----------------------| | Adatom residence | $\tau_\text{ad} = \nu^{-1}e^{E_\text{ad}/k_BT}$ | $\nu \sim 10^{12}$ s$^{-1}$, $E_\text{ad}$ vdW regime | | Nucleation rate | $J = A\exp(-\Delta G^*/k_BT)$ | $A$, $\Delta G^*$ system/material-specific | | Lattice mismatch | $$\delta = (a_\text{film} - a_\text{sub})/a_\text{sub}$$ | $\delta$ up to $\sim$15% tolerated(Ribeiro et al., 2021) |

3. Interface Structure, Registry, and Orientation Control

Classically, in-plane registry in vdW epitaxy is only weakly selected, producing multiple domain orientations. However, systems have been identified and engineered wherein interfacial chemistry leads to enhanced orientation control ("locked vdW epitaxy"), mediated by two principal mechanisms:

• Interfacial Dative Bonding: As shown for CdTe/NbSe$_2$, a two-step process occurs: (1) net electron transfer from Cd dangling bonds into the Fermi-level Nb d-states of NbSe$_2$, creating empty acceptor states on Cd; (2) formation of directional dative bonds (Cd $\leftarrow$ Se) in the interface, enhancing registry locking and yielding a per-CdTe binding energy five times that of CdTe/graphene, but still lower than full covalent bonds (Xie et al., 2016). Similar effects were demonstrated in Cr$_5$Te$_8$/WSe$_2$ epitaxy, with interfacial Cr–Se dative bonds ($\sim$1 eV/Cr) driving the formation of monocrystalline, commensurate moiré superlattices (Bian et al., 2022).
• Interstitial Registry Anchoring: Mo interstitial incorporation in MoS$_2$ bilayers under Mo-rich MOCVD conditions creates tetrahedrally bonded defects at the vdW gap. This substantially increases the local energy barrier for sliding and rotational misalignments ($\sim$1.6 eV/interstitial), converting a 2H/3R stacking landscape with meV-scale difference into a locked 2H crystal even after transfer-induced mechanical perturbations (Yoo et al., 22 Jul 2025).

A quantitative thermodynamic framework for orientation control/locking has been developed, introducing predictive indices ($I_\text{pre}$ and $I_\text{lock}$) that combine electrostatic, chemical, vdW, and strain contributions. Systems with $I_\text{lock}>1$ (e.g., STO(111)/mica, MoS$_2$/sapphire) show locked facet or in-plane rotational order; those with $I_\text{lock}<1$ (e.g., MoS$_2$/HOPG, Fe$_4$N(001)/mica) do not (Liang et al., 26 Dec 2025).

4. Growth Methodologies, Substrate Strategies, and Process Control

vdW epitaxy has been successfully implemented across diverse film–substrate pairs and deposition modalities:

• MBE/Pulsed Laser/Sputter Deposition: Atomically flat films of Fe$_5$GeTe$_2$, Bi$_2$Te$_3$, α-MoO$_3$, Sb, GaSe, InSe, and PbI$_2$ have been grown by molecular beam or pulsed-laser methods on substrates ranging from sapphire, mica, and silicon to graphene, h-BN, and layered oxides (Lahiji et al., 14 Feb 2025, Yimam et al., 2023, Claro et al., 2022, Tsotezem et al., 6 Jun 2025).
• Template/Seed Layer Strategies: On amorphous or non-layered substrates, thin crystalline seed layers (e.g., Sb$_2$Te$_3$ for Sb, MoSe$_2$ for MoSe$_2$) provide a vdW template to initiate epitaxy and transfer registry—or, in multi-step "solid-phase" methods, enable subsequent epitaxial multilayer growth (Vergnaud et al., 2019, Yimam et al., 2023).
• Selective-Area and Custom-Feature Growth: Lithographically patterned, fluorinated mica regions with altered surface free energy enable spatially selective vdW epitaxy, producing micron-scale features of topological insulators (Bi$_2$Te$_2$S$_1$) with controlled domain orientation and armchair/zigzag edges (Trivedi et al., 2017). He$^+$ defect engineering in graphene delivers deterministic nucleation points for SAvdWE, attaining nucleation yield and quality control at the nanometer scale (Heilmann et al., 2020).
• “Virtual Substrate” and Membrane Release: α-PbO vdW films serve as virtual substrates for oxide perovskite growth, supporting large ($|\delta|>2\%$) lattice mismatches and enabling subsequent mechanical exfoliation or spontaneous spalling to yield free-standing oxide membranes (Claro et al., 20 Nov 2025).

5. Structure–Property Relationships and Device Implications

vdW epitaxy yields heterostructures with highly tunable physical properties and device functionality:

• Quantum Well and Superlattice Integration: GaSe/InSe superlattices and quantum wells, grown vdW-epitaxially on Si(111) or c-sapphire, show miniband formation and confinement-tunable photoluminescence, demonstrating atomically sharp interfaces and visible–NIR photodetection at wafer scale (Claro et al., 2022).
• Functional Magnetic, Topological, and Optical Layers: Layered Fe$_5$GeTe$_2$ and Cr$_5$Te$_8$ films, grown via vdW epitaxy and dative epitaxy respectively, support robust room-temperature ferromagnetism and low-defect, orientation-locked monocrystalline order, with direct implications for spintronics and valleytronics (Ribeiro et al., 2021, Bian et al., 2022).
• Interface-Driven Excitations and Tunneling: Double-sided vdW epitaxy across suspended atomic membranes (e.g., Sb$_2$Te$_3$/hBN/Bi$_2$Se$_3$) yields quantum devices with crystal-momentum-conserving tunneling, with magneto-tunneling spectroscopy revealing resonant Landau-level transitions and gate-tunable interfaces (Park et al., 2024).
• Lattice Coherence, Disorder and Strain: Advanced x-ray methodologies demonstrate that lateral domain size and in-plane atomic displacement can be optimized via substrate temperature, chalcogen overpressure, and chemical flux ratios to tune the mobility, defect density, and conduction-type in Bi$_2$Te$_3$ and related films (Kycia et al., 2018).

6. Predictive Frameworks, Model Systems, and Design Criteria

Recent thermodynamic frameworks provide criteria for engineering the degree of registry, orientation locking, and facet selection:

• Two-Tier Predictive Indices: The tier-1 predictive index $I_\text{pre}=P_\text{coupling}+4C_\text{affinity}$ (mixing surface potential and chemical affinity descriptors) and the tier-2 locking criterion $I_\text{lock}$ (ratio of non-vdW to vdW/surface energy terms) enable quantitative forecasting of locked vs. free vdW epitaxy (Liang et al., 26 Dec 2025).
• Materials Selection for Registry Control: Candidates for enhanced vdW epitaxy or dative epitaxy are chosen for (i) a substrate with sufficient work function and density of low-energy acceptor states, (ii) an overlayer whose surface atoms supply readily emptied or filled states (dangling bonds or lone pairs), and (iii) weak overall lattice matching to avoid misfit dislocations despite strong interfacial coupling (Xie et al., 2016, Bian et al., 2022).
• Defect-Engineered Epitaxy: Mo interstitials (and, by extension, other covalently bonding interstitials) can be introduced at the interface to fix multilayer stacking, provided their site-specific incorporation energy exceeds the bulk stacking energy difference by at least 2–3 orders of magnitude (Yoo et al., 22 Jul 2025).
• Process Knobs: Growth temperature, chalcogen/metal flux ratio, defect ion fluence, and surface functionalization/chemical passivation are rational levers for crossing the regime boundaries identified by the predictive indices [$I_\text{pre}\approx20$, $I_\text{lock}=1$], with system-specific kinetic limitations at boundaries (Liang et al., 26 Dec 2025, Mortelmans et al., 2020).

7. Challenges, Limitations, and Research Directions

While vdW epitaxy mitigates the severe lattice-matching prerequisites of conventional heteroepitaxy, several challenges are being actively addressed:

• Twin Domain and Grain Boundary Control: In weakly bound systems (e.g., WSe$_2$), low barriers to in-plane rotation favor 60° twin domain formation, but enhanced coupling or lower growth temperature suppresses this, as seen for Bi$_2$Se$_3$ (Mortelmans et al., 2020).
• Registry and Interlayer Defect Engineering at Scale: Interstitial-driven registry locking has been demonstrated for MoS$_2$ bilayers, but extension to higher-order multilayers or other 2D materials requires precise in situ control over precursor stoichiometry and step-directed epitaxy (Yoo et al., 22 Jul 2025).
• Integrated Heterostructure Complexity: Strategies including double-sided epitaxy, virtual vdW substrates, and selective-area approaches are extending vdW epitaxy toward scalable, arbitrary, heterointegrated devices, though challenges in domain size scaling, edge state control, and interlayer transport remain (Trivedi et al., 2017, Claro et al., 20 Nov 2025, Park et al., 2024).
• Coupled Kinetic–Thermodynamic Modelling: While thermodynamic frameworks provide clear boundaries and design rules for locked/free registry, kinetic effects—nucleation rates, adatom diffusion, coalescence dynamics—determine the accessible structures and domain sizes, mandating coupled phase-field or kinetic Monte Carlo approaches for further predictive power (Liang et al., 26 Dec 2025, Wang et al., 2015, Llopez et al., 2024).

The field is rapidly converging on a unified picture in which atomically precise control over interfacial chemistry, defect incorporation, and substrate engineering can enable deterministic registry and orientation in a wide palette of layered/2D materials, greatly expanding the design scope for heterostructured electronics, optoelectronics, quantum, and spintronic devices.