Adsorption-Controlled Growth

• Adsorption-controlled growth is a regime where surface processes—adsorption, desorption, and incorporation kinetics—dominate over simple flux matching to determine film composition.
• In epitaxy, this method achieves self-regulation by supplying a volatile constituent in excess, allowing unwanted species to desorb while stabilizing the targeted phase.
• Thermodynamic maps and kinetic models validate the approach across various materials, enabling precise control over film morphology, defect density, and functional performance.

Adsorption-controlled growth denotes a regime in which incorporation at a surface is governed primarily by adsorption, desorption, and interfacial incorporation kinetics rather than by exact flux matching alone. In epitaxy, the usual consequence is self-regulation: one constituent is supplied in excess, the excess volatile species desorb, and the stable phase is selected by the surface chemical potential and the least volatile or rate-limiting species. In other settings, the same term refers to wall-film formation in pores, substrate-modulated adatom attachment, or adsorption-limited crystal growth under constant chemical potential (Choo et al., 4 Oct 2025, Lapano et al., 2020, Kityk et al., 2021, Gargari et al., 2 Dec 2025).

1. Definition and conceptual variants

In oxide and chalcogenide epitaxy, adsorption-controlled growth usually means that the film can reject excess volatile species while retaining the target compound. In hybrid MBE of BaTiO$_3$, Ti is supplied from volatile TTIP, excess Ti-containing species can desorb, and a plateau in the out-of-plane lattice parameter at $4.040 \pm 0.003\ \text{Å}$ for TTIP/Ba BEP $= 96$–$155$ identifies the adsorption-controlled window near the bulk BTO $c$-axis of $4.036\ \text{Å}$ (Choo et al., 4 Oct 2025). In MnTe(Bi$_2$Te$_3$)$_n$, Mn is the limiting incorporated species, whereas excess Bi and Te are not incorporated under stoichiometric growth conditions and desorb from the surface (Lapano et al., 2020).

The term does not always imply full control of all sublattices. FeVSb is explicitly described as a semi adsorption-controlled system because only the Sb sublattice is self-limiting while the Fe/V ratio is not (Shourov et al., 2020). In ICSSE growth of CdTe, self-regulation is limited by desorption rather than absorption: a self-regulated regime of $2\ \text{ML/cycle}$ is reached only for longer purge times and/or short Cd exposure times (Larramendi et al., 2019).

Taken together, these cases suggest that adsorption-controlled growth is best understood as a family of self-limiting incorporation regimes rather than a synonym for perfect stoichiometric control. The decisive question is which species is volatile, which species is incorporation-limiting, and whether rejected material leaves the surface before it can stabilize a secondary phase or defect population.

2. Thermodynamic and kinetic framework

Adsorption-controlled growth is commonly rationalized with thermodynamic phase maps that identify a region where the target phase is stable but excess volatile species are not. For FeVSb, an Ellingham-style analysis places the useful regime between Sb sublimation and FeVSb decomposition; experimentally, at $4.040 \pm 0.003\ \text{Å}$0C the growth window is approximately Sb/V $4.040 \pm 0.003\ \text{Å}$1 to $4.040 \pm 0.003\ \text{Å}$2 by RHEED and about $4.040 \pm 0.003\ \text{Å}$3 to $4.040 \pm 0.003\ \text{Å}$4 by XRD, substantially narrower than equilibrium thermodynamics predicts (Shourov et al., 2020). For $4.040 \pm 0.003\ \text{Å}$5-GaSe on GaAs $4.040 \pm 0.003\ \text{Å}$6, the observed phase boundaries qualitatively match an Ellingham diagram, but growth above about $4.040 \pm 0.003\ \text{Å}$7C produced a sharp decrease in Ga and Se sticking coefficients and no crystalline growth (Eickhoff et al., 6 Mar 2026). For LaInO$4.040 \pm 0.003\ \text{Å}$8 on DyScO$4.040 \pm 0.003\ \text{Å}$9(110), a TOMBE diagram similarly overestimated the practical growth window; the best films were obtained at $= 96$0C in an oxygen-flux range of roughly $= 96$1 to $= 96$2, and the usable window was narrowed by kinetics, surface roughness, oxygen sensitivity, and domain formation (Hoffmann et al., 2022). A laser-heated epitaxy proposal extends the same logic to perovskites such as SrTiO$= 96$3, arguing for a self-limited window above roughly $= 96$4C and below about $= 96$5 oxygen, with ozone greatly expanding the accessible temperature range (Braun, 2024).

Kinetic models complement these thermodynamic maps by specifying how adsorbates are transported and incorporated. For a circular 2D domain fed by diffusing adsorbates, the moving-boundary Stefan formulation gives

$= 96$6

so the domain area grows linearly in time, while finite attachment kinetics add an extra resistance term through $= 96$7 (Seki, 2019). In rejection-free kMC for MoS$= 96$8, adsorption, desorption, on-substrate diffusion, attachment, and edge migration all follow

$= 96$9

whereas in full-diffusion kMC for WS$155$0 on ST-X quartz, adsorption and diffusion energies vary spatially with local substrate registry (Aldana et al., 2024, Wu et al., 2018).

This combination of a thermodynamic window and a kinetic pathway is a recurring feature. Thermodynamics determines whether excess species can desorb without destabilizing the target phase; kinetics determines whether they do so rapidly enough to preserve smooth, single-phase, or domain-selective growth.

3. Epitaxial implementations across materials classes

Hybrid MBE of BaTiO$155$1 demonstrates adsorption control in a membrane architecture. The heterostructure $155$2 uses SrO as a binary oxide sacrificial layer that is MBE-compatible, thermally stable during growth, and selectively dissolvable in water. Within the stoichiometric window the films are single-crystalline and epitaxial, water-droplet lift-off yields submillimeter- to millimeter-sized membranes, and the transferred membranes remain phase-pure and single-crystalline with bulk-like lattice parameters. The membranes show tetragonal Raman modes, $155$3, $155$4, and $155$5, with the dielectric and ferroelectric response interpreted in relation to mixed c- and a-domain configurations (Choo et al., 4 Oct 2025).

In La-doped BaSnO$155$6, adsorption control is realized by supplying Sn in excess as volatile SnO$155$7, which desorbs from the surface within the BaSnO$155$8 stability region. A $155$9 La-doped film on a $c$0 undoped BaSnO$c$1 buffer on $c$2 DyScO$c$3 showed $c$4, room-temperature mobility of $c$5, $c$6 at $c$7, and a much lower concentration of $c$8 Ruddlesden–Popper shear faults than earlier PLD-grown films (Paik et al., 2017).

Adsorption control can also select among competing magnetic and topological phases. In MnTe(Bi$c$9Te$4.036\ \text{Å}$0)$4.036\ \text{Å}$1, MnBi$4.036\ \text{Å}$2Te$4.036\ \text{Å}$3 forms for about $4.036\ \text{Å}$4 at $4.036\ \text{Å}$5C, MnBi$4.036\ \text{Å}$6Te$4.036\ \text{Å}$7 is stabilized at $4.036\ \text{Å}$8, and Mn-rich growth with $4.036\ \text{Å}$9 produces ferromagnetic hysteresis although XRD still mostly shows the MnBi$_2$0Te$_2$1 structure (Lapano et al., 2020). In FeVSb, the highest electron mobility and lowest background carrier density occur toward the Sb-rich bound of the semi adsorption-controlled window, with a maximum reported mobility of $_2$2 at $_2$3 (Shourov et al., 2020).

Oxide variants emphasize different volatile intermediates but the same self-limiting logic. Suboxide MBE of Ga$_2$4O$_2$5 supplies Ga$_2$6O directly from a Ga + Ga$_2$7O$_2$8 source with $_2$9, bypasses the rate-limiting on-surface formation of Ga$_3$0O, and reaches growth rates up to $_3$1 for phase-pure, smooth, high-purity films thicker than $_3$2 (Vogt et al., 2020). Homoepitaxial c-plane sapphire becomes adsorption-controlled above about $_3$3C under sufficiently oxidizing conditions; the ideal regime is approximately $_3$4–$_3$5C, where the films are atomically smooth, Al-terminated, and show RMS roughness as low as $_3$6, a single-crystal-like bandgap, and a low density of F$_3$7 centers (Majer et al., 2024).

4. Morphology and coverage control in two-dimensional growth

In 2D materials, adsorption control often governs flake shape and edge evolution more directly than bulk stoichiometry. For monolayer WS$_3$8 on ST-X quartz, full-diffusion kMC attributes anisotropy to substrate-induced modulation of adsorption, desorption, diffusion, and edge stabilization. The substrate is reduced to strong-adsorption Si and ordinary-adsorption O domains with an adsorption contrast $_3$9 of about $_n$0. The anisotropic growth ratio (AGR) is positively proportional to the C/M ratio, and $_n$1 can produce either perfect isotropy or high anisotropy depending on the linear relation between gas flux and temperature, with $_n$2 near perfect isotropic growth and $_n$3 near extremely anisotropic growth (Wu et al., 2018).

For MoS$_n$4, rejection-free kMC reaches a closely related conclusion. Growth speed increases strongly with adsorption rate and is reported as

$_n$5

Compact triangles persist only when edge migration is sufficiently rapid; otherwise higher adsorption produces defective triangles and then branched flakes. On patterned substrates, adsorption asymmetry directs preferential growth, but the practical window for retaining compactness is roughly adsorption ratios below $_n$6 (Aldana et al., 2024).

Continuum theories recover analogous control laws at larger length scales. For a circular single domain fed by diffusing adsorbates, the Stefan problem gives $_n$7, while the reaction-limited limit becomes

$_n$8

Stopping deposition reverses the sign of the driving term and yields shrinkage (Seki, 2019). In catalytic CVD of graphene on Cu, Langmuir adsorption theory and 2D crystallization lead to a self-limited saturation coverage

$_n$9

which separates no-graphene, partial-coverage, and continuous-layer regimes (Kim et al., 2013).

These models collectively indicate that adsorption-controlled growth in 2D systems is not reducible to flux maximization. The decisive balance is among supply, residence time, edge mobility, and the substrate’s local adsorption landscape.

5. Beyond epitaxy: confined adsorption, framework assembly, and physical adsorption

Adsorption-controlled growth also describes progressive occupation of confined media. In mesoporous silica with $2\ \text{ML/cycle}$0 pores, adsorption of 5CB from 5CB/methanol mixtures produces a type-II-like capacitance isotherm that is fitted at low to intermediate concentration by a generalized BET-type relation,

$2\ \text{ML/cycle}$1

The fitted monolayer capacity $2\ \text{ML/cycle}$2 corresponds to $2\ \text{ML/cycle}$3, consistent with flat-lying 5CB molecules at the pore wall. At higher 5CB concentration, the model underestimates the measured adsorption, which was interpreted as a transition from wall-film growth to pore-center filling analogous to capillary condensation (Kityk et al., 2021).

Constant-chemical-potential simulations of ZIF-8 proto-crystal growth extend the concept to framework assembly. The simulation combines C$2\ \text{ML/cycle}$4MD with particle insertion to maintain reactant concentrations, detects short oligomers that adsorb and then rearrange at the growth front, and finds defect-rich layers containing 3-, 5-, and 7-membered rings. Higher concentration and higher temperature increase the Kullback–Leibler deviation from the crystal template, favor larger rings, and produce a non-linear dependence of growth rate on concentration that was taken to suggest adsorption-controlled rather than diffusion-controlled growth (Gargari et al., 2 Dec 2025).

At the nanoscale, the adsorption energetics that underlie such regimes can themselves become nonlocal. Many-body analyses of physical adsorption show deviations from local-dielectric Lifshitz–Zaremba–Kohn power laws over experimentally relevant distances, extending up to $2\ \text{ML/cycle}$5–$2\ \text{ML/cycle}$6 and, for graphene and related 2D substrates, beyond $2\ \text{ML/cycle}$7. Because adsorption strength then depends on substrate dimensionality, collective response, and adsorbate excitation frequency, this suggests that physical adsorption can itself be engineered as a control parameter for nucleation, wetting, and deposition (Ambrosetti et al., 2017).

6. Experimental signatures, limitations, and recurring misconceptions

Experimental identification of adsorption-controlled growth usually relies on plateaus, invariances, or direct desorption signatures rather than on nominal source ratios. In BaTiO$2\ \text{ML/cycle}$8, the central signature is the plateau in $2\ \text{ML/cycle}$9 at $4.040 \pm 0.003\ \text{Å}$00 for TTIP/Ba BEP $4.040 \pm 0.003\ \text{Å}$01–$4.040 \pm 0.003\ \text{Å}$02 (Choo et al., 4 Oct 2025). In FeVSb, the 002 peak position and the out-of-plane lattice parameter plateau near $4.040 \pm 0.003\ \text{Å}$03 within the growth window (Shourov et al., 2020). In c-plane sapphire, the adsorption-controlled regime is marked by a reduced growth rate, growth-rate independence from Al supply at $4.040 \pm 0.003\ \text{Å}$04C and $4.040 \pm 0.003\ \text{Å}$05, and a growth-rate increase with oxygen pressure over $4.040 \pm 0.003\ \text{Å}$06 to $4.040 \pm 0.003\ \text{Å}$07 (Majer et al., 2024). In LaInO$4.040 \pm 0.003\ \text{Å}$08, line-of-sight QMS directly tracks the indium-containing desorption signal that makes the self-limiting regime possible (Hoffmann et al., 2022).

A common misconception is that adsorption control automatically implies a broad and forgiving process window. Several systems show the opposite. The experimental FeVSb window has a width of only a factor of about $4.040 \pm 0.003\ \text{Å}$09 to $4.040 \pm 0.003\ \text{Å}$10 in Sb partial pressure even though the thermodynamic prediction spans several decades (Shourov et al., 2020). For LaInO$4.040 \pm 0.003\ \text{Å}$11, the experimental window is significantly narrower than the TOMBE prediction (Hoffmann et al., 2022). For $4.040 \pm 0.003\ \text{Å}$12-GaSe, increasing growth and annealing temperature decreases mosaicity and smooths the surface, but also drives a transition from singly oriented $4.040 \pm 0.003\ \text{Å}$13 to twinned $4.040 \pm 0.003\ \text{Å}$14 with $4.040 \pm 0.003\ \text{Å}$15 rotated domains (Eickhoff et al., 6 Mar 2026).

A second misconception is that adsorption control necessarily fixes all stoichiometric degrees of freedom. FeVSb remains only semi adsorption-controlled because Fe/V control is unresolved (Shourov et al., 2020). CdTe in ICSSE reaches its self-regulated regime only after desorption reduces a larger BET-type Cd coverage to a stable $4.040 \pm 0.003\ \text{Å}$16 residual layer (Larramendi et al., 2019). BaTiO$4.040 \pm 0.003\ \text{Å}$17 membranes likewise show that stoichiometric control, membrane release, and functional response are coupled: Ba-rich films degrade the SrO sacrificial layer and transfer poorly, whereas stoichiometric films transfer successfully and retain crystallinity (Choo et al., 4 Oct 2025).

These results suggest that adsorption-controlled growth is best treated as a design principle. The target phase must be stable, at least one competing species or intermediate must remain volatile, and the surface kinetics must permit rejected material to desorb before defect formation, twinning, roughening, or phase separation lock it into the film. When that balance is achieved, adsorption control provides reproducible routes to stoichiometric oxides, magnetic chalcogenides, ferroelectric membranes, compact 2D domains, and regulated filling of confined media.