Sub-monolayer tracking of molecular states at buried interfaces

Direct, quantitative sensing of molecular state with depth

• The model’s three-slab analysis directly estimates tilt and density across energy, using 6 parameters rather than the Free model’s 84.The Free model fits four uniaxial tensor components per energy per slab; ML-DFT uses two parameters per slab.Source: Direct, quantitative sensing of… · p. 2, Figure 2 · p. 3
• The ML-DFT model fits the resonant series better than the Free model (average deviation 1.7σ vs 2.2σ) and indicates no measurable contamination or oxidation.It directly reads molecular tilt and density from a physically constrained model, while the Free model requires secondary interpretation.Source: Direct, quantitative sensing of… · pp. 2–3
• The bulk layer matches herringbone ZnPc, while surface and buried layers show distinct orientations and densities yet retain resonant anisotropy characteristic of oriented ZnPc.Unlike the Free model’s uncertain, sometimes unphysical optical parameters, the ML-DFT model reads these states directly; the Free model’s low-energy trends can also imply conflicting orientations.Source: Direct, quantitative sensing of… · pp. 3–4, Figure 3 · p. 4

Sub-monolayer interfacial physics

• The gradient model removes the slab model’s fringe phase shift, better reproduces the Brewster angle, and achieves the best fit with fewer parameters.It represents orientation as a smooth depth profile transitioning toward pinned states at the interfaces.Source: Sub-monolayer interfacial physics · p. 4
• The buried interface has lower density and a more face-on orientation, while the free surface relaxes to a lower tilt angle and slightly higher density than the bulk.The profile is consistent across independent films; the interfacial tilt requires sub-monolayer coverage and is below the diffraction limit, yet the model constrains it through energy- and polarization-dependent scattering.Source: Sub-monolayer interfacial physics · pp. 4–5, Figure 4 · p. 5

Surface vs bulk dynamics in film growth

• The observed gradient challenges substrate-patterning explanations of bulk orientation and instead supports competition between substrate adhesion and intermolecular π–π cohesion during growth.The proposed crossover is from low-dimensional interfacial coupling to the three-dimensional growth mechanism that sets bulk texture; boundary layers may also reflect a distinct, incompletely crystallized state rather than contamination or oxidation.Source: Surface vs bulk dynamics in film growth · p. 5
• The analysis is presented as applicable beyond ZnPc films, including other molecular systems, polymers, alloys, mixed oxidation states, and scattering geometries beyond reflectivity.The authors also identify crystal growth, kinetic deposition, and solvent interaction as areas for quantitative study; supplementary materials and data are available online.Source: Surface vs bulk dynamics in film growth · pp. 5–6, Online content · p. 6

Film growth

• ZnPc films were deposited by physical vapor deposition on silicon, either directly or over a 3 nm CuI patterning layer, with substrate temperature varied for CuI samples.Films were approximately 20 nm thick; RSoXS samples were stored under inert nitrogen and transported under vacuum.Source: Methods · p. 8

Pre-characterization

• VASE, GIXRD, AFM, and angle-resolved NEXAFS provided complementary measurements of optical constants, crystal texture, surface morphology, and molecular orientation.NEXAFS tilt was refined using DFT-derived transition-dipole cluster orientations against the experimental spectra.Source: Methods · p. 8

RSoXS collection and reduction

• Polarized reflectivity was collected across 21 photon energies, reduced into continuous profiles, and assigned uncertainties combining per-pixel intensity error with a q-dependent envelope.The envelope accounts for increasing ambiguity between specular and diffuse reflectivity at higher q.Source: Methods · pp. 8–9

RSoXS modeling

• A global fit compared free tensor optical parameters with a DFT-based model that represents each slab by molecular orientation and density.All energies and polarizations share structural parameters; the DFT model uses 101 varying parameters, versus 350 for the free tensor model.Source: Methods · p. 9

Structural reconstruction

• A relaxed ZnPc unit cell and force field informed a molecular-dynamics reconstruction that combines fitted depth profiles with structural measurements for visualization.The illustrated packing density is made self-consistent with the fitted density and orientation gradients; the reported spacing comparison is a secondary consistency check.Source: Methods · pp. 9–10

1.1. Variable angle spectroscopic ellipsometry

• The VASE-derived optical constants show a split Q band at 1.98 and 1.80 eV, and the higher-energy peak is more intense, consistent with edge-on herringbone ZnPc.The ZnPc layer thickness was 21.4(5) nm.Source: §1.1 · p. 11, Figure S1 · p. 11

1.2. Grazing incidence wide angle X-ray scattering

• GIWAXS reflections at d = 12.6 Å out of plane and at 11.8 Å in plane, together with π–π stacking, agree with edge-on textured ZnPc on weakly interacting oxides.The 12.6 Å spacing matches relaxed γ-ZnPc rather than the strained spacing reported for initial growth layers.Source: §1.2 · p. 11, Figure S2 · p. 11

1.3. Atomic force microscopy

• AFM was used to pre-characterize film surface morphology and roughness for the reflectivity measurements.The same-batch ZnPc sample used for RSoXS had 0.8 nm RMS roughness.Source: Figure S3 · p. 11, §1.3 · p. 12

1.4. Effect or growth parameters for Copper (II) Iodide patterned films

• CuI-grown films had height variations exceeding 20 nm, indicating incomplete wetting and island-like Volmer–Weber growth; off-specular signal prevented reliable specular reflectivity reduction.At 100 °C, morphology depended most on deposition rate, with higher rate producing elongated domains and greater RMS roughness.Source: §1.4 · p. 12, Figure S4 · p. 12

1.5. NEXAFS Spectroscopy

• DFT-cluster refinement against NEXAFS yielded a molecular polar tilt of 74° and reduced χ² of 0.213, consistent with the study’s other ZnPc characterizations.The tilt is used as the coarse-grained molecular orientation for films measured under RSoXS.Source: §1.5 · p. 12, Figure S5 · p. 12

2. Optical Tensor Construction

• Experimental NEXAFS supplies imaginary β through mass absorption, while density scaling sets the specific-volume index and Kramers–Kronig calculation supplies δ.The absorption spectra are scaled to bare-atom mass absorption at density one before evaluating the index at a material density.Source: §2 · pp. 12–13
• Experimental dichroism, formed by averaging differences between incident-angle spectra, augments isotropic β to recover molecular-frame tensor components.The coefficients are chosen to accommodate the off-axis transition-dipole angle.Source: §2 · p. 13
• The DFT tensor uses directly calculated components for each transition-dipole cluster, requiring no auxiliary analyses.Source: §2 · p. 13

3. DFT Methods

• The ZnPc calculation used a crystallographic molecular geometry because it initially agreed better with experiment than thermodynamically relaxed or force-field-relaxed structures.StoBe transition-potential calculations used HCH for transition energies, transition-dipole moments, and oscillator strengths, with ΔKS fixing absolute transition energies.Source: §3 · p. 13
• Four chemically distinct carbon atoms reproduce ZnPc’s possible transitions in a useful scattering-analysis optical model; larger sets offered no accuracy gain.The tested larger sets used eight carbons of the outer wing or sixteen carbons from half the molecule.Source: §3 · p. 13, Figure S6 · p. 13

3.1. Clustering and Refinement

• Clustering parameters were selected by reduced chi square against experimental NEXAFS, then checked for small differences from the original DFT parameters.The chosen values were OS = .25 and OVP = 52.5; OVP values from 50 to 55 converged well, while larger OS degraded agreement with the originating DFT.Source: §3.1 · p. 13

4. Optical model parameterization

• The model assumes single-molecule DFT represents the film’s available electronic states, and its agreement with the experimental optical model suggests packing- or alignment-induced states are not dominant in ZnPc.Source: §4 · p. 13
• For a uniaxial film, molecular order is parameterized by tilt γ, and the molecular tensor is rotated and uniformly averaged over azimuth.The tensor is azimuthally symmetric, so its off-diagonal components vanish; a density scale factor is applied.Source: §4 · pp. 13–14
• The model’s isotropic orientation condition occurs at the 54.7° magic angle, consistent with Stöhr.Source: §4 · p. 14

5.1. RSoXS Collection

• Measurements began in s-polarization at 250 eV, with axis realignment every ten energies and recalibration between polarizations after a 30-minute wait.Polystyrene transmission NEXAFS calibration at the start and end showed no energy drift during the 12-hour experiment.Source: §5.1 · p. 14

5.2. Reflectivity Reduction

• Reflectance is calculated from background-subtracted specular intensity divided by incident intensity; overlapping q subsets provide effective incident intensity for long scans.Source: §5.2 · p. 14

5.3. Error Approximations

• Per-pixel photon-counting uncertainty is approximated as √N, with a Fano factor scaling Poisson noise and a q-dependent envelope increasing uncertainty at higher q.The envelope accounts for specular/off-specular discrimination uncertainty from surface scattering and roughness.Source: §5.3 · p. 14
• The optical-constant comparison shows tensor components β and δ, alongside extracted orientation and density; density has lower inter-energy variance than orientation.The caption compares direct DFT-refined orientation with per-energy orientation from a secondary full-tensor refinement.Source: Figure S8 · p. 15

5.4. RSoXS Analysis Methods

• The film model contains surface, bulk, and interface ZnPc layers above native SiO2 and silicon, with layer thickness and roughness parameterizing structure.A 4×4 transfer-matrix formalism computes reflection and transmission; interfacial roughness is represented with Nèvot–Croce attenuation.Source: §5.4 · p. 15
• The DFT model describes the same structure with 17 parameters versus 266 for the free-tensor model, reducing optical-model complexity by more than an order of magnitude.These counts describe the model before the per-energy experimental correction terms, which bring totals to 101 for DFT and 350 for the free-tensor model.Source: §5.4 · pp. 15–16
• The free-tensor model uses full tensor complexity, whereas earlier dichroic-ratio approaches do not enforce cross-energy Kramers–Kronig or molecular-orientation consistency.Experimental correction parameters can correlate with structure and optics without appropriate bounds; the authors recommend adding them only when realistic structural and optical parameters cannot reproduce the first fringe.Source: §5.4 · pp. 15–16

• The model represents density and orientation as deviations from bulk values and uses gradient penalties to oppose abrupt changes through the film.Source: §6 · p. 16
• Density and orientation deviations are coupled through a quadratic expansion of the bulk free energy, with a bilinear term linking the two fields.Source: §6 · p. 16
• Minimizing the free energy yields coupled second-order equations; Robin boundary conditions relate order-parameter gradients to surface fields, while strong anchoring fixes interfacial values.Source: §6 · pp. 16–17
• Coupling gives density and orientation shared coherence lengths; the proposed profiles sum exponential contributions decaying from the vacuum and silicon interfaces.Source: §6 · p. 17
• The model is an empirical approximation; determining anchoring potentials requires resolving boundary conditions, and interfacial realignment may follow another mechanism.Source: §6 · p. 17
• Non-resonant X-ray reflectivity on a second sample supports a density gradient, but a single energy cannot independently determine the orientation gradient.Source: Figure S10 · p. 17
• Reconstructed packing is compared with GIWAXS sector cuts and measured d-spacings; the passage does not state the comparison outcome.Source: Figure S11 · p. 18
• Molecular-dynamics simulations use constructed ZnPc crystal cells, including an alpha-phase cell relaxed with LAMMPS at 300 K.Source: Figure S12 · p. 18, §6 · p. 18