DFT–FDTD Framework for Optoelectronic Simulation

• The DFT–FDTD framework is an integrated method that combines quantum-mechanical DFT for dielectric properties with FDTD to simulate full-field electrodynamics in complex devices.
• It converts atomistic electronic responses into wavelength-dependent refractive indices and extinction coefficients, enabling accurate predictions of absorption, emission, and field enhancement.
• Its applications span perovskite solar cells, PeLEDs, and plasmonic devices, offering a parameter-free route to optimize nanoscale optoelectronic performance.

A Density Functional Theory–Finite-Difference Time-Domain (DFT–FDTD) framework combines ab initio electronic-structure calculations with electrodynamics simulations to deliver predictive, composition-specific modeling of optical phenomena in functional materials and devices. DFT determines the atomistic dielectric response by resolving band structure and electronic transitions, while FDTD propagates Maxwell’s equations using those material parameters to simulate device or nanostructure–level performance. This integrated workflow enables parameter-free prediction and optimization of properties such as absorption, emission, and field enhancement in photovoltaics, light-emitting diodes (LEDs), plasmonic pixel arrays, and other optoelectronic systems (Saffari et al., 2017, Debnath et al., 19 Dec 2025, Islam et al., 9 Jun 2025).

1. Fundamental Elements of the DFT–FDTD Workflow

The DFT–FDTD methodology is a two-stage computational pipeline:

1. Electronic-structure calculation (DFT) computes the complex dielectric tensor $$\varepsilon(\omega)=\varepsilon_1(\omega)+i\varepsilon_2(\omega)$$, bandgap, and dispersion directly from the atomic arrangement and composition. Optical constants—the real refractive index $n(\omega)$ and extinction coefficient $k(\omega)$—are extracted via:

$$n(\omega)=\sqrt{\frac{\sqrt{\varepsilon_1^2+\varepsilon_2^2}+\varepsilon_1}{2}},\qquad k(\omega)=\sqrt{\frac{\sqrt{\varepsilon_1^2+\varepsilon_2^2}-\varepsilon_1}{2}}$$

2. Electrodynamics simulation (FDTD) uses $n(\omega)$ and $k(\omega)$ as wavelength-dependent inputs. FDTD numerically solves Maxwell’s equations in complex device geometries with actual atomic-scale, material-specific electromagnetic response, enabling accurate predictions for light absorption, reflection, and emission.

This decoupling allows first-principles accuracy at the electronic/material scale and full-field propagation at the device scale (Saffari et al., 2017, Debnath et al., 19 Dec 2025, Islam et al., 9 Jun 2025).

2. DFT Protocols for Dielectric Function Extraction

DFT calculations employ periodic-boundary plane-wave codes (e.g., CASTEP) with GGA-PBE functionals, sometimes augmented by van-der-Waals corrections or Grimme’s D2 for dispersion interactions. Core electrons are treated with norm-conserving or ultrasoft pseudopotentials.

Key parameters:

• Plane-wave cutoff energy: 200 Ry (2,720 eV) for perovskites (Saffari et al., 2017), 500 eV for CsSn$_x$Ge$_{1-x}$I$_3$ (Debnath et al., 19 Dec 2025).
• Brillouin-zone sampling: Dense Monkhorst–Pack grids (e.g., 8×8×8 for relaxations, 50×50×50 for optical spectra in perovskites (Saffari et al., 2017)).
• Geometry optimization: Energy and force convergence below 1×10⁻⁶ eV and 0.01 eV/Å (Debnath et al., 19 Dec 2025), or similar.
• For polymers, 1D supercells with k-meshes tailored for each chain’s symmetry (Islam et al., 9 Jun 2025).

The imaginary part $\varepsilon_2(\omega)$ is assembled from interband transition matrix elements in the long-wavelength limit. The real part $\varepsilon_1(\omega)$ is then retrieved via the Kramers–Kronig transform. These permit a direct, atomistically grounded linkage to measured optical constants (Debnath et al., 19 Dec 2025, Islam et al., 9 Jun 2025).

3. Interfacing DFT Output to FDTD: Data Processing and Import

DFT-derived $\varepsilon_1(\omega)$ and $\varepsilon_2(\omega)$ are tabulated across the relevant spectral window (typ. 400–1,000 nm). Data processing involves:

• Interpolating (e.g., via cubic splines) and smoothing (e.g., Savitzky–Golay filters) to remove DFT artifacts while retaining resonances (Islam et al., 9 Jun 2025).
• Computing $n(\lambda)$ and $k(\lambda)$ as per the relations above.
• Outputting ASCII files of the format: wavelength (nm), $n$, $k$.
• Importing these files into the FDTD solver as user-defined dispersive materials (“multi-coefficient” or “imported refractive index”), ensuring the FDTD engine can apply piecewise-dispersive or auxiliary-differential-equation models at every step (Saffari et al., 2017, Debnath et al., 19 Dec 2025, Islam et al., 9 Jun 2025).
• For metals (e.g., Au, TiN), Drude–Lorentz parameterizations are used; see the cited work for the equations and implementation (Islam et al., 9 Jun 2025).

4. FDTD Simulation Methodology: Structure, Meshing, and Analysis

FDTD simulations proceed on an explicit Yee mesh, where spatial and temporal steps are chosen by the Courant criterion ($\Delta t = S \cdot \Delta x / (c\sqrt{3})$ with $S < 1$ for stability).

Device architecture and boundary conditions are system-specific:

• Perovskite solar cells and LEDs: Layer stacks (AR, TCO, transport layers, absorber, reflector) of nanometric thicknesses, with meshing at $\sim$5–10 nm, refined below 2 nm at plasmonic hotspots (Saffari et al., 2017, Debnath et al., 19 Dec 2025).
• Plasmonic nanopixels: Core-shell geometries with conductive polymers, mesh refinement in the near-field gap, custom geometries including bow tie and gear for spectral engineering (Islam et al., 9 Jun 2025).

Boundary treatments include perfectly matched layers (PMLs) for open boundaries and periodic (or Bloch) conditions to mimic extended arrays. Broadband sources (total-field/scattered-field or plane wave) are used, with spectral monitoring of transmission, reflection, scattering cross-section, and local fields.

Post-processed quantities include:

• Absorption spectra: $A(\lambda) = 1 - R(\lambda) - T(\lambda)$
• Photogenerated current: $$J_{\rm ph} = e \int_\lambda A(\lambda)\Phi_{\rm ph}(\lambda)\,d\lambda$$, with $\Phi_{\rm ph}$ photon flux from AM1.5G
• Purcell factor and light-extraction efficiency (LEE) for emitters, calculated using power integrals over solid angles and spectral overlap integrals (Debnath et al., 19 Dec 2025).

5. Paradigmatic Applications: Perovskite Solar Cells, LEDs, Nanopixels

Perovskite Solar Cells: DFT–FDTD modeling reveals that increasing Cl content in CH$_3$NH$_3$PbI$_{3-x}$Cl$_x$ increases the bandgap (from 1.50 to 2.60 eV for $x=0 \rightarrow 3$) and decreases both lattice constant and refractive index ($n_{\rm max}:2.6\rightarrow1.8$). FDTD simulations show optimized anti-reflection and light-trapping layers (e.g., SiO$_2$/Si$_3$N$_4$ pyramids) can boost absorption from 72% to 83.13% and $J_{\rm sc}$ from 20.8 to 23.34 mA/cm$^2$ (Saffari et al., 2017).

PeLEDs and Plasmonic Enhancement: The DFT–FDTD workflow supports compositional tuning and engineered nanostructuring. In CsSn$_x$Ge$_{1-x}$I$_3$ PeLEDs, $n$ varies from 2.55 to 2.20 (over $\lambda_{\rm em} = 643$–931 nm), with Purcell factors reaching 12.1×, LEE up to 25%, and 36% enhancement versus planar reference. Spectral overlap between emitter and plasmonic resonance can be maximized (up to 96%) by tuning the Au/SiO$_2$ nanorod aspect ratio. CsSn$_{0.5}$Ge$_{0.5}$I$_3$ offers a balance between extraction efficiency, Purcell enhancement, and stability (Debnath et al., 19 Dec 2025).

Plasmonic Nanopixels: For core-shell electrochromic devices, the framework enables nm-precision tuning of coloration, with 40–100 nm spectral shifts and systematic CIE color analysis. The DFT–FDTD protocol produces an atomistically rigorous pathway from molecular structure (polymer redox state) to optical color rendering (Islam et al., 9 Jun 2025).

6. Generalization and Impact Across Material Systems

The DFT–FDTD architecture is generalizable to a wide range of functional materials, including but not limited to perovskites, chalcogenides, conductive polymers, and emerging LED constituents:

• DFT or TD-DFT determines $\varepsilon(\omega)$ for arbitrary compositions and configurations.
• Standardized processing and import pipelines allow device-agnostic FDTD simulation.
• Output metrics (absorption spectra, $J_{\rm sc}$, Purcell enhancement, LEE, or colorimetric parameters) are directly comparable with experimental and design targets.

A principal consequence is rapid, in silico optimization of both composition and nanostructure for targeted spectra, efficiency, or field enhancement, linking atomistic detail with device-scale photonics. This enables rational discovery and engineering of optoelectronic materials beyond empirical tuning (Saffari et al., 2017, Debnath et al., 19 Dec 2025, Islam et al., 9 Jun 2025).

7. Tables: Summary of Key DFT–FDTD Framework Parameters

Material/System	DFT Parameters (cutoff, $k$-mesh)	Device/FDTD Stack and Highlights
CH$_3$NH$_3$PbI$_{3-x}$Cl$_x$ SCs	200 Ry, 8×8×8 (geom), 50×50×50 (opt)	SiO$_2$/ITO/PEDOT:PSS/Perovskite/PC$_{60}$BM/Ag; LT pyramids, $J_{\rm sc}$ boosts to 23.34 mA/cm$^2$
CsSn$_x$Ge$_{1-x}$I$_3$ PeLEDs	500 eV, 6×6×6	Ag/ZnO/Perovskite/Spiro-OMeTAD/ITO; Au/SiO$_2$ nanorods, LEE 25%, Purcell $12.1\times$
Au/Polymer Nanopixels	CASTEP, PBE-GGA, k-mesh 2–32 points	Au core/polymer shell/(mirror), TFSF source, 100 nm tuning, CIE color evaluation