Density functional theory has become an indispensable tool for modeling nanoscale interfaces due to its ability to predict electronic structure with reasonable computational cost. The method provides atomic-scale insights into interface formation, charge redistribution, and electronic states that govern interfacial phenomena. Three major classes of interfaces benefit particularly from DFT analysis: metal-semiconductor junctions important for contacts, semiconductor-semiconductor interfaces crucial for heterostructures, and organic-inorganic hybrids relevant for emerging devices.

For metal-semiconductor interfaces, DFT calculations focus on Schottky barrier formation and charge transfer mechanisms. The Schottky barrier height is determined by calculating the potential difference between the metal Fermi level and semiconductor band edges after interface equilibration. Supercell models must include sufficient vacuum layers to prevent artificial interactions between periodic images. Typical calculations use slab models with 5-10 atomic layers of metal and semiconductor, where the central layers maintain bulk properties while interfacial atoms relax. Charge density difference plots reveal electron accumulation and depletion regions, with common observations of metal-induced gap states in the semiconductor near the interface. Work function modifications occur through interface dipole formation, where charge transfer between materials creates an electrostatic potential step. For example, DFT studies of Au-CdS interfaces show a 0.3 eV interfacial dipole reducing the Schottky barrier by 0.5 eV compared to the ideal metal work function prediction.

Semiconductor-semiconductor interfaces require accurate band alignment predictions through careful treatment of band gaps and offsets. The standard approach involves separate bulk calculations of each material using the same exchange-correlation functional, followed by interface calculations with aligned reference potentials. Two methods dominate: the core level alignment technique compares atomic core states deep within each material slab, while the potential lineup method integrates the electrostatic potential across the interface. Hybrid functionals or GW corrections often become necessary to overcome DFT band gap underestimation, particularly for type-II heterojunctions where both conduction and valence band offsets determine carrier confinement. In GaAs-AlAs interfaces, DFT predicts a valence band offset of 0.45 eV and conduction band offset of 0.35 eV, consistent with experimental measurements within 0.1 eV error. Interface states appear as localized electronic states within the band gap, analyzed through projected density of states calculations that decompose contributions from specific atomic layers.

Organic-inorganic interfaces present unique challenges due to weak van der Waals interactions and molecular flexibility. DFT treatments require dispersion-corrected functionals to properly describe physisorption energetics. Charge transfer at these interfaces often involves partial electron donation quantified through Bader analysis or Mulliken population methods. The electronic coupling between molecular orbitals and inorganic substrate states determines interfacial transport properties, evaluated through overlap integrals of frontier orbitals. For instance, benzene adsorbed on Cu(111) shows charge transfer of 0.05 electrons per molecule through DFT calculations, with the molecular LUMO hybridizing with metal surface states. Band alignment methods adapt to molecular systems by referencing the highest occupied molecular orbital to the inorganic valence band maximum.

Supercell design critically impacts all interface calculations. The in-plane lattice constant typically matches one material or adopts an average value with tolerable strain below 3%. A 5x5 surface unit cell often suffices to isolate defects or adsorbates, while 1x1 cells may suffice for perfect interfaces. Convergence tests must verify that slab thickness and vacuum spacing exceed 10 Å to minimize finite-size effects. Dipole corrections apply when asymmetric charge distribution creates spurious electric fields across periodic boundaries. For polar interfaces like ZnO-ZnS, careful atomic termination and stoichiometry preservation prevent unphysical divergences in the electrostatic potential.

Work function modifications at interfaces arise from multiple mechanisms. Charge transfer creates interfacial dipoles that shift electrostatic potentials, while surface reconstruction or adsorption alters surface dipole layers. DFT calculations decompose these contributions through local potential analysis along the surface normal direction. Metal-oxide interfaces often exhibit work function changes exceeding 1 eV due to strong ionic bonding and charge redistribution. At Al-MgO interfaces, DFT predicts a 1.2 eV work function reduction compared to pristine Al surfaces, attributed to electron transfer from metal to oxide conduction band.

Schottky barrier predictions combine bulk and interface calculations. The bulk metal work function and semiconductor electron affinity provide initial estimates, while interface calculations account for chemical bonding effects. Barrier heights correlate with metal electronegativity, with reactive metals like Ti forming lower barriers on n-type semiconductors due to stronger interfacial bonding. For Au-Si interfaces, DFT predicts a Schottky barrier of 0.7 eV for electrons, matching experimental values within 0.1 eV accuracy when using hybrid functionals.

Heterojunction band offsets follow systematic trends across material systems. Lattice-matched semiconductors like GaAs-AlAs show minimal strain effects on band alignment, while lattice-mismatched systems like CdS-ZnO require strain compensation in supercells. The transitivity rule for band offsets holds within 0.1 eV for most DFT predictions across ternary compounds. Strain effects can modify offsets by up to 0.3 eV in highly mismatched systems like Ge-Si, where 4% compressive strain increases the conduction band offset by 0.2 eV according to DFT calculations.

Interface state analysis distinguishes intrinsic states from defect-related features. Intrinsic states arise from chemical bonding discontinuities and decay exponentially into both materials. Their energy distribution and localization length provide critical insights for carrier recombination and Fermi level pinning. Defect states introduce additional peaks in the gap region, with their charge transition levels calculated through total energy differences between charge states. At TiO2-metal interfaces, DFT identifies gap states 0.8 eV below the conduction band that facilitate electron transfer while inhibiting hole recombination.

Advanced techniques extend standard DFT interface modeling. Non-equilibrium Green's function methods enable charge transport calculations across interfaces, though these approach device-level analysis. Constrained DFT calculations isolate specific charge transfer processes by fixing charge densities in selected regions. Time-dependent DFT tracks electron dynamics during interfacial charge separation processes, particularly relevant for photovoltaic applications. Machine learning potentials trained on DFT data enable larger-scale interface simulations while preserving quantum mechanical accuracy.

The predictive power of DFT for nanoscale interfaces continues improving through methodological advancements and computational resources. Careful attention to convergence parameters, appropriate exchange-correlation functionals, and systematic validation against experimental data ensures reliable results. Future developments will address temperature effects, dynamic interface restructuring, and more accurate treatment of strongly correlated systems while maintaining computational feasibility for realistic interface models.