This tracks what I’ve learned about method capabilities and failure modes through direct use.

Each entry documents what a method constrains well, what it can’t distinguish, and when I’ve seen it fail (or almost fail) in my own work.

Not exhaustive. Not authoritative. Just what I’ve encountered so far across 5 undergraduate projects and 1 industry internship.

Last updated: March 2026  ·  Experience: ~2 years computational materials science, 1 summer semiconductor metrology

Quick reference

Filter by domain or click a method to jump to the full entry.

Method Primary limit Used in
DFT (PBE) Band gap underestimation, self-interaction error AlN, g-C₃N₄, alloy sampling
DFT (HSE06) No excitonic effects, cost limits cell size g-C₃N₄, AlN (planned)
Optical response (DFT) Independent-particle approximation, frozen lattice g-C₃N₄, AlN
RCWA Inverse non-uniqueness, periodicity assumption Inverse RCWA metrology
XRD Amorphous/nanocrystalline ambiguity, thin film limits AlN
UV–Vis Depth averaging, scattering vs absorption ambiguity AlN
AFM Surface only, tip convolution, single-area bias AlN
Dispersion models Non-unique mechanism assignment, extrapolation failure Inverse RCWA metrology
Identifiability Model class not tested, single-run optimization Inverse RCWA, port metasurface
Configuration sampling Combinatorial explosion, non-equilibrium synthesis Alloy sampling, g-C₃N₄
EM simulation Environment non-identifiability, single-scenario overfit Port metasurface

DFT (PBE)

Reference: Perdew, Burke, Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

Constrains well:

  • Relative energies of similar structures (<50 meV/atom when converged)
  • Equilibrium geometries for covalent/ionic solids (~0.02 Å bond lengths)
  • Qualitative orbital character and bonding trends

Cannot distinguish:

  • Optical gaps from transport gaps (systematic 30-100% underestimation)
  • Defect ionization energies (±0.5 eV uncertainty)
  • Strongly vs. weakly correlated regimes (self-interaction error)

Assumptions:

  • Ground-state density uniquely determines properties (Hohenberg-Kohn)
  • Non-interacting quasiparticles in effective potential
  • Semi-local exchange-correlation functional
  • Born-Oppenheimer approximation (classical nuclei)

Fails when:

  • Open-shell transition metals, stretched bonds (static correlation)
  • van der Waals interactions dominate (unless dispersion-corrected)
  • Predicting optical spectra without experimental calibration
  • Energy differences <10 meV/atom used as definitive

Trust when:

  • Comparing energies within same structure class
  • Explicit convergence tests (k-points, cutoff, cell size, smearing)
  • Cross-validated against experiment or higher-level methods for calibration

Misleading when:

  • Band gap “agreement” within 0.5 eV claimed as validation (error cancellation)
  • Single relaxed structure treated as representative under disorder
  • Small energy differences used to rank mechanisms without uncertainty

Used in: AlN electroabsorption, g-C₃N₄ optical, Alloy sampling

DFT (hybrid functionals)

Reference: Heyd, Scuseria, Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

Constrains well:

  • Band gaps (typically within 0.2-0.5 eV of experiment for semiconductors)
  • Band-edge placement relative to vacuum level
  • Localized vs. delocalized state character in defect systems

Cannot distinguish:

  • Excitonic effects (needs BSE or TDDFT)
  • Correct gaps when structural model is wrong
  • Optical vs. fundamental gaps (missing electron-hole interaction)

Assumptions:

  • Screened exact exchange improves self-interaction error
  • Mixing parameter (α = 0.25) and screening length (ω) are system-transferable
  • Frozen-ion approximation (no vibronic coupling)

Fails when:

  • Strong correlation remains (Mott insulators, f-electron systems)
  • Computational cost forces small supercells (finite-size errors)
  • Applied to systems where PBE structural prediction was already wrong

Trust when:

  • Finite-size convergence demonstrated (supercell size, k-points)
  • Structural model independently validated
  • Calibrated against experiment for similar material class

Misleading when:

  • Better numbers on wrong structure interpreted as improved physics
  • Quantitative optical predictions made without excitonic corrections
  • Computational cost prevents proper convergence testing

Used in: g-C₃N₄ optical, AlN electroabsorption (planned)

Optical response from electronic structure

Reference: Gajdoš et al., Phys. Rev. B 73, 045112 (2006) [for VASP implementation]

Constrains well:

  • Qualitative trends: how symmetry breaking, doping, defects shift absorption onset
  • Relative oscillator strength changes under perturbations
  • Selection rule violations from symmetry breaking

Cannot distinguish:

  • Specific peak assignments under structural disorder
  • Contributions from different defect species with similar energetics
  • Excitonic vs. single-particle transitions (independent-particle approximation)

Assumptions:

  • Independent-particle transitions (no electron-hole interaction)
  • Dipole approximation (long-wavelength limit)
  • Frozen lattice (no vibronic coupling or thermal disorder)
  • Structural model represents measured sample

Fails when:

  • Excitonic effects dominate (requires BSE)
  • Multiple structural motifs contribute to same spectral region
  • Local-field effects are strong (needs full GW-BSE)
  • Disorder averaging is significant but not sampled

Trust when:

  • Structural model space tightly constrained by independent measurements
  • Claims restricted to trends, not absolute peak positions
  • Configuration sampling performed when disorder expected

Misleading when:

  • Single-configuration spectrum treated as “the material’s spectrum”
  • Peak agreement used to validate structural model (circular reasoning)
  • Effective parameters adjusted to match experiment without physical justification

Used in: g-C₃N₄ optical, AlN electroabsorption (defect level analysis)

RCWA

Reference: Moharam et al., J. Opt. Soc. Am. A 12, 1068 (1995)

Constrains well:

  • Forward spectral response of periodic structures (exact within numerical precision when converged)
  • Sensitivity of reflectance/transmittance to geometric parameters
  • Angle and polarization dependence for periodic media

Cannot distinguish:

  • Multiple (geometry, index) pairs producing identical far-field spectra (inverse non-uniqueness)
  • Material dispersion mechanisms (all effective models fit equally well)
  • Sub-wavelength defects (spatial averaging over unit cell)

Assumptions:

  • Perfect periodicity (Floquet-Bloch boundary conditions)
  • Linear optical response (no saturation, no nonlinear effects)
  • Local material response (no spatial dispersion)
  • Layers laterally infinite (edge effects ignored)

Fails when:

  • High aspect ratios without sufficient Fourier orders (need 50-100+)
  • Plasmonic resonances near ε ≈ -1 (numerical instability)
  • Real samples violate periodicity (roughness, line-edge roughness, thickness variation)
  • Convergence not verified (under-resolved features mimic physical effects)

Trust when:

  • Convergence explicitly tested (<1% change with added Fourier orders)
  • Forward modeling with independently characterized materials
  • Comparing relative trends (design A vs. B), not absolute parameter extraction

Misleading when:

  • Inverse fitting without identifiability analysis (covariance, multi-start, posterior)
  • Effective dispersion used to absorb modeling error, then interpreted physically
  • Single best-fit geometry reported without uncertainty or degeneracy analysis

Used in: Inverse RCWA metrology

XRD

Reference: Standard X-ray diffraction technique

Constrains well:

  • Presence/absence of crystalline phases (above detection limit)
  • Lattice parameters and preferred orientation (well-crystallized samples)
  • Phase identification via peak indexing against databases

Cannot distinguish:

  • Amorphous structure details beyond “no crystalline peaks”
  • Thin film crystallinity when substrate peaks dominate
  • Nanocrystalline (<3-5 nm domains) from truly amorphous

Assumptions:

  • Sufficient scattering volume and crystallite size
  • Bragg condition satisfied (constructive interference from periodic lattices)
  • Known reference phases for identification
  • Negligible texture (or corrected for)

Fails when:

  • Film thickness <50 nm without grazing-incidence geometry
  • Low atomic number contrast (e.g., carbon-based materials, light-element compounds)
  • Mixed amorphous/nanocrystalline regimes without complementary probes
  • Substrate peaks misidentified as film phases

Trust when:

  • Appropriate scan geometry for thin films (GIXRD, not symmetric θ-2θ)
  • Detection limits explicitly stated (integration time, background level, signal-to-noise)
  • Multiple reflections confirm phase assignment (not single-peak identification)

Misleading when:

  • “No peaks observed = amorphous” without reporting detection limits
  • Quantitative crystallinity claims without Rietveld refinement or calibrated standards
  • Thin film measurements without accounting for substrate contribution

Used in: AlN electroabsorption

UV–Vis spectroscopy

Reference: Standard optical transmission/reflection spectroscopy

Constrains well:

  • Relative spectral changes under controlled perturbations (bias, temperature, processing)
  • Absorption onset identification (when background stable)
  • Spectral weight redistribution under systematic variations

Cannot distinguish:

  • Depth-localized absorption mechanisms (averages over penetration depth)
  • Surface vs. bulk contributions without angle-resolved measurements
  • Absorption from scattering when both present

Assumptions:

  • Beer-Lambert law applies (linear regime, uniform absorption)
  • Baseline drift and instrument response stable
  • Sample homogeneity over beam spot size
  • Reflected/transmitted intensity accurately measured

Fails when:

  • Scattering dominates (Mie scattering, surface roughness comparable to λ)
  • Strong baseline drift or calibration errors mask real changes
  • Film thickness variations across sample produce effective spectral broadening
  • Absorption length « film thickness (saturation effects)

Trust when:

  • Reproducibility demonstrated across multiple samples/cycles
  • Baseline and instrument response carefully characterized
  • Complementary structural probes verify no morphology changes
  • Absorption changes >3× measurement noise

Misleading when:

  • Spectral agreement claimed without uncertainty quantification
  • Single measurement treated as definitive without reproducibility check
  • Scattering-driven changes misinterpreted as absorption changes
  • Depth-averaged signal used to infer depth-localized mechanism

Used in: AlN electroabsorption

AFM

Reference: Standard atomic force microscopy

Constrains well:

  • Surface topography at nm-scale vertical resolution
  • RMS roughness statistics (when sampling representative)
  • Relative morphology changes across processing conditions

Cannot distinguish:

  • Bulk vs. surface-localized features (surface-only probe)
  • Material composition (purely topographic)
  • Whether imaged region represents full sample

Assumptions:

  • Tip-sample interaction well-modeled (contact, tapping, non-contact modes)
  • Scan parameters (speed, setpoint, gain) properly optimized
  • Surface features within tip bandwidth and z-range

Fails when:

  • Tip convolution for high-aspect-ratio features (>3:1 typically)
  • Limited scan area misses dominant length scales
  • Surface contamination or adsorbates alter apparent topography
  • Soft samples deform under tip force

Trust when:

  • Multiple scan regions confirm representativity
  • Roughness reported with uncertainty across regions
  • Tip condition verified (sharp, not damaged or contaminated)
  • Scan parameters stable and appropriate for sample

Misleading when:

  • Single small-area scan claimed as representative
  • Tip artifacts misidentified as sample features
  • Surface roughness extrapolated to bulk structure claims
  • Quantitative height measurements without calibration

Used in: AlN electroabsorption

Dispersion models

Reference: Various (Drude, Lorentz, Sellmeier, Tauc-Lorentz, Cauchy, etc.)

Constrains well:

  • Compact parametric representation for interpolation within measured range
  • Smooth refractive index/extinction vs. wavelength for forward modeling

Cannot distinguish:

  • Physical mechanism uniquely (multiple model forms fit identically)
  • Extrapolation behavior outside fitted range
  • Whether parameters have physical meaning vs. being effective

Assumptions:

  • Model functional form captures relevant physics
  • Parameters are wavelength/angle-independent (within model domain)
  • Kramers-Kronig consistency enforced (or assumed negligible violation)

Fails when:

  • Over-parameterization hides non-uniqueness (more parameters → better fit, worse identifiability)
  • Extrapolated beyond measurement range (unphysical behavior common)
  • Model selection based only on χ² without complexity penalty

Trust when:

  • Model comparison performed (AIC, BIC, or cross-validation)
  • Parameters physically motivated, not just free fits
  • Uncertainty propagated from measurement noise to model parameters
  • Used only for interpolation within measured range

Misleading when:

  • Best-fit parameters interpreted physically without justification
  • Multiple models fit equally well but claimed to reveal different physics
  • Dispersion model absorbs systematic errors (geometry, roughness, etc.)

Used in: Inverse RCWA metrology

Identifiability and uncertainty

Reference: Sethian & Wiegmann (concept); Tarantola (inverse problems); see also “Practical identifiability” literature

Constrains well:

  • Which parameters data can actually resolve
  • Sensitivity and covariance structure
  • Whether multiple solutions exist with similar fit quality

Cannot distinguish:

  • Truth of model class itself (only parameters within chosen model)
  • Out-of-sample generalization without new data

Assumptions:

  • Forward model adequately represents system
  • Measurement noise characterized correctly
  • Parameter space explored sufficiently (local vs. global minima)

Fails when:

  • Only single optimization run performed (misses multimodality)
  • Covariance ignored (independent-parameter assumption breaks)
  • Sensitivity calculated at single point (not representative of parameter space)

Trust when:

  • Multi-start optimization or posterior sampling shows convergence
  • Parameter sensitivity and covariance explicitly reported
  • Failure cases documented (which parameters are non-identifiable)
  • Priors stated explicitly and sensitivity to priors tested

Misleading when:

  • Good fit quality equated with unique parameter recovery
  • Uncertainty bars from fit statistics only (ignore model error)
  • Identifiable parameters claimed without covariance analysis

Used in: Inverse RCWA metrology, Port metasurface

Configuration sampling

Reference: Various (special quasirandom structures, cluster expansion, Monte Carlo)

Constrains well:

  • Representative trends within sampled configuration space
  • Ensemble-averaged properties when sampling weighted by energy
  • Sensitivity to structural motifs within model class

Cannot distinguish:

  • Rare but important configurations (if not sampled)
  • True equilibrium distribution without thermodynamic integration
  • Whether sampled space captures experimental reality

Assumptions:

  • Sampled configurations cover relevant configuration space
  • Supercell size sufficient (no strong finite-size effects)
  • Energy landscape adequately explored (no major metastable states missed)
  • Boltzmann weighting appropriate (thermal equilibrium assumed)

Fails when:

  • Configuration space grows faster than sampling can cover (combinatorial explosion)
  • Rare motifs with high impact are systematically missed
  • Kinetic barriers trap system in non-equilibrium configurations
  • Supercell too small for target property (artificial periodicity artifacts)

Trust when:

  • Sampling strategy justified by target property and system
  • Convergence with sample size demonstrated
  • Uncertainty quantified across sampled configurations
  • Results compared to experimental distributions where available

Misleading when:

  • Single configuration treated as ensemble representative
  • Sample size inadequate for statistical claims (e.g., <10 for variance estimates)
  • Equilibrium sampling applied to non-equilibrium synthesis

Used in: Alloy sampling, g-C₃N₄ optical

EM simulation in deployment settings

Reference: Various (CST, HFSS, COMSOL, custom FDTD/FEM codes)

Constrains well:

  • Forward trends under assumed boundary conditions and material models
  • Sensitivity to design parameters in idealized environments
  • Relative performance comparisons (design A vs. B)

Cannot distinguish:

  • Real-world performance under environment variability
  • Whether simulated environment matches deployment
  • Contributions from unmodeled effects (clutter, multipath, time-variation)

Assumptions:

  • Environment geometry and materials known/assumed
  • Boundary conditions representative of deployment
  • Static or quasi-static scene (no rapid time variation)
  • Linear material response (unless nonlinearity explicitly modeled)

Fails when:

  • Environment approximation dominates error (unknown clutter, ground properties)
  • Optimization overfits to specific simulated scenario
  • Hardware nonidealities not captured (fabrication tolerances, losses, coupling)
  • Dynamic scenes change faster than simulation update rate

Trust when:

  • Simulations validated against controlled measurements
  • Sensitivity to environment assumptions explicitly tested
  • Performance reported across scene ensemble, not single case
  • Hardware limitations included in model

Misleading when:

  • Single-scenario simulation treated as deployment guarantee
  • Environment idealized without justification or sensitivity analysis
  • Optimization produces designs brittle to small deviations

Used in: Port metasurface

Notes on this ledger

What this is: My working reference for methods I’ve actually used. Built from mistakes I’ve made or almost made.

What this isn’t: A comprehensive methods review. Authoritative assessments. Static — I expect to revise as I learn more.

How to use it: If you’re encountering similar problems, this might help. If you’re an expert, you’ll probably find things I got wrong — let me know.

Contact: anuraag.sharma22 [at] student.xjtlu.edu.cn

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