CD-SEM · 17,280 model combinations · MPI

Uncertainty Quantification for Simulation Metrology

A systematic uncertainty programme that tests how physical-model choices move simulated semiconductor-metrology signals.

Goal

Why this problem matters

The research is organised by scientific question rather than career stage, so the methods and results form one continuous programme.

Determine whether simulated nanometre-scale measurements remain reliable when their scattering and energy-loss models change.

Separate physical-model uncertainty from geometry effects and Monte Carlo statistical noise.

Method

How the problem is approached

01
Enumerate
Reproduce the published 17,280-profile campaign: 384 ELSEPA elastic-potential combinations × 3 dielectric models × 5 work functions × 3 optical ELF datasets.
02
Simulate
Run ensemble Monte Carlo campaigns with MPI and apply structured statistical post-processing to the resulting spatial fields.
03
Extend
Compare that published campaign with the broader catalogue of 3 inelastic formalisms × 4 available ELF datasets = 12 inelastic combinations, together with reported work-function and electron-affinity values.
04
Quantify
Build confidence intervals that expose how model-form choices affect the simulated measurement and how the spread changes with scan position.

Results

What the programme has established

Result 01The elastic-potential and work-function choices materially shift absolute signal intensity; the optical ELF and dielectric-model choices contribute a smaller spread in the published study.
Result 02The uncertainty envelope is non-uniform across the line scan, so a single constant error band would conceal the spatial dependence of model sensitivity.
Result 03Normalisation reduces intensity-scale variation while preserving the edge-sensitive line-shape comparison, separating model-driven spread from Monte Carlo noise.
Result 04Established a reusable framework for comparing emission and metrology predictions across candidate physics models.

Scientific animation

The mechanism, made visible

This interactive figure is an explanatory schematic. It is clearly separated from the peer-reviewed quantitative figures below.

Conceptual visualization

From model ensemble to a position-dependent uncertainty band

Candidate physical inputs produce a family of CD-SEM line-scan profiles. Their spread is strongly position-dependent: it widens near high-sensitivity edges and changes across the feature instead of forming a constant-width band.

Ready

Candidate model realizationOne elastic-potential, dielectric, optical-ELF, and work-function choice
Position-dependent uncertainty bandIts width changes with scan position—the key result
Mean line-scan profile, Ī(x)Central profile across the candidate model set

Published campaign: 17,280 model combinationsThe paper's 384 × 3 × 5 × 3 input campaign
Elastic model space: 384 ELSEPA potential combinationsUsed for comparison and model-selection uncertainty
Broader inelastic catalogue: 3 formalisms × 4 ELF datasets = 12LLM, FPA, and SMA with the supplied optical-data catalogue
Main finding: Band width varies with xA constant uncertainty band would erase the result

The profile shape follows the supplied CD-SEM evidence: a lateral line scan with edge-sensitive, non-uniform model spread. The animation is explanatory and does not reproduce numerical values from a single run.

Evidence