WS₂ is the TMD people reach for when they want a bright, direct-gap monolayer with strong spin–valley physics, and the one they fight with when they try to make it into a process. Growth leaves sulfur vacancies. Transfer leaves strain. Patterning leaves a damage halo that is invisible under the optical microscope and very visible in the device.

Raman and photoluminescence maps see all three, which is why every WS₂ team owns a confocal Raman system. The problem is turning a few thousand spectra into a decision. This post walks through what Atlas does with one real pair of maps, using the same analysis Blocks that run inside the Matter42 app, and states the limits of each result along the way.

The sample

A multilayer WS₂ flake on Si/SiO₂, patterned with a plasma focused-ion beam (PFIB) and then mapped on a Horiba LabRAM HR Evolution at 532 nm by a collaborating lab. Two LabSpec exports at roughly 1 µm pixel pitch, covering a 21 × 49 µm field:

Atlas parsed both into the same hyperspectral dataset model, identified the material as WS₂ from the Raman modes, and detected Si substrate lines in every pixel — this flake is thin enough for the 520 cm⁻¹ line to come through. Because the sample was PFIB-processed, the parse was told to expect a 2.5 µm damage buffer around milled boundaries; that value is stored on the dataset and inherited by every downstream Block.

The PFIB pattern is the useful part. Milled bands are total damage, the halo around them is partial damage, and the interior is as-grown material. One map contains the whole quality range a process engineer cares about.

First look: what is film, what is halo, what is bare substrate

Before any physics, Atlas needs to know which pixels to trust. Segment regions uses the quality mask, the stored boundary buffer, and the substrate lines to label the field.

Half the map is intact interior, a third is the transition halo, and a fifth is substrate the ion beam exposed. Every number below was computed on the interior only unless stated. That single choice is what separates "what is my WS₂ like" from "what is the average of my WS₂ and the damage I did to it".

A resonance trap, and how Atlas avoids it

At 532 nm, WS₂ is excited near its B exciton. That double-resonantly enhances the second-order 2LA(M) band at ~350 cm⁻¹, which sits directly on top of the E₂g mode most linewidth analyses depend on. Fit the region with one peak and you measure a composite that is almost twice as wide as the phonon.

Estimate defect density knows this. It checks the laser wavelength against the material's resonance table, fits the E₂g window with two components when it has to, and reports both numbers.

Three things in that card matter more than the headline percentage.

First, the resonance correction is applied and reported, not silently assumed. A 13.5 cm⁻¹ composite linewidth would have read as a badly disordered film; 7.7 cm⁻¹ is a respectable multilayer flake carrying a modest native vacancy population.

Second, the two independent estimators disagree, and Atlas says so. The E₂g-linewidth inversion uses a calibration built from simulated WS₂ defect supercells. The LA(M) ratio method uses constants transferred from MoS₂ because no direct WS₂ calibration exists. When they diverge by a factor of three, the honest statement is "roughly one percent by the better-supported method, and the population may not be the defect type either calibration assumes". That is what the Block returns.

Third, the density is a map. The interior mean is 1.02% with a 0.12% spread, and the spread is spatially structured rather than noise — which is what the next two Blocks pick apart.

Strain or doping?

The E₂g and A₁g modes respond differently to strain and to carrier density, so a scatter of their per-pixel shifts can be decomposed along two axes. Decompose strain vs doping does the inversion and reports the response coefficients it used and where they came from.

The interior of this flake is close to relaxed: a strain spread of ±0.12% between the 5th and 95th percentiles, with a weak correlation (r = 0.41) between the two mode shifts. There is no large uniform strain and no large doping gradient. For a company checking whether a transfer process left the film under tension, this is the readout — and the strain map shows where the residual sits.

The caveat is repeated because it is real. The doping axis for WS₂ borrows MoS₂ coefficients. Atlas flags this on every run rather than presenting a doping density to two decimal places.

What the PL says about carriers

The photoluminescence map answers a different question: how many of those excitons are charged? Fit exciton/trion decomposes each pixel's emission into the neutral A exciton, the trion, and, when the fit demands it, a bound-exciton band further to the red.

This is the result that connects back to the Raman defect estimate. A ~1% chalcogen-vacancy-scale defect population is exactly the kind of thing that donates electrons, and a trion-dominated PL spectrum is exactly what a heavily n-doped WS₂ flake emits. Two independent measurements, two independent Blocks, one consistent picture.

The splitting check is the quiet safeguard. If the fit had returned a 60 meV "trion" splitting, the Block would have flagged that the second component is probably something else. It returned 32 meV, so the labels mean what they say.

How far does the damage reach?

The PFIB boundaries are a built-in experiment: as-grown material meets a sharp edge of total damage. Profile a metric vs distance from film edge bins any per-pixel quantity by its distance from the nearest edge and fits a decay length.

The two profiles disagree on the reach of the damage, and the disagreement is the finding. PL intensity recovers within about one pixel of the edge — the emission is either there or it is not. The exciton energy, by contrast, stays blueshifted for nearly 4 µm into the interior before relaxing to the bulk value. Something with a several-micron footprint — strain relaxation at the free edge, ion-induced charging, or a diffuse defect population — perturbs the exciton well beyond the zone where emission is killed.

This is the kind of statement that decides a layout rule. If your process keeps active regions 1 µm from any cut edge because that is where the PL comes back, the exciton-energy profile says the material is not back to normal until 4 µm.

Do Raman and PL agree about where the bad material is?

The two maps were acquired separately, on grids that do not quite coincide. Correlate modalities estimates the spatial offset between them, pairs pixels within a tolerance, and computes rank correlations across every feature pair.

A 7 µm offset between the two exports would have scrambled any pixel-by-pixel comparison done by hand. With it corrected, the picture is clear: where the lattice scatters, the excitons emit (ρ = +0.73), and where the E₂g mode broadens, the PL dims (ρ = −0.38). The weaker second correlation is physically meaningful too — electronic quenching and phonon disorder are related but not the same thing, which is why a Raman-only or PL-only quality metric can mislead.

Letting the data draw the regions

Finally, with both maps aligned, Cluster map groups interior pixels on all eleven spectral features at once, without being told what "good" looks like.

The clusters are not dramatic, and Atlas says so: the silhouette score is low because the interior really is fairly uniform. What makes the result useful is the coherence number. Overlapping populations that nonetheless form contiguous spatial domains are regions, not noise, and the third region is the inner edge of the damage halo that the fixed 2.5 µm buffer did not fully exclude.

What this gives a WS₂ team

From two map files and about seven minutes of compute, the interior of this flake now has:

• a region mask separating as-grown material from a 5.5 µm damage halo and bare substrate,
• a resonance-corrected E₂g linewidth of 7.7 cm⁻¹ and a defect-density estimate near 1%, with the disagreement between two estimators recorded rather than hidden,
• a strain spread of ±0.12% and no evidence of a large doping gradient, with the borrowed coefficients flagged,
• a PL picture of a heavily n-type flake — 63% of pixels trion-dominated, 32 meV splitting inside the literature band, a defect band present in three quarters of pixels,
• a 4 µm exciton-energy recovery length versus a 0.6 µm intensity recovery length at every cut edge,
• a 7 µm registration offset between the two instruments' exports, corrected, and cross-modal correlations that show Raman and PL are seeing the same population,
• and three data-driven regions whose spatial coherence, not their statistical separation, is what makes them trustworthy.

There are things Atlas did not do here. It did not count layers: the Si line visible through the flake and the ~68 cm⁻¹ E₂g–A₁g separation both place it in the multilayer regime, where the mode-separation calibration saturates and stops being informative. It did not identify which defect species dominates — the classifier ran, ranked S→C substitution first, and warned that its estimated density falls outside the calibration range, so we have not quoted it. It did not measure absolute doping. Each of those limits is stated in the Block output, which is the point: the numbers you can build a process on are separated from the ones you cannot.

The Blocks used here are documented at Segment regions, Estimate defect density, Decompose strain vs doping, Fit exciton/trion, Profile edge, Correlate modalities, and Cluster map. Every figure above was generated from the two source files through the same Atlas analysis functions the Blocks run.

If you grow, transfer, or pattern WS₂ and have maps like these sitting in a LabSpec folder, we would like to run them. Request access or get in touch.