Deep Learning to Automate Parameter Extraction and Model Fitting of Two-Dimensional Transistors

Andrew J. Mannix; Asir Intisar Khan; Eric Pop; Harmon F. Gault; Jan-Lucas Uslu; Kathryn Neilson; Lauren Hoang; Robert K. A. Bennett; Tara Pe\~na; Young Suh Song

REVIEW 2 major objections 5 minor 2 references

Deep Learning to Automate Parameter Extraction and Model Fitting of Two-Dimensional Transistors

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that reverse-engineering transistor parameters from current-voltage curves can be done with about 500 physics-based simulations instead of 20,000 to 1,000,000, using a surrogate-trained inverse network that achieves…

desk verdict Solid data-efficiency result for ML-based TCAD parameter extraction, anchored by strong experimental validation; the simulated-test scaling curves need a TCAD-based check before the >40x claim is fully secure. read the letter →

arxiv 2507.05134 v1 pith:EUEUPLZG submitted 2025-07-07 cs.LG cond-mat.mtrl-sciphysics.app-ph

Robert K. A. Bennett , Jan-Lucas Uslu , Harmon F. Gault , Asir Intisar Khan , Lauren Hoang , Tara Peña , Kathryn Neilson , Young Suh Song

show 3 more authors

Zhepeng Zhang Andrew J. Mannix Eric Pop

This is my paper · ORCID

classification cs.LGcond-mat.mtrl-sciphysics.app-ph

keywords deeplearninginverseparameterextractionTCADtandemneuralnetworksurrogatemodeltwo-dimensionaltransistorsmonolayerWS2high-electron-mobility

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

To fit a transistor model to measured current-voltage data, one normally must tune many physical parameters, such as mobility, contact barrier height, and defect densities, by hand or through optimizer loops that require expensive simulations. This paper claims that a neural network can learn the inverse map, from measured $I_d$-$V_{gs}$ curves straight to those parameters, using only about 500 physics-based simulations, more than 40 times fewer than earlier deep-learning extraction efforts. The enabling move is to train a cheap surrogate network that imitates the physics-based simulator, use the surrogate to mass-produce a pre-training set, and only then fine-tune the inverse network on the real simulation data. If this works as claimed, rigorous TCAD-based parameter extraction becomes practical for 2D semiconductors and other emerging devices where one simulated curve can cost minutes to hours.

What carries the argument

The load-bearing object is the tandem inverse network: the inverse network outputs a candidate set of device parameters, and those candidate parameters are fed into a pre-trained forward neural network that approximates the TCAD simulator. The training loss penalizes errors in both the output parameters and the predicted current curves, including log-current and derivatives, which is how the network copes with the fact that different parameter sets can produce nearly identical $I_d$-$V_{gs}$ curves. A second component is the pre-training scheme: the forward surrogate generates about 100,000 augmented curves in under 30 seconds, the inverse network is pre-trained on these, and then fine-tuned on the original set of about 500 physics-based simulations. The input representation also matters: each device enters as eight feature vectors at 32 gate voltages, namely current, log-current, and their derivatives at two drain biases.

What would settle it

Train the same pipeline on simulations from a deliberately incomplete forward model, for example omitting nonlocal tunneling through the Schottky barrier, fit the measured WS2 curves, and check whether the extracted barrier heights still land in the physically expected 170-400 meV range; if high $R^2$ persists while the parameters shift unphysically, the fit metric is not validating the physics. Likewise, applying the trained network without retraining to a transistor with a different channel length or oxide thickness should degrade markedly; failure to degrade would contradict the paper's stated limitation.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that pre-training on surrogate-generated data makes high-quality inverse fits achievable with dramatically less expensive simulation data: training on simulated $I_d$-$V_{gs}$ data from only about 500 devices yields median $R^2=0.995$ on a simulated test set and $R^2=0.990$ when reverse-engineering measured monolayer WS2 transistors, with median absolute extraction errors of 0.88 cm$^2$ V$^{-1}$ s$^{-1}$ for mobility and 18.4 meV for Schottky barrier height. The authors show that the pre-training step is worth roughly a doubling of the physics-based training set, and that the same pipeline scales to 35-parameter fits of GaN high-electron-mobility transistors when the training set is enlarged to about 16,000 devices. They state the caveat that a fit is only physically meaningful if the forward simulator accurately describes the measured transistors.

Load-bearing premise

The entire extraction is only as sound as the TCAD model used to generate its training data; if that drift-diffusion, Schottky-contact, defect-profile model does not describe the measured WS2 transistors, the network can still achieve high $R^2$ fits while returning physically wrong parameters, a caveat the paper states in its training-set section.

Editorial extensions

If this is right

TCAD model fitting for emerging semiconductors becomes feasible when a single simulated curve takes minutes to hours: a 500-device training set can be generated in about 30 minutes on 32 cores.
The method is forward-model-agnostic, so it can import drift-diffusion, Monte Carlo, or quantum-transport simulators rather than being restricted to cheap compact models.
Once trained, the network can rapidly screen large numbers of devices; the authors use it to map mobility and barrier-height distributions across 51 WS2 transistors.
For more complex models, the required training set grows roughly fourfold per ten additional fitted parameters, so 35-parameter fits remain achievable with about 16,000 simulations.
Pre-training provides an accuracy gain roughly equivalent to doubling the size of the physics-based training set.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the paper shows the surrogate pre-training is what breaks the data bottleneck, the same two-network recipe is a natural template for other inverse problems with expensive forward simulators, such as photonic nanostructures, batteries, or thermoelectrics, though that is an extension the paper does not make.
The non-uniqueness the paper acknowledges implies that parameter-error metrics understate the true ambiguity, especially for correlated defect parameters; downstream users should treat extracted defect densities as effective values rather than unique physical truths.
A strong test of physical meaningfulness would be to compare extracted parameters against independently measured values, such as Hall mobility or Kelvin-probe barrier heights, on the same devices; the paper does not do this.
Requiring retraining for each geometry is a real limitation; conditioning the network on channel length, oxide thickness, or gating configuration would remove that cost, and the scaling data here suggest it is worth trying.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know: the central data-efficiency claim is real but is partly measured through a surrogate, and the experimental validation is the strongest part of the paper. The key idea is to train a fast forward network on a small TCAD training set, use it to generate 100k cheap curves for pretraining, then fine-tune on the real simulations. That is a simple, sensible use of established tandem-network training, and the combination applied to TCAD-based extraction for 2D FETs is new enough to be worth reporting.

The paper does several things well. The bootstrap study across training sizes is careful. The authors include a well-reasoned feature-engineering ablation. The experimental test is genuinely convincing: 51 WS2 transistors, with predicted parameters re-simulated in Sentaurus, median R2 = 0.990. They also show scaling to 35-parameter HEMT extraction, which is a useful stress test.

Now the soft spots. The simulated-test R2 in Figure 4a is computed by passing predicted parameters through a well-trained forward network, not through Sentaurus. That is a surrogate-on-surrogate evaluation. The stress-test note worries the inverse network could exploit weaknesses in the forward network. That concern is muted by the fact that the evaluation surrogate is trained on all 25k simulations and reproduces Sentaurus with worst 0.5% R2 of 0.9915, and the experimental validation at the 500-device size independently confirms the headline. But the claim that pretraining roughly doubles effective training size, and the detailed scaling curve, rest only on surrogate evaluation. A determined referee should ask for a TCAD re-evaluation of at least a subset of the bootstrap conditions, or an explicit statement that Figure 4a is an estimate.

A second, more important omission in my view: there is no baseline against conventional optimization-based fitting. For 51 experimental devices, how many Sentaurus calls would a standard Levenberg-Marquardt or derivative-free fit need, and how do the resulting R2 and parameter values compare? The paper sells "automate parameter extraction," but without a traditional-fit comparison, the reader cannot judge whether the ML approach is actually faster or better for someone who only has dozens of devices. This is not a fatal flaw—the method's value for expensive simulators stands on the data-efficiency argument—but the missing baseline makes the engineering advantage less crisp.

The paper is transparent about the TCAD model assumptions and the need to retrain for new geometries. Code and sample data are public, which earns credit. The full training sets are not, but the experimental fits make the core results reproducible in spirit.

Bottom line: this is a solid, useful engineering paper. It deserves a serious referee. I would send it to review, and I would ask the authors to add the TCAD-based check on the bootstrap curve and a conventional-fitting baseline. This will be a useful reference for anyone doing ML-based transistor characterization.

Referee Report

2 major / 5 minor

Summary. The paper presents a deep-learning pipeline for inverse parameter extraction in transistor TCAD modeling. A forward neural network is trained on physics-based Sentaurus Device simulations and is then used to generate a large augmented dataset for pretraining an inverse network that maps Id-Vgs curves to model parameters; the inverse network is fine-tuned on the original physics-based data, and during training the forward network is called in a tandem manner to evaluate current-mismatch losses. The authors report bootstrap experiments showing that pretraining yields high simulated-test R2 after training on roughly 500 physics-based simulations, claim a greater-than-40x reduction in required training data relative to prior work, and validate on 51 experimental monolayer WS2 transistors by re-simulating in Sentaurus with predicted parameters (median R2 = 0.990). They also demonstrate scaling to a 35-parameter ASM-HEMT compact model. The central data-efficiency claim rests on simulated-test R2 values that are computed through the surrogate forward network rather than through direct TCAD re-simulation, which is the main technical concern.

Significance. If the central claims hold, the paper makes a practical contribution: it shows that a surrogate-based pretraining strategy can substantially reduce the number of expensive physics-based simulations needed to train an inverse parameter-extraction network, and it provides a direct experimental check by re-simulating 51 measured WS2 devices in Sentaurus with extracted parameters. The bootstrapped experimental design, the held-out simulated test set, and the public release of code and sample data are clear strengths that support reproducibility. The significance would be strengthened if the simulated-test evaluation were verified by direct TCAD re-simulation, and if the wording distinguished 'physical parameters' from 'effective TCAD model parameters' given the acknowledged model assumptions.

major comments (2)

[After training / Supplementary Section 5] The simulated-test R2 values in Figure 4, including the headline median R2 = 0.995 and the 5th-quantile R2 = 0.98 for 500-device training, are computed by feeding predicted parameters into a forward neural network surrogate rather than into Sentaurus Device. The paper says this allows accuracy to be estimated 'without having to re-run Sentaurus Device simulations,' but this is not an independent check: the inverse network is itself trained in tandem with a forward surrogate, so the evaluation can be optimistic if the inverse network exploits regions where the surrogate is inaccurate. The forward surrogate trained on 500 devices has a 5th-quantile R2 of only about 0.94 (Supplementary Figure S2b), so the surrogate error is non-negligible at the training sizes that anchor the greater-than-40x data-efficiency claim. I request that the authors re-run Sentaurus Device on the predicted parameters for at least the 500- and 1,000-device training settings, or on a random subset of the 1,000-device test set, and report direct TCAD R2 values. The main text should also state explicitly which forward network is used for evaluation at each training size.
[Experimental validation and abstract] The paper claims to extract 'physical parameters' such as mobility, Schottky barrier height, and defect densities. The experimental validation establishes that Sentaurus simulations using the predicted parameters reproduce measured Id-Vgs curves with high R2, but high curve-fitting R2 does not by itself establish that the extracted values are the physically true parameters, especially given the acknowledged model assumptions (e.g., zero-mobility band-tail acceptor states, absence of a Fermi-level pinning model, effective-mass density of states, and fixed geometry and parameter ranges). The authors already caution about model validity in the 'Generating the training set' section, but the abstract and title make unqualified claims of physical parameter extraction. To make the central claim proportioned to the evidence, the authors should either validate a subset of extracted parameters against independent measurements (e.g., Hall mobility, Kelvin-probe barrier height, or defect spectroscopy) or explicitly reframe the results as extraction of effective TCAD model parameters whose physical interpretation is conditional on the validity of the Sentaurus model.

minor comments (5)

[Supplementary Section 4] The sentence 'In Eq. (7) the main text' should refer to Eq. (6) in the main text, which is the loss function for the inverse network.
[Figure 4 and main text] The standard deviation of the mobility error is quoted as 1.9 cm2 V-1 s-1 in the text, but Figure 4f reports 1.6 cm2 V-1 s-1; please reconcile these numbers.
[Main text, parameter accuracy paragraph] The sentence 'Actual vs. predicted values for (e) mobility, (f) Schottky contact barrier height, and (g) peak donor density in Figures 4f-h' has panel labels inconsistent with the figure; panels f through h show mobility, barrier height, and ND0, respectively.
[Introduction and conclusion] When claiming a greater-than-40x reduction in training devices, please specify in the main text that the comparison is to prior compact-model parameter-extraction efforts and that the factor refers to the number of physics-based simulations for a fixed geometry and parameter range, so that the claim is not misread as a general computational-cost reduction.
[Supplementary Section 7 / main text] The exclusion of the one device that could not reach an on-state current of 1 uA/um at Vgs = 50 V is a selection criterion; please state this criterion in the main text when describing the 51-device test set, since it affects how the reported median R2 should be interpreted.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the inverse network is validated by fresh Sentaurus runs on experimental data, and the surrogate-based simulated-test metric is a disclosed approximation rather than a definitional loop.

full rationale

The central derivation is not circular. Physics-based Sentaurus TCAD simulations are the external ground truth used to train the forward surrogate and to fine-tune the inverse network, and the inverse network is tested on an unseen Sentaurus test set as well as on 51 measured monolayer WS2 transistors by running new Sentaurus simulations with the predicted parameters (main text, 'Experimental validation: measured Id-Vgs data from monolayer WS2 transistors'). This external check closes the loop against experiment, not against the network's own outputs. The only methodological concern is that the simulated-test R2 in Figure 4a is obtained by passing predicted parameters through the forward neural network rather than through Sentaurus: 'we take these extracted parameters and estimate their corresponding Id-Vgs curves using a well-trained forward neural network that was trained on all 25,000 devices in our original physics-based training set.' The same forward network participates in training as the tandem loss evaluator and as the generator of the augmented pretraining set, so the simulated-test metric is not fully independent of the training machinery. However, the forward network is itself benchmarked against Sentaurus (Supplementary Section S5, worst 0.5% R2 = 0.9915 for the 25,000-device network), and the experimental validation uses actual Sentaurus simulations, yielding median R2 = 0.990. Thus the shared-surrogate evaluation is a disclosed limitation in one secondary metric rather than a definitional circularity in the main claim. Self-citations (e.g., refs. 3, 9, 20 and the GitHub repository) supply background parameter ranges and experimental data, but none carries the burden of proving the inverse-extraction result. Overall circularity burden is minimal.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method has no fitted physical constants of its own; the listed free parameters are user choices that define the extraction domain and preprocessing. The axioms capture the modeling assumptions that give the extracted parameters physical meaning. No new physical entities are introduced; donor/acceptor defect states are modeled with standard distributions from prior literature.

free parameters (4)

Training parameter range bounds (Table I) = 8 parameters with ranges, e.g., mobility 1-35 cm2/V/s, barrier 10-510 meV
Chosen by hand from prior literature and the authors' prior estimates (Supp. Sec. 2). The network cannot predict parameters outside these ranges, so the ranges set the extractable domain and directly bound the experimental results.
Noise floor = 5e-5 μA/μm
Manually imposed on both simulated and experimental data to match the measurement instrument; affects all curves and the R2 calculation (Supp. Sec. 4).
Training set size for 2D FETs = 500 physics-based devices (plus 100,000 augmented samples)
Chosen based on bootstrap studies (Fig. 4a); the paper's headline result depends on this operating point.
Vgs range and grid points = -6 to +50 V, 32 points
Chosen to match experimental sweep; the shallow-defect parameter extraction depends on this window (Supp. Sec. 3-4).

assumptions (5)

domain assumption Drift-diffusion transport is valid for the 500 nm channel and describes the measured devices.
Invoked in Supp. Sec. 2 ('which is valid for the relatively long 500 nm channel lengths considered in this work'). Load-bearing for the meaning of the extracted mobility.
domain assumption The Sentaurus Schottky contact model with nonlocal tunneling and no Fermi-level pinning adequately represents the real Ni/WS2 contacts.
Supp. Sec. 1; the paper notes Sentaurus lacks an established pinning model and instead tunes electron affinity to set the nominal barrier. This simplification feeds every barrier-height extraction.
ad hoc to paper Defect states are parameterized as truncated Gaussian donors and exponential acceptors with zero-mobility band tails.
Main text Eqs. (4)-(5); this parameterization is a modeling choice not directly validated against spectroscopy for these devices.
domain assumption The forward surrogate neural network approximates the physics-based simulator closely enough for pretraining and tandem loss evaluation.
Validated in Supp. Sec. 5 (median R2 >= 0.98, worst 0.5% R2 = 0.9915 on test set) but remains an approximation; all simulated-test R2 values in Fig. 4 inherit its error.
domain assumption The 51 measured WS2 devices are described by the same geometry and physics as the training simulations.
The training set uses fixed back-gated geometry (Fig. 2a), channel length 500 nm, 100 nm SiO2; experimental devices match this geometry (Supp. Sec. 7). Any mismatch (e.g., gate leakage, fringing fields not modeled) would bias extracted parameters.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Deep Learning to Automate Parameter Extraction and Model Fitting of Two-Dimensional Transistors." pith.science (2026). https://pith.science/paper/EUEUPLZG

@misc{pith2026250705134,
  author       = {Pith},
  title        = {Pith review of: Deep Learning to Automate Parameter Extraction and Model Fitting of Two-Dimensional Transistors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EUEUPLZG}},
  note         = {Machine review of arXiv:2507.05134}
}

abstract

We present a deep learning approach to extract physical parameters (e.g., mobility, Schottky contact barrier height, defect profiles) of two-dimensional (2D) transistors from electrical measurements, enabling automated parameter extraction and technology computer-aided design (TCAD) fitting. To facilitate this task, we implement a simple data augmentation and pre-training approach by training a secondary neural network to approximate a physics-based device simulator. This method enables high-quality fits after training the neural network on electrical data generated from physics-based simulations of ~500 devices, a factor >40$\times$ fewer than other recent efforts. Consequently, fitting can be achieved by training on physically rigorous TCAD models, including complex geometry, self-consistent transport, and electrostatic effects, and is not limited to computationally inexpensive compact models. We apply our approach to reverse-engineer key parameters from experimental monolayer WS$_2$ transistors, achieving a median coefficient of determination ($R^2$) = 0.99 when fitting measured electrical data. We also demonstrate that this approach generalizes and scales well by reverse-engineering electrical data on high-electron-mobility transistors while fitting 35 parameters simultaneously. To facilitate future research on deep learning approaches for inverse transistor design, we have published our code and sample data sets online.

Figures

Figures reproduced from arXiv: 2507.05134 by the authors.

**Figure 2.** Summary of transistors considered in this work [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Inverse neural network and tandem network training approach [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Performance of the inverse network on the simulated test set [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Performance of the inverse network on experimentally measured test devices. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

the forward neural network

Here, we find that for all training set sizes considered, our forward neural network can achieve a median R2 ≥ 0.98 on the test set ( Supplementary Figure S2b), indicating a good match between the original simulated current and the approximation from the forward neural network. We are also interested in the network’s performance across the vast majority o...

work page
[10]

curse of dimensionality,

space, e.g., for a parameter with lower and upper bounds A and B, we drew a random number c sampled uniformly between log10A and log10B and assigned the parameter a value y = 10c. 32 We plot the 5th quantile (worst 5%), 10th quantile (worst 10%), and median R2 fit as functions of the number of fitting parameters in Supplementary Figure S4a-c for various t...

work page arXiv 2017

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

the forward neural network

Here, we find that for all training set sizes considered, our forward neural network can achieve a median R2 ≥ 0.98 on the test set ( Supplementary Figure S2b), indicating a good match between the original simulated current and the approximation from the forward neural network. We are also interested in the network’s performance across the vast majority o...

work page

[2] [10]

curse of dimensionality,

space, e.g., for a parameter with lower and upper bounds A and B, we drew a random number c sampled uniformly between log10A and log10B and assigned the parameter a value y = 10c. 32 We plot the 5th quantile (worst 5%), 10th quantile (worst 10%), and median R2 fit as functions of the number of fitting parameters in Supplementary Figure S4a-c for various t...

work page arXiv 2017