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

This paper presents a deep learning framework that automates the extraction of physical parameters and model fitting for two-dimensional transistors by leveraging a pre-trained neural network to approximate physics-based simulators, achieving high accuracy with significantly fewer training samples than previous methods.

Original authors: Robert K. A. Bennett, Jan-Lucas Uslu, Harmon F. Gault, Asir Intisar Khan, Lauren Hoang, Tara Peña, Kathryn Neilson, Young Suh Song, Zhepeng Zhang, Andrew J. Mannix, Eric Pop

Published 2026-09-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Robert K. A. Bennett, Jan-Lucas Uslu, Harmon F. Gault, Asir Intisar Khan, Lauren Hoang, Tara Peña, Kathryn Neilson, Young Suh Song, Zhepeng Zhang, Andrew J. Mannix, Eric Pop

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of modern electronics, the tiny transistors that power our devices are becoming increasingly difficult to understand. Scientists are moving beyond traditional silicon to explore new materials, such as ultra-thin sheets of atoms only a single layer thick. These two-dimensional materials hold great promise for faster, more efficient electronics, but they behave in complex ways that are hard to predict. To make these new materials work, researchers must measure how electricity flows through them and then work backward to figure out the hidden physical properties inside, such as how easily electrons move or how high the energy barriers are at the points where metal meets the material. This process of working backward is essential for designing better devices, but it has traditionally been a slow, manual task that requires experts to guess and check, often taking hours or days to get a single answer right.

A team of researchers at Stanford University has developed a new method to speed up this process dramatically using artificial intelligence. Instead of asking a computer to guess the answer, they trained a digital system to learn the relationship between the electrical measurements and the physical properties of the transistor. The challenge was that the computer simulations needed to teach this system are incredibly slow and expensive to run, often taking minutes or hours to generate a single data point. To solve this, the researchers created a clever two-step training system. First, they trained a fast, simple neural network to mimic the slow, complex physics simulator. They used this fast mimic to generate a massive amount of practice data for free. Then, they used this practice data to teach the main system how to work, before finally fine-tuning it with a small number of real, expensive simulations.

The result is a system that can extract the hidden physical parameters of a transistor in a fraction of a second. In their tests, the researchers used this method on a set of 500 simulated devices to train the network. Once trained, the system could look at electrical measurements from a real transistor and instantly predict the values of eight different physical properties with high accuracy. When they tested this on actual experimental transistors made from a material called tungsten disulfide, the system successfully reverse-engineered the device's behavior, matching the measured data with a precision that indicates a near-perfect fit. The researchers found that the system could determine how fast electrons move through the material and the height of the energy barriers at the contacts, revealing variations between different devices that would have been difficult to spot otherwise.

This approach is particularly powerful because it drastically reduces the amount of computing power needed. Previous methods required training on data from tens of thousands or even millions of simulated devices to achieve similar results. By using the fast mimic to pre-train the system, the researchers achieved excellent results with data from only 500 devices, a reduction of more than forty times. This makes it feasible to use the most rigorous and accurate physics models, which are usually too slow to be used for training large datasets. The method also proved flexible; the researchers showed it could be scaled up to handle much more complex transistors with up to thirty-five different unknown parameters, suggesting it could be applied to a wide variety of electronic components beyond the specific materials tested.

The researchers validated their work by applying the trained system to fifty-one real-world transistors fabricated on three different chips. The system successfully matched the electrical curves of these devices, allowing the team to map out the distribution of mobility and contact barriers across the chips. This level of detail helps scientists understand how the manufacturing process affects the final product, such as how the metal contacts interact with the semiconductor. While the system is highly accurate at matching the electrical curves, the authors note that a perfect match does not guarantee that every single extracted number is physically perfect, as different combinations of properties can sometimes produce similar electrical results. However, for the purpose of characterizing large groups of devices and understanding their performance limits, the method provides a robust and rapid tool.

By making their code and data available to the public, the researchers hope to encourage further development of these techniques. This work represents a shift from manual, time-consuming analysis to an automated, high-throughput approach for understanding next-generation electronics. It allows scientists to focus less on the tedious work of fitting curves and more on interpreting the physical insights those curves provide. As the field of two-dimensional electronics continues to grow, tools like this will be essential for turning experimental discoveries into reliable, high-performance technology. The ability to quickly and accurately understand the inner workings of these tiny devices is a critical step toward bringing the next generation of electronics to life.

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

Problem Statement
Emerging semiconductor technologies, such as two-dimensional (2D) transition metal dichalcogenides (TMDs), require rigorous characterization to extract physical parameters (e.g., mobility, Schottky barrier height, defect profiles) from electrical measurements. Traditionally, this is achieved by fitting measured current-voltage ( $I_d$ - $V_{gs}$ ) characteristics to physics-based models. However, this process is iterative, time-consuming, and often inaccessible to non-experts. While recent deep learning approaches have automated this inverse problem, they typically require training sets comprising 20,000 to 1,000,000 unique devices. For emerging technologies modeled by computationally expensive physics-based simulators (e.g., Sentaurus Device, quantum transport solvers), generating such large datasets is often intractable, as a single simulation can take minutes to hours.

Methodology
The authors propose a deep learning framework that drastically reduces the required number of expensive physics-based simulations by employing a "surrogate" pretraining strategy. The workflow consists of five key steps:

Physics-Based Data Generation: A small initial dataset is generated using a comprehensive physics-based simulator (Sentaurus Device) for 2D field-effect transistors (FETs). This dataset maps input model parameters (8 parameters including mobility, barrier height, and defect profiles) to output $I_d$ - $V_{gs}$ curves.
Forward Surrogate Training: A forward neural network is trained to approximate the physics-based simulator. This network learns to predict $I_d$ - $V_{gs}$ curves given a set of input parameters.
Augmented Pretraining: The trained forward network is used to generate a massive, computationally inexpensive augmented dataset (e.g., 100,000 curves) by sampling random parameters. An inverse neural network is pre-trained on this augmented data.
Tandem Fine-Tuning: The inverse network is fine-tuned using the original, small set of physics-based simulations. Crucially, this training utilizes a tandem neural network approach: the inverse network's predicted parameters are fed into the forward network to estimate the resulting current. The loss function penalizes both the error in the predicted parameters and the error in the reconstructed current ( $I_{pred}$ vs. $I_{actual}$ ), addressing the non-uniqueness of the inverse problem where multiple parameter sets can yield similar curves.
Inference: Once trained, the inverse network directly maps experimental $I_d$ - $V_{gs}$ data to the underlying physical parameters without requiring further physics-based simulations.

Key Contributions

Data Efficiency: The method achieves high-quality fits using training sets of only ~500 devices, representing a >40× reduction compared to previous deep learning efforts that required tens or hundreds of thousands of devices.
Physics-Rigorous Training: Unlike methods restricted to compact models, this approach enables training on complex, self-consistent physics-based models (TCAD) that include geometry, transport, and electrostatic effects, without prohibitive computational costs.
Generalizability: The framework is demonstrated to scale to more complex models, successfully reverse-engineering 35 parameters for Gallium Nitride (GaN) high-electron-mobility transistors (HEMTs) using the ASM-HEMT compact model.
Open Science: The authors have released the code and sample datasets on GitHub to facilitate future research in inverse transistor design.

Results

Simulated and Experimental Performance: When tested on a set of 1,000 unseen devices simulated with Sentaurus Device, the approach achieved a median coefficient of determination ( $R^2$ ) of 0.995. On the experimental test set of 51 monolayer WS₂ transistors, the approach achieved a median $R^2$ of 0.990. The pretraining step was shown to provide an accuracy boost equivalent to doubling the size of the physics-based training set.
Parameter Extraction Accuracy: The median absolute errors for key parameters were low: mobility (0.88 cm² V⁻¹ s⁻¹) and Schottky barrier height (18.4 meV). Errors were slightly higher for defect density parameters, attributed to mutual redundancy in the model, though the overall $I_d$ - $V_{gs}$ fit remained excellent.
Experimental Validation: The method was applied to 51 experimental monolayer WS₂ transistors. The reverse-engineered parameters produced simulated curves that closely matched experimental data, with a median $R^2$ of 0.990. The extracted distributions of mobility and barrier height qualitatively matched the expected experimental variations.
Scalability: The approach successfully handled high-dimensional problems, fitting 35 parameters for GaN HEMTs with a training set of ~16,000 devices, demonstrating that the method scales with model complexity provided the training set generation remains computationally feasible.

Significance and Claims
The paper claims that this approach makes automated parameter extraction feasible for emerging technologies where generating large datasets via rigorous physics-based simulation was previously a bottleneck. By reducing the training requirement from days or weeks of simulation time to under an hour, the method enables the use of complex, physically accurate models for device characterization and technology computer-aided design (TCAD) fitting.

The authors emphasize that while the method automates the fitting process, it does not automatically select the correct physical model; the user must still ensure the underlying physics-based model is appropriate for the device. Furthermore, they note that while the method is highly efficient for characterizing large distributions of devices (e.g., for yield analysis or process monitoring), for fitting a single device, traditional optimization methods might still be computationally cheaper. The work positions deep learning as a practical tool for bridging the gap between complex physical simulations and experimental data analysis in next-generation electronics.

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

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