Physics-informed AI Accelerated Retention Analysis of Ferroelectric Vertical NAND: From Day-Scale TCAD to Second-Scale Surrogate Model

This paper introduces a Physics-Informed Neural Operator (PINO) surrogate model that accelerates the retention analysis of Ferroelectric Vertical NAND devices by over 10,000 times compared to traditional TCAD simulations while maintaining physical accuracy, thereby enabling efficient optimization of device designs against charge detrapping and ferroelectric depolarization.

The Gist

Here is an explanation of the paper, translated into simple language with creative analogies.

The Big Picture: The "Crystal Ball" for Computer Memory

Imagine you are trying to build a super-dense, 3D skyscraper of computer memory (called Fe-VNAND). This new type of memory is amazing because it's smaller and uses less power than current memory. However, it has a major flaw: it forgets things too quickly.

In the world of memory chips, "forgetting" is called Data Retention Loss. It's like writing a note on a whiteboard, but the ink starts fading or the board gets wiped clean by itself over time.

To fix this, engineers need to tweak the design of the chip (changing layer thicknesses, temperatures, etc.). But there's a problem: Testing these designs is agonizingly slow.

The Problem: The "Slow Motion" Simulator

Traditionally, engineers use a super-complex software called TCAD (Technology Computer-Aided Design) to simulate how the chip behaves.

• The Analogy: Imagine you want to know how a specific recipe tastes. To test it, you have to bake a cake, wait for it to cool, taste it, and then wait 24 hours to see if it goes stale.
• The Reality: In this paper, running just one simulation to see how the memory holds data for a few days takes 24 hours on a supercomputer. If you want to test 100 different designs, that's 100 days of waiting. It's too slow to ever find the perfect design.

The Solution: The "Physics-Informed AI" (The Smart Apprentice)

The researchers (from Georgia Tech, Samsung, and NVIDIA) built an AI Surrogate Model. Think of this AI not as a magic black box that guesses, but as a super-smart apprentice who has studied the laws of physics.

They call it PINO (Physics-Informed Neural Operator). Here is how it works:

1. The "Physics Teacher" (The Secret Sauce)

Standard AI is like a student who just memorizes flashcards. If you ask it a question it hasn't seen before, it might hallucinate a wrong answer.

• The PINO approach: Instead of just memorizing, they taught the AI the Laws of Physics (like gravity or electricity rules) directly into its brain.
• The Analogy: Imagine teaching a student to predict the weather.
  • Normal AI: "It rained yesterday, so it will rain today." (Guessing based on patterns).
  • PINO AI: "It rained yesterday, and I know the laws of thermodynamics say the air pressure is dropping, so it must rain today." (Reasoning based on rules).
• Because the AI knows the rules, it can't make "silly" mistakes. It ensures the predictions make physical sense.

2. The Speed Boost (From Days to Seconds)

Once the AI is trained, it doesn't need to "bake the cake" every time. It just looks at the recipe and instantly knows the result.

• The Result: What used to take 60 hours (2.5 days) to simulate a full range of designs now takes 10 seconds.
• The Speedup: That is a 10,000x speedup. It's like going from walking to the store to teleporting there.

How They Did It (The Three-Step Process)

The researchers built a pipeline to train this AI:

1. The Data Generator (The Slow Way): They ran the slow TCAD simulator a few times (about 120 times) to create a "textbook" of what happens inside the chip. They tracked things like electric fields and trapped charges.
2. The Physics Engine (The Brain): They used a special AI architecture (Fourier Neural Operator) that learns to predict the 2D maps of the chip's internal physics. Instead of just guessing a number, it draws a picture of what the electricity looks like inside the chip.
   • Crucial Step: They forced the AI to obey the Poisson Equation (a law of electricity) and Monotonicity (a rule that says data loss should always get worse over time, never better). This prevents the AI from predicting impossible scenarios.
3. The Translator (The Output): The AI takes those internal physics maps and translates them into the final result: How much memory is lost? (Threshold Voltage shift).

The Results: Why It Matters

• Accuracy: The AI's predictions were almost identical to the slow, expensive simulations (99.8% accurate).
• Generalization: Because the AI learned the rules of physics, it could predict how the chip would behave at temperatures or sizes it had never seen before. It didn't just memorize; it understood.
• Smoothness: Without the physics rules, the AI's predictions were "jittery" and unstable (like a shaky video). With the physics rules, the predictions were smooth and realistic.

The Bottom Line

This paper is about breaking the bottleneck of chip design.

By using an AI that respects the laws of physics, the team turned a process that took days into one that takes seconds. This allows engineers to explore thousands of design variations instantly, helping them build faster, more reliable, and higher-capacity memory for our future devices much faster than ever before.

In short: They taught a computer to understand the rules of the universe so it could stop guessing and start predicting, saving us years of waiting time.

Technical Summary

Here is a detailed technical summary of the paper "Physics-informed AI Accelerated Retention Analysis of Ferroelectric Vertical NAND: From Day-Scale TCAD to Second-Scale Surrogate Model."

1. Problem Statement

The semiconductor industry faces significant bottlenecks in scaling 3D Vertical NAND (VNAND) memory due to high programming voltages required by conventional charge trap layers. Ferroelectric Field-Effect Transistors (FeFETs) offer a promising alternative with lower operating voltages and faster switching. However, data retention in Fe-VNAND is a critical reliability challenge caused by the complex, time-dependent interplay between:

• Ferroelectric Depolarization: The gradual loss of remnant polarization ($P_r$) over time.
• Charge Detrapping: The leakage of trapped charges at dielectric interfaces, which exacerbates the internal depolarization field.

The Core Challenge: Optimizing device designs (e.g., Tunnel Dielectric Layer thickness, geometry) to mitigate these effects requires exploring a vast parameter space. Traditional Technology Computer-Aided Design (TCAD) simulations are physically accurate but computationally prohibitive. A single simulation sweeping temperature and time can take over 24 hours, making comprehensive Design Space Exploration (DSE) infeasible. Furthermore, standard "black-box" machine learning models often fail to capture physical laws (e.g., predicting non-monotonic charge detrapping), leading to unreliable extrapolations.

2. Methodology

The authors propose a Physics-Informed Neural Operator (PINO) framework to create a high-fidelity AI surrogate model. The approach integrates physical laws directly into the learning architecture to ensure accuracy and generalizability.

A. Device Physics & Data Generation

• Device Structure: A single FeFET with an engineered gate stack (HZO/TDL/HZO). The Tunnel Dielectric Layer (TDL) acts as a charge-screening region.
• TCAD Simulation: High-fidelity data was generated using Synopsys Sentaurus TCAD, integrating the ferroelectric Preisach model and Fowler-Nordheim (FN) tunneling.
• Input Parameters: The dataset was synthesized by sweeping three variables:
  • HZO Thickness ($t_{HZO}$): 5–9 nm
  • Temperature ($T$): 300–473 K
  • Retention Time ($\tau$): 0 to $10^4$ seconds.
• Output Targets: The TCAD solver provided 2D spatial physics maps (electrostatic potential, polarization, trapped carrier densities) and $I_D-V_G$ electrical characteristics.

B. AI Architecture (Three-Phase Pipeline)

Built on the NVIDIA PhysicsNeMo™ framework, the model operates in three phases:

1. Phase 1 (Input Embedding): Scalar inputs ($t_{HZO}$, $T$, $\log(\tau)$) are embedded.
2. Phase 2 (Physics Surrogate Engine):
   • Utilizes a Fourier Neural Operator (FNO) backbone. Unlike CNNs that process local pixels, FNOs perform global convolutions in the Fourier domain, allowing the network to learn continuous solution operators of Partial Differential Equations (PDEs).
   • Output: Resolution-invariant 2D physical fields (Potential, Polarization, Charge Density, Current Density).
   • Regularization: To prevent overfitting on the sparse dataset (120 TCAD sweeps), the FNO uses low-frequency mode cutoffs and narrow latent channels.
3. Phase 3 (Electrical Readout):
   • An IV-Net (hybrid CNN + MLP) predicts final electrical metrics ($I_D-V_G$ curves).
   • Scalar Context Injection: A critical innovation where original scalar inputs (temperature, time) are injected directly into a parallel MLP and fused with the CNN-extracted spatial features. This ensures the model retains global thermodynamic context that cannot be inferred solely from 2D electrostatic maps.

C. Physics-Informed Loss Function

To transition from a data-driven FNO to a PINO, a dual-loss formulation is used:
$$\mathcal{L}_{total} = \mathcal{L}_{data} + \mathcal{L}_{physics}$$

• $\mathcal{L}_{data}$: L2 norm error between predictions and TCAD ground truth.
• $\mathcal{L}_{physics}$: Enforces physical consistency via two constraints:
  1. Poisson Residual: Penalizes deviations from Poisson's equation ($\nabla \cdot (\epsilon \nabla \phi) + (\rho - \nabla \cdot P) = 0$), ensuring electrostatic validity.
  2. Monotonicity Constraints: Enforces the physical law that remnant polarization and trapped charge must decay monotonically over time, preventing unphysical temporal oscillations.

3. Key Contributions

• First PINO for Fe-VNAND Retention: Demonstrates the application of Physics-Informed Neural Operators to model the complex retention loss mechanisms (depolarization + detrapping) in 3D FeFETs.
• Hybrid Architecture: Introduces a "Scalar Context Injection" mechanism in the readout network, allowing the model to accurately predict global thermal effects that 2D maps alone cannot capture.
• Physical Regularization: Successfully embeds Poisson's equation and monotonicity constraints to eliminate unphysical artifacts (e.g., ripples in transfer curves) common in black-box ML models.
• Interpretable Digital Twin: The model outputs intermediate 2D physics maps, allowing engineers to visualize and verify localized charge detrapping dynamics, rather than just predicting a final number.

4. Results

• Reconstruction Accuracy: The PINO model reconstructs 2D physics maps (potential, charge, current) with a relative error of ~0.1% compared to TCAD.
• Electrical Prediction: Achieves an $R^2 > 0.998$ for threshold voltage ($V_{th}$) prediction across the full parameter sweep.
• Generalization: The model successfully interpolates retention loss for unseen temperatures (e.g., 350K) between trained data points (300K and 400K), maintaining physical consistency.
• Artifact Elimination: Unlike purely data-driven models which exhibited unstable ripples in $I_D-V_G$ curves due to overfitting, the PINO model produced smooth, physically valid curves.
• Error Reduction: The physics-informed approach improved the Root-Mean-Squared-Error (RMSE) by >40% compared to a data-driven baseline.

5. Significance and Impact

• Computational Speedup: The AI surrogate reduces inference time from 60 hours (TCAD full sweep) to approximately 10 seconds. This represents a >10,000× speedup (from day-scale to second-scale).
• Enabling Continuous DSE: The speed and mesh-free interpolation capability allow for continuous Design Space Exploration, eliminating "blind spots" inherent in discrete TCAD sampling.
• Scalability: While validated on a single FeFET, the framework provides a scalable pathway for modeling full-scale 3D Fe-VNAND arrays, accelerating the development of next-generation high-density, low-voltage memory.

In summary, this work bridges the gap between high-fidelity physics simulation and the computational efficiency required for modern semiconductor design, establishing a robust, physics-compliant AI framework for reliability analysis.