DDNet: A Unified Physics-Informed Deep Learning Framework for Semiconductor Device Modeling

TL;DR

DDNet tackles forward drift-diffusion simulations and inverse device design by unifying physics-informed neural networks with a mesh-free PDE solver for the Poisson–drift–diffusion system. It uses three coupled subnetworks for the electrostatic potential and carrier densities, trained with a physics-based loss that enforces the governing equations and boundary conditions, and augmented with inverse constraints for design tasks. The framework achieves forward accuracy comparable to commercial TCAD in 1D and 2D, while enabling parametric learning and inverse design of doping profiles, APDs, and binarized structures with minimal overhead. This approach supports rapid device discovery and optimization, can incorporate fabrication constraints and experimental data, and offers a scalable path toward multi-physics semiconductor design.

Abstract

The accurate modeling of semiconductor devices plays a critical role in the development of new technology nodes and next-generation devices. Semiconductor device designers largely rely on advanced simulation software to solve the drift-diffusion equations, a coupled system of nonlinear partial differential equations that describe carrier transport in semiconductor devices. While these tools perform well for forward modeling, they are not suitable to address inverse problems, for example, determining doping profiles, material, and geometrical parameters given a desired device performance. Meanwhile, physics-informed neural networks (PINNs) have grown in popularity in recent years thanks to their ability to efficiently and accurately solve inverse problems at minimal computational cost compared to forward problems. In this study, we introduce the Drift-Diffusion Network (DDNet), a unified physics-informed deep learning solver for the forward and inverse mesh-free solutions of the drift-diffusion equations of semiconductor device modeling. Using prototypical device configurations in one- and two spatial dimensions, we show that DDNet achieves low absolute and relative error compared to traditional simulation software while additionally solving user-defined inverse problems with minimal computational overhead. We expect that DDNet will benefit semiconductor device modeling by facilitating exploration and discovery of novel device structures across comprehensive parameter sets in a fully automated way.

Figures (6)

• Figure 1: The Drift-Diffusion Network (DDNet) architecture for forward semiconductor device modeling. The spatial inputs are passed to the three subnetworks $\phi$-Net, $n$-Net, and $p$-Net, which learn the three functions $\hat{\phi}$, $\hat{n}$, and $\hat{p}$, respectively. The three functions are then used to satisfy the physical constraints imposed by the Poisson-drift-diffusion equations via PDE and boundary conditions. If experimental data is available, it can be employed to further inform the DDNet solution. The PDE, boundary, and experimental residuals are then evaluated with a suitable loss function metric, which is then used to train DDNet using backpropagation. The process is repeated until a certain number of iterations (epochs) have passed or the loss has decreased below a threshold error $\sigma$.
• Figure 2: One-dimensional forward device simulation with DDNet. a, Schematics of the $pn$ junction geometry employed for validating the network's forward modeling capabilities. b, Overlayed plot of TCAD Sentaurus and DDNet’s reconstruction of the electric potential. c, d, Comparison of the densities of electrons and holes simulated by TCAD Sentaurus (left) and DDNet (right). The relative $L_1$ errors are below 2% for all cases.
• Figure 3: Two-dimensional forward device simulation with DDNet. a, Schematics of the 2D $p$-$n$ junction geometry employed with its doping profile shown in b. c, The different boundary conditions used when training DDNet on this geometry. Each line segment corresponds to 3 additional PDE equations that DDNet solves simultaneously. d, g, l, The reference solution computed by using TCAD Sentaurus, with DDNet's solution shown below in panels e, h, and k. The 3D contour plots of the DDNet solutions are shown in panels f, i, and l. The integrated relative $L_1$ errors between d, g, j and e, h, k were below 5%.
• Figure 4: Inverse design capabilities of DDNet. a, Modified DDNet architecture to tackle inverse design and parametric learning tasks. The input space has been expanded to accept device parameters $P_1,\dots,P_n$, and the output space of the $p$-Net and $n$-Net now enables the retrieval of the doping profile $\hat{C}=\hat{N}_d^++\hat{N}_a^-$. b, Example of parametric learning for a $pin$ junction, where DDNet extrapolates the maximal electric field behavior as a function of the intrinsically doped region width after training on 4 widths. c, Example of inverse design of a doping profile to achieve the maximal user-defined target performance from only three data points. d, Example of device discovery, where a $pnp$ BJT-like structure is retrieved to match the user's performance criteria on the electric field and carrier concentrations.
• Figure 5: Inverse design of APDs and binarized structures using DDNet. a, Multiscale electric field target performance dataset for a prototypical RF sensing device. b, DDNet's inverted doping profile with a comparison to a true APD doping and corresponding APD device schematic.