Ferroelectric transistor compact models train on measured current: spectral normalization smooths derivatives, and commercial SPICE runs large memory arrays
Synopsis
Compact models for ferroelectric field-effect transistors (FeFETs) have required either deriving physics-based equations term by term or training neural networks on smooth high-order derivatives from numerical solvers. This work trains a neural network on measured drain current instead, using scaled spectral normalization to constrain the network weights, smooth derivatives and filter measurement noise, covering the full range of polarization amplitudes and supporting dynamic polarization switching in transient simulations. Write and read operations of memory arrays up to large scale, including parasitics, complete transient simulation in commercial SPICE, and all converge.
Interpretation
A neural network can be trained directly on measured transistor current into a SPICE-usable compact model, without clean derivatives from a numerical solver as the training target. Earlier neural-network transistor models relied mainly on synthetic data generated by numerical solvers, which carries high-precision derivative information; measured data instead contains anisotropic, sweep-dependent structured noise that makes derivative extraction difficult. Training data came from transfer-characteristic measurements of a fabricated FeFET, covering the full range of polarization amplitudes; the resulting log-residuals approximate a zero-mean normal distribution, indicating the network captured the deterministic drain-current behavior while filtering measurement noise.
Training constrains each layer's weight matrix spectral norm with scaled spectral normalization, controlling the network's Lipschitz constant so derivatives stay smooth and stable. With derivative terms removed, the loss reduces to an L1 margin term plus a saturation-region scaling term and contains nothing that constrains derivative behavior, so a network can fit well yet still produce wildly oscillating derivatives. The three hidden layers use scaling coefficients of 1.0, 2.0 and 4.0, with the input layer left unnormalized; trained weights can be fused with the normalization layer, adding no runtime cost at inference.
The model links polarization amplitude, an internal state, to the gate-to-drain voltage difference, implementing real-device polarization boundary conditions through gating functions and a differential equation. A physical FeFET has only drain, gate, source and body terminals, so polarization amplitude cannot be set directly from terminal voltages and needs a conversion path from terminal voltage to polarization state. The polarization-speed function is fitted to ERS switching-time data from a different FeFET, growing exponentially with voltage difference and asymptotically bounded, avoiding the zero denominator and overflow of the original switching-time formula.
The model runs write and read transient simulations of large FeFET memory arrays with parasitic resistances and capacitances in commercial SPICE. The source notes that custom frameworks exist for SPICE-based FeFET array simulation, while all simulations here ran in a general commercial SPICE simulator with the neural-network Verilog-A model. An array with FeFETs and more than 1.5 million parasitic elements simulates in about 15 minutes, all array sizes converge under the same simulation options, and disabling polarization logic cuts simulation time for large arrays by up to 17%.
Perspective
The demonstrated scope is transfer-characteristic measurements of one fabricated FeFET and write/read transient simulations in commercial SPICE of memory arrays up to large scale with parasitics; the intended readers are researchers and engineers working on compact modeling and circuit simulation of emerging devices.
Because training data are noisy, standard quantitative metrics such as mean absolute error are dominated by noise and lose meaning, so fit quality is judged mainly by visual inspection of every sweep and by residual statistics; only positive polarization amplitudes were measured, with the negative side handled by a symmetric-device assumption; the polarization-speed function is fitted to switching-time data from a different device and differs somewhat from the original formula.