Feed-forward neural basis model delivers most accurate held-out temperature predictions for Schottky diode curves

In the crowded arena of architectures competing to learn a semiconductor device’s behavior, the winner turned out to be neither the deepest nor the flashiest. In a new study of Schottky barrier diodes, a feed-forward neural network built from stacked basis-expansion blocks, known as N-BEATS, delivered the numerically lowest descriptive mean errors for predicting current–voltage behavior at temperatures never seen during training — outperforming classical machine-learning models, recurrent and convolutional neural networks, and physics-based benchmark methods under a rigorous leave-one-temperature-out validation protocol. The work suggests that for small, structured datasets typical of device characterization, simpler architectures can hold their own against the deep sequential models that dominate other domains of artificial intelligence.

The research focused on aluminum/cadmium zinc oxide/p-type silicon diodes fabricated by a sol-gel route. Schottky barrier diodes are indispensable for high-speed rectification, radio-frequency detection, and photodetection, and their performance hinges on the metal–semiconductor interface. Three parameters govern that behavior: the effective barrier height, the ideality factor, and parasitic resistances. These quantities are sensitive to interfacial chemistry, defect states, and microstructure, and they all shift with temperature, making temperature-dependent current–voltage (I–V) measurements a demanding test of any predictive model.

Cadmium doping of zinc oxide plays a distinctive role in this system. The larger ionic radius of cadmium red-shifts the bandgap, alters the conduction-band edge alignment, and can relieve lattice mismatch at the heterointerface. Previous studies across several deposition methods have consistently reported bandgap narrowing and microstructural tuning with increasing cadmium content. In the present work, cadmium acetate and zinc acetate precursors were dissolved in 2-methoxyethanol, spin-coated onto ohmic-contacted p-type silicon at 3000 rpm, and annealed at 500 °C for one hour. Aluminum top contacts completed the Al/Cd0.1Zn0.9O/p-Si structures.

Measurements were carried out across an unusually broad temperature range. Forward and reverse I–V curves were recorded from −3.0 to +4.0 volts in 20-millivolt steps at eleven temperatures spanning 110 to 380 kelvin, inside a cryostat maintained at roughly 10⁻³ torr. Temperature was monitored continuously with a type-T thermocouple near the sample. This dataset — eleven temperature levels, each a full I–V sweep — became the substrate for a head-to-head comparison of ten prediction methods.

The seven data-driven contenders included Support Vector Regression, a multi-layer perceptron (MLP), Random Forest, three recurrent or hybrid architectures (LSTM-Many2One, CNN-LSTM, and Attention-LSTM), and N-BEATS, a feed-forward residual basis-expansion model. Each model received a fixed window of 30 consecutive voltage values together with the target temperature and was asked to predict the natural logarithm of the absolute current at the next voltage step. Crucially, the inputs contained no preceding current values, so the recurrent and convolutional models functioned as nonlinear regressors on ordered voltage-domain data rather than as genuine time-series forecasters.

The evaluation used a leave-one-temperature-out (LOTO) protocol: for each fold, all data at one temperature were held out entirely, and the model was trained only on the remaining ten temperatures. Held-out temperatures included boundary extrapolation cases at 110 and 380 kelvin as well as nine interior interpolation cases. Z-score normalization was fitted exclusively on training data of each fold to prevent leakage, and hyperparameter tuning was performed with Optuna on fold-specific validation blocks. Three additional benchmarks — nearest-temperature transfer, a two-dimensional polynomial-ridge response surface, and a thermionic-emission single-diode model with series and shunt resistances — shared the same outer folds.

N-BEATS produced the lowest descriptive mean errors: RMSE of 0.461 ± 0.236 on the logarithmic current scale and R² of 0.989 ± 0.008, with bias near zero. The MLP followed closely at RMSE 0.519 ± 0.269 and R² 0.986, with LSTM-Many2One and Attention-LSTM close behind. However, the authors were careful about claiming statistical superiority: a Friedman test across the eleven folds confirmed overall differences among methods, but after Holm correction, N-BEATS differed significantly from Random Forest, CNN-LSTM, and the three benchmarks — not from MLP, SVR, or the other recurrent models. The paired N-BEATS–MLP difference of −0.048 RMSE had a 95 percent confidence interval spanning zero.

The starkest result was a negative one. The CNN-LSTM, the most architecturally complex model, collapsed at held-out temperatures, with RMSE of 4.223 ± 2.707 and R² of just 0.128 — an over-parameterized network struggling with a small dataset. At the boundary folds, the picture was also nuanced: the 110-kelvin lower boundary proved harder for most methods, while the 380-kelvin upper boundary was method-dependent and not uniformly worse than interior interpolation. The physics-based thermionic-emission benchmark was respectable (RMSE 0.755, R² 0.961) but did not capture all measured deviations as accurately as the strongest data-driven models.

Beyond raw curve prediction, the team extracted the underlying diode physics from both experimental and model-generated curves. For the ideality factor — which exceeded unity throughout, a signature of barrier inhomogeneity and interface traps — N-BEATS achieved a mean relative error of about 7.5 percent, versus roughly 13.7 percent for MLP and 14.2 percent for LSTM-Many2One. Barrier heights were recovered remarkably well by all three representative models, with mean relative errors near 1.1 to 1.8 percent. Saturation-current errors were comparable for MLP and N-BEATS, while the LSTM deviated by more than an order of magnitude at higher temperatures. The models also reproduced the energy-dependent interface-state density profile obtained through the Card–Rhoderick treatment, with N-BEATS tracking the experimental decay most closely in descriptive terms, particularly in the mid-energy regions at 200 and 290 kelvin.

The authors are transparent about limitations. The dataset covers a single device architecture and fabrication route, so the findings speak to temperature generalization within this system, not device-to-device portability. Only DC measurements were considered, N-BEATS used a fixed configuration without hyperparameter search, and with only eleven temperature folds the statistical power of paired comparisons is limited. Still, the study offers a compelling message for the device-modeling community: when the goal is predicting behavior at temperatures never seen during training, a leakage-controlled validation protocol matters as much as the architecture itself, and a modest feed-forward network — supplied only with voltage windows and temperature — can faithfully preserve the transport physics buried in a diode’s I–V signature.

Subject of Research: Machine learning prediction of temperature-dependent current–voltage behavior in CdZnO Schottky barrier diodes

Article Title: Temperature-aware learning of current–voltage behavior in Schottky diodes: From classical machine learning to neural basis-expansion models under a leave-one-temperature-out validation protocol

Article References: Tulum, G., & Taşçıoğlu, İ. (2026). Temperature-aware learning of current–voltage behavior in Schottky diodes: From classical machine learning to neural basis-expansion models under a leave-one-temperature-out validation protocol. Machine Learning with Applications, 26, Article 101039. https://doi.org/10.1016/j.mlwa.2026.101039

Image Credits: AI Generated

DOI: 10.1016/j.mlwa.2026.101039

Keywords: Schottky barrier diode, machine learning, N-BEATS, leave-one-temperature-out, CdZnO, current–voltage characteristics, ideality factor, barrier height, interface-state density, neural networks, zinc oxide, thermionic emission