cond-mat.mes-hallApr 15, 2026
SaveAutomatic Charge State Tuning of 300 mm FDSOI Quantum Dots Using Neural Network Segmentation of Charge Stability Diagram
Organizations: CEA-Leti, Univ. Grenoble Alpes, F-38000 Grenoble, France
Abstract
Tuning of gate-defined semiconductor quantum dots (QDs) is a major bottleneck for scaling spin qubit technologies. We present a deep learning (DL) driven, semantic-segmentation pipeline that performs charge auto-tuning by locating transition lines in full charge stability diagrams (CSDs) and returns gate voltage targets for the single charge regime. We assemble and manually annotate a large, heterogeneous dataset of 1015 experimental CSDs measured from silicon QD devices, spanning nine design geometries, multiple wafers, and fabrication runs. A U-Net style convolutional neural network (CNN) with a MobileNetV2 encoder is trained and validated through five-fold group cross validation. Our model achieves an overall offline tuning success of 80.0% in locating the single-charge regime, with peak performance exceeding 88% for some designs. We analyze dominant failure modes and propose targeted mitigations. Finally, wide-range diagram segmentation also naturally enables scalable physic-based feature extraction that can feed back to fabrication and design workflows and outline a roadmap for real-time integration in a cryogenic wafer prober. Overall, our results show that neural network (NN) based wide-diagram segmentation is a practical step toward automated, high-throughput charge tuning for silicon QD qubits.
Figures & tables
Figure 1: Schematic summary of the offline auto-tuning pipeline. Top (Data acquisition): experimental setup and device illustrations (left) show the measurements done using cryogenic wafer prober on the gate-defined FDSOI QD geometry; the dataset panel (right) displays representative measured CSDs used for training. Bottom (Inference): the wide-diagram segmentation flow. Preprocessing produces a normalized input, which is fed to a U-Net with a MobileNetV2 encoder; the network outputs a predicted probability map that is binarized and refined by morphological post-processing; the algorithm then extracts transition-line skeletons and identifies the single-electron (1e - ) regime (highlighted in red here), returning gate-voltage targets for automatic charge tuning. The pipeline is trained and validated on a large, heterogeneous set of experimental CSDs and produces per-pixel line maps that enable both tuning and physics-based feature extraction.
Figure 2: (a) Charge stability diagram: a 2D current map associated to a QD . The x and y axes represent the voltage sweep applied to the gates, and the color bar represents the measured current value at every pixel in the map. The numbers represent the charges that are trapped in the dot, separated by charge transition lines. The area highlighted in light blue corresponds to the single-electron regime. (b) Ground truth mask of the CSD obtained by manually labeling the transition lines.
Figure 3: Offline auto-tuning pipeline. From left to right: (1) Cryogenic data acquisition of full CSDs . (2) Manual annotation and dataset assembly (1015 labeled CSDs ). (3) U-Net model training with five-fold group cross-validation. (4) Inference and postprocessing, (thresholding, morphological closing, dynamic component filtering, skeletonization) to extract the single-charge regime and return gate-voltage targets. Side panels show typical intermediate outputs produced by the pipeline.
Figure 4: Plot showing inference and the main postprocessing steps. (a) Input CSD as an image. (b) Expert annotated ground-truth transition-line mask used for training. (c) Raw model output: per-pixel probability map (colormap indicates model confidence between that the specific pixel belongs to a transition line). (d) Binary map obtained by thresholding the probability map at . (e) Morphological closing (to bridge small gaps) followed by dynamic area filtering / connected-component area thresholding (to remove small spurious detections) that connects broken segments and suppresses parasitic features. (f) Final cleaned binary mask from which the first two transition lines are extracted, and the center of mass of the single charge (1e - ) regime is computed (highlighted here in green). This center gives the gate-voltage target proposed by the pipeline for charge tuning.
Figure 5: Representative offline auto-tuning inference. (a) Measured CSD (input). (b) Expert-annotated ground truth transition line binary mask. (c) Model prediction after binarization and post-processing; the detected single charge regime center is marked with a red square. The single charge regime is highlighted with red, blue, and green for (a), (b), and (c), respectively. The example highlights how the pipeline extracts the relevant transition lines and proposes gate-voltage coordinates for tuning.
| Mask | Design | Success/Total CSDs | Success (%) |
|---|---|---|---|
| I | Design A | 70/83 | 84% |
| I | Design B | 52/61 | 85% |
| I | Design C | 64/81 | 79% |
| I | Design D | 130/147 | 88% |
| I | Design E | 122/138 | 88% |
| I | Design F | 121/142 | 85% |
Table 1: Per-design aggregate tuning success computed over five folds. “Success (%)” is the fraction of CSDs for which the predicted single charge regime center falls within the annotated charge region. The third column lists the raw successful detections and total diagrams per design.
| Failure Mode | Associated Causes | Failure Mitigation |
|---|---|---|
| Bad Quality CSD | Defective device / Noisy measurements Large regions with no signal (low SNR ) | Train a good vs. bad CSD classifier Re-measure noisy CSDs |
| Missed Lines | Stochastic lines Faint lines | Add contrast / gradient channels as inputs Expand / relabel dataset for stochastic lines |
| Spurious Lines | Noise-induced false positives Instrumentation or measurement artefacts | Confirm during online tuning Use FFT to spot lines with different slopes and spatial frequencies |
| Fragmented Lines | Low contrast leading to broken lines Interrupted transitions | Use row-sweep grouping to merge fragmented segments |
| Ambiguous Labeling | Human annotation inconsistencies | Multi-annotator Zoom / re-scan during online tuning |
Table 2: Summary of common failure modes observed in our stability diagrams, their associated causes, and suggested mitigations.
Figure 6: Representative failure-mode examples. Column 1: a stochastic/faint transition that intermittently disappears in the prediction; Column 2: a spurious line-like measurement artefact that can be misclassified as a transition; Column 3: a true transition whose predicted line is fragmented. Each column shows (top) the input CSD with a red arrow indicating the problematic feature, (middle) the hand-annotated ground-truth transition-line mask, and (bottom) the model’s binary prediction and extracted transition contours (blue/green) with the red dot marking the computed single charge target.
Figure 7: Distribution of our CSDs data across mask designs, device polarity, batches, wafers, and device design, respectively, from top left to bottom right.
| Mask | Polarity | Batch | Wafer | Design | Count |
|---|---|---|---|---|---|
| Mask I | n-type | B1 | i | Design A | 83 |
| Design B | 61 | ||||
| Design C | 81 | ||||
| Design D | 147 | ||||
| Design E | 138 | ||||
| Design F | 104 |
Table 3: Hierarchical breakdown of CSD counts across masks, polarity, batches, wafers, and specific device designs.
Figure 8: Representative stability diagram examples across masks, wafers and device geometries.
Figure 9: Schematic of the U-Net segmentation model (encoder, bottleneck, skip connections, and four-stage decoder) used to predict per-pixel transition probabilities from input CSD measurements.
| Model | Params |
|---|---|
| MobileNetV2-U-Net ( ) (total params) | 2,057,489 |
| Trainable params | 2,032,497 |
| Non-trainable params | 24,992 |
Table 4: Model parameter count
| Hyperparameter | Value |
|---|---|
| Optimizer | Adam [ 17 ] |
| Learning rate | |
| Loss function | Dice loss |
| Batch size | 8 |
| Epochs | 50 |
| Input size | 1024x1024 |
Table 5: Fixed hyperparameters used for all folds.
Figure 10: Examples of successful detection of the single charge regime across a variety of CSDs. Column 1 includes the original CSD used as input. Column 2 represents the corresponding hand-annotated ground truth mask. And column 3 is the model’s prediction of transition lines and subsequent detection of the single charge regime by our auto-tuning pipeline.
| Fold | Design A | Design B | Design C | Design D | Design E |
|---|---|---|---|---|---|
| 1 | 11/12 (92%) | 14/16 (88%) | 17/17 (100%) | 39/42 (93%) | 24/24 (100%) |
| 2 | 17/19 (89%) | 10/11 (91%) | 15/20 (75%) | 21/26 (81%) | 37/41 (90%) |
| 3 | 11/15 (73%) | 7/12 (58%) | 12/15 (80%) | 25/30 (83%) | 25/31 (81%) |
| 4 | 12/14 (86%) | 9/9 (100%) | 13/15 (87%) | 21/25 (84%) | 17/21 (81%) |
| 5 | 19/23 (83%) | 12/13 (92%) | 7/14 (50%) | 24/24 (100%) | 19/21 (90%) |
| Total | 70/83 (84%) | 52/61 (85%) | 64/81 (79%) | 130/147 (88%) | 122/138 (88%) |
Table 6: Inference Summary per Design and per Fold. For each device and fold we report the ratio of the number of diagrams with successful single charge detection to the total number of diagrams, followed by the percentage value.