A method for screening metal / gallium oxide contact resistivity based on quantum kernel residual

Abstract

The application discloses a metal / gallium oxide contact resistivity screening method based on quantum kernel residual. In view of the problems of high cost and limited samples of high-fidelity transport label under fixed doping concentration and interface template, joint query scores are constructed based on the boundary of candidate element records, distribution gain, batch diversity and physical priori to determine the priority of the object to be labeled. A first-level residual is predicted by using a material-level leave-one-out pre-reference prediction. Quantum kernel residual prediction is obtained through standardization, principal component analysis, Pauli Z-phase encoding, fidelity quantum kernel and support vector regression. The quantum kernel residual regression basic prediction value is formed by combining the pre-reference prediction, and the low contact resistivity candidate ranking is output. Further, the applicable domain state can also be output. The new target value is called by subsequent model training tasks after external high-fidelity calculation, artificial verification and archiving, so as to improve the low-resistance contact metal screening efficiency under the limited calculation budget.

Description

Technical Field

[0001] This invention belongs to the fields of materials informatics, gallium oxide (Ga2O3) power device contact engineering, quantum kernel machine learning, and computational materials science. It relates to a metal / gallium oxide contact resistivity screening method based on quantum kernel residuals. In particular, it relates to a quantum-kernel residual regression (QK-RR) method that combines material-level extra-refractive baseline residuals with Pauli-Z fidelity quantum kernels under fixed doping concentration and fixed interface template conditions to predict and rank metal / β-Ga2O3 contact candidates. Background Technology

[0002] β-Ga₂O₃ possesses a wide bandgap, high critical breakdown field strength, and high figure of merit for power devices, making it an important candidate material for high-voltage, high-power electronic devices. The potential barrier, interface states, Fermi level pinning, and quantum transport behavior at the metal / β-Ga₂O₃ contact interface directly affect the device's on-resistance, power consumption, and reliability. Even with unchanged doping concentration, β-Ga₂O₃ crystal orientation, interface termination mode, and device configuration, significant differences in contact transport performance can still exist for different contact metals. Therefore, it is necessary to identify low-resistance contact materials from a broad range of candidate metals.

[0003] Obtaining contact transport tags at the metal / β-Ga2O3 interface using density functional theory—non-equilibrium Green's function (DFT-NEGF) typically requires sequential steps including interface lattice matching, atomic structure optimization, open-boundary device construction, transmission spectrum calculation, zero-bias conductivity extraction, and lateral area normalization. The computational resources and manual configuration costs for a single candidate are substantial. Furthermore, results obtained from different crystal orientations, termination methods, doping concentrations, device lengths, or tag extraction methods cannot usually be directly mixed as training tags for the same screening task.

[0004] Under the constraints of a unified interface template and a unified labeling standard, the number of labeled contact metals that can be obtained is often only a few dozen to a few dozen, while the number of elemental physicochemical descriptors may be higher than the number of labeled metals, forming a regression problem with extremely small samples, high dimensionality, and target values ​​that vary across orders of magnitude. If high-fidelity calculations are performed on each candidate metal, the screening cost is high; if candidates are excluded in advance based solely on experience, work function, or a single barrier index, low-resistivity materials affected by interface bonding, interface dipoles, metal-induced bandgap states, and tunneling effects may be missed.

[0005] Existing patents have proposed several solutions for the design and transport simulation of semiconductor contact interfaces. For example, CN119129219A discloses a design and simulation method for two-dimensional semiconductor nanotransistors, which analyzes the band structure, carrier mobility, and contact resistance of two-dimensional semiconductor devices through material selection, surface treatment, metal contact design, device structure optimization, and first-principles and non-equilibrium Green's function transport simulation. CN118332873A discloses a method for simulating heterojunction tunneling current under stress, which introduces macroscopic stress and strain information obtained from COMSOL multiphysics simulation software into first-principles band structure calculations to obtain the tunneling barrier and tunneling current variations with stress. The above solutions focus on the design, simulation, and performance analysis of a given two-dimensional device or a given heterojunction structure, and do not provide a same-aperture contact transport tag prediction and ranking process for establishing a candidate metal library for fixed metal / β-Ga2O3 interface tasks.

[0006] CN114997092B discloses a simulation method for the electrical characteristics of semiconductor devices based on machine learning and models. It predicts the input model parameters of a compact model based on device structural parameters or process parameters, and then substitutes the predicted model parameters into the device model to complete the electrical characteristic simulation. In its GaN high-electron-mobility transistor (GaN HEMT) implementation, the compact model parameters include source and drain contact resistances. The machine learning object of this scheme is the mapping between process parameters, structural parameters, and compact model parameters, aiming to accelerate device or circuit-level simulation. It does not use different metal elements as discrete candidate objects, nor does it disclose the use of a unified DFT-NEGF area-normalized zero-biased transport index to train the contact material screening model.

[0007] CN118522374A discloses a machine learning method for screening chalcogenide phase change memory materials based on amorphous structures. The method trains a machine learning model using first-principles modeling, molecular dynamics simulations, and features such as local structure, material stacking ratio, and electronegativity differences to identify and screen phase change materials. This approach demonstrates that first-principles features and machine learning can be used for material screening; however, its material system, sample labels, and screening targets are all specific to chalcogenide phase change memory materials, without addressing the quantum transport resistance of the metal / semiconductor interface, nor solving the problems of contact metal regression and labeling order selection for extremely small samples under fixed interface conditions.

[0008] CN122133481A discloses a heat dissipation optimization method for Ga2O3 power devices based on heterostructures. This method combines first-principles calculations, thermal conductivity calculations, machine learning potential functions, non-equilibrium molecular dynamics, and finite element thermal simulations to perform multi-scale screening and optimization of Ga2O3 heterostructure materials, interfacial thermal conductivity, and device thermal field. While this approach is related to the screening of Ga2O3 materials and candidate materials, its core objective is to optimize high thermal conductivity substrates and interfacial thermal transport. Evaluation metrics include thermal conductivity, interfacial thermal conductivity, and device junction temperature, but it does not involve zero-bias conductivity, contact transport parameters, or low contact resistance candidate ranking for metal / β-Ga2O3 electrical contacts.

[0009] Previous studies have proposed machine learning schemes for screening low-contact electrodes for 2D semiconductors under limited data conditions [Li PH, Dong LP, Li C, et al. Machine Learning to Promote EfficientScreening of Low-Contact Electrode for 2D Semiconductor Transistor UnderLimited Data[J]. Advanced Materials, 2024, 36(26): 2312887.]. This study constructed a material space containing 513 2D electrode candidates from a computational 2D material database, used feature-adaptive variational active learning (FAVAL) to select representative training samples, and combined it with an autoencoding regularized adversarial neural network (ARANet) to predict the vertical or lateral Schottky barrier and tunneling probability. This study shows that active learning can improve the efficiency of labeled sample utilization, and reports that when FAVAL and ARANet are combined, good prediction performance can be obtained using only 15% of the total samples. However, its overall candidate space reaches hundreds of items, and even with a 15% sampling, there are still dozens of high-fidelity labeled samples. For tasks where the number of elemental candidates that can be included in the initial screening is only on the order of hundreds, and where only a few to a dozen transport tags of the same diameter can usually be obtained under a unified metal / β-Ga2O3 interface template, this data scale and deep network training method are still difficult to apply directly; its prediction targets are also mainly the barrier and tunneling probability, rather than the normalized zero-biased transport index of the complete device area.

[0010] Another study applied quantum kernel learning to model ohmic contacts in semiconductor manufacturing processes [Wang ZH, Wang F Z, Li L, et al. Quantum Kernel Learning for Small Dataset Modeling in Semiconductor Fabrication: Application to Ohmic Contact[J]. Advanced Science, 2025, 12(35): e06213.]. Based on 159 sets of experimental samples of ohmic contacts in GaN high electron mobility transistors, this study, after principal component analysis preprocessing and variational autoencoder data augmentation, used a shallow Pauli-Z eigenmap and a trainable quantum kernel alignment layer to construct a quantum kernel alignment regressor to predict contact resistance under different metal stacking, annealing conditions, and device parameters. This study demonstrates that the quantum kernel method can express complex nonlinear correlations in data-constrained semiconductor contact modeling and shows predictive potential compared to several classical regression models. However, this scheme is based on the 159 sets of experimental samples and their augmentation data that have been obtained. It focuses on the contact resistance regression of the given process samples. It does not solve the problem of which high-fidelity labels should be prioritized when facing unlabeled candidate metals, nor does it establish a sample determination mechanism between active candidate selection, external labeling, and quantum kernel model training.

[0011] For metal / β-Ga2O3 contact screening under a fixed interface template, the number of labeled data is small, the material descriptor has a high dimension, and the contact transport is affected by factors such as elemental properties, interface bonding, Fermi level pinning, metal-induced bandgap states and tunneling behavior. There may be nonlinear coupling across metal groups between the descriptor and the area-normalized zero-biased transport index.

[0012] In summary, the existing patents and academic literature cover two-dimensional semiconductor contact design and quantum transport simulation, device compact model parameter prediction, stress coupling tunneling analysis, phase change material machine learning screening, Ga2O3 heterostructure substrate heat dissipation optimization, FAVAL active learning and ARANet prediction for hundreds of two-dimensional electrode candidates, and quantum kernel regression based on existing GaN ohmic contact process samples. While existing active learning schemes can improve label utilization, their candidate space and training sample size are still significantly larger than the number of labels of the same caliber typically obtainable for elemental metal contact tasks with fixed templates. Existing quantum kernel contact modeling schemes rely on existing experimental samples and data augmentation, failing to address the priority acquisition and determination of new candidate metal labels. Furthermore, modeling contact materials with very small samples also presents problems in evaluation and candidate selection. Using a fixed ratio to randomly divide the training, validation, and test sets further reduces the number of materials available for fitting; if the same metal identity or its derived records appear simultaneously in both the training and evaluation sets, the model's generalization ability to new metals is easily overestimated. Directly employing high-degree-of-freedom deep networks or directly fitting quantum kernels to all targets across orders of magnitude may be affected by a few extreme labels in extremely small sample sizes. Selecting candidates solely based on predicted values ​​will cause new labels to concentrate in the low-resistivity region perceived by the current model, while selecting candidates solely based on distance may repeatedly select similar boundary points or result in over-extrapolation. Furthermore, the aforementioned publicly available solutions do not provide a unified audit output to determine whether candidates are within the training distribution, near the boundary, or in a clearly extrapolated region.

[0013] Based on this, the present invention proposes a screening scheme for metal / β-Ga2O3 contact materials with fixed doping concentration and fixed interface template: using the normalized zero-bias transport index of the complete device area of ​​the same aperture as a label, the priority supplementary label candidates with coverage value are determined by descriptor space query, the cross-metal group main trend is extracted by a low-degree-of-freedom physical partitioning pre-benchmark model, and the residuals not explained by the pre-benchmark model are learned by using the Pauli-Z fidelity metric quant kernel, thereby forming a prediction and ranking for new metal identities under a limited high-fidelity computation budget.

[0014] Furthermore, the present invention can also output the applicable domain state of each candidate element and use descriptor space query to determine the supplementary label object with coverage value from the finite candidate elements, so as to reduce the amount of high-fidelity computation required to form an effective training set and prioritize the allocation of limited external DFT-NEGF computing resources to candidate metals with training value or performance verification value. Summary of the Invention

[0015] This invention aims to solve the problem of high-fidelity area-normalized zero-biased transport index ρ at the metal / β-Ga2O3 interface. cTo address the problems of high tag acquisition costs, limited number of available labeled metals under fixed interface conditions (which may be less than the effective material descriptor dimension), and difficulty in describing cross-metal group trends through direct regression with extremely small samples, this paper proposes a metal / gallium oxide contact resistivity screening method based on material-level extrapolation pre-benchmark residuals and Pauli-Z fidelity quantum kernel regression.

[0016] The technical solution adopted in this invention is as follows:

[0017] A method for screening the contact resistivity of metal / gallium oxide (Ga2O3) based on quantum nuclear residuals includes:

[0018] Acquire labeled contact metal data and candidate element records for metal / β-Ga2O3 contact systems under the same physical task. The labeled contact metal data includes a pre-reference auxiliary descriptor, an effective material descriptor, and a target value corresponding to the area-normalized zero-biased transport index. The candidate element records include the corresponding pre-reference auxiliary descriptor and effective material descriptor.

[0019] For the labeled contact metal data, based on its preceding benchmark auxiliary descriptor, for each contact metal as a reserved unit of material-level extrapolation prediction, the contact metal is reserved from the current training set, the preceding benchmark model is trained using the remaining labeled contact metal data, and the reserved contact metal is predicted using the trained preceding benchmark model to obtain the preceding benchmark prediction value of material-level extrapolation for each labeled contact metal; the difference between the target value and the corresponding preceding benchmark prediction value of material-level extrapolation is determined as the first-level residual;

[0020] Based on the effective material descriptor and the first-order residual, a quantum kernel residual regression model using Pauli Z-phase encoding and a fidelity metric quantum kernel is trained.

[0021] Based on the labeled contact metal data, a pre-benchmark model is fitted, and the pre-benchmark predicted value and the quantum kernel first-level residual predicted value of the candidate element record are obtained by using the fitted pre-benchmark model and the trained quantum kernel residual regression model, respectively.

[0022] For candidate element records that can obtain the aforementioned baseline prediction value and quantum kernel first-level residual prediction value, the aforementioned baseline prediction value is added to the quantum kernel first-level residual prediction value scaled by the residual scaling factor to obtain the quantum kernel residual regression baseline prediction value, and the candidate element records are sorted in ascending order according to the quantum kernel residual regression baseline prediction value.

[0023] In the above technical solution, further, the same physical task refers to having at least the following conditions that are the same: doping concentration, β-Ga2O3 crystal orientation, interface termination method, interface template conditions, and target value extraction rules.

[0024] Furthermore, the area-normalized zero-bias transport index is determined based on the zero-bias differential resistance of the intact metal / β-Ga2O3 template device and the transverse periodic supercell area perpendicular to the transport direction. The target value is the area-normalized zero-bias transport index multiplied by Ω·nm. 2 The commonly used logarithm of the ratio.

[0025] Furthermore, the determination of the preceding benchmark model includes:

[0026] Multiple candidate configurations of the pre-benchmark are constructed with different parameter schemes. Taking the contact metal as the leave-out unit, material-level extra-blurred pre-benchmark prediction is performed for each candidate configuration of the pre-benchmark.

[0027] Based on the material-level extrapolation prediction error corresponding to each candidate pre-prepared baseline configuration, the pre-prepared baseline configuration used to construct the first-level residual and predict the candidate element record is optimally determined; then, the labeled contact metal data is fitted under the pre-prepared baseline configuration to obtain the pre-prepared baseline model; furthermore, the material-level extrapolation prediction error includes the internal sum of squared errors (SSE), internal mean absolute error, and internal root mean square error. The optimal determination is as follows: first, the candidates are sorted in ascending order by the internal sum of squared errors (SSE); if they are the same, they are sorted in ascending order by the internal mean absolute error; if they are still the same, they are sorted in lexicographical order by the candidate configuration name, and the first item is taken as the pre-prepared baseline configuration.

[0028] Furthermore, the physical partitioning pre-benchmark model divides the labeled contact metals and candidate element records into different physical partitions based on the element category attributes of the contact metals. Each labeled contact metal or candidate element record is predicted only by the pre-benchmark sub-model corresponding to its physical partition. The element category attributes include transition metal labels and periodic table family numbers. The physical partitions include a first physical partition and a second physical partition. Transition metals with periodic table family numbers from group 8 to group 11 are assigned to the second physical partition, and the pre-benchmark sub-model used is a ridge regression regularized linear regression model. The rest are assigned to the first physical partition, and the pre-benchmark sub-model used is a radial basis function kernel support vector regression (RBF-SVR) nonlinear kernel regression model. Each pre-benchmark sub-model uses the pre-benchmark auxiliary descriptor corresponding to the physical partition as input.

[0029] Furthermore, the training of the quantum nuclear residual regression model includes:

[0030] The effective material descriptors are standardized and subjected to principal component dimensionality reduction to obtain dimensionality-reduced coordinates;

[0031] The components of the reduced-dimensional coordinates are mapped to phase angles, and the corresponding qubits are encoded using phase rotations generated by the Pauli Z operator. The Pauli Z phase encoding does not set entanglement coupling terms between qubits.

[0032] Construct a fidelity quantum kernel based on the fidelity between quantum encoded states corresponding to different dimensionality reduction coordinates;

[0033] Based on the pre-calculated fidelity metric kernel, a ν-support vector regression residual regression model with the first-level residual as the supervision target is trained.

[0034] Furthermore, the residual scaling factor, as a parameter of the quantum nucleus residual branch candidate configuration, is determined based on the material-level extrapolation evaluation results of each quantum nucleus residual branch candidate configuration.

[0035] Furthermore, it also includes:

[0036] The applicable domain state of the candidate element record is determined based on the spatial distance of the candidate element record relative to the descriptor of the labeled contact metal data, and the degree to which the effective material descriptor of the candidate element record exceeds the corresponding value range of the labeled contact metal data.

[0037] The applicable domain states include interpolation type, near-boundary type, and extrapolation type.

[0038] Furthermore, it also includes a descriptor space query method for selecting candidate element records for the target value to be supplemented, including:

[0039] Retrieve seed metal records, candidate element records, and query master descriptors that do not contain target values ​​for the same physical task;

[0040] A descriptor query space is constructed based on the query master descriptor, and the current query coverage set is formed by the seed metal records;

[0041] Without using the target value of the candidate element record, the quantum kernel residual regression prediction value, the model residual, and the model uncertainty, determine the boundary score, the overall distribution gain, the intra-batch diversity score, and the auxiliary physical prior score of the candidate element record, respectively.

[0042] The boundary score, overall distribution gain, intra-batch diversity score, and auxiliary physical prior score are combined into a joint query score, and candidate element records of the target value to be supplemented are selected in sequence according to the joint query score to form a descriptor coverage query batch.

[0043] After each candidate element record is selected, the candidate element record is added to the current query batch and the current query coverage set. The boundary score, overall distribution gain, intra-batch diversity score, auxiliary physical prior score, and joint query score of the remaining candidate element records are re-determined based on the updated current query coverage set, until the descriptor coverage query batch is formed.

[0044] Furthermore, the seed metal record and candidate element record are determined as the overall distribution reference set, which remains unchanged during the same descriptor space query process;

[0045] The boundary score is determined based on the descriptor space distance between the candidate element record and the current query coverage set;

[0046] The overall distribution gain is determined based on the change in the distribution difference between the current query coverage set and the overall distribution reference set before and after the candidate element records are added to the current query coverage set.

[0047] The intra-batch diversity score is determined based on the descriptor space distance between the candidate element record and the selected candidate element record in the current query batch; when no candidate element record has been selected in the current query batch, the same initial intra-batch diversity score is applied to the remaining candidate element records.

[0048] The auxiliary physical prior score is determined based on the actual available physical properties of the elements in the candidate element record.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] QK-RR utilizes a pre-baseline model to extract cross-metallic family main trends. The Pauli-Z fidelity metric sub-kernel support vector regressor only learns the first-order residuals not explained by the pre-baseline model, thus reducing the difficulty of directly fitting all orders of magnitude targets. Material-level out-of-fold residuals and outer single-fold retention are implemented in a layered manner, allowing auditing of the label isolation of the fitting process of each fold model under frozen hyperparameter combinations. The original ranking of the trained models is used to screen low-ρ models awaiting external validation. c Candidate prediction. In the implementation of setting up an applicable domain audit, the applicable domain state is also output based on the candidate's position relative to the training distribution. In the implementation using descriptor space query, the query process prioritizes supplementing training samples based on descriptor space coverage to avoid training label acquisition being completely biased towards the current low-resistivity prediction region; after the newly added labels are externally calculated with high fidelity, manually verified, and archived, an updated labeled dataset and corresponding data version are formed. After subsequent model training completes candidate configuration selection, model fitting, and result freezing, a corresponding model version is formed. In the implementation using nested evaluation of terminal residuals, this evaluation is only used as a nested error analysis tool on a fixed dataset and does not propagate to the deployment ranking of unlabeled candidates. The supplementary label calculation and performance verification are both manually configured by independent external processes; this method does not automatically complete DFT calculation, label backhaul, manual verification, or archiving, and the archiving of newly added target values ​​does not automatically trigger subsequent model training or model version establishment. Attached Figure Description

[0051] Figure 1In a preferred embodiment of the present invention, candidates for covering labels are first selected by independent descriptor space query, new labels are calculated and archived by external manual configuration of DFT-NEGF, and then QK-RR is trained to filter low-p values. c A flowchart illustrating the process of predicting candidates and validating them using externally configured DFT-NEGF.

[0052] Figure 2 To fix the QK-RR basic prediction model at 1×10 19 e / cm 3 Figure showing the consistency between predicted and actual values ​​when performing material-level retention-one-out reproduction on 13 labeled metals under certain conditions;

[0053] Figure 3 for Figure 2 The diagram shows the QK-RR basic prediction external residual generated by leave-one-out reproduction at the material level;

[0054] Figure 4 for Figure 2 The figure shown is a graph of the metal-by-metal multiplicative error results for the basic prediction of QK-RR material-level leave-one-out reproduction;

[0055] Figure 5 for Figure 2 The figure shows the material-level bootstrap sensitivity interval results for the QK-RR basic prediction reproducibility index of 13 metals.

[0056] Figure 6 for Figure 2 The figure shown is a consistency result chart of the sorting of 13 labeled metals in the QK-RR basic prediction material-level leave-one-out reproduction.

[0057] Figure 7 To utilize the fixed-parameter QK-RR basic model fitted to all currently labeled contact metals, the original ranking of the top 15 unlabeled candidate elements with complete and valid material descriptors, capable of obtaining the previous benchmark prediction value from the previous benchmark model, and capable of obtaining the quantum nucleus first-level residual prediction value is given.

[0058] Figure 8 for Figure 7 The diagram shows the rule-based applicable domain audit diagram of the QK-RR basic prediction candidate element record with fixed parameters;

[0059] Figure 9 In this embodiment of the invention, a fixed doping concentration of 1×10⁻⁶ is used. 19 e / cm 3Under the conditions of fixed target definition and leave-one-out verification for 13 kinds of metal materials, the predictive performance of the quantum kernel residual regression model (QK-RR) is compared with that of gradient boosting regression, nearest neighbor regression, random forest regression, ridge regression, radial basis function support vector regression, radial basis function kernel ridge regression, and Gaussian process regression. Subplot (a) shows the comparison of root mean square error (RMSE), subplot (b) shows the comparison of mean absolute error (MAE), and subplot (c) shows the coefficient of determination (R²). 2 )contrast. Detailed Implementation

[0060] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to illustrate the specific implementation and effects of the present invention and do not constitute a limitation on the present invention.

[0061] The metal / gallium oxide (Ga2O3) contact resistivity screening method based on quantum kernel residuals proposed in this invention includes quantum-kernel residual regression (QK-RR) basic prediction and low-ρ... c Candidate output. In the QK-RR basic prediction stage, the main prediction is obtained from the pre-baseline model, and a first-level residual is constructed through material-level out-of-place predictions within the training set. This is then combined with in-place normalization, principal component dimensionality reduction, and Pauli-Z phase encoding. A support vector regressor with a fidelity metric nucleus as the pre-computation kernel is used to learn the first-level residual. The pre-baseline prediction value is added to the scaled quantum nucleus first-level residual prediction value to obtain the QK-RR basic prediction. The target contact resistivity is the area-normalized zero-biased transport index ρ under a fixed β-Ga2O3 interface template and a fixed doping concentration. c The regression objective is ρ c Relative to Ω·nm 2 The commonly used logarithm. In the method of this invention, the number of labeled contact metals is limited and can be less than the dimension of the effective material descriptor; data with different crystal orientations, interface terminations, doping concentrations, or target value extraction rules are labeled separately and not directly mixed into the same fixed-condition training task. That is, the screening method is only performed as the same physical task when the doping concentration, β-Ga2O3 crystal orientation, interface termination method, interface template conditions, and target value extraction rules are all the same.

[0062] In a preferred embodiment, the support vector regressor is a ν-support vector regression (NuSVR); after training, the original ranking of the model is output.

[0063] In another preferred embodiment, an applicable domain audit is set up. For candidate element records that meet the QK-RR numerical prediction conditions, an interpolated, near-boundary, or extrapolated applicable domain status is output. For candidate element records that do not meet the QK-RR numerical prediction conditions, an unsupported status is output, so that external processes can manually configure high-fidelity verification.

[0064] In other preferred embodiments, descriptor space query, nested evaluation, and candidate verification stages are also included. The descriptor space query stage independently generates a coverage query batch using the geometric relationships of descriptors in the query feature table. This batch is manually configured and supplemented by operators of the external high-fidelity calculation process. Newly added target values ​​obtained from external calculations are manually verified and archived according to physical task identifiers, fixed doping concentrations, interface template conditions, and target value extraction rules, forming an updated labeled dataset and corresponding data version. The external high-fidelity calculation, manual verification, and archiving are performed by processes outside this method. The archiving of new target values ​​does not automatically trigger new QK-RR model training or model version creation. Subsequent model training uses the updated labeled dataset by an explicitly initiated training task and performs candidate configuration selection, model fitting, result freezing, and candidate prediction according to this method, forming the corresponding model version. The nested evaluation stage only performs terminal residual nested evaluation within the fixed labeled dataset, used to audit the error structure without modifying the deployment ranking of unlabeled candidate element records.

[0065] The following points will be discussed in detail.

[0066] I. (1) Candidate element record library, interface template and current annotation set

[0067] In the metal / β-Ga2O3 contact minimal sample task, this embodiment uses

[100] β-Ga2O3 with oxygen termination at the interface, and does not limit the number of candidate metals, feature dimension and model parameters to unique values.

[0068] Construct a main pool of candidate element records, and distinguish between descriptor space query records used for active learning of complementation and records used for low-ρ records after training. c The QK-RR deployment records selected and the candidate electrode material records that have been externally verified and are ready for contact interface review. Unmarked records are indicated as (c, x). c , b c , p c , a c (Does not contain unknown target label y) c ; Add corresponding y to the already marked record c fields, where The identifier for the candidate element is recorded, such as the element symbol Ga or V. Record for elements The corresponding effective material descriptor vector, i.e., the material property vector used by the quantum kernel residual branch after screening for non-finite values, near-constant values, and redundant fields, b c For the preceding baseline auxiliary descriptor, i.e., the element attributes used by the preceding baseline model, p c To query the physical prior auxiliary descriptor, a c This process marks the initial usability status and related field availability at the code level. In one specific embodiment of the invention, the QK-RR deployment candidate pool includes 93 element records sorted by element symbol, of which 13 are labeled training metals. 52 element records meet the QK-RR numerical prediction conditions, meaning that each candidate element record simultaneously possesses a complete and valid material descriptor, can obtain a baseline prediction value from the baseline model, and can obtain a quantum kernel first-level residual prediction value from the quantum kernel residual regression model, thus enabling the output of basic QK-RR prediction values. 28 element records do not meet any of the above QK-RR numerical prediction conditions, and therefore only output an unsupported state. This deployment candidate pool is used for basic QK-RR prediction, initial model sorting, and domain auditing. Independent of the deployed candidate pool, the descriptor space query uses a fixed query feature table provided by the query version. In this embodiment, the fixed query program reads 88 element records and 15 query master descriptor fields. Pt, Pd, silver (Ag), gold (Au), copper (Cu), Sc, titanium (Ti), and magnesium (Mg) constitute the initial query coverage set, while the remaining 80 element records constitute non-seed query candidates. Even if a descriptor space query record does not meet the QK-RR numerical prediction conditions, it can still be used as a coverage supplementary label when a complete query master descriptor is available. Externally added labels, after manual confirmation and archiving, can form an updated labeled dataset and corresponding data version. Subsequent model training tasks call the updated labeled dataset and complete candidate configuration selection, model fitting, and result freezing to form the next model version. The model input support status only indicates whether numerical calculations can be performed and is not equivalent to the final feasibility of the material or task.

[0069] Create a master descriptor vector x for each candidate element record. The list of valid descriptor fields is provided without using any ρ. c In the case of a target value, the frozen feature table is used to determine the following: fields containing non-finite values ​​and near-constant fields are deleted, and redundancy screening is performed on the remaining fields without reading the target value; if redundancy screening is performed, a scaling transformation is performed, which is only used to determine the field list and is not used as a normalization parameter for model training. The model normalizer still only fits within the corresponding training iteration. The cleaning described in the fixed embodiment only utilizes the frozen descriptor rows corresponding to the 13 labeled metals and does not read any ρ cThe target value, and unlabeled candidates, are not included in the determination of the 24-dimensional effective field list; within each model evaluation layer, the normalizer and principal component analyzer are trained only on the metal fit of that layer. The fixed 13-metal task yields the 24-dimensional effective descriptors listed in Table 1 from the 32-field feature source; the effective dimension can change after changing the metal set or feature source. The candidate main pool contains 93 element records.

[0070] This embodiment employs a hierarchical versioning system. The physical task identifier is determined by the material system, fixed interface template, target definition, and fixed n-type doping concentration; the candidate element identifier system is managed separately as a data recording specification; the data version is determined by the physical task identifier, labeled dataset content, and archived records; the model version is determined by the called data version, model feature table, pre-reference candidate library, quantum core candidate configuration set and its frozen selection results, end-residual nested evaluation rules, and applicable domain rules; the query version is determined by the query feature table, query algorithm, scoring weight, and batch size. Active learning query batches are used for external manual supplementation of training labels; newly added labels, after manual verification and archiving, establish a new data version. Subsequent model training tasks call this data version, and after completing candidate configuration selection, model fitting, and result freezing, establish the corresponding model version. Performance verification candidate results can be output based on this model version. When the content of the labeled dataset is changed, a new data version is created; when the query feature table, query algorithm, weight, or batch size is changed, a new query version is created; when the model input, candidate configuration generation, internal selection, or applicable domain rules are changed, a new model version is created; the results of different physical task identifiers, data versions, model versions, or query versions are recorded separately.

[0071] Table 1. 24-dimensional effective descriptors for the first-order residual branch of the QK-RR quantum kernel with fixed parameters.

[0072] The fields in Table 1 of the Mendeleev element database, the material genome analysis library element table (pymatgen), and the material-independent informatics and exploration platform (Magpie) are based on the stored values ​​in the fixed static feature table; the same archived feature table is used for model training and candidate prediction, and the field values ​​are not automatically updated during the prediction process.

[0073] For candidate element records, establish a code-level preliminary usability status marker 'a', a set of prerequisite auxiliary descriptors 'b', and a set of query physics prior auxiliary descriptors 'p', and establish corresponding field availability markers. The prerequisite auxiliary descriptor 'b' includes at least the corresponding fields from Pauling electronegativity, atomic mass, and tenth-order ionization energy; the continuous physics prior fields 'p' for querying the descriptor space without reading target labels only include Fermi level, bulk modulus, shear modulus, melting point, and Pauling electronegativity. The code-level preliminary usability status marker 'a' can be formed based on preset material category, stability, radioactivity, or task constraint fields, and is used as an auxiliary marker for the candidate list; this status does not change QK-RR prediction, model ranking, or active learning joint scoring, nor does it constitute the final task eligibility judgment. Whether a candidate is suitable for actual interface calculation is still confirmed externally by manual verification based on specific task conditions.

[0074] Missing candidate fields are handled according to the rules frozen in the corresponding model version or query version: all non-seed candidate element records in the specified query feature table can participate in the descriptor space query without reading the target label, and they are not required to have QK-RR basic model fields at the same time; QK-RR candidate deployment only combines and outputs the QK-RR basic prediction value for candidate element records that have complete and valid material descriptors, can obtain the previous baseline prediction value from the previous baseline model, and can obtain the quantum kernel first-level residual prediction value; for candidate element records that do not meet any of the above conditions, the "not supported" status is output. When a candidate lacks auxiliary fields required for query physical priors, no fictitious filling is performed, and only the actual available fields are used to calculate the availability ratio and physical prior gain; when there are no available auxiliary fields, the original physical prior score is 0, and the remaining query score items can still be used for the candidate.

[0075] (2) Data source, processing and freezing

[0076] In this embodiment, the data source, processing, and freezing process are distinct from model training, candidate prediction, and descriptor space querying. The fixed query master descriptor used for active learning is based on predefined metal element records, extracted using the Magpie Dataset from the materials informatics toolkit (matminer) after constructing single-element chemical formulas by element symbols. The fixed query master feature table retains 15 complete fields and 88 element records. Among the auxiliary fields used for querying physical priors, the Fermi level, bulk modulus, and shear modulus are taken from single-element records matching the corresponding elements in the Materials Project database, prioritizing stable records and selecting from available records according to energy priority rules when necessary. Melting point and Pauling electronegativity are obtained from the MagpieData fields.

[0077] The static element descriptor tables used for QK-RR were obtained by Mendeleev, pymatgen, and MagpieData, respectively. The fixed 13-metal embodiment does not read ρ. c Under the condition of target values, a 24-dimensional list of valid descriptors is formed from 32 feature source fields; model training, material-level leave-one-out evaluation, and candidate prediction all read the stored values ​​in this frozen table, without reconnecting to the network to obtain or update the element fields during the prediction process. The target labels of the 13 training metals are derived from the density functional theory-nonequilibrium Green's function (DFT-NEGF) calculation results archived under fixed physics task conditions, rather than from the aforementioned element attribute database.

[0078] During data processing, multi-source records are first merged by element symbol and atomic number, and material number and fields duplicated with element identity are removed. For bulk modulus and shear modulus, values ​​not greater than zero or greater than 1000 GPa are marked as missing values. The active learning query master feature table performs zero-tolerance removal on feature columns containing missing values, without filling with the mean, median, or model estimate, thus freezing 15 query master descriptors without missing values. Missing physical prior auxiliary fields are allowed; missing fields do not participate in the physical prior calculation of the candidate, and the original score of the physical prior is zero when no available auxiliary fields exist.

[0079] QK-RR candidate deployments only accept element records whose 24-dimensional valid descriptors are all finite values ​​and simultaneously meet the conditions of baseline prediction and quantum kernel first-level residual prediction. If any required field is missing or any numerical prediction condition is not met, the output does not support the state and is not included in the original model sorting, and no fictitious filling or missing value imputation is performed. The number of records and fields in each frozen file is shown in Table 1-1.

[0080] Table 1-1 Data Source, Processing, and Freezing Records for Fixed Implementation Examples

[0081] A fixed computational template for the metal / β-Ga2O3 interface is established. To differentiate between different computational tasks, the task template can also record the β-Ga2O3 crystal orientation and termination mode, metal crystal orientation and lattice matching rules, interface lateral matching mode, structure optimization and device fabrication, exchange-correlation functional, pseudopotential, basis set, k-point sampling, doping concentration, spin handling, convergence parameters, energy sampling, and ρ. c Extraction and area normalization rules, etc. New data should be categorized into the corresponding physical task identifier based on the fixed doping concentration, label definition, and computational task conditions; data for different physical task identifiers should be recorded separately. Table 4 lists the computational settings that can be confirmed by existing data in this embodiment; other parameters can be further recorded in different implementations.

[0082] The metals and their model labels from the historical frozen archives used in the fixed embodiments of this application constitute the initial or current labeled dataset A. t The frozen archive includes 13 metals: Ag, Al, Au, Cs, Cu, Fe, Mg, Nb, Pd, Pt, Sc, Ti, and Y. The implementation of the frozen QK-RR configuration only extracts 1×10⁻⁶ samples. 19 e / cm 3 The corresponding 13 metal tags are used as the target vector. The historical frozen archive is used to illustrate the model construction, evaluation, and candidate ranking in this embodiment; the newly added data obtained by subsequent active learning and labeling should be manually confirmed by external parties and archived according to the physical task identifier, label definition, and calculation task conditions, thereby forming a corresponding new data version; the subsequent model training task calls the new data version, completes the candidate configuration selection, model fitting, and result freezing to form a corresponding new model version.

[0083] For a task with a fixed doping concentration, the target value of the i-th labeled contact metal is determined according to the following formula:

[0084]

[0085] Where, ρ c,i Let be the area-normalized zero-bias transport index of the complete metal / β-Ga2O3 template device corresponding to the i-th labeled contact metal, and satisfy:

[0086]

[0087] Among them, G 0,i R is the zero-bias total differential conductance of the template device. 0,i A is the reciprocal of the zero-bias total differential conductance. ⊥,i The area of ​​the transverse periodic hypercell perpendicular to the transport direction is defined. The current labeled dataset records element identifiers, valid material descriptors, prior baseline auxiliary descriptors, query physics prior auxiliary descriptors, preliminary usability states, and target values. The currently labeled set of contact metal identifiers is managed by the corresponding data version and associated with the corresponding physics task identifier. The descriptor space query candidate set and the QK-RR deployment candidate set are managed by the query version and model version, respectively. Active learning query batches are first used for external manual configuration to supplement training labels. After external calculation results are manually verified and archived, an updated label set and corresponding data version are formed. Subsequent training tasks call upon these data versions to complete the selection of candidate configurations for the corresponding QK-RR model, model fitting, and result freezing, forming the model version. The trained model outputs performance verification candidate results for external manual verification of low-ρ... c predict.

[0088] The initial labeled dataset A0 can be derived from existing computational results. The fixed query feature table in this embodiment includes 88 element records and 15 query master descriptor fields. Eight metals (Pt, Pd, Ag, Au, Cu, Sc, Ti, and Mg) constitute the initial query coverage set, while the remaining 80 element records are non-seed query candidates. The descriptor space query step, which does not read the target label, directly selects the query batch using the geometric relationship between the initial set and all non-seed element records in the fixed query feature table, without invoking QK-RR predictions or residuals. QK-RR standardization and principal component transformation are performed within each training fold, using only that fold for metal fitting. The list of effective descriptor fields is numerically cleaned before evaluation based on the frozen descriptor sub-table corresponding to the 13 labeled metals, without reading target values. Query space standardization is performed using the fixed query feature table specified by the query version for fitting.

[0089] II. QK-RR Pre-benchmark, Quantum Kernel First-Level Residual Learning, and Nested Evaluation of Terminal Residuals

[0090] This section will detail the physical partitioning, parameter set, configuration selection, quantum kernel first-level residual learning, and other aspects of the preceding benchmark.

[0091] When training the QK-RR base model using the currently labeled metals, the following steps are performed sequentially: fitting the pre-baseline model, generating the pre-baseline extrapolated residuals within the training set, learning the quantum kernel first-level residuals, and summing the pre-baseline predictions with the scaled quantum kernel first-level residual predictions. Separately, material-level extrapolated terminal residual generation and thresholded terminal residual nested evaluation are performed on the base predictions; the folding evaluation rules in the nested evaluation are not used for ranking unlabeled candidates.

[0092] For the current training metal set, a preliminary benchmark candidate configuration is pre-determined. One fixed-parameter implementation uses a hard-gated physical partitioning preliminary benchmark model: training metals or candidate element records that meet the transition metal label and are from group 8 to group 11 of the periodic table are divided into a second physical partition, and the remaining training metals or candidate element records are divided into a first physical partition. The first physical partition uses a radial basis function support vector regression (RBF-SVR) sub-model based on Pauling electronegativity and atomic mass, while the second physical partition uses a ridge regression sub-model based on Pauling electronegativity and the tenth-order ionization energy. Table 2 shows four C-parameter grids, four ε-parameter grids, and four αR-parameter grids, respectively. A complete candidate configuration is selected from each of the three grid types, and the median or mean is aggregated. For the first physical partition, multiple RBF-SVR sub-models are trained using the combined Cartesian product parameters of the selected C-grid and ε-grid; for the second physical partition, multiple Ridge sub-models are trained using all parameters in the selected αR-grid; target records are predicted only by the sub-models of their respective physical partitions and aggregated according to the selected statistics. Thus, the total number of candidates is 4×4×4×2=128. The inputs of each sub-model are fitted to a normalizer within the corresponding training fold; in this fixed-parameter implementation, the kernel coefficients γ of RBF-SVR are determined using a scale-adaptive rule according to the following formula; Ridge uses intercept fitting. Candidate names are encoded by C-grid, ε-grid, αR-grid, and aggregation method, and are used for final tie-breaking.

[0093]

[0094] Where, d b X is the input dimension of the preceding baseline sub-model. b For the corresponding training in-fold normalized input matrix, Var(X) b ) represents the total variance of all elements in the matrix.

[0095] The purpose of employing the hard-gated physics partitioning benchmark model is to reduce the model degrees of freedom of minimal sample benchmarks and to distinguish the differences between Group 8 to Group 11 transition metals and other metals in terms of valence electron occupation and higher-order ionization behavior. For records in the second physics partition, the tenth-order ionization energy is used as a low-dimensional physical proxy feature related to the difference in d-electron binding during the continuous removal of electrons; for the remaining records in the first physics partition, Pauling electronegativity and atomic mass form the main trends. The partitioning rules, input features, and candidate parameter set are frozen before the task begins, and are not based on the true ρ of the metal to be predicted. c The label has been temporarily changed.

[0096] The pre-benchmark internal material-level leave-one-out evaluation requires that each physical partition to which a metal is left out retains at least one metal in its corresponding sub-training set. If a candidate configuration cannot fit or produce a prediction in any material-level leave-one-out sub-trade, that configuration is skipped; if no successful candidates exist, the current round of pre-benchmark fitting is terminated and the configuration is output as unavailable. The number of samples in the pre-benchmark partition is determined by the affiliation of the current 13 labeled metals in each physical partition and is independent of the initial coverage set of the descriptor space query.

[0097] Table 2. Set of Fixed Parameters for the Candidate Library of Physical Partition Pre-Bachelorship

[0098] For the current training metal set S, a pre-set candidate benchmark library is compared using material-level leave-one-out predictions within S, and a unified pre-benchmark configuration is selected. This configuration chooses to utilize the internal summation error on S; for each metal i in S, the sub-model that produces the prediction for that metal uses only a sub-training set that does not contain that metal. Fit the selected configuration to obtain the out-of-range prediction of the preceding baseline. And construct the first-order residual Therefore, the first-order residual is called the internal out-of-place residual of the current training set. For the metal c to be predicted, the selected uniform configuration is fitted using all currently trained metals to obtain the preceding baseline prediction. In the evaluation of the outer metal layer, a unified configuration is adopted. The selection must be made only within the outer training set; the outer metal set is not included in the above configuration selection.

[0099] For each available candidate configuration of the preceding benchmark, the sum of squared errors (SSE), the mean absolute error, and the root mean square error are calculated based on the material-level leave-one-out predictions on the current training set S; each metal contributes only one material-level out-of-the-box prediction. The three evaluation metrics are as follows:

[0100]

[0101]

[0102]

[0103] Candidate configurations are first sorted in ascending order of internal sum of squared errors, then in ascending order of internal mean absolute errors if they are the same, and finally in lexicographical order of their names if they are still the same. The first item is taken as the unified pre-reference configuration. The 4 C-grids, 4 ε-grids, 4 αR-grids, and 2 aggregation methods listed in Table 2 form 128 fixed candidate configurations. No other pre-reference combinations are added during the evaluation phase. The subscript "inner" indicates evaluation within the current training set, and the superscript "oof" indicates material-level extrapolation prediction.

[0104] Based on the effective material descriptor and the first-order residual, a quantum kernel residual regression model using Pauli Z-phase encoding and a fidelity metric quantum kernel is trained, including:

[0105] The effective material descriptors are standardized and subjected to principal component dimensionality reduction to obtain dimensionality-reduced coordinates;

[0106] The components of the reduced-dimensional coordinates are mapped to phase angles, and the corresponding qubits are encoded using phase rotations generated by the Pauli Z operator. The Pauli Z phase encoding does not set entanglement coupling terms between qubits.

[0107] Construct a fidelity quantum kernel based on the fidelity between quantum encoded states corresponding to different dimensionality reduction coordinates;

[0108] Based on the pre-calculated fidelity metric kernel, a ν-support vector regression residual regression model with the first-level residual as the supervision target is trained.

[0109] Specifically:

[0110] The quantum kernel first-level residual learning process only uses the current training metals to calculate the mean and overall standard deviation of the effective descriptors for each dimension; when the overall standard deviation of a certain dimension is zero, the scaling factor for that dimension is set to 1. The unlabeled candidate metals to be predicted and the validation reserved metals are transformed using only the scaling parameters obtained from the training set, and no arbitrary ε-smoothing term is added in this step.

[0111] A principal component analyzer is fitted onto the training matrix normalized by a quantum kernel-level residual learning process, mapping the descriptors to low-dimensional vectors zi. A fixed-parameter implementation employs three-dimensional principal component analysis (PCA) and three qubits; when the number of training samples limits the number of effective principal components, insufficient dimensions can be padded with zeros, but unlabeled candidates to be predicted or validation reserves are not used to fit the PCA model.

[0112] Let Q be the number of qubits, and then consider the q-th dimension of the m-th low-dimensional coordinate. This is mapped to the phase angle. Each qubit is first initialized by an Adamarc (Hadamard) gate H. The state is prepared as an equal-amplitude superposition state, and then a single-qubit phase rotation R generated by the Pauli Z operator is applied. Z (θ m,q Furthermore, no entanglement coupling terms between qubits or quantum nucleus alignment parameters are set. The phase angle is determined according to the following formula:

[0113]

[0114] In this context, the subscripts m and q of the symbol z represent the m-th reduced-dimensional coordinate and its q-th dimension component, respectively, s is the angle scaling factor, and Q is the number of qubits.

[0115]

[0116] For the m-th and n-th quantum encoded states, the fidelity quantum kernel is defined as:

[0117]

[0118]

[0119] in, This represents the initial computational ground state of a single quantum bit. This represents the Q-qubit quantum state encoded by the m-th dimension-reduced coordinate. A fixed-parameter implementation uses Q = 3 and s = 1. The analytical expression can be derived from the definition of quantum state fidelity and can be evaluated on classical computing devices.

[0120] The ν-SVR is trained using a training kernel matrix (i.e., a fidelity metric kernel matrix, where each element represents the fidelity between quantum states of pairwise metal samples after quantum encoding) as the pre-computed kernel and the prior benchmark out-of-place residual as the supervised target. For candidate element record c, a kernel vector relative to the training metal is constructed using a normalizer, PCA, and quantum feature mapping fitted to the same training set, and the quantum kernel first-order residual prediction is obtained from the ν-SVR; the QK-RR basic prediction is:

[0121]

[0122] in, This represents the QK-RR baseline prediction value of candidate element record c. Record the previous baseline prediction value of c for the candidate element. The quantum kernel first-order residual prediction value of candidate element c is recorded, where λ is the residual scaling factor; in a fixed-parameter implementation, λ is 0.8.

[0123] After the QK-RR basic prediction is formed, a material-level extrapolation prediction is performed again on the current training metal to generate the terminal residual:

[0124]

[0125] Among them, the QK-RR basic forecast discount value in the terminal residual formula , is the predicted value generated from the corresponding training data that does not contain the i-th metal.

[0126] To avoid residual leakage, when generating the i-th terminal residual, the selection of the preceding benchmark configuration, the preceding benchmark fitting, the quantum kernel preprocessor, the quantum kernel matrix, and the ν-SVR training do not include the i-th metal; in the outer leave-one evaluation, each terminal residual support sample used to form the correction amount of the outer leave-one metal evaluation should also be generated separately within the outer training range.

[0127] This embodiment uses nested residual evaluation to audit the local error structure on a fixed-label dataset using nested material-level protocol auditing. Local evaluations can use pre-frozen residual inputs, support sample selection, weighting, shrinkage, and truncation rules; the specific candidate composition and parameters are recorded according to the corresponding evaluation configuration and are not limited to a fixed number, fixed three feature spaces, or fixed values ​​in this specification. The in-fold evaluation correction is only used for calculating the prediction error of the corresponding nested evaluation fold and is not used for basic predictions of unlabeled candidates, original model rankings, or active learning queries.

[0128] In nested evaluation of terminal residuals, missing inputs, insufficient supporting samples, and ties are all handled according to the corresponding frozen evaluation configuration. When the corresponding evaluation configuration cannot generate an effective in-flight evaluation correction, the uncorrected result of that flight is recorded. Nested evaluation of terminal residuals is only used for nested evaluations on fixed labeled datasets and does not temporarily switch unlabeled candidates or extrapolate the nested evaluation rules of terminal residuals.

[0129] In this embodiment, the nested evaluation of terminal residuals uses a 24-dimensional effective material descriptor as the basic input and employs a material-level nested leave-one-out protocol. The preprocessing, local support set, and evaluation parameters within each outer layer are determined only by the corresponding source training set and its frozen evaluation configuration; the nested evaluation rules of terminal residuals determined in the evaluation stage are not used to form a unified deployment rule for unlabeled candidates.

[0130] The candidate library of pre-defined benchmarks and its selection protocol, as well as the candidate configuration set and selection protocol for the quantum kernel residual branch, are all predetermined before the task begins. The final quantum kernel configuration is determined by the candidate selection results on the current labeled dataset and is frozen with the corresponding model version. Within each outer training set, the pre-defined benchmark is first selected and the quantum kernel first-level residual model is trained using only that training set. Subsequently, metals are reserved one by one within that training set to form the inner layer validation. The preprocessing, local support set, and evaluation parameters for the nested evaluation of the terminal residuals are determined only by the corresponding source training set and its frozen evaluation configuration, and the evaluation results are not written into the deployment ranking of unlabeled candidates.

[0131] For tasks with fixed doping concentrations, data is partitioned into groups of whole metals. The out-of-fold prediction within the training set is used to construct the residuals required for model training, where the target metal does not participate in the sub-model fitting that generates the predicted value. In each material-level leave-one-outer-fold, the preceding baseline configuration is only reselected and fitted within the remaining training metals; the normalizer, principal component analyzer, fidelity kernel matrix, and ν-SVR also only utilize the remaining training metals for fitting. The left-out metal label is not included in the model fitting, kernel matrix construction, first-order residual generation, determination of the nested evaluation rules for the terminal residual, or generation of the in-fold evaluation correction; it is only used to calculate the corresponding evaluation error after the prediction for that fold is completed. Since the frozen hyperparameter combination of the quantum kernel branch has already completed candidate selection using the same 13 metals, the left-out metal label may still indirectly affect the frozen configuration through the selection of the full data configuration. Therefore, the summarized results only belong to the material-level leave-one-out reproduction of the posterior frozen configuration and do not belong to the nested model selection evaluation, unbiased generalization error, or independent external testing. Data with different doping concentrations are labeled separately and corresponding fixed-condition tasks are established; records of different concentrations are not split into the training and test sets of the same fixed doping concentration task. The field list before evaluation consists of 13 descriptor lines for labeled metals without reading ρ. c Freezing is performed under the target value condition, so the descriptor of the outer metal layer can participate in the judgment of non-finite, near-constant, and redundant fields; but its true ρ c Labels must not be included in the preceding benchmark selection and fitting, standardization, principal component analysis, kernel matrix construction, ν-SVR fitting, determination of nested evaluation rules for terminal residuals, or generation of evaluation correction quantities within the corresponding outer layer.

[0132] In this embodiment, the quantum core residual branch uses a pre-determined set of candidate configurations. Each candidate configuration consists of the number of qubits Q, the angle scaling factor s, the first-order residual scaling factor λ, the support vector regression penalty parameter C, and the parameter ν of ν-support vector regression or the parameter ε of ε-support vector regression (ε-SVR). The specific parameter values, candidate names, and selection results for each candidate configuration are frozen and archived with the corresponding model version. Candidate configurations are arranged in ascending order of material-level leave-one-out RMSE, ascending order of MAE, and lexicographical order of candidate names. The candidate values ​​for the first-order residual scaling factor λ are 0.6, 0.7, 0.8, 0.9, and 1.0, selected according to the ascending order of material-level leave-one-out RMSE, ascending order of MAE, and lexicographical order of candidate names; λ is chosen as 0.8. The freezing parameter combination in this embodiment is a 24-dimensional effective material descriptor space, in-fold 3D PCA, three qubits, Pauli-Z entanglement-free mapping, angle scaling factor 1, pre-computation kernel (ν-SVR (C=5, ν=0.55)), and first-order residual scaling factor 0.8. Since the candidate configuration selection and subsequent 13-fold index both use the same 13 metal data, the results belong to the material-level leave-one-out reproduction of the posterior frozen configuration, and do not belong to the nested model selection evaluation or independent external testing. The terminal residual nested evaluation uses the 24-dimensional effective material descriptor as input and is performed within the fixed labeled dataset according to the material-level nesting protocol; its results are only used for error structure diagnosis and do not form a unified deployment correction rule for unlabeled candidates.

[0133] Table 3 Recording range of nested evaluation of terminal residuals

[0134] III. Independent descriptor space sample query without reading target tags

[0135] The descriptor space query step is used to select candidates that improve descriptor space coverage and reduce intra-batch repetition within a limited subsequent computational budget. The query batch, as descriptor coverage candidates, is manually configured by operators of the external high-fidelity computation process to perform DFT-NEGF calculations with supplementary training labels; the sampling and scoring process does not access QK-RR predictions, model residuals, or ρ. c Target value or model uncertainty. External calculation results, after manual verification and archiving, form an updated labeled dataset and corresponding data version. The external high-fidelity calculation, manual verification, and archiving are performed outside of this method's procedures; archiving does not automatically trigger new model training or model version creation. Subsequent model training involves an explicitly initiated training task calling the updated labeled dataset and completing candidate configuration selection, model fitting, result freezing, and candidate prediction according to this method, forming the corresponding model version. The trained QK-RR model outputs low p-values ​​for unlabeled candidates. cPredict rankings; in the implementation of setting up applicable domain audits, the applicable domain audit status is also output for performance review.

[0136] During the step-by-step construction of the descriptor space query batch, the seed metal preset in the query version is used as the initial query coverage set, and the selected candidates in this batch are incorporated into the coverage set. The material descriptors of the selected candidates are used to update the boundary positions and overall distribution coverage relationships of subsequent candidates in this batch. The sampling and scoring process does not access the target label field.

[0137] In one implementation, descriptor space sampling reads seed metal records and candidate element records from a fixed query feature table specified by the query version. In this embodiment, the fixed query procedure directly reads 88 element records and 15 query master descriptor fields from the query feature table; these fields do not include element identifiers, p... c The fields include target value, model predicted value, model residual, model uncertainty, applicable domain status, code-level preliminary usability status, and manual verification results. The fixed query feature table is provided before the query runs; the query program does not re-execute non-finite field deletion, near-constant field deletion, or Pearson correlation redundancy screening during sampling, nor does it change the field order during runtime. The query space normalizer fits the fixed query master descriptor using all seed metal records and candidate element records, without reading ρ. c Target label; the standardized full query master descriptor vector is used for boundary scoring, overall distribution gain, and intra-batch diversity scoring.

[0138] Descriptor space sampling can be implemented using a candidate pool of general element records specified by the query version. The element range, stability filtering, or exclusion fields of the candidate pool are pre-recorded by the query version; the filtering is only used to define the query input and does not constitute the final material category or task eligibility judgment in this method. Different candidate pools form different query versions.

[0139] When the candidate pool, query feature table, preprocessor, scoring rules, or batch size changes, the corresponding descriptor space sampling results form a new query version and are recorded separately from the existing query results, without mixing query batches of different query versions into the same fixed batch.

[0140] All element records in the complete query feature table specified in the query version are pre-determined as the overall distribution reference set P. This set includes both seed metal records and candidate element records, and remains unchanged within the same query version. Let... μ represents the original query master descriptor vector of element record p. P,k and σ P,kLet these represent the mean and population standard deviation of the k-th dimension query master descriptor in the overall distribution reference set, respectively; to avoid division by zero due to zero standard deviation, a scaling factor is defined. When σ P,k When σ is greater than zero P,k Otherwise, take 1:

[0141]

[0142]

[0143] The vector after query space standardization is denoted as q. p Its feature dimension is d. At step t, the current query coverage set is denoted as C. t The set of candidates selected in the current query batch is denoted as B. t The remaining candidate set to be evaluated is denoted as U. t The candidate to be evaluated is denoted as c.

[0144] The original boundary score of candidate c at step t. The minimum normalized Euclidean distance from the candidate to the current query coverage set:

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] in, For the first The current query coverage set of the step, For a fixed reference set of the overall distribution, These are the current candidate records to be evaluated. To cover the record index in the collection, The overall distribution reference set is used as the record index; , and These are the standardized query master descriptor vectors for the corresponding records. To query the dimension of the main descriptor, Let be the number of records in the overall distribution reference set. For the _th Dimensional standardized query master descriptor, and Representing sets respectively The mean and population variance of this dimension. and Representing sets respectively The mean and overall variance of the corresponding dimension. , and These represent the mean deviation term, variance deviation term, and coverage distance term, respectively. The sum of three terms represents the overall distribution error of the current covered set relative to the overall distribution reference set; This represents the maximum nearest distance from the record in the overall distribution reference set to the coverage set. It is only recorded as a monitoring indicator for coverage blind spots and is not included in the overall distribution error or joint query score. Overall distribution raw gain. Indicates candidate records The reduction in overall distribution error before and after adding to the coverage set; a larger value indicates a greater effect of the candidate on improving the overall descriptor distribution coverage. This is used in the gradual formation of descriptor coverage query batch B. t At step t, the original score for intra-batch diversity of candidate c is defined as:

[0153]

[0154] in, Candidate records to be evaluated The standardized query master descriptor vector, For the current query batch Selected candidate records The standardized query master descriptor vector is used. When there are no selected candidates in the current batch, the original intra-batch diversity score of all remaining candidates is set to 0, and then normalized to 0.5 because this score is the same across all candidates. After each candidate element record is added, it is added to the current query batch and the current query coverage set. The boundary score, overall distribution gain, intra-batch diversity score, and auxiliary physical prior score of the remaining candidate element records are recalculated, and the joint query score is recalculated accordingly.

[0155] Let J P The set of predefined auxiliary physical fields can include Fermi level, bulk modulus, shear modulus, melting point, and Pauling electronegativity. Only if candidate element record c has an actual value in the j-th auxiliary physical field and the current query covers the set C... t A field is included in the effective field set J of candidate c only if both the overall distribution reference set P and the overall distribution reference set P have at least one non-missing value for that field, and the field in the overall distribution reference set P has discriminative dispersion. eff(c) . Let uc,j For each candidate element, record the actual value of c in the j-th auxiliary physical field, μ Ct,j and μ P,j The current query coverage set C is respectively t Compared with the mean of non-missing values ​​in the overall distribution reference set P in this field, σ Ct,j For the current query coverage set C t The overall standard deviation of non-missing values; to avoid unstable standardized distance due to an excessively small standard deviation of an auxiliary physical field in the current query coverage set, a scaling factor is defined. :when Time to take ;when When taking the standard deviation of the population distribution reference set in this field When the standard deviation of the corresponding field in the overall distribution reference set is approximately zero, that field is not included in the set of valid fields.

[0156]

[0157]

[0158]

[0159]

[0160] To simplify notation, the following auxiliary physical prior score correlation quantities omit explicit markings for query step t, and are all based on the current query coverage set C. t Calculation. Among them... Indicates the candidate record at the th The standardized deviation of each valid field from the mean of the current query coverage set. This indicates the degree of standardization of the record relative to the mean of the overall distribution reference set. The field can be set to scale a. avail(c) The values ​​are determined according to the ratio of the number of valid fields to the total number of preset auxiliary physical fields; D(c) and E(c) are respectively taken from the set of valid fields J. eff(c) The arithmetic mean of the absolute value of the standardized deviation and the absolute value of the standardized extreme values. When J eff(c) When empty, the field can be used with the proportion and the physical prior raw score. All values ​​are treated as 0; no fictitious padding values ​​are used.

[0161]

[0162]

[0163]

[0164] The descriptor space query score consists of boundaries, overall distribution, intra-batch diversity, and auxiliary physical priors; rule-based applicability audits and code-level preliminary usability status can be recorded along with candidate results, but are not used as input for actively learning query scores.

[0165] The original scores for boundary, overall distribution gain, intra-batch diversity, and auxiliary physical prior are respectively subjected to min-max normalization, and the resulting normalized scores are denoted as s. B (c), s D (c), s V (c) and s P (c). For the current remaining candidate set U t Non-constant raw scores are normalized according to the following formula;

[0166] When a given original score is indistinguishable among all remaining candidates, its normalized value is uniformly set to 0.5. The joint query score is defined as follows. Candidates are arranged in descending order of joint query score, overall distribution gain, and boundary score; the program in this embodiment does not set separate rules for juxtaposing element symbols. Each score does not read unknown true targets that are not labeled as candidates, nor does it take the lowest predicted target as a necessary condition for training the query.

[0167]

[0168]

[0169] in, For rating category index, These correspond to boundary, overall distribution gain, intra-batch diversity, and auxiliary physical prior scores, respectively. For the current remaining candidate set Candidate record index in For record In the The original score under the category score. For candidate records Normalized score, For its joint active learning score (i.e., joint query score); where , , and These are the preset weights for boundary, overall distribution gain, intra-batch diversity, and auxiliary physical prior score in this embodiment. In other embodiments, different boundary, representativeness, or diversity scoring functions can be used for descriptor space queries without reading target labels; different query algorithms or weights form different query versions, and their point selection results are not mixed.

[0170] Query candidates are selected progressively from high to low based on the preset joint query score. Each time a candidate record is added, it is added to the current query batch and the current query coverage set. The boundary score, overall distribution gain, intra-batch diversity score, and auxiliary physical prior score of the remaining candidate records are recalculated, and the joint query score is recalculated accordingly. The batch size is preset by the query version until the specified batch size is reached or no remaining candidate records are found.

[0171] IV. Output of external high-fidelity verification candidate results

[0172] The descriptor coverage candidates and performance verification candidates correspond to different stages of external high-fidelity computation. The descriptor coverage query batch output by this method must at least include candidate element record identifiers and query scores, which are used by operators of the external high-fidelity computation process to manually construct and execute DFT-NEGF supplementary calculations. After manual verification, the newly added target values ​​obtained from external computation are archived according to the physical task identifier, fixed doping concentration, interface template conditions, target value definition, and computation task conditions. The external manual archiving process forms an updated labeled dataset and corresponding data version. This method only receives, saves, or calls the archived results; it does not automatically perform external high-fidelity computation, does not automatically generate or return target values, does not automatically merge candidate element records into the labeled dataset, and does not automatically perform manual verification and archiving. The archiving behavior does not automatically trigger new model training or model version establishment. When the updated labeled dataset is explicitly designated for a new model training task, each training step calls upon this dataset to perform candidate configuration selection, model fitting, result freezing, and candidate prediction according to this method, forming a corresponding model version. After training, the performance verification candidate results output by this method at least include candidate element record identifiers, fixed doping concentrations, QK-RR base prediction values, and the original model ranking. In the implementation of setting applicable domain audits, it also includes the applicable domain audit status. The performance verification candidate results are provided for manual construction and execution of low-ρ calculations by operators of external high-fidelity computing processes. c Verification calculation of predicted candidates.

[0173] The purpose of external computation for descriptor coverage candidates is to supplement training labels, while the purpose of external computation for performance verification candidates is to verify the low-ρ QK-RR of the trained dataset. c Prediction; the two are not confused due to the use of the same physical task identifier, candidate element identifier system, and fixed doping concentration. External operators can decide whether to configure the actual task based on the specific interface template, material category, and calculation conditions; this method does not perform final task qualification verification, screening for the same task label, or automatic merging of multiple roles.

[0174] In an optional implementation where the positive and negative bias sequences are fixed separately and the self-consistent inputs and outputs of each bias are saved, the bias-related transmission function can be recalculated and the current-voltage (I-V) characteristic can be constructed based on the Landauer formula. This bias analysis is used to assist in judging contact nonlinearity and does not replace the zero-bias definition of this fixed machine learning label. The total differential conductance of the unified metal / β-Ga2O3 two-electrode NEGF device under zero-bias linear response is denoted as G0, the corresponding differential resistance is defined as the reciprocal of the total zero-bias differential conductance, and the normalized zero-bias transport index of the complete device area is defined as the product of the differential resistance and the transverse supercell area perpendicular to the transport direction. The index is expressed in Ω·nm. 2 This indicates the area-normalized zero-bias transport response corresponding to the complete template device; training, prediction, and sorting under the same physical task identifier are distinguished according to fixed doping concentration, target value definition, and corresponding model version or query version.

[0175] The zero-biased linear response conductance is determined according to the Landauer formula. Where E is the electron energy, e is the elementary charge, h is Planck's constant, and f(E,μ,T) is the linear response conductance. e ) represents the Fermi-Dirac distribution function, μ is the chemical potential and corresponds to the Fermi level under zero bias conditions, and T e T is the electron temperature; T(E) is the total supercell transmission function obtained by summing all k samples from the transverse Brillouin zone according to their respective integral weights. For spin polarization, T... σ (E) represents the total transmission function of the corresponding spin channel after weighting by the same transverse k-points, where σ is the spin channel identifier. In the non-spin polarized implementation that takes into account double spin degeneracy:

[0176]

[0177] In the spin-polarized implementation, the transmission of each spin channel is calculated and summed separately:

[0178]

[0179] In a specific implementation using the atomic-scale materials simulation software QuantumATK, the DFT-NEGF calculation employs the Perdue-Burke-Enzehoff generalized gradient approximation exchange-correlated functional (PBE-GGA), the gauge-conserved pseudopotential library (PseudoDojo pseudopotential), and the medium linear combination of atomic orbitals (LCAO) basis set. The Brillouin zone sampling of the DFT calculator used for structure optimization is 3×9×1; the periodic electrodes for the self-consistent NEGF device calculation use a 12×5×215 Monkhorst-Pack grid, where 215 corresponds to the periodic electrode sampling along the C transport direction, and the central scattering region uses an open boundary along the C direction. After the device Hamiltonian reaches self-consistent convergence, the projected local density of states (PLDOS) and transmission spectrum analysis are post-processed using 21×8×1 lateral sampling. Therefore, the two sets of grids correspond to the self-consistent device calculation and the spectroscopic post-processing, respectively, and are not repeated settings in the same calculation step. The density grid cutoff energy is 125 Hartree, and the maximum residual force is no higher than 0.02 eV / Å as the geometric optimization convergence condition.

[0180] The zero-biased differential conductance G0 is directly read or calculated from the zero-biased linear response of the object analyzed by transmission spectroscopy, without being replaced by an arbitrary finite bias fitting window, nor is it limited by ρ. c The lower limit for transmittance or conductivity is artificially set on an order of magnitude. When the self-consistent calculation fails to converge, G0 is a non-finite value, or its value is zero or below the resolvable range of the used calculation precision, the result is marked as invalid and excluded from the training label, instead of using the preset maximum ρ. c Instead, a complete computational task can further record parameters such as electron temperature, doping compensation method, spin processing, and device structure; this embodiment only discloses parameters that can be confirmed by existing data as fixed values, and other parameters are not specifically limited.

[0181] Table 4 lists the calculation parameters that can be confirmed by existing data in this embodiment; in other embodiments, other calculation settings can be further recorded in conjunction with specific task templates.

[0182] Table 4. Calculation parameters for template T-1 that can be confirmed from existing data.

[0183] PLDOS was calculated along the device transport direction to observe band alignment and metal-induced bandgap states. Both PLDOS and transmission spectra were calculated in the range of -4 to +4 eV near the Fermi level, using the same 21×8×1 lateral Monkhorst-Pack k-point sampling; 401 energy sampling points were used within this energy range. The macroscopically averaged Hartley differential potential was superimposed on the PLDOS to show band bending; since there is no clear electronic boundary between metallic and semiconductor states near the interface, the barrier was not directly read from the PLDOS. When a clear potential maxima exist, the energy difference between this maxima and the Fermi level was used to estimate the n-type effective barrier under the current PBE-GGA calculation caliber. Generally, the energy at which the transmittance first reaches 1% of the maximum transmittance within the energy range is used as a proxy index for the 1% relative transmission turn-on energy; when tunneling is significant in highly doped states, this index is only used to compare transport turn-on behavior and is not directly interpreted as the conventional Schottky barrier height.

[0184] Bias transmission spectra and I–V characteristics were calculated according to the aforementioned optional bias sequences; ρ c Still based solely on the zero-biased linear response conductance G0 and the transverse supercell area A perpendicular to the transport direction ⊥ The unified definition is extracted. PLDOS and the effective barrier are only used to assist in contact physics analysis.

[0185] To illustrate the examples with a fixed doping concentration, Table 5 discloses... Figure 2 The horizontal axis corresponds to the 13 training metal archive labels. In the table, ρ... c The numerical values ​​in the fixed archive dataset are used, and the target value is calculated according to the aforementioned dimensionless logarithmic formula. Model training uses the complete numerical values ​​in the archive, without using the precision shown in the table for inverse transformation or recalculation. The numerical values ​​shown in Table 5 are used to illustrate the model construction, evaluation, and candidate ranking in this embodiment. New data should be classified into the corresponding physical task identifier according to the fixed doping concentration, target value definition, and calculation task conditions, and data for different physical task identifiers should be recorded separately.

[0186] Table 5 1×10 19 e / cm 3 Fixed doping concentration training labels

[0187] If the doping concentration, label definition, interface template, or other calculation conditions affecting transmission of a candidate change, its label will be recorded according to the corresponding physical task identifier and will not be directly incorporated into the current fixed-condition training task.

[0188] Descriptor coverage query batches, performance review candidate results, and terminal residual nested evaluation records are stored separately. The former is used for independent external high-fidelity computation to manually supplement training labels; after manual verification and archiving, the newly added labels form an updated labeled dataset and corresponding data version. Subsequent model training tasks, after candidate configuration selection, model fitting, and result freezing, form the corresponding model version. Performance review candidate results are used for independent external high-fidelity computation to manually verify low-ρ... c Prediction; nested evaluation of terminal residuals does not change the deployment ranking of the current candidate element record.

[0189] If new labels are obtained in an independent external computing process, they can be archived separately according to the physical task identifier, label definition and computing task conditions to form an updated labeled dataset and corresponding data version; the data version can be called by subsequent model training tasks, and after training is completed and frozen, it forms the corresponding model version.

[0190] Subsequent descriptor space query batches are managed by the corresponding query version, and QK-RR model evaluation is managed by the corresponding model version. When it is necessary to compare continuous model versions, the QK-RR basic prediction error can be recorded on a pre-determined audit set using the same material grouping protocol.

[0191] In this embodiment, the QK-RR basic prediction adopts a structure that adds the previous benchmark prediction to the first-order residual prediction of 0.8 times the quantum core. Figure 7 , Figure 8 Both the base prediction and the unlabeled candidate deployment table use this base prediction. The material-level outer-fold terminal residuals of the base prediction are only used for nested material-level residual evaluation based on 24-dimensional effective material descriptors, and do not summarize the different rules for each outer fold selection into a single unlabeled candidate deployment rule. The descriptor space query batch first serves to supplement the descriptor coverage training labels; after the external high-fidelity calculation results are manually verified and archived to form an updated labeled dataset and corresponding data version, the subsequent model training task completes candidate configuration selection, model fitting, and result freezing to form the corresponding model version; the QK-RR prospective candidates output by this model version are used for low-ρ c Performance verification of the prediction.

[0192] V. Using QK-RR basic prediction to screen and audit candidate element records

[0193] Using all currently labeled contact metals, a baseline model is determined and fitted to obtain baseline prediction values ​​for candidate element records. Quantum kernel first-order residual prediction values ​​are obtained using a normalizer and principal component analyzer fitted with all currently labeled contact metals, a Pauli-Z fidelity metric quantum kernel, and ν-SVR. These two methods are combined to obtain the QK-RR basic prediction value. Only for candidate element records with complete and valid material descriptors, capable of obtaining baseline prediction values ​​from the baseline model, and capable of obtaining quantum kernel first-order residual prediction values, the QK-RR basic prediction value is combined and output. The conversion relationship between the QK-RR basic prediction value and the area-normalized zero-biased transport index prediction value is as follows:

[0194]

[0195] in, Record the QK-RR baseline prediction value of c for the candidate element. The area-normalized zero-biased transport index prediction value is obtained by inverse transformation of the dimensionless logarithmic prediction value. For candidate elements that do not meet any of the above QK-RR numerical prediction conditions, a "not supported" status is recorded in the output. The terminal residual nested evaluation described in Table 3 is only used for error structure diagnosis on the fixed labeled dataset and is not superimposed on the deployment output of unlabeled candidates.

[0196] Figures 2 to 6 The 13 labeled metal predictions are derived from material-level leave-one-out reproduction and can be used to calculate reproduction metrics. The 13 labeled metal reference predictions retained in the final deployment output are generated by a frozen model refitted using all 13 labels and are used only for coverage and output consistency auditing, not for recalculating R. 2 RMSE, MAE, or prediction-actual value consistency. The 52 unlabeled candidate element records that meet the above QK-RR numerical prediction conditions are prospective predictions after refitting all 13 metals. Since there are no real labels of the same caliber, candidate error is not calculated. The 52 records are only candidate element records and are not represented as a whole as confirmed candidate contact metals.

[0197] The preprocessing space of the QK-RR deployment model is used for the applicable domain audit. A normalizer and principal component analyzer are fitted using all currently labeled contact metals' valid material descriptors, and each labeled contact metal and candidate element record is mapped to the same normalized principal component space. The normalizer and principal component analyzer are different from the query space normalizer fitted using the complete query feature table in the descriptor space query step; they belong to the model version and query version respectively and are not used together.

[0198] Let N be the number of labeled contact metals, and let z be the coordinates of the i-th labeled contact metal in the normalized principal component space. iLet z be the coordinates of the candidate element record c in the same space. c The training nearest neighbor reference distance for the i-th labeled contact metal is defined as:

[0199]

[0200] When calculating the training nearest neighbor reference distance, zero distances from labeled contact metals to themselves are excluded; equivalently, in the pairwise Euclidean distance matrix of labeled contact metals, the diagonal distances are set to infinity, and then the minimum distance of each row is extracted. The empirical reference distribution is constructed from the training nearest neighbor reference distances of all N types of labeled contact metals.

[0201]

[0202] For a candidate element record c, whose coordinates in the same normalized principal component space represent the corresponding candidate record, the nearest neighbor distance from the candidate element record to the currently labeled contact metal is defined as:

[0203]

[0204] The nearest neighbor distance empirical percentile of candidate element record c is determined according to the discrete empirical cumulative distribution function of the empirical reference distribution:

[0205]

[0206] The indicator function takes the value 1 if the condition within the parentheses is true, and 0 otherwise. When the training nearest neighbor reference distance is equal to the nearest neighbor distance of the candidate element record, it is counted as less than or equal to the nearest neighbor distance. The empirical percentile represents the discrete position of the nearest neighbor distance of the candidate element record in the training nearest neighbor empirical reference distribution, and does not represent the prediction confidence, error probability, statistical significance, or prediction interval coverage.

[0207] In the implementation with 13 fixed contact metals, Ag, Al, Au, Cs, Cu, Fe, Mg, Nb, Pd, Pt, Sc, Ti, and Y constitute the current training set, N=13, and the dispersion measure of the empirical percentile is:

[0208]

[0209] For example, when there are 10 training nearest neighbor references in the empirical reference distribution whose distances are less than or equal to the nearest neighbor distance of the candidate element record, its empirical percentile is 76.923%; when there are 12 training nearest neighbor references whose distances are less than or equal to the nearest neighbor distance of the candidate element record, its empirical percentile is 92.308%. The empirical percentiles of Na and Er in the fixed output are 76.923% and 92.308%, respectively, which are consistent with the calculation results of the discrete empirical cumulative distribution.

[0210] In addition to the nearest neighbor distance empirical percentile, in the original effective material descriptor space that is neither standardized nor subjected to PCA dimensionality reduction, the proportion of out-of-bounds fields that exceed the original value range of the current training set in each dimension of the candidate element record is calculated. The proportion of out-of-bounds fields is also called the field out-of-range proportion, and is defined according to the following formula:

[0211]

[0212] Where, d QK x represents the effective material descriptor dimension used in the corresponding model version. c,q Record the q-th effective material descriptor for candidate element c, x i,q It is the q-th dimension effective material descriptor for the i-th type of labeled contact metal.

[0213] The first distance threshold, the second distance threshold, the first proportional threshold, and the second proportional threshold can be preset according to the physical task identifier, the current labeled dataset size, and the applicable domain audit requirements, and are frozen with the corresponding model version; wherein, the first distance threshold is lower than the second distance threshold, and the first proportional threshold is not higher than the second proportional threshold. In this embodiment, the first distance threshold, the second distance threshold, the first proportional threshold, and the second proportional threshold are set to 75%, 90%, 0, and 10%, respectively.

[0214] When the nearest neighbor distance empirical percentile is not higher than 75% and the out-of-bounds field ratio is zero, the candidate element record is marked as interpolated; when the candidate element record does not meet the interpolated type condition, and the nearest neighbor distance empirical percentile is not higher than 90% or the out-of-bounds field ratio is not higher than 10%, it is marked as near-boundary type; the remaining candidate element records that meet the above QK-RR numerical prediction conditions are marked as extrapolated type.

[0215] Candidate outputs employ a three-level terminology system. Objects in the descriptor table, query pool, and model numerical outputs are collectively referred to as candidate element records; objects whose candidate material categories have been preliminarily confirmed by external personnel and are suitable for further evaluation are called candidate electrode material records; objects confirmed by external personnel in conjunction with specific interface and task conditions and entering actual verification are called candidate contact metals. The initial model ranking is based on all candidate element records with complete and valid material descriptors, capable of obtaining baseline prediction values ​​from the baseline model, and capable of obtaining quantum core first-level residual prediction values. In implementations with applicable domain auditing, candidate element records are further output as interpolated, near-boundary, extrapolated, or unsupported states. Code-level preliminary usability states are only used for auxiliary marking; candidate electrode material records and candidate contact metals are not automatically determined by model ranking or query batches.

[0216] Figure 7 and Figure 8The candidate rankings and proposed review batches shown are from the base prediction model with the frozen QK-RR configuration, used to demonstrate the base predictions, rule-based application domain audits, and low-ρ predictions after training. c The prospective validation batch formation method for predicted candidates. The original model ranking only includes candidate element records that meet the above QK-RR numerical prediction conditions, and is determined in ascending order according to the predicted dimensionless target value; if the predicted values ​​are the same, they are determined in ascending order according to the element symbol. In an example of external manual review, the operator, based on the original model ranking and the applicable domain status, comprehensively considers low ρ c To meet the requirements of prediction, material diversity, and ranking comparison, six candidate elements—gallium (Ga), vanadium (V), manganese (Mn), erbium (Er), holmium (Ho), and bismuth (Bi)—were selected for recording. Among them, Ga, V, and Mn were used to observe low-ρ... c The performance of the predicted candidates is reviewed, with Er and Ho used to expand material category diversity, and Bi used as a ranking control. The formation of this manually reviewed batch does not change the original ranking of the QK-RR model, nor is it part of the descriptor space joint query scoring. The batch consisting of the above six candidate element records is used for externally configured DFT-NEGF calculations to verify the QK-RR ranking and its mobility across different applicable regions; this is not equivalent to ranking by the lowest predicted ρ. c The final recommended list of metals directly formed. Cadmium (Cd), Ga, V, Mn, Zinc (Zn), Molybdenum (Mo), Tin (Sn), Chromium (Cr), Rhenium (Re), and Indium (In) remain in the low-prediction ρ range of the basic model. c Priority review sequence.

[0217] VI. Model Evaluation Results

[0218] like Figure 1 The diagram illustrates a specific implementation process based on the method of this invention. It includes: first, selecting covering label candidates using an independent descriptor space query; second, manually configuring and archiving newly added labels using DFT-NEGF; and third, training QK-RR to filter low-p values. c The complete process of predicting candidates and verifying them through external manual configuration of DFT-NEGF involves adding labels, which are then manually verified and archived to form an updated labeled dataset and corresponding data version, which can be used for the next round of descriptor space query. Subsequent model training tasks call the updated labeled dataset to complete candidate configuration selection, model fitting, and result freezing to form the corresponding model version. The loop requires external manual confirmation and configuration. External high-fidelity calculation, manual verification, and archiving are not automatically performed by this method, and the archiving of newly added target values ​​does not automatically trigger subsequent model training.

[0219] Figures 2 to 6Based on 13 labeled metals and a frozen QK-RR configuration. Since only 13 labeled metals of the same diameter exist at a fixed doping concentration, and their number is less than the 24-dimensional effective descriptor dimension, this embodiment does not use a fixed-ratio random partitioning. For each material-level leave-one-fold, only the remaining 12 metals are used to reselect and fit the pre-reference model, generating the pre-reference out-of-fold residual within the training set. The normalizer, PCA, fidelity kernel matrix, and ν-SVR are refitted using only the 12 training metals. The pre-reference prediction is added to the 0.8 times quantum kernel first-level residual prediction to obtain the QK-RR basic prediction and its terminal out-of-fold residual. The left-out metal label does not enter the pre-reference selection and fitting, model preprocessing, kernel matrix construction, or regressor fitting for that fold; however, the frozen hyperparameter combination of the quantum kernel branch has already completed candidate selection using the same 13 metals, and the left-out label may indirectly affect the frozen configuration through the full data configuration selection. Therefore, this evaluation belongs to the material-level leave-one-fold reproduction of the posterior frozen configuration, and does not belong to nested model selection evaluation, unbiased generalization error, or independent external testing. This reproducibility is used for audit prediction, terminal residuals, and sorting, but not for quantifying the label efficiency of descriptor space sampling relative to random sampling.

[0220] In 1×10 19 e / cm 3 In the fixed doping concentration task, the frozen QK-RR configuration employs a hard-gated physical partitioning pre-reference candidate library, a 24-dimensional effective descriptor, an in-fold normalizer, a three-dimensional principal component space, a Pauli-Z fidelity kernel, and a pre-computed kernel ν-SVR. The first-order residual scaling factor λ = 0.8. The 13-fold material-level leave-one-out reproduction is reported to four decimal places, with a determination coefficient R² = 0.9811 and RMSE = 0.5645; the RMSE corresponds to a dimensionless logarithmic objective. The above indicators are for leave-one-out reproduction configured posteriorly on the same 13 metal datasets, applicable only to the fixed target field definition, fixed doping concentration, fixed feature version, and fixed dataset reproduction protocol, and do not constitute independent external test errors.

[0221] Figure 2 To fix the QK-RR basic prediction model at 1×10 19 e / cm 3 The figure shows the consistency between predicted and actual values ​​for material-level leave-one-out reproduction of 13 labeled metals under certain conditions. The basic prediction is obtained by summing the preceding baseline prediction and the first-order residual prediction of 0.8 times the quantum kernel. The result is the QK-RR basic prediction and does not include the nested evaluation results of the terminal residual. As can be seen from the figure, the QK-RR basic prediction values ​​of most of the left-out metals are close to the identity line, indicating that under the extremely small sample conditions in this embodiment, the sum of the preceding baseline and the Pauli-Z fidelity kernel ν-SVR first-order residual can reproduce ρ. cThe main relative trends across orders of magnitude are presented, providing the main predictions for subsequent nested evaluation of terminal residuals. This result does not imply reliable extrapolation of any distant candidate without auditing the applicable domain. In the figure, the dark gray inner shading represents the preset logarithmic error reference band of ±0.5 on both sides of the identity line, and the light gray outer shading represents the preset logarithmic error reference band of ±1.0. Both are used only for visual comparison and do not participate in model training or candidate selection.

[0222] Figure 3 Give directly Figure 2 The marginal residuals of the QK-RR baseline prediction are defined as follows: the marginal residual equals the true value minus the marginal value of the QK-RR baseline prediction. Pt, Al, and Sc show large positive residuals, indicating that the baseline prediction is lower than the true value; Nb and Pd show negative residuals, indicating that the baseline prediction is higher than the true value. These marginal residuals are only used for nested material-level residual evaluation based on 24-dimensional effective material descriptors and are not used for... Figure 7 and Figure 8 The deployment predictions are shown for candidates that are not labeled.

[0223] Figure 4 for Figure 2 The graph showing the metal-by-metal multiplicative error results for leave-one-out reproduction of QK-RR basic predictions converts the absolute logarithmic error of QK-RR basic predictions into a multiplicative error with a base of 10 and an exponent representing the absolute logarithmic error. The median multiplicative error for the 13 metals is approximately 2.2 times. The dashed lines at 3.16 times and 10 times in the graph correspond to absolute logarithmic errors of the order of 0.5 and 1.0, respectively, and are for visual reference only, not for model evaluation or candidate selection. The results are used to illustrate the error scale of QK-RR basic predictions and to conduct terminal residual error structure diagnosis. The final candidates still need to be calculated or verified experimentally using the same caliber.

[0224] Figure 5 The results of material-level bootstrap sensitivity intervals are provided; 10,000 resampling operations are performed with metals as the resampling unit, and the 95th percentile interval is reported.

[0225] Figure 6 for Figure 2The figure shows the consistency results of the labeled metal ranking for the leave-one-out reproduction of the QK-RR basic prediction. Both the true and predicted ranks are determined in ascending order of the target values. In this embodiment, the relative sizes of the true labels and the QK-RR basic predictions are compared for all 78 metal pairs formed for 13 metals; no tied values ​​were found. The figure shows the Spearman rank correlation coefficients for the two sets of ranking ranks, and the Kendall-type pairwise ranking coefficient calculated by dividing the difference between the number of metal pairs with consistent ranking directions and the number of metal pairs with inconsistent ranking directions by the total number of metal pairs. The basic prediction has 70 metal pairs with consistent directions, corresponding to a pairwise ranking accuracy of 89.7%; the Spearman rank correlation coefficient is 0.912, and the Kendall-type pairwise ranking coefficient is 0.795.

[0226] In a fixed implementation with 24-dimensional effective material descriptor input, the QK-RR basic prediction has a material-level leave-one-out-of-place RMSE of 0.5645 on the same 13-metal fixed dataset. The nested evaluation of terminal residuals is only used to identify local error structures; it does not generate uniformly deployed correction rules across the entire dataset and is not considered an independent external test result.

[0227] To ensure uniqueness of the evaluation criteria, the RMSE=0.5645 result described in this specification is limited to a 24-dimensional effective material descriptor, fixed doping concentration, fixed label definition, and a leave-one-out-of-reproducibility protocol for 13 metal materials. The nested evaluation of terminal residuals is only used for error structure diagnosis; when expanding input features, changing the evaluation level, or changing the nested evaluation rules of terminal residuals, it should be considered as another model protocol and re-evaluated, and its result should not replace the result of this embodiment. Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the substantive content of the present invention. In the absence of conflict, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0228] Figure 7 To utilize the fixed-parameter QK-RR baseline model fitted to all currently labeled contact metals, a raw ranking chart of the top 15 unlabeled candidate elements with complete and valid material descriptors, capable of obtaining baseline predictions from the baseline model, and capable of obtaining quantum nucleus first-order residual predictions is provided. The horizontal axis represents the dimensionless logarithmic target value of the prediction. This raw ranking is not equivalent to a contact metal list that has undergone material category confirmation or external high-fidelity verification.

[0229] Figure 8 for Figure 7The diagram shows the regular application domain audit of the fixed-parameter QK-RR baseline prediction candidate element records. Only candidate element records with complete and valid material descriptors, capable of obtaining baseline predictions from the baseline model, and capable of obtaining quantum kernel first-order residual predictions are plotted. Candidate element records that do not meet any of the above conditions are output as unsupported and are not shown in this diagram. The 75th percentile vertical dashed line and the 90th percentile vertical dashed line are the empirical distance percentile reference lines, respectively.

[0230] Figure 9 Under the same 13 metals, fixed doping concentrations, fixed target definitions, and a material-level leave-one-out verification outer layer protocol, the reproducibility metrics of seven classical regression models and a fixed-configuration QK-RR were summarized. The seven classical regression models include gradient boosting, K-nearest neighbors, random forest, ridge regression, radial basis function support vector regression, radial basis function kernel ridge regression, and Gaussian process regression; their input descriptor spaces and model selections all followed their respective archived freezing procedures. Among them, the root mean square error (RMSE) of QK-RR was 0.5645, the mean absolute error (MAO) was 0.4195, and the coefficient of determination (COR) was 0.9811. The best classical regression model illustrated is gradient boosting regression, with an RMS of 2.1635, an MAO of 1.8577, and a COR of 0.7227. This comparison illustrates the reproducibility differences between the frozen QK-RR and multiple classical models within the fixed embodiment; the selection of internal candidate configurations for different models still follows their respective freezing procedures.

[0231] The embodiments described above are merely some preferred embodiments of the present invention, and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A method for screening the contact resistivity of metal / gallium oxide (Ga2O3) based on quantum nuclear residuals, characterized in that, include: Acquire labeled contact metal data and candidate element records for metal / β-Ga2O3 contact systems under the same physical task. The labeled contact metal data includes a pre-reference auxiliary descriptor, an effective material descriptor, and a target value corresponding to the area-normalized zero-biased transport index. The candidate element records include the corresponding pre-reference auxiliary descriptor and effective material descriptor. For the labeled contact metal data, based on its preceding benchmark auxiliary descriptor, for each contact metal as a reserved unit of material-level extrapolation prediction, the contact metal is reserved from the current training set, the preceding benchmark model is trained using the remaining labeled contact metal data, and the reserved contact metal is predicted using the trained preceding benchmark model to obtain the material-level extrapolation preceding benchmark prediction value of each labeled contact metal. The difference between the target value and the corresponding material-level pre-deflation baseline prediction value is determined as the first-level residual; Based on the effective material descriptor and the first-order residual, a quantum kernel residual regression model using Pauli Z-phase encoding and a fidelity metric quantum kernel is trained. Based on the labeled contact metal data, a pre-benchmark model is fitted, and the pre-benchmark predicted value and the quantum kernel first-level residual predicted value of the candidate element record are obtained by using the fitted pre-benchmark model and the trained quantum kernel residual regression model, respectively. For candidate element records that can obtain the aforementioned baseline prediction value and quantum kernel first-level residual prediction value, the aforementioned baseline prediction value is added to the quantum kernel first-level residual prediction value scaled by the residual scaling factor to obtain the quantum kernel residual regression baseline prediction value, and the candidate element records are sorted in ascending order according to the quantum kernel residual regression baseline prediction value.

2. The method according to claim 1, characterized in that, The same physical task refers to having at least the following identical conditions: doping concentration, β-Ga2O3 crystal orientation, interface termination method, interface template conditions, and target value extraction rules.

3. The method according to claim 1, characterized in that, The area-normalized zero-bias transport index is determined based on the zero-bias differential resistance of the intact metal / β-Ga2O3 template device and the transverse periodic supercell area perpendicular to the transport direction. The target value is the area-normalized zero-bias transport index multiplied by Ω·nm. 2 The commonly used logarithm of the ratio.

4. The method according to claim 1, characterized in that, The determination of the preceding benchmark model includes: Multiple candidate configurations of the pre-benchmark are constructed with different parameter schemes. Taking the contact metal as the leave-out unit, material-level extra-blurred pre-benchmark prediction is performed for each candidate configuration of the pre-benchmark. Based on the material-level extrapolation prediction error corresponding to each candidate pre-prepared baseline configuration, the pre-prepared baseline configuration used to construct the first-level residual and predict the candidate element record is optimally determined; then, the labeled contact metal data is fitted under the pre-prepared baseline configuration to obtain the pre-prepared baseline model; furthermore, the material-level extrapolation prediction error includes the internal sum of squared errors (SSE), internal mean absolute error, and internal root mean square error. The optimal determination is as follows: first, the candidates are sorted in ascending order by the internal sum of squared errors (SSE); if they are the same, they are sorted in ascending order by the internal mean absolute error; if they are still the same, they are sorted in lexicographical order by the candidate configuration name, and the first item is taken as the pre-prepared baseline configuration.

5. The method according to claim 1, characterized in that, The preceding benchmark model is a physical partitioning preceding benchmark model. The physical partitioning preceding benchmark model divides the labeled contact metals and candidate element records into different physical partitions based on the element category attributes of the contact metals. Each labeled contact metal or candidate element record is predicted only by the preceding benchmark sub-model corresponding to its physical partition. The element category attributes include transition metal labels and periodic table family numbers. The physical partitions include a first physical partition and a second physical partition. Transition metals with periodic table family numbers from group 8 to group 11 are assigned to the second physical partition, and the preceding benchmark sub-model used is a ridge regression regularized linear regression model. The rest are assigned to the first physical partition, and the preceding benchmark sub-model used is a radial basis function kernel support vector regression (RBF-SVR) nonlinear kernel regression model. Each preceding benchmark sub-model uses the preceding benchmark auxiliary descriptor corresponding to the physical partition as input.

6. The method according to claim 1, characterized in that, The training of the quantum nuclear residual regression model includes: The effective material descriptors are standardized and subjected to principal component dimensionality reduction to obtain dimensionality-reduced coordinates; The components of the reduced-dimensional coordinates are mapped to phase angles, and the corresponding qubits are encoded using phase rotations generated by the Pauli Z operator. The Pauli Z phase encoding does not set entanglement coupling terms between qubits. Construct a fidelity quantum kernel based on the fidelity between quantum encoded states corresponding to different dimensionality reduction coordinates; Based on the pre-calculated fidelity metric kernel, a ν-support vector regression residual regression model with the first-level residual as the supervision target is trained.

7. The method according to claim 1, characterized in that, The residual scaling factor, as a parameter of the quantum nucleus residual branch candidate configuration, is determined based on the material-level extrapolation evaluation results of each quantum nucleus residual branch candidate configuration.

8. The method according to claim 1, characterized in that, Also includes: The applicable domain state of the candidate element record is determined based on the spatial distance of the candidate element record relative to the descriptor of the labeled contact metal data, and the degree to which the effective material descriptor of the candidate element record exceeds the corresponding value range of the labeled contact metal data. The applicable domain states include interpolation type, near-boundary type, and extrapolation type.

9. The method according to claim 1, characterized in that, It also includes a descriptor space query method for selecting candidate element records for the target value to be supplemented, including: Retrieve seed metal records, candidate element records, and query master descriptors that do not contain target values ​​for the same physical task; A descriptor query space is constructed based on the query master descriptor, and the current query coverage set is formed by the seed metal records; Without using the target value of the candidate element record, the quantum kernel residual regression prediction value, the model residual, and the model uncertainty, determine the boundary score, the overall distribution gain, the intra-batch diversity score, and the auxiliary physical prior score of the candidate element record, respectively. The boundary score, overall distribution gain, intra-batch diversity score, and auxiliary physical prior score are combined into a joint query score, and candidate element records of the target value to be supplemented are selected in sequence according to the joint query score to form a descriptor coverage query batch. After each candidate element record is selected, the candidate element record is added to the current query batch and the current query coverage set. The boundary score, overall distribution gain, intra-batch diversity score, auxiliary physical prior score, and joint query score of the remaining candidate element records are re-determined based on the updated current query coverage set, until the descriptor coverage query batch is formed.

10. The method according to claim 9, characterized in that, The seed metal records and candidate element records are determined as the overall distribution reference set, which remains unchanged during the same descriptor space query process; The boundary score is determined based on the descriptor space distance between the candidate element record and the current query coverage set; The overall distribution gain is determined based on the change in the distribution difference between the current query coverage set and the overall distribution reference set before and after the candidate element records are added to the current query coverage set. The intra-batch diversity score is determined based on the descriptor space distance between the candidate element record and the selected candidate element record in the current query batch; when no candidate element record has been selected in the current query batch, the same initial intra-batch diversity score is applied to the remaining candidate element records. The auxiliary physical prior score is determined based on the actual available physical properties of the elements in the candidate element record.

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