Artificial intelligence-driven phase stability evaluation and new dopants identification of hafnium oxide-based ferroelectric materials

Development of DFT datasets and ferroelectric phase fractions

Various the dopant and doping focus in HfO₂ crystals can result in modifications within the crystal construction, and the vitality distinction between completely different phases is a necessary foundation for his or her stability. To analyze the stability of completely different phases in HfO₂ crystals, we utilized DFT calculations and chosen some 2-valent to 5-valent parts as dopants for HfO₂, presenting the doping scenario of HfO₂ on a big scale. The crystal buildings of Ca-, Al-, Zr-, and Nb-doped monoclinic and ferroelectric phases are proven in Fig. 2a, the vitality distinction relative to the ground-state monoclinic phase can be proven below the situation of a doping focus of 12.5%. This method enabled us to realize insights into the stability of completely different phases in HfO₂ and examine the results of dopants and doping focus on the crystal construction. The stability of completely different phases on this work is evaluated by the vitality distinction between the corresponding phase and the m phase, which is obtained by calculating the overall vitality of every phase and the m phase. Right here, we calculated E_f-m and E_t-m, the place a constructive vitality distinction signifies that the phase has a better vitality than the m phase, whereas a destructive vitality distinction signifies that the phase has a decrease vitality than the m phase. Though the phase formation vitality can be utilized to match the stability of completely different materials, when evaluating completely different phases of the identical materials, the formation vitality of a phase could solely signify the transformation of absolute vitality, making it troublesome to immediately examine relative stability. Subsequently, for HfO₂, which requires the existence of a metastable ferroelectric phase, the phase vitality distinction can extra immediately mirror the chance of ferroelectric phase formation. The decrease the vitality of the ferroelectric phase, the larger the chance of its incidence. It’s because the phase vitality distinction immediately compares the relative stability between completely different phases with out contemplating the widespread reference state within the formation vitality. If the vitality of f-phase is decrease than the vitality of another phase, then f-phase is the bottom state phase, however it’s troublesome to guage whether or not it’s the floor state phase by way of the formation vitality.

In Fig. 2, we current the circumstances of undoped and doped HfO₂ with m phase because the reference state. The vitality variations between f phase and m phase and t phase and m phase are 63.6 meV and 136 meV, respectively. The overall energies proven listed here are the minimal energies obtained after construction optimization, and solely doping concentrations within the vary of 0–12.5% are displayed. In experiments, solely Zr dopant can obtain excessive doping concentrations, the doping focus shouldn’t be too excessive as a result of the tetragonal t-phase fashioned in the course of the crystal annealing course of can’t be reworked right into a ferroelectric f-phase in the course of the cooling course of²³. Typically, the dopants can have a ferroelectric phase construction solely within the case of a doping focus of 12.5%, and to simply examine the distinction in energies of the completely different dopants, the doping focus of lower than 12.5% is subsequently chosen. In Fig. 2b, c, we plotted the vitality variations for 12 sorts of dopants collected in keeping with their valence states. We seen that trivalent dopants exhibit extra important benefits in phrases of vitality distinction, and elemental doping of HfO₂ blocks can cut back the free vitality distinction between the f phase or t phase and the m phase. Earlier research have reported that bodily components akin to dopant dimension and electronegativity have an effect on the phase transition course of^24,25,26, and trivalent dopants have a transparent benefit as a result of their ionic radii being akin to that of Hf. Moreover, in Fig. 2b, c, the vitality distinction impact of tetravalent silicon dopants (with out cost carriers) is considerably weaker than that of divalent and trivalent dopants, which can be attributed to the provider impact of low-valence dopants.

We now have computed the overall density of states (TDOS) for the f-phase of HfO₂ at a doping focus of 12.5% (see Supplementary Fig. S1 within the Supplementary Data (SI)). It’s evident that below low-valence doping (2-valent and 3-valent) and high-valence doping circumstances, the Fermi degree enters the valence and conduction bands, respectively. This leads to the introduction of holes and electrons in hafnium oxide. Along with the vitality variations proven in Fig. 2, introducing these hole-doping results considerably enhances the ferroelectricity of hafnium oxide. This remark aligns with latest analysis by Cao et al.²⁷, which means that gap doping enhances ferroelectric stability in hafnium oxide. The quantity of holes might be obtained by integrating the density of states close to the Fermi degree, and the quantity of holes launched by 2-valent doping is twice that of 3-valent doping. Consequently, on the identical doping focus proven in Fig. 2, the vitality distinction between the f phase and m phases is decrease below 2-valent doping. Ba doping supplies a greater illustration of this phenomenon. In contrast to Ca and Sr, the density of states signifies that Ba doesn’t introduce holes below high-concentration doping however as an alternative kinds hole states throughout the bandgap. Moreover, these states are situated nearer to the conduction band, resembling the conduct of Ta. Consequently, the vitality distinction between the f phase and m phases (E_f-m) will increase, which is detrimental to the stability of the ferroelectric f phase. Particularly, doping with Sr induces a decrease focus of ferroelectricity ²⁸, which is attributed to the truth that divalent Sr has extra holes in comparison with trivalent Y, as mirrored within the lowering pattern of vitality distinction in Fig. 2b. Alternatively, provider injection can be one of the explanations for the fatigue or failure of ferroelectricity in ferroelectric materials. Earlier research usually managed the focus of low-valence dopants within the low-concentration vary.

In present preparation strategies, the vitality barrier variations between the assorted crystalline phases (together with the orthorhombic phase, monoclinic phase, tetragonal phase, cubic phase, and many others.) fashioned throughout annealing of ferroelectric skinny movies are comparatively small. Subsequently, regardless of whether or not the hafnium oxide ferroelectric movies are ready by bodily or chemical vapor deposition, they exhibit the traits of multi phase coexistence. That is the principle issue resulting in the inhomogeneous ferroelectric properties and poor repeatability of hafnium oxide-based movies, significantly hindering the sensible gadget purposes and business growth of hafnium oxide-based ferroelectric movies. To successfully consider the macroscopic ferroelectric efficiency of hafnium oxide-based ferroelectric movies, acquiring the proportion of the ferroelectric phase within the multi-phase construction can be crucial, along with utilizing parameters akin to polarization magnitude. The proportion of the ferroelectric phase can successfully reveal the stability and sturdiness of the polarization of hafnium oxide-based ferroelectric movies on a macroscopic scale and shortly remove false polarization brought on by varied interfering components. On this work, we used the Boltzmann distribution to calculate the proportion of the ferroelectric phase below completely different doping parts and doping quantities. We evaluated the ferroelectric efficiency of HfO₂-based movies by contemplating the proportion of the ferroelectric phase and the magnitude of polarization. The calculation course of for the ferroelectric phase fraction is proven within the SI, which requires the vitality distinction of every phase below completely different doping parts, these summary energies are then transformed into visualized ferroelectric phase fraction distribution mapping.

The Boltzmann distribution can be utilized to calculate the proportions of completely different phases in the identical system, as completely different phases might be considered completely different states of the system, every with its particular vitality. By calculating the vitality of every phase, their possibilities of incidence, i.e., the phase fractions, might be derived utilizing the Boltzmann distribution components. Determine 3 reveals the ferroelectric phase fractions of HfO₂ below varied dopants and doping concentrations. To make sure comparability of the polarization and ferroelectric phase fraction below completely different doping circumstances, we normalized the utmost values of the polarization magnitude. Subsequently, the normalized polarization and the ferroelectric phase fraction proven within the determine signify relative magnitudes. Relating to Fig. 3, a concise remark is that the nearer to the excessive polarization and excessive ferroelectric phase fraction area (i.e., the crimson area close to the highest), the extra more likely to obtain higher ferroelectric efficiency. This remark underscores the sturdy correlation between ferroelectric phase fractions and polarization. As proven in Fig. 3a, the world of excessive ferroelectric phase fraction for hafnium oxide doped with Ba is tiny and ferroelectric efficiency solely seems in a slender, low doping area, which is troublesome to realize experimentally. Subsequently, Ba shouldn’t be a perfect dopant for ferroelectric hafnium oxide as a result of its doping window is just too small. For hafnium oxide doped with Al, as proven in Fig. 3d, the world of the excessive ferroelectric phase fraction is considerably bigger. Good ferroelectric efficiency could happen within the vary of 2% to 10% Al doping, which is in good settlement with our experimental information (see Supplementary Fig. S2 and Supplementary Desk S1 the SI for particulars). For hafnium oxide doped with Zr, the area with a excessive ferroelectric phase fraction proven in Fig. 3j is extra in depth and tends to happen within the excessive doping vary of 30% to 50%, which is in good settlement with different associated research, thus offering additional proof that Zr is one of the optimum dopants for ferroelectric hafnium oxide movies. Equally, the ferroelectric phase fraction plot depicted in Fig. 3n signifies that Nb gentle doping is extra more likely to end in ferroelectric efficiency. It’s evident from the evaluation of Fig. 3 that by correlating the doping focus with the ferroelectric phase fraction, we are able to assess the effectiveness of completely different dopants and predict the optimum doping focus vary, thus guiding optimizing the doping focus in experiments.

Goal properties of hafnium oxide primarily based ferroelectric materials

The efficient doping focus ranges of completely different parts diverse considerably primarily based on DFT calculations. In all the workflow, it’s unreasonable to imagine the existence of ferroelectric phase buildings exterior the efficient doping focus. Subsequently, step one of this work is to display screen for dopants and doping concentrations that exhibit ferroelectric phase buildings. Within the second step of this work, to raised examine the energies of the three competing phases in doped hafnium oxide, we outline the relative vitality of α regarding the floor state m phase with dopant A on the identical doping focus as

the place ({E}_{A}^{alpha }) and ({E}_{A}^{m}) are the calculated whole DFT energies of the doped α phase and m phase, respectively. We obtained the vitality variations E_f-m and E_f-t between the ferroelectric and monoclinic phases and between the ferroelectric and tetragonal phases, respectively, primarily based on the outcomes from DFT calculations. The vitality variations are thought-about to be important foundations for the formation and secure existence of the ferroelectric phase^29,30. Polarization is an important criterion for assessing the ferroelectric efficiency of the HfO₂ system, which is highlighted on this research. The polarization magnitude of f phase HfO₂ doped samples was calculated by multiplying the Born efficient cost (BEC, Z*) with the atomic displacement (d) relative to the reference centrosymmetric t phase³¹.

The place i represents the ith atom and e is denoted because the digital cost and the thought-about cell quantity, respectively. Density generalized perturbation idea calculates the BEC within the course alongside the c-axis. As a result of full rest of the doped construction, the f phase hafnium oxide crystal construction undergoes particular modifications relying on the sort of doped atoms and the doping focus. Though most of these f phases preserve their ferroelectric phase construction traits when doped, at increased doping concentrations of sure doping parts, important phase construction modifications happen in the course of the rest course of, it’s troublesome to establish the non-contrastive ferroelectric phase construction traits, and in such circumstances, we outline its polarization magnitude as zero.

Particular presentation and evaluation of the machine studying mannequin

The multi-stage materials design framework is introduced in Fig. 1c. It combines classification and regression strategies and integrates characteristic development methods with typical machine studying strategies. The design framework consists of two important components: a classification process to foretell whether or not doped HfO₂ has a ferroelectric phase construction and a regression process to foretell phase vitality variations and polarization magnitudes. The enter information for this research, obtained from first-principles calculations, consist of related information for 15 sorts of doping parts which are divided into classification and regression datasets. As a standard course of in machine studying, characteristic engineering is a necessary step. Right here, the bodily traits of the doping parts, together with electronegativity (χ), ionization vitality (IE), electron affinity (EA), atomic radii (R), atomic mass (m), ionic radii (r), and valence state, are used. The machine studying mannequin can take benefit of the available bodily options, which can be utilized as probably the most direct and accessible enter for the mannequin.

To make sure the credibility of the following predictions, we first targeted our efforts on the classification of ferroelectric buildings. Earlier than developing the classification mannequin, we used the SISSO methodology to construct the characteristic house (see the SI for particulars). In comparison with conventional machine studying strategies for giant information evaluation, SISSO can generate efficient descriptors even when utilizing comparatively sparse information. It needs to be famous that SISSO might be break up into SIS and SO. SIS selects the subspace S_1D with the best correlation with the goal property, whereas the n-dimensional descriptors are chosen from the subspace S_nD with a response of Δ_(n-1)D. Then, SO extracts one of the best n-dimensional descriptors from the union of all beforehand chosen subspaces ({{rm{S}}}_{{rm{nD}}}cup {{rm{S}}}_{(({rm{n}}-1){rm{D}})}cup cdots cup {{rm{S}}}_{1{rm{D}}}) within the house. SISSO searches for easy and efficient characteristic descriptors within the house, and the screened characteristic descriptors shall be used to assemble the classification mannequin. To some extent, deciding on two descriptors within the characteristic house simplifies the classification mannequin and makes it extra interpretable. In Fig. 4c, the density distribution of the ferroelectric phase buildings and their bodily characteristic values reveals a powerful correlation between atomic radius and ferroelectric phase buildings. The atomic radius related to ferroelectric phases is primarily concentrated round R ~ 155 pm, clearly distinguishing from the atomic radius in non-ferroelectric phases. Subsequently, we chosen descriptors associated to R from the SISSO characteristic house and used them to assemble SVC fashions. To make sure simplicity and interpretability, we constructed every mannequin utilizing solely two descriptors from the characteristic house. Additional characteristic choice optimization was carried out, and a characteristic descriptor primarily based on R and χ was preliminarily established. The classification mannequin was constructed utilizing the SVC methodology and optimized by way of standardization and grid search. The accuracy of the mannequin in predicting the presence of ferroelectric buildings was 96.5% (Fig. 5a). We famous that the standardized characteristic descriptors within the classification mannequin are ({{(R}_{O}+{chi }_{A})}_{S}) and ({{(chi }_{A}-{R}_{A})}_{S}), that are immediately associated to the atomic radii and electronegativity of the doping parts.

Determine 5b reveals the affect of composition on lattice constants and quantity modifications (see the SI for particulars). The doping of impurities into HfO₂ crystals may cause native deformation of the crystal construction and modifications in quantity³². The quantity discount or enlargement brought on by the doping element might be thought-about as a relative compressive pressure change and a quantity enlargement change. The relative compressive pressure change makes the monoclinic phase transition unstable, which additionally impacts the orthorhombic phase to some extent. When the quantity change shouldn’t be important, a phase transition happens and the orthorhombic phase step by step stabilizes.

Nevertheless, with growing doping focus, this relative compressive pressure change can even have a destructive influence, and the vitality of the nonpolar phase satisfies the optimum secure situation, inflicting the crystal phase to shift in the direction of the nonpolar phase, the place the polar phase is at a drawback. For the phase transition brought on by quantity enlargement, the pressure vitality brought on by the scale mismatch between the m phase and t phase as a result of quantity enlargement is extra important³³. The lattice distortion is comparatively giant, so the cubic phase dominates on this case. Subsequent, we used Pearson correlation coefficients (PCCs) to measure the diploma of correlation between options. It’s price noting that we launched quantity modifications on this correlation evaluation. Determine 5c reveals the heatmap of the correlation coefficients between bodily options, and the excessive correlation (PCCs = 0.946) between atomic radii and quantity change hyperlinks the bodily mannequin with the ML mannequin (see the SI for particulars). This work not solely demonstrates the wonderful efficiency of SVC in classification issues but additionally supplies necessary bodily insights from the “black field” mannequin by way of the new method combining SISSO with SVC.

Subsequent, we employed the random forest methodology to foretell E_f-m and E_f-t, incorporating the valence states of doping parts as a characteristic. The valence state is the rationale for the technology of holes or electrons within the HfO₂ construction. It performs a necessary function in predicting vitality variations, so it was a beneficial addition to the related options. To judge the efficiency of the regression mannequin, we used two evaluation metrics: the coefficient of willpower (R²) and the imply absolute error (MAE). The check outcomes of the random forest mannequin are proven in Fig. 5d, e, with the R² and MAE values for the E_f-m mannequin being 92.9% and 3.671 meV, respectively, and for the E_f-t mannequin being 95.3% and 1.801 meV, respectively. These outcomes reveal the wonderful efficiency of our random forest mannequin in predicting vitality variations. Subsequently, we skilled a polarization prediction mannequin utilizing the identical enter options however discovered the mannequin efficiency unsatisfactory. We noticed that vitality distinction and polarization are carefully associated (the vitality distinction displays the stability of the ferroelectric phase). To deal with this, we added E_f-m and E_f-t as enter options to the polarization mannequin, and the check outcomes are proven in Fig. 5f, with R² and MAE of 90.7% and 0.926 μC/cm², respectively. This demonstrates that the mannequin can predict polarization magnitude inside a suitable error vary (particulars of the machine studying mannequin might be discovered within the SI).

Bodily insights of the machine studying mannequin

The SHAP methodology supplies a unified strategy to clarify the output of any machine studying mannequin by connecting recreation idea and native interpretation, calculating the contributions of every participant primarily based on their marginal results with or with out participation^34,35. Though random forests have characteristic significance to elucidate the significance of related options (see Supplementary Fig. S3 within the SI), it isn’t simple to realize the native contributions of every characteristic. Subsequently, we performed SHAP evaluation on the fashions for vitality variations (E_f-m, E_f-t) and polarization (P_s).

Determine 6a, b reveals the SHAP values for particular person options on the samples. Unsurprisingly, the valence state of the factor contributes considerably to the vitality distinction since Hf is tetravalent, and the doping of different valence states can introduce holes or electrons. From Fig. 6a, b, destructive SHAP values for the doping of divalent and trivalent parts might be noticed, indicating that they might promote the proportion of the ferroelectric phase. This means that trivalent doping could also be extra appropriate as dopants for HfO₂, which is per the findings of Batra et al.³⁶. It’s famous that the excessive electron affinity (EA) can considerably improve the vitality distinction, as proven in Fig. 6a. EA is outlined because the vitality launched when an electron is added to a impartial atom. The excessive EA values noticed below pentavalent doping exhibit a constructive contribution to E_f-m and E_f-t of over 100 meV. Though different options exhibit conduct that lowers the vitality distinction, no reversal is noticed. The excessive EA values could have a detrimental impact on phase stability.

Moreover, SHAP evaluation can reveal the influence of ionic radii below completely different coordination environments on the goal property. Single-sample SHAP evaluation was performed on completely different ionic radii of Sn, Ti, and Si in the identical valence state, as proven in Fig. 6c. The impact of completely different dopant ionic radii on E_f-m and E_f-t was important (see Supplementary Figs. S4 and S5 within the SI). Because the dopant ionic radii will increase, the SHAP worth of the ionic radii reveals a pattern of initially destructive and then constructive. For ionic radii alone, smaller ionic radii could have a extra important benefit than a bigger ionic radius in stabilizing the ferroelectric phase. Nevertheless, in phrases of the general vitality distinction, the vitality variations for the three ions are 47.27, −11.62, and 54.12 meV, respectively. Merely utilizing ionic radii to argue that smaller is healthier shouldn’t be complete. We observe that the E_f-m worth for Sn is barely bigger than that for Si. Though the destructive characteristic contribution related to smaller ionic radii could have an absolute benefit in E_f-m, in conditions the place the distinction in ionic radii shouldn’t be important, different options akin to electronegativity and electron affinity can have an absolute influence on the goal property, and this influence is advanced. The numerous influence of doping ionic radii on E_f-m and E_f-t is clear in Fig. 6a, b, exhibiting reverse traits for the 2 properties. A smaller E_f-m worth signifies a larger chance of forming the ferroelectric phase from an vitality perspective, whereas a smaller E_f-t worth suggests larger stability of the ferroelectric phase on the vitality degree. The connection between doping ionic radii and phase vitality distinction doesn’t exhibit a strict linear dependence, as proven in Fig. 7, the place a linear relationship is barely noticed inside a sure vary. An reverse impact emerges with additional will increase in ionic radii, which may very well be an important issue within the disappearance of the ferroelectric phase construction. SHAP evaluation revealed that increased dopant ionic radii inside a selected vary may successfully stabilize the polar phase, whereas excessive ionic radii can result in a rise within the phase vitality distinction, inflicting instability of the ferroelectric phase construction. Starschich et al.³⁷ noticed experimentally that the bigger the dopant ionic radii inside a sure vary, the extra important the residual polarization. The outcomes obtained from the SHAP evaluation are per the experimental observations, indicating that the mannequin has extracted related insights on the bodily degree.

Functions of the machine studying mannequin

To reveal the use of the multistage materials design framework in screening high-value HfO₂ dopants and their doping concentrations, we chosen a subset of dopants as examples and computed their corresponding E_f-m, E_f-t, and calculated ferroelectric phase proportions, as proven in Fig. 8. We screened a complete of 22 dopants, together with 52 completely different valences. Following earlier experiences, we restricted the dopant concentrations to 2%-25%. Determine 8b clearly reveals that the secure ferroelectric phases are principally discovered within the low doping states with decrease E_f-t. Though Ag, Cd, and Sc exhibit low E_f-t at excessive doping concentrations, they don’t seem to be perfect as HfO₂ dopants within the calculated ferroelectric phase fraction, notably for Ag²⁺, Cd²⁺, and Sc²⁺. Curiously, Sc³⁺ exhibited a unique outcome. We examined the corresponding ionic radii and discovered that the ionic radii of Sc³⁺ in an octahedral coordination setting is 0.87 Å, which is nearer to that of Hf⁴⁺ (0.83 Å). Determine 8 lists many unconfirmed doping candidates for HfO₂ in phrases of first-principles calculations or experiments and some candidates which have been confirmed to be doubtlessly beneficial^19,36,38.

Within the mapping of ferroelectric phases predicted by the machine studying mannequin, we discover that Ga³⁺ doping stabilizes increased ferroelectric phase fractions, implying that there’s a doubtlessly good ferroelectric efficiency in HfGaO. To evaluate the effectiveness and accuracy of the machine studying mannequin, we chosen Ga as a new factor for DFT calculations and multi-gradient doping experiments, as proven in Fig. 9. DFT calculations had been carried out for various doping ratios of HfGaO, and the outcomes had been in contrast with the predictions of machine studying mannequin. From Fig. 9a, it may be seen that the errors of E_f-m and E_f-t are inside a small vary. To additional validate the efficiency of Ga doping in experiments, we ready Ga-doped HfO₂ movies with completely different Hf:Ga cycle ratios by utilizing plasma enhanced atomic layer deposition (PEALD) system (the precise experimental strategies are offered within the SI). The XPS spectra are proven in Supplementary Fig. S6 within the SI, by way of XPS evaluation we are able to verify the efficient doping of Ga parts and the doping focus. After calculations we decided the doping concentrations of Ga to be 1.2%, 3.1%, 4.5%, and 9.2%, which correspond to completely different Hf:Ga deposition cycles, respectively (particulars of the Ga³⁺ valence affirmation and the XPS evaluation might be discovered within the SI). Supplementary Fig. 9b reveals a comparability between the ferroelectric phase fraction of the experimentally ready HfGaO movies and the ferroelectric phase fraction predicted by the machine studying mannequin, and we are able to see that the experimentally decided variation traits of ferroelectric phase fraction and polarization properties with Ga doping focus are in good settlement with the predictions given by machine studying. It’s clear that the excessive ferroelectric phase fraction is accompanied by good polarization properties, showing within the predicted excessive ferroelectric phase fraction and giant polarization area (crimson area), and displaying a pattern of enhancement adopted by weakening with growing doping focus (from 0% to 9.2%), which is in excessive consistency with the pattern predicted by machine studying.

The phase composition of the HfGaO movies was analyzed utilizing grazing incidence extensive angle X-ray scattering (GIWAXS) method, and the corresponding phase fractions with completely different Ga doping concentrations had been obtained (Fig. 9c), and the small print of the calculations concerning the phase compositions are given within the SI. It’s noteworthy that the ferroelectric phase fraction reaches a most (61%) because the doping focus will increase as much as 4.5%, and the ferroelectric phase fraction decreases virtually to be akin to that of the doping focus of 1.2% because the doping focus will increase as much as 9.2%, however the composition of the phase fractions shouldn’t be the identical at these two doping concentrations. This is because of the truth that the fraction of the m-phase decreases and the fraction of the t-phase will increase because the doping focus will increase, which is per the pattern of the vitality distinction demonstrated in Fig. 9a, the place the m-phase is dominant and the ferroelectric phase will increase at low doping concentrations decrease than 4.5%, and the t-phase is dominant and the ferroelectric phase decreases because the Ga doping focus continues to extend. The GIWAXS patterns and the corresponding polarization-voltage curves of HfGaO movies with completely different Ga doping concentrations are given in Fig. 9d. We will clearly see the traits of the diffraction peak intensities equivalent to the o-phase (i.e., ferroelectric phase), t-phase, and m-phase, respectively, various with the Ga doping focus, and the precise phase fractions have been introduced in Fig. 9c. The polarization-voltage curves we measured by the PUND (Constructive­Up­Destructive­Down) methodology in order that the impact of dielectric properties on the polarization efficiency might be excluded. With the rise of the ferroelectric phase, the polarization magnitude of the HfGaO movies will increase and reveals typical hysteresis traits, and the polarization curve reaches a most at 4.5% Ga doping focus, with the remnant polarization 2P_r reaching 17.8 μC/cm², which is in excellent settlement with the method of ferroelectric phase variation. We use Ga as a model new dopant below the prediction of the machine studying mannequin, and experimentally achieve acquiring the variation patterns of ferroelectric properties and ferroelectric phase with completely different Ga doping concentrations, which totally demonstrates that constructing machine studying fashions with glorious predictive capabilities can facilitate the seek for beneficial hafnium oxide doping candidates within the big chemical house, which is orders of magnitude quicker than first-principles calculations.