Pushing the Pareto front of band gap and permittivity: ML-guided search for dielectric materials

TL;DR

The paper tackles the dual challenge of achieving high dielectric permittivity while maintaining a large band gap in dielectrics, a classic trade-off that hinders device voltage tolerance. It introduces a scalable ML-guided funnel that uses Wyckoff-based structure representations and ensemble models to pre-screen candidates for formation energy, band gap, and dielectric constants, then applies element substitution to generate a vast pool of candidates for high-throughput DFPT validation, finally incorporating expert judgment in synthesis choices. The workflow yields a larger set of high-$\Phi_M$ materials than prior DFPT-only studies and validates two novel dielectrics, Bi2Zr2O7 (E_gap = 2.27 eV; ε_tot = 20.5 at 1 MHz) and CsTaTeO6 (E_gap = 1.05 eV; ε_tot = 26), with CsTaTeO6 illustrating successful de novo design and Bi2Zr2O7 demonstrating practical dielectric potential. The work highlights the value of combining ML prescreening with first-principles validation and human expertise to efficiently explore unknown chemical space, while noting current ML band gap limitations and proposing avenues for improvement such as higher-level theory and spectrum-based predictions. The approach paves the way for accelerated discovery of high-performance dielectrics suitable for advanced electronic devices.

Abstract

Materials with high-dielectric constant easily polarize under external electric fields, allowing them to perform essential functions in many modern electronic devices. Their practical utility is determined by two conflicting properties: high dielectric constants tend to occur in materials with narrow band gaps, limiting the operating voltage before dielectric breakdown. We present a high-throughput workflow that combines element substitution, ML pre-screening, ab initio simulation and human expert intuition to efficiently explore the vast space of unknown materials for potential dielectrics, leading to the synthesis and characterization of two novel dielectric materials, CsTaTeO6 and Bi2Zr2O7. Our key idea is to deploy ML in a multi-objective optimization setting with concave Pareto front. While usually considered more challenging than single-objective optimization, we argue and show preliminary evidence that the $1/x$-correlation between band gap and permittivity in fact makes the task more amenable to ML methods by allowing separate models for band gap and permittivity to each operate in regions of good training support while still predicting materials of exceptional merit. To our knowledge, this is the first instance of successful ML-guided multi-objective materials optimization achieving experimental synthesis and characterization. CsTaTeO6 is a structure generated via element substitution not present in our reference data sources, thus exemplifying successful de-novo materials design. Meanwhile, we report the first high-purity synthesis and dielectric characterization of Bi2Zr2O7 with a band gap of 2.27 eV and a permittivity of 20.5, meeting all target metrics of our multi-objective search.

Figures (11)

• Figure 1: Diagram of our dielectric material discovery workflow, integrating ML pre-screening and elemental substitution for generating novel crystals with high-throughput DFPT validation. The discovery pipeline can operate in two modes: screening and generation. Screening mode searches for large permittivity among known materials. In generation mode, we feed the top 1k MP structures by figure of merit $\Phi_\text{M}$ into an element substitution process.
• Figure 2: Violin plot showing Gaussian KDEs of DFPT-computed electronic (blue left halves) and ionic (orange right halves) contributions to the dielectric constant split by crystal system. The dashed horizontal lines in each violin show the median. Below each crystal system is the number of materials we have for it as well as its share of the total DFPT dataset in percent. The colored bold numbers (blue = low, red = high) show the mean of the top 30 electronic/ionic dielectric constants for each crystal system.
• Figure 3: Log-log plot of PBE band gap ${E_\text{gap}}$ vs. total dielectric constant $\epsilon_\text{tot}$ visualizing the hit rates for high-$\Phi_\text{M}$ materials from different studies. Many of our DFPT data points (blue circles) reach into regions far beyond the 240eV isoline. The orange diamonds and green squares show results from *petousis_high-throughput_2017petousis_high-throughput_2017 and *qu_high_2020qu_high_2020 which produce fewer $\Phi_\text{M}> 240$ materials, both in absolute numbers and as a fraction of dataset size (see \ref{['tab:hit-rate-comparison']}). The dark blue lines indicate constant figure of merit $\Phi_\text{M}= {E_\text{gap}} \cdot \epsilon_\text{tot}$. The stacked marginal rugs along the top and right show the distribution of band gaps and dielectric constants in each dataset.
• Figure 4: Structural determination of CsTaTeO6 (\ref{['fig:exp-rietveld-CsTaTeO6-Fd3m']}) and Bi2Zr2O7 (https://materialsproject.org/materials/mp-756175) (\ref{['fig:exp-rietveld-Bi2Zr2O7-Fm3m']}) using XRD and Rietveld refinement. $Q = 2 \pi \cdot d^{-1}$$[\text{Å}^{-1}]$ is the scattering vector. \ref{['fig:CsTaTeO6-whole-cell']}) Crystal structure of the best Rietveld fit for CsTaTeO6. with \ref{['fig:CsTaTeO6-a-site']}) and \ref{['fig:CsTaTeO6-b-site']}) showing the pyrochlore A and B site octahedra. \ref{['fig:Bi2Zr2O7-whole-cell']}) Crystal structure of the best Rietveld fit for Bi2Zr2O7 with \ref{['fig:Bi2Zr2O7-polyhedra']}) showing the isolated Zr/BiO8 polyhedra. Notable Ta2O5 impurities were detected in the CsTaTeO6 XRD scan (\ref{['fig:exp-rietveld-CsTaTeO6-Fd3m']}). Ta2O5 has many $hkl$ reflections, most of which are not distinguishable from the background noise. The most prominent observable Ta2O5 peak at $Q = 1.7$ as marked by the orange arrow. The absence of a (111) peak in the Bi2Zr2O7 Rietveld fit (\ref{['fig:exp-rietveld-Bi2Zr2O7-Fm3m']}) suggests a fluorite structure, in contrast to the literature-proposed pyrochlore model.
• Figure 5: Dielectric measurements of Bi2Zr2O7 and CsTaTeO6. (\ref{['fig:exp-diffuse-reflectance']}) Diffuse reflectance spectra for both compounds exhibit distinctive absorption edges, indicating ordered crystalline structures. (\ref{['fig:exp-tauc-bandgaps']}) Tauc plot measuring absorption coefficient $\alpha(E_\text{ph})$ vs photon energy $E_\text{ph} = h \nu$ for both compounds.The extracted optical band gaps are ${E_\text{gap}} = 2.27eV$ for Bi2Zr2O7 and 1.05eV for CsTaTeO6. (\ref{['fig:exp-CSTaTeO6-diel-real-imag-loss-vs-freq']}) Dielectric response of CsTaTeO6 as a function of frequency. We measure $\epsilon_\text{tot} = 26$ at 1MHz electric field (compared to 67 from DFPT) Its unwelcome high dielectric loss of $\tan(\delta) = 0.23$ at 1MHz confirms the semiconducting nature observed in the Tauc plot's spectroscopic data. (\ref{['fig:exp-Bi2Zr2O7-diel-real-imag-loss-vs-freq']}) Dielectric response of Bi2Zr2O7 as a function of frequency yields $\epsilon_\text{tot} = 20.5$ at 1MHz (compared to 206 from DFPT) We highlight Bi2Zr2O7's dielectric loss of less than 0.1 above 1kHz, a sufficiently low value for many practical applications.