Fundamental band gap and alignment of two-dimensional semiconductors explored by machine learning

Two-dimensional (2D) semiconductors isoelectronic to phosphorene has been drawing much attention recently due to their promising applications for next-generation (opt)electronics. This family of 2D materials contains more than 400 members, including (a) elemental group-V materials, (b) binary III-VII and IV-VI compounds, (c) ternary III-VI-VII and IV-V-VII compounds, making materials design with targeted functionality unprecedentedly rich and extremely challenging. To shed light on rational functionality design with this family of materials, we systemically explore their fundamental band gaps and alignments using hybrid density functional theory (DFT) in combination with machine learning. First, GGA-PBE and HSE calculations are performed as a reference. We find this family of materials share similar crystalline structures, but possess largely distributed band-gap values ranging approximately from 0 to 8 eV. Then, we apply machine learning methods, including Linear Regression (LR), Random Forest Regression (RFR), and Support Vector Machine Regression (SVR), to build models for prediction of electronic properties. Among these models, SVR is found to have the best performance, yielding the root mean square error (RMSE) less than 0.15 eV for predicted band gaps, VBMs, and CBMs when both PBE results and elemental information are used as features. Thus, we demonstrate machine learning models are universally suitable for screening 2D isoelectronic systems with targeted functionality and especially valuable for the design of alloys and heterogeneous systems.

[1]  Zhixian Zhou,et al.  Improved carrier mobility in few-layer MoS2 field-effect transistors with ionic-liquid gating. , 2013, ACS nano.

[2]  B. Gorman,et al.  Using heterostructural alloying to tune the structure and properties of the thermoelectric Sn1−xCaxSe , 2017 .

[3]  Likai Li,et al.  Black phosphorus field-effect transistors. , 2014, Nature nanotechnology.

[4]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[5]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[6]  Giuseppe Iannaccone,et al.  Electronics based on two-dimensional materials. , 2014, Nature nanotechnology.

[7]  Alok Choudhary,et al.  A General-Purpose Machine Learning Framework for Predicting Properties of Inorganic Materials , 2016 .

[8]  A. Radenović,et al.  Single-layer MoS2 transistors. , 2011, Nature nanotechnology.

[9]  P. Ye,et al.  Semiconducting black phosphorus: synthesis, transport properties and electronic applications. , 2014, Chemical Society Reviews.

[10]  Wei Kang,et al.  Ferroelectricity and Phase Transitions in Monolayer Group-IV Monochalcogenides. , 2016, Physical review letters.

[11]  Tanmoy Das,et al.  Superconductivity and topological Fermi surface transitions in electron-doped cuprates near optimal doping , 2007, 0711.1504.

[12]  Gustavo E. Scuseria,et al.  Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)] , 2006 .

[13]  Andrew G. Glen,et al.  APPL , 2001 .

[14]  Wenhui Wang,et al.  Two-dimensional antimonene single crystals grown by van der Waals epitaxy , 2016, Nature Communications.

[15]  F. Xia,et al.  The renaissance of black phosphorus , 2015, Proceedings of the National Academy of Sciences.

[16]  Stefano Curtarolo,et al.  High-throughput electronic band structure calculations: Challenges and tools , 2010, 1004.2974.

[17]  D. Tománek,et al.  Tiling phosphorene. , 2014, ACS nano.

[18]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[19]  H. Zeng,et al.  Atomically thin arsenene and antimonene: semimetal-semiconductor and indirect-direct band-gap transitions. , 2015, Angewandte Chemie.

[20]  Xianfan Xu,et al.  Phosphorene: an unexplored 2D semiconductor with a high hole mobility. , 2014, ACS nano.

[21]  Zhen Zhu,et al.  Semiconducting layered blue phosphorus: a computational study. , 2014, Physical review letters.

[22]  D. Tománek,et al.  Designing Isoelectronic Counterparts to Layered Group V Semiconductors. , 2015, ACS nano.

[23]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.

[24]  Cormac Toher,et al.  Charting the complete elastic properties of inorganic crystalline compounds , 2015, Scientific Data.

[25]  Paolo Ruggerone,et al.  Computational Materials Science X , 2002 .

[26]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[27]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[28]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[29]  Michael P. Short,et al.  Current Opinion in Solid State and Materials Science , 2013 .

[30]  J. Shan,et al.  Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides , 2016, Nature Photonics.

[31]  A. H. Castro Neto,et al.  Electric field effect in ultrathin black phosphorus , 2014 .

[32]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[33]  James E. Gubernatis,et al.  Multi-fidelity machine learning models for accurate bandgap predictions of solids , 2017 .

[34]  P. Kim,et al.  Experimental observation of the quantum Hall effect and Berry's phase in graphene , 2005, Nature.

[35]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[36]  Ryan O'Hayre,et al.  Predicting density functional theory total energies and enthalpies of formation of metal-nonmetal compounds by linear regression , 2016 .

[37]  Engineering,et al.  Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques , 2016 .

[38]  Christopher M Wolverton,et al.  Atomistic calculations and materials informatics: A review , 2017 .

[39]  L. Bellaiche,et al.  Photostrictive Two-Dimensional Materials in the Monochalcogenide Family. , 2017, Physical review letters.

[40]  Marco Buongiorno Nardelli,et al.  The high-throughput highway to computational materials design. , 2013, Nature materials.

[41]  A S Rodin,et al.  Strain-induced gap modification in black phosphorus. , 2014, Physical review letters.

[42]  Chiho Kim,et al.  Machine learning in materials informatics: recent applications and prospects , 2017, npj Computational Materials.

[43]  C. Goodman.  The prediction of semiconducting properties in inorganic compounds , 1958 .

[44]  James Theiler,et al.  Materials Prediction via Classification Learning , 2015, Scientific Reports.

[45]  Shu Zhong,et al.  Epitaxial Growth of Single Layer Blue Phosphorus: A New Phase of Two-Dimensional Phosphorus. , 2016, Nano letters.

[46]  Anubhav Jain,et al.  Phosphates as Lithium-Ion Battery Cathodes: An Evaluation Based on High-Throughput ab Initio Calculations , 2011 .