Lee et al. (Nature 494, 336 (2013)) established dicalcium nitride, Ca2N{\rm Ca_2N}, as the first bulk two-dimensional electride, in which anionic excess electrons form a two-dimensional sheet in the interlayer space of the layered ionic host [Ca2N]+⋅e−[{\rm Ca}_2{\rm N}]^{+}\cdot e^{-}, and reported anisotropic, low work functions of 3.5 eV (single-crystal (00ℓ)(00\ell) basal surface) and 2.6 eV (polycrystal) by ultraviolet photoemission spectroscopy. Thirteen years of subsequent work has neither prepared nor microscopically characterized a clean, atomically defined surface of this compound: the orientation dependence of the work function, the assignment that low-work-function (100)-type lateral facets terminate at and expose the anionic electron layer, the surface atomic structure (reconstruction and termination) beyond one slab-model and one cleaved-crystal photoemission study, and the chemical stability and passivation of a free anionic-electron surface under ambient conditions all remain experimentally undetermined. The open problem is: establish the surface physics and surface chemistry of Ca2N{\rm Ca_2N} — which terminations exist, which expose anionic electrons, what their absolute work functions are, and whether the exposed anionic electron layer can be stabilized in reactive environments.

Background

An electride is an ionic crystal in which some valence electrons occupy interstitial voids instead of belonging to any atom, so that these 'anionic' or excess electrons act as the anion of the ionic lattice. Their physical properties are governed by the topology of the cavity or plane that confines the anionic electrons. Before 2013, known inorganic electrides confined electrons in zero-dimensional cages (e.g. the mayenite-based electride [{{\rm Ca}_{24}{\rm Al}_{28}{\rm O}_{64}]^{4+}\cdot 4e^{-}) or in weakly linked one-dimensional channels; a two-dimensional electron system confined at an interface had been realized only in artificially fabricated semiconductor heterostructures. The work function is the minimum energy needed to remove an electron from a surface to vacuum; it is conventionally measured by ultraviolet photoemission spectroscopy (UPS), in which the width of the photoemission onset yields the energy difference between the Fermi level and the vacuum level at that surface. Because photoemission is surface-sensitive, the measured value can be shifted by surface reconstruction (a rearrangement of the topmost atomic layers), by band bending, and by the surface photovoltage effect (a light-induced flattening of surface band bending that distorts photoemission thresholds, especially in low-carrier-density systems).

Dicalcium nitride crystallizes in a rhombohedral layered structure of alternating [{{\rm Ca}_2{\rm N}]^{+} cationic slabs and interlayer sheets of anionic electrons, giving the formal composition [{{\rm Ca}_2{\rm N}]^{+}\cdot e^{-}. In hexagonal axes, the (00ℓ)(00\ell) (basal) planes are the natural cleavage planes parallel to the [{{\rm Ca}_2{\rm N}]^{+} slabs, whereas (100)-type lateral planes cut perpendicularly through both the slabs and the anionic electron sheets. Electronic-structure calculations by Uijttewaal, de Wijs and de Groot in 2004 had already predicted that a surface of Ca2N{\rm Ca_2N} which terminates the anionic electron layer has a work function roughly half an eV lower than metallic calcium, making it a candidate low-work-function cathode for polymer light-emitting diodes. Lee, Kim, Toda, Matsuishi and Hosono (2013) synthesized single crystals and polycrystalline Ca2N{\rm Ca_2N}, demonstrated two-dimensional diffusive transport of the dense anionic electron layer (mobility 520 cm2 V−1s−1520\ {\rm cm^2\,V^{-1}s^{-1}}, quadratic-in-temperature resistivity indicating electron-electron scattering, and anisotropic magnetoresistance), and used UPS to measure work functions of 3.5 eV on the (00ℓ)(00\ell) surface and 2.6 eV on the polycrystal, attributing the lower value to (100)-related facets that expose anionic electrons, by analogy with the first-principles prediction.

The authors of the 2013 paper acknowledged that these surface conclusions were indirect: the UPS thresholds could be affected by surface reconstruction and by surface photovoltage, so the exact surface electronic structure and the absolute orientation dependence of the work function were not established; the facet assignment was inferred from data and calculations rather than imaged; and the compound is so reactive toward oxygen and water vapour that all handling required a glove box and ultrahigh vacuum, leaving open how an exposed anionic electron layer could survive device-relevant conditions. Subsequent theoretical work confirmed that Ca2N{\rm Ca_2N} and the analogous strontium compound Sr2N{\rm Sr_2N} are stable down to monolayer thickness, with work functions that depend strongly on thickness and termination, and that the basal cleavage surface of quasi-two-dimensional electrides such as Ca2N{\rm Ca_2N} and Y2C{\rm Y_2C} hosts floating, Tamm-like surface states (surface-localized electron states created by the abrupt termination of the bulk potential at the surface) derived from the anionic electrons. Experimentally, however, the only surface probe of Ca2N{\rm Ca_2N} after 2013 has been an angle-resolved photoemission spectroscopy (ARPES) study — a technique that resolves electron energy versus momentum — on an in-situ-cleaved crystal, which found band dispersions consistent with theory except for a chemical potential shift attributed to the reactivity of the surface excess electrons. Reviews of inorganic electrides continue to list the extreme air and moisture sensitivity of two-dimensional electrides as the principal obstacle to their application as low-work-function cathodes, electron injectors, and electron-donating catalysts, while a 2018 silver-passivation study showed one route to temporarily stabilize the compound.

Problem Statement

Establish the surface physics and surface chemistry of the two-dimensional electride [{{\rm Ca}_2{\rm N}]^{+}\cdot e^{-} on clean, atomically defined surfaces. Specifically: (1) prepare and determine the atomic structure — termination and any reconstruction — of the principal low-index surfaces of Ca2N, namely the (00ℓ)(00\ell) basal cleavage plane and the (100)-type lateral planes that intersect the anionic electron sheets, under conditions where surface reactivity does not dominate; (2) measure the absolute work function of each orientation by surface-sensitive techniques (photoemission, or Kelvin-probe methods, which measure the contact potential difference between the surface and a vibrating reference electrode) with the surface photovoltage and band-bending artifacts that affected the original UPS thresholds identified and corrected, thereby fixing the true orientation dependence of the work function; (3) determine, microscopically and spectroscopically (e.g. by scanning tunneling microscopy, low-energy electron diffraction, or spatially resolved photoemission), which surface facets actually terminate at and expose the anionic electron layer, testing the 2013 inference that the lowest work function of polycrystalline Ca2N arises from (100)-related facets; and (4) establish the chemical stability of an exposed anionic electron layer under device-relevant oxygen and water exposure, including whether passivation routes exist that preserve the low work function and the two-dimensional anionic electron layer rather than burying it. These four sub-goals are jointly required for completion; progress on any single sub-goal is not by itself a resolution of the problem. The companion direction named in the source — a broad search for other stoichiometric [{{\rm AE}_2{\rm N}]^{+}\cdot e^{-} electrides with tunable interlayer spacing, carrier density, and terminations, and their translation into device prototypes such as low-work-function cathodes — is an open-ended exploration program rather than part of this problem's completion boundary, and is treated as context.

References

  1. Kimoon Lee, Sung Wng Kim, Yoshitake Toda, Satoru Matsuishi, Hideo Hosono, 'Dicalcium nitride as a two-dimensional electride with an anionic electron layer', Nature 494, 336-340 (2013). DOI: 10.1038/nature11812, https://doi.org/10.1038/nature11812
  2. M. A. Uijttewaal, G. A. de Wijs, R. A. de Groot, 'Low work function of the (1000) Ca2N surface', Journal of Applied Physics 96, 1751-1753 (2004). DOI: 10.1063/1.1767611, https://doi.org/10.1063/1.1767611
  3. Ji Seop Oh, Chang-Jong Kang, Ye Ji Kim, Soobin Sinn, Moonsup Han, Young Jun Chang, Byeong-Gyu Park, Sung Wng Kim, Byung Il Min, Hyeong-Do Kim, Tae Won Noh, 'Evidence for Anionic Excess Electrons in a Quasi-Two-Dimensional Ca2N Electride by Angle-Resolved Photoemission Spectroscopy', Journal of the American Chemical Society 138, 2496-2499 (2016). DOI: 10.1021/jacs.5b12668, https://doi.org/10.1021/jacs.5b12668
  4. Takeshi Inoshita, Seiji Takemoto, Tomofumi Tada, Hideo Hosono, 'Surface electron states on the quasi-two-dimensional excess-electron compounds Ca2N and Y2C', Physical Review B 95, 165430 (2017). DOI: 10.1103/PhysRevB.95.165430, https://doi.org/10.1103/PhysRevB.95.165430
  5. Shan Guan, Shengyuan A. Yang, Liyan Zhu, Junping Hu, Yugui Yao, 'Electronic, Dielectric and Plasmonic Properties of Two-Dimensional Electride Materials X2N (X = Ca, Sr): A First-Principles Study', Scientific Reports 5, 12285 (2015). DOI: 10.1038/srep12285, https://doi.org/10.1038/srep12285
  6. K. P. Faseela, Ye Ji Kim, Seong-Gon Kim, Sung Wng Kim, Seunghyun Baik, 'Dramatically Enhanced Stability of Silver Passivated Dicalcium Nitride Electride: Ag-Ca2N', Chemistry of Materials 30, 7803-7812 (2018). DOI: 10.1021/acs.chemmater.8b03202, https://doi.org/10.1021/acs.chemmater.8b03202
  7. Jongho Park, Kimoon Lee, Seung Yong Lee, Chandani N. Nandadasa, Sungho Kim, Kyu Hyoung Lee, Young Hee Lee,, Hideo Hosono, Seong-Gon Kim, Sung Wng Kim, 'Strong Localization of Anionic Electrons at Interlayer for Electrical and Magnetic Anisotropy in Two-Dimensional Y2C Electride', Journal of the American Chemical Society 139, 615-618 (2017). DOI: 10.1021/jacs.6b11950, https://doi.org/10.1021/jacs.6b11950
  8. Daniel L. Druffel, Adam H. Woomer, Kaci L. Kuntz, Jacob T. Pawlik, Scott C. Warren, 'Electrons on the surface of 2D materials: from layered electrides to 2D electrenes', Journal of Materials Chemistry C 5, 11196-11213 (2017). DOI: 10.1039/C7TC02488F, https://doi.org/10.1039/C7TC02488F
  9. Xiaohua Zhang, Guochun Yang, 'Recent Advances and Applications of Inorganic Electrides', The Journal of Physical Chemistry Letters 11, 3841-3852 (2020). DOI: 10.1021/acs.jpclett.0c00671, https://doi.org/10.1021/acs.jpclett.0c00671
  10. Biao Wan, Yangfan Lu, Zewen Xiao, Yoshinori Muraba, Junghwan Kim, Dajian Huang, Lailei Wu, Huiyang Gou, Jingwu Zhang, Faming Gao, Ho-kwang Mao, Hideo Hosono, 'Identifying quasi-2D and 1D electrides in yttrium and scandium chlorides via geometrical identification', npj Computational Materials 4, 77 (2018). DOI: 10.1038/s41524-018-0136-1, https://doi.org/10.1038/s41524-018-0136-1
  11. Zhujun Zhang, Shiyao Wang, Jiang Li, Masato Sasase, Masaaki Kitano, Hideo Hosono, 'Creation of an air-stable surface electrene and its application to ammonia synthesis', Nature Communications 17, 7896 (2026). DOI: 10.1038/s41467-026-74820-4, https://doi.org/10.1038/s41467-026-74820-4
  12. Qianwen Zhang, Xia Cheng, Zhenzhou Guo, Weiyao Jia, Ying Yang, Zhenxiang Cheng, Weizhen Meng, '2D Inorganic Electrides: Interstitial Electrons as Key Drivers of Multifunctional Properties and Applications', Advanced Science 13, e76098 (2026). DOI: 10.1002/advs.76098, https://doi.org/10.1002/advs.76098