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Structural and electronic properties of the random alloy ZnSexS1−x

S. Sarkar, O. Eriksson, D. D. Sarma, and I. Di Marco
Phys. Rev. B 105, 184201 – Published 6 May 2022
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  • INTRODUCTION
  • METHODOLOGY
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • Supplemental Material
    References

    Abstract

    In this article we employ density functional theory in the generalized gradient approximation to investigate the structural and electronic properties of the solid solution alloy ZnSexS1−x in the wurtzite structure. We analyzed the character of the bond lengths and angles at the atomic scale, using a supercell approach that does not impose any constraint on the crystal potential. We show that the bond lengths of pristine ZnS and ZnSe compounds are almost preserved between nearest neighbors, which is different from what would be anticipated if Vegard's law were valid at the atomic level. We also show that bond lengths start behaving in accordance with Vegard's law from the third shell of nearest neighbors onward, which in turn determines the average lattice parameters of the alloys determined by diffraction experiments. Fundamental building blocks around the anions are identified and are shown to be nonrigid but still volume preserving. Finally, the geometrical analysis is connected to the trend exhibited by the electronic structure, and in particular by the band gap. The latter is found to exhibit a small deviation from linearity with respect to the Se concentration, in accordance with available experimental data. By assuming a quadratic dependence, we can extract a bowing parameter and analyze various contributions to it with various calculations under selected constraints. The structural deformation in response to the doping process is shown to be the driving force behind the deviation from linearity. The difference in stiffness between ZnS and ZnSe is shown to play a key role in the asymmetric behavior of the bowing parameter observed in the S-rich and Se-rich regions.

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    • Received 1 March 2022
    • Accepted 27 April 2022

    DOI:https://doi.org/10.1103/PhysRevB.105.184201

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Chemical bondingCompositionDoping effectsElectronic structureFirst-principles calculationsStructural properties
    1. Physical Systems
    AlloysSemiconductors
    1. Techniques
    Density functional theory
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    S. Sarkar1, O. Eriksson2,3, D. D. Sarma4,5, and I. Di Marco1,2,6,*

    • 1Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
    • 2Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
    • 3School of Science and Technology, Örebro University, SE-70182 Örebro, Sweden
    • 4Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru 560012, India
    • 5CSIR-National Institute for Interdisciplinary Science and Technology (CSIR-NIIST), Industrial Estate P.O., Pappanamcode, Thiruvananthapuram 695019, India
    • 6Department of Physics, POSTECH, Pohang 37673, Korea

    • *igor.dimarco@apctp.org; igor.dimarco@physics.uu.se

    Article Text

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    Issue

    Vol. 105, Iss. 18 — 1 May 2022

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    • Figure 1
      Figure 1

      Left: Variation of the lattice parameter a=b (bottom) and c (top) as a function of increasing Se concentration in ZnSexS1−x solid solutions. The linear variation of both is in agreement with Vegard's law. Right: Variation of the volume per formula unit as a function of increasing Se concentration in wurtzite and cubic phases, as reported in different theoretical (athis work, bRef. [17], cRef. [21]) and experimental (d,eRef. [41], fRef. [17]) studies.

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    • Figure 2
      Figure 2

      (a) Variation in the Zn-S and Zn-Se nearest-neighbor bond length as a function of increasing Se concentration in ZnSexS1−x solid solutions. (b) Average nearest-neighbor Zn-X (X=S or Se) bond length (down triangles) compared to a hypothetical VCA-like average Zn-X bond length (dashed line) obtained connecting the Zn-X bond lengths of the pure end members; the Zn-S bond length (up triangles) calculated by imposing optimized lattice parameters in the ZnS wurtzite unit cell is also shown. (c) Distribution of the nearest-neighbor Zn-S and Zn-Se bonds in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bonds per Zn atom (4); the unfilled blue outlines represent data for the zinc blende structure. The details of the ranges and averages for each composition in the wurtzite phase are also tabulated in the SM [24].

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    • Figure 3
      Figure 3

      Variation in the (a) Zn-Zn second-nearest-neighbor bond length and (b) X−X (X=S or Se) second-nearest-neighbor bond length as a function of increasing Se concentration in ZnSexS1−x. (c) Distribution of the nearest-neighbor Zn-Zn bonds in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bonds per Zn atom (12); the unfilled blue outlines represent data for the zinc blende structure. For the alloy systems we see a clear bimodal distribution corresponding to the Zn-Zn bonds coming from ZnS- and ZnSe-type clusters, respectively. More quantitative details on the range and averages of the distributions are provided in the SM [24].

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    • Figure 4
      Figure 4

      Distribution of the (a) S-S, (b) Se-Se, and (c) S-Se second-nearest-neighbor bonds in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bonds per S or Se atom (12), weighted by their relative concentration. More quantitative details on the range and averages of the distributions are provided in the SM [24].

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    • Figure 5
      Figure 5

      Variation in the (a) X-Zn-X and (b) Zn-X-Zn (X=S or Se) average bond angles as a function of increasing Se concentration in the ZnSexS1−x solid solutions.

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    • Figure 6
      Figure 6

      (a) Variation in the Zn-X (X = S or Se) bond distance between Zn and S or Se atoms from the third coordination shell around Zn atoms, as a function of increasing Se concentration. (b) Variation in the Zn-Zn bond distance corresponding to the fourth coordination shell as a function of increasing Se concentration. The details of the average and range for these Zn-S, Zn-Se, and Zn-Zn bonds are given in the SM [24].

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    • Figure 7
      Figure 7

      (a) Distributions of the third-nearest-neighbor short and long Zn-S bonds in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bonds per Zn atom (10). The two vertical dashed lines in the bottom panel represent the corresponding values in pristine ZnSe. (b) Distributions of the third-nearest-neighbor short and long Zn-Se bonds in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bonds per Zn atom (10). The two vertical dashed lines in the top panel represent the corresponding values in pristine ZnS. (c) Distributions of the fourth-nearest-neighbor Zn-Zn bond distances in the system with increasing Se concentration (top to bottom), normalized with respect to the number of bonds per Zn atom (6). More quantitative details on the range and averages of the distributions are provided in the SM [24].

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    • Figure 8
      Figure 8

      (a) Substitution of a Se atom in a S-rich region leading to a larger SeZn4 tetrahedral unit (red triangle) and rotation of the surrounding SZn4 tetrahedral units shown by black curved arrows. (b) Substitution of a S atom in a Se-rich region leading to a smaller SZn4 tetrahedral unit (blue triangle) and rotation of the surrounding SeZn4 tetrahedral units shown by black curved arrows.

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    • Figure 9
      Figure 9

      Distribution of the calculated volumes associated with the (a) XZn4 and (b) ZnX4 units (X=S or Se) in the alloy systems, normalized to 1.

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    • Figure 10
      Figure 10

      Variation in the band gap as a function of increasing Se concentration calculated using (a) PBE and (b) mBJ as exchange-correlation functional. The black dotted line represents a quadratic fit, which is used to extract the bowing parameter b. As reported in the legends, b=0.44 eV for PBE and b=0.60 eV for mBJ.

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    • Figure 11
      Figure 11

      (a) Decomposition of various mechanisms contributing to the bowing parameter. As indicated in the legend, volume changes and structural distortions as a result of substitution in the ZnSexS1−x alloy, pure ZnS, and ZnSe are considered. See main text for comprehensive details. (b) Total energy vs atomic volume curves for ZnS and ZnSe in the wurtzite phase. Zero volume corresponds to the equilibrium atomic volume of each compound, for a better comparison of the relative stiffness.

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    • Figure 12
      Figure 12

      (a) Distributions of the S-Zn-S bond angles in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bond angles centered on a Zn atom (six) weighted by the S concentration. (b) Distributions of the Se-Zn-Se bond angles in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bond angles centered on a Zn atom (six) weighted by the Se concentration. (c) Distributions of the S-Zn-Se bond angles in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bond angles centered on a Zn atom (six) weighted by the pair concentration of S and Se. The details of the average and range for these angles are given in the SM [24].

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    • Figure 13
      Figure 13

      (a) Distributions of the Zn-S-Zn bond angles in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bond angles centered on a S atom (6). (b) Distributions of the Zn-Se-Zn bond angles in the solid solution alloy for increasing Se concentration (top to bottom), normalized with respect to the number of bond angles centered on a Se atom (6). The details of the average and range for these angles are given in the SM [24].

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    • Figure 14
      Figure 14

      (a) Atom-projected partial density of states corresponding to the Zn and S states in ZnS. (b) Magnified view around the Fermi energy to show the contributions at the valence band maximum (VBM) and conduction band minimum (CBM).

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    • Figure 15
      Figure 15

      Atom-projected partial density of states corresponding to the S and Se s and p states in ZnS, ZnSe, and the alloy systems.

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