BeSiN2

Contents

• Crystal Structures

• Synthesis and Growth Methods

• Electronic Band Structure

• Vibrational Properties

• Optical Properties

• Dielectric Properties

Crystal Structures

Space Group: Pbn2₁ NOTE: see discussion of crystal structures

_{Point Group: C2v}

_{Lattice constants:}

_{Note: we use the a>b>c choice discussed in the section "Crystal Structures". In the references, a and b are interchanged.}

Wyckoff positions: from [6]

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Alternative crystal structures

Ref. [2] studied the relative stability of the chalcopyrite structure vs. the orthorhombic Pbn2₁.

They obtain a= 4.073 Å, c=8.164 Å for this tetratogonal phase. They find this phase to be higher in energy than the Pbn2₁ by about 25 meV. They also report calculations for a phase which they label as fcc or zincblende. However, they did not explain how the cations were arranged in this phase, which has a calculated energy of formation higher by 0.1 eV. These numbers are extracted from their fig. 1. The enthalpies of formation in their table 1 do not match up with this calculation and it is also unclear whether these calculations were done in LDA or GGA.

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_{Synthesis and growth methods}

Eckerlin [4] reports the first synthesis by a powder ceramic method:

using ball milling to mix Si₃N₄ and Be₃N₂ powders in CCl₄ with SiO₂, then heating to 1700 ^oC in N₂ to produce the solid state reaction:

Be₃N₂ + Si₃N₄ → 3BeSiN₂

This procedure resulted in crystallites of micron size.

See also Ref.[5] pgs 52-54

Single crystals of about 1mm by 0.1 mm were obtained by a sublimation method at 1900 ^oC from the previous micron sized powders

as reported in [1] and were used for the X-ray diffraction studies that allowed observation of the weak superlattice peaks, evidencing the ordering of the cations. Prior work with powder X-ray diffraction spectra had determined the structure to be wurtzitic.

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Electronic band structure

The FLAPW calculations of [2] give an indirect band gap for BeSiN₂. The valence band maximum (VBM) occurs at Γ but the conduction band minimum (CBM) occurs along Γ-Y with a slightly higher minimum along Γ-Z. This Y corresponds to their choice of b axis, which is interchanged with our a axis, so their Y would be labeled X in the convention that we have followed for other compounds. The paper gives only the Γ-Z and Γ-Γ gaps. The lowest, indirect gap (from the valence band Γ point to the Γ-Y minimum in the conduction band) is estimated from the figure. The CASTEP plane wave pseudopotential calculations of [3] give almost the same CBM near Z, T and X. The direct gap is about 0.5 eV higher. The authors do not mention which density functional they used.

Recently quasiparticle self-consistent QS-GW band structures were presented by Sai Lyu et al. [6] at both LDA and GGA lattice constants. The latter are assumed to be more accurate. The paper also explains why the CBM occurs at 2/3 Γ-X by comparison to wurtzite BN.

Band Gaps:

Figure 1: Band structure of BeSiN₂ calculated by the FLAPW

method with GGA. [2]

Figure 2: Band structure of BeSiN₂ calculated by GW@GGA. [6]

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_{Vibrational Properties}

Phonon frequencies at Γ in cm^-1 [7]

Raman and Infrared spectra can be found in [7] for different scattering geometries and polarizatons

Phonon dispersion curbes and DOS can also be found in [7]

Born effective charges can be found in [7]

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Elastic Properties

Bulk modulus B and its pressure derivative B':

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_{Optical Properties}

_{Dielectric Constants (at high frequency, electronic screening only, from DFT calculations)}

_{εxx = 4.72 εyy = 4.77 εzz = 4.90 [3] LDA}

_{εxx = 4.42 εyy = 4.46 εzz = 4.61 [7] LDA}

_{Index of refraction}

_{nx=2.10 ny=2.11 nz=2.15}

_Figure:

_{Figure 2: Real (ε1) and imaginary (ε2) parts of the dielectric function versus photon energy of BeSiN2 for different light polarizations, calculated by FLAPW with GGA.}

_{Second order nonlinear optical coefficients, in pm/V [3]:}

_References

_{[1] P. Eckerlin, Zeitschrift für anorgische und allgemeine Chemie, 353, 225-336 (1967).}

_{[2]. V. L. Shaposhnikov, A.V. Krivosheeva, F. Arnaud D'Avitaya, J.-L. Lazzari and V.E. Borisenko, Phys. Stat. Sol. (b) 245, 142–148 (2008).}

_{[3]. Jung Y Huang,L.C Tang and M.H Lee, J. Phys.: Condens. Matter 13, 10417-0431 (2001).}

_{[4]. P. Eckerlin, A. Rabenau, H. Normann, Z. anorg. allg. Chem. 353, 113 (1967)}

_{[5] Friedrich Schröder, June 29, 2013, Si Silicon: System Si-N. Binary and Ternary Silicon Nitrides, Springer, ISBN 9783662069974.}

[6] Sai Lyu and Walter R. L. Lambrecht, J. Phys. Condensed Matter 31,335501 (2019).

[7] Sai Lyu, Yuheng Liu and Walter R. L. Lambrecht, J. Phys. D 52, 285106 (2019)