ZnGeN2

Contents

- Crystal Structures

Synthesis and Growth Methods
Electronic Band Structure
Vibrational Properties
Raman Spectra
Elastic Properties
Dielectric Properties
Index of Refraction
Non-Linear Optical Coefficients

Crystal Structures:

Spacegroup: Pna2₁ (or Pbn2₁ with current axes choice).

(NOTE: For the crystal modeling purposes, select the spacegroup as Pbn2₁ )

Point group: C_2v

Lattice constants:

[2]

Wyckoff positions

Hypothetical alternative structure; space group Pmc2₁ [8],[15]

Also disordered wurtzite structure.[14]

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Synthesis and growth methods

- poly crystalline powder synthesis: Maunaye and Lang in 1970 [16] using the reaction

3 Zn₂GeO₄+8NH₃→3ZnGeN₂ +N₂+3Zn+12 H₂O at 700-650 ⁰C.

- polycrystalline film growth, Larson et al. [4] (1974) using a CVD process exposing the metals to HCl-N₂ gas at 550 C for Zn and 950 C for Ge and subsequently mixing with NH₃/N₂ atmosphere and deposited at 850 C on sapphire using the reaction ZnCl2+GeCl4+2NH3->ZnGeN2+6HCl
- high pressure bulk growth Endo et al. (1992) [17] starting from Zn3N₂+Ge₃N₄ 6 GPa and 1000⁰C
- MOCVD growth Zhu et al. [18] (1999) precursors: diethylZn and germane, NH₃, substrates: r -plane and c-plane saphhire with GaN buffer layer
- Misaki et al.[ 19] remote plasma enhanced MOCVD
- Kikkawa and Morisaka [20] RF-sputtering on Si
- Vapor liquid solid growth Du et al. [21]

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Electronic band structure.

Band gap:

The band gap is direct at Gamma.

Effective masses:

Conduction band minimum:

m_cx=0.22, m_cy=0.20, m_cz=0.15 [2]

Valence band maximum splittings and effective masses:

[2]

Figures :

Figure 1: Band structure of ZnGeN2. From data published in [2].

Figure 2: Band structure near valence band maximum [2].

Figure 3: Density of states and partial density of states.[2]

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Vibrational properties

There are 12 modes of a₂, 11 of a₁, b₁ and b₂ symmetry.

All modes are Raman active. The a₁, b₁, b2 are IR active and exhibit LO-TO splitting.

The Raman tensors for a₁ have xx, yy, zz components, for a₂, xy, for b₁ xz and for b₂ yz components with x||a, y||b, z||c.

a₁ is IR active for z polarization E||c

b₁ is IR active for x polarization E||a

b₂ is IR active for y polarization E||b

Table 1: a₂ modes frequencies in cm^-1

calc. A: [7] abinit, Fritz-Haber-Institute pseudopotential,M. Fuchs and M. Scheffler, Comput. Phys. Commun.119,67(1999).

calc. B: [8] abinit, HGH pseudopotential, C. Hartwigsen, S. Goedecker, and J. Hutter, Phys. Rev.B 58, 3641 (1998).

Expt. : [8] Raman on platelets

Table 2: a₁ mode frequencies in cm^-1.

Calc.A : [7] abinit, Fritz-Haber-Institute pseudopotential

Calc. B: [8] abinit, HGH pseudopotential

Expt. 1: [9] Raman on needles

Expt. 2: [8] Raman on platelets

T: tranverse, L: longitudinal

* this mode was not identified in this paper but can be seen in the spectrum

Table 3: b₁ modes in cm^-1.

Calc. A: [7], Calc. B:[8]

Table 4: b₂ modes in cm^-1

Calc. A: [7], Calc. B:[8]

Expt. [9] Raman on needles with crossed polarizers

Born effective charge tensors.

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Raman Spectra

Predicted Raman spectra and Raman intensities can be found in [10], [11].

Predicted Raman spectra for Pmc2₁ structure can be found in [11].

Measured Raman spectra for needles can be found in [9].

Measured Raman spectra for polycrystalline material can be found in [9] and in [12].

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Elastic Properties

Bulk moduli and pressure derivative

Elastic stiffness constants C_ij(Mbar=100GPa)

Elastic compliances S_ij (Mbar^-1)

Reference: [13]

Piezo-electric constants and spontaneous polarization (cm^-2)

Reference: [13]

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Dielectric Properties.

High frequency

ε^∞_xxand static dielectric constants ε⁰

Reference: [10]

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Index of refraction

n_x

2.273

n_y

2.289

n_z

2.393

Reference: [10]

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Non-linear optical coefficients.

Second order non-linear optics coefficients (pm/V)

d₁₅=d₃₁

-2.63

d₃₄=d₃₂

-3.17

d₃₃

6.98

Reference:[13]

Linear electro-optical coefficients (pm/V)

References:

[1]. M. Wintenberger, M. Maunaye, and Y. Laurent, Mat. Res. Bull. 8, 1049 (1973).

[2]. A. Punya, W. R. L. Lambrecht, and M. van Schilfgaarde, Phys. Rev. B 84, 165204 (2011).

[3]. K. Du, C. Bekele, C. C. Hayman, J. C. Angus, P. Pirouz, and K. Kash, J. Cryst. Growth 310, 1057 (2008).

[4]. W. L. Larson, H. P. Maruska, and A. Stevenson, J. Electrochem. Soc. 121, 1683 (1974).

[5]. A.Osinsky,V.Fuflyigin, L.D. Zhu,A.B.Goulakov, J.W.Graff, and E. F. Schubert, in High Performance Devices, 2000. Proceedings 2000 IEEE/Cornell Conference on (IEEE, Piscataway, NJ, 2000),pp. 168–172

[6]. T. Misaki, K. Tsuchiya, D. Sakai, A. Wakahara, H. Okada, and Y. A., Phys. Status Solidi C 0, 188 (2000).

[7]. W. R. L. Lambrecht, E. Alldredge, and K. Kim, Phys. Rev. B 72, 155202 (2005).

[8]. E. W. Blanton, M. Hagemann, K. He, J. Shan, W. R. L. Lambrecht, and K. Kash, unpublished

[9]. T. J. Peshek, T. R. Paudel, K. Kash, and W. R. L. Lambrecht, Phys. Rev. B 77, 235213 (2008)

[10]. T. R. Paudel and W. R. L. Lambrecht, Phys. Rev. B 78,115204 (2008).

[11]. M. Hagemann, C. Bhandari and W. R. L. Lambrecht, Solid State Commun. 233, 46 (2016).

[12]. R. Viennois, T. Taliercio, V. Potin, A. Errebbahi, B. Gil, S. Charar, A. Haidoux, and J.-C. Tédenac, Mater. Sci. Eng., B 82,45(2001).

[13]. T. R. Paudel, W. R. L. Lambrecht, Phys. Rev. B 79, 245205 (2009).

[14]. E. Blanton, K. He, J. Shan, and K. Kash, in Symposium E/H—Photovoltaic Technologies,Devices and Systems Based on Inorganic Materials,

Small Organic Molecules and Hybrids, Mater.Res. Soc. Proc., Vol. 1493 (MRS Online Proceedings Library, Cambridge University Press, New York, 2013),pp. 237–242.

[15]. P. C. Quayle,E.W. Blanton,A. Punya,G. T. Junno,K. He,L.Han,H. Zhao,J. Shan,W.R.L. Lambrecht, K. Kash,Phys.Rev.B91,205207(2015).

[16]. M. Maunaye and J. Lang, Mat. Res. Bull. 5, 793-796 (1970).

[17]. T. Endo, Y. Sato, H. Takizawa, M. Shimada, J. Mater. Sci. Lett. 11, 424 (1992).

[18]. L. D. Zhu, P. H. Maruska, P. E. Norris, P. W. Yip and L. O. Bouthillette, MRS Internet J. Nitride Semiconductor Res.4S1:G3.8 (1999)

[19]. T. Misaki, A. Wakahara, H. Okada, A. Yoshia, J. Cryst. Growth 260,1049 (2004)

[20]. S. Kikkawa abd G. Morisaka, Solid State Commun. 112, 513 (1999)

[21]. K. Du, C. Bekele, C. C. Hayman, J. C. Angus, P. Pirouz and K. Kash, J. Cryst. Growth 310, 1057 (2008).

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