M Benaida, K E Aiadi, S Mahtout, S Djaadi, W Rammal, M Harb, Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study[J]. J. Semicond., 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101.

M. Benaida^{
1, , }
, K. E. Aiadi^{
1, }
, S. Mahtout^{
2, }
, S. Djaadi^{
1, }
, W. Rammal^{
3, }
and M. Harb^{
4, , }

**Abstract: **We present a systematic computational study based on the density functional theory (DFT) aiming to high light the possible effects of one As doping atom on the structural, energetic, and electronic properties of different isomers of Ge_{n + 1} clusters with *n* = 1–20 atoms. By considering a large number of structures for each cluster size, the lowest-energy isomers are determined. The lowest-energy isomers reveal three-dimensional structures starting from *n* = 5. Their relative stability versus atomic size is examined based on the calculated binding energy, fragmentation energy, and second-order difference of energy. Doping Ge_{n + 1} clusters with one As atom does not improve their stability. The electronic properties as a function of the atomic size are also discussed from the calculated HOMO–LUMO energy gap, vertical ionization potential, vertical electron affinity, and chemical hardness. The obtained results are significantly affected by the inclusion of one As atom into a Ge_{n} cluster.

**Key words:**
density functional theory, As–Ge clusters, structural properties, electronic properties

**Abstract: **We present a systematic computational study based on the density functional theory (DFT) aiming to high light the possible effects of one As doping atom on the structural, energetic, and electronic properties of different isomers of Ge_{n + 1} clusters with *n* = 1–20 atoms. By considering a large number of structures for each cluster size, the lowest-energy isomers are determined. The lowest-energy isomers reveal three-dimensional structures starting from *n* = 5. Their relative stability versus atomic size is examined based on the calculated binding energy, fragmentation energy, and second-order difference of energy. Doping Ge_{n + 1} clusters with one As atom does not improve their stability. The electronic properties as a function of the atomic size are also discussed from the calculated HOMO–LUMO energy gap, vertical ionization potential, vertical electron affinity, and chemical hardness. The obtained results are significantly affected by the inclusion of one As atom into a Ge_{n} cluster.

**Key words:**
density functional theory, As–Ge clusters, structural properties, electronic properties

**References:**

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Wang J, Han J G. The growth behaviors of the Zn-doped different sized germanium clusters: a density functional investigation. Chem Phys, 2007, 342: 253 |

[2] |
Mahtout S, Tariket Y. Electronic and magnetic properties of CrGe n ⩽ 29) clusters: a DFT study. Chem Phys, 2016, 472: 270 |

[3] |
Schmude R W, Gingerich K A. Thermodynamic study of small silicon carbide clusters with a mass spectrometer. J Phys Chem A, 1997, 101: 2610 |

[4] |
Samanta P N, Das K K. Electronic structure, bonding, and properties of Sn |

[5] |
Kingcade J Jr, Gingerich K. Knudsen effusion mass spectrometric investigation of palladium-germanium clusters. Inorg Chem, 1989, 28: 89 |

[6] |
Yadav P S, Yadav R K. Ab initio study of the physical properties of binary Si |

[7] |
Bandyopadhyay D, Kumar M. The electronic structures and properties of transition metal-doped silicon nanoclusters: a density functional investigation. Chem Phys, 2008, 353: 170. |

[8] |
Han J G, Hagelberg F. Recent progress in the computational study of silicon and germanium clusters with transition metal impurities. J Comput Theor Nanosci, 2009, 6: 257 |

[9] |
Bals S, Van Aert S, Romero C P, et al. Atomic scale dynamics of ultrasmall germanium clusters. Nat Commun, 2012, 3: 897. |

[10] |
Siouani C, Mahtout S, Safer S, et al. Structure, stability, and electronic and magnetic properties of VGe |

[11] |
Brack M. The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches. Rev Mod Phys, 1993, 65: 677. |

[12] |
Han J G, Zhang P F, Lic Q X, et al. A theoretical investigation of Ge |

[13] |
Singh A K, Kumar V, Kawazoe, Y. Thorium encapsulated caged clusters of germanium: The Ge |

[14] |
Wang J, Han J G. A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory. J Chem Phys, 2005, 123: 244303. |

[15] |
Zhao W J, Wang, Y X. Geometries, stabilities, and magnetic properties of MnGe |

[16] |
Jaiswal S, Kumar V. Growth behavior and electronic structure of neutral and anion ZrGe |

[17] |
Mahtout S, Siouani C, Rabilloud F. Growth behavior and electronic structure of noble metal-doped germanium clusters. J Phys Chem A, 2018, 122: 662 |

[18] |
Djaadi S, Aiadi K E, Mahtout S. First principles study of structural, electronic and magnetic properties of SnGe |

[19] |
Ordejón P, Artacho E, Soler J M. Self-consistent order-N density-functional calculations for very large systems. Phys Rev B, 1996, 53: R10441. |

[20] |
Soler J M, Artacho E, Gale J D, et al. The siesta method for ab initio order-n materials simulation. J Phys Cond Matter, 2002, 14: 2745. |

[21] |
Troullier N, Martins J L. Efficient pseudopotentials for plane-wave calculations. Phys Rev B, 1991, 43: 1993. |

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Perdew J P, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B, 1981, 23: 5048. |

[23] |
Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77: 3865. |

[24] |
Bandyopadhyay D, Sen P. Density functional investigation of structure and stability of Ge |

[25] |
Shi S, Liu Y, Zhang C, et al. A computational investigation of aluminum-doped germanium clusters by density functional theory study. Comput Theor Chem, 2015, 1054: 8 |

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Kapila N, Garg I, Jindal V K, et al. First principle investigation into structural growth and magnetic properties in Ge |

[27] |
Wang J, Wang G, Zhao J. Structure and electronic properties of Ge |

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Yoshida M, Aihara J I. Validity of the weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes with up to 120 carbon atoms. Phys Chem Chem Phys, 1999, 1: 227 |

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Parr R G, Pearson R G. Absolute hardness: companion parameter to absolute electronegativity. J Am Chem Soc, 1983, 105, 7512 |

[30] |
Sosa-Hernández E, Alvarado-Leyva P. Magnetic properties of stable structures of small binary Fe |

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Li X, Su K, Yang X, et al. Size-selective effects in the geometry and electronic property of bimetallic Au-Ge nanoclusters. Comput Theor Chem, 2013, 1010: 32 |

[32] |
Kingcade J E, Nagarathna-Naik H M, Shim I, et al. Electronic structure and bonding of the dimeric germanium molecule from all-electron ab initio calculations and equilibrium measurements. J Phys Chem, 1986, 90: 2830 |

[33] |
Nagendran S, Sen S S, Roesky H W, et al. RGe(I)Ge(I)R Compound (R = PhC(NtBu) |

[34] |
Gadiyak G V, Morokov Y. N, Mukhachev A G, et al. Electron density functional method for molecular system calculations. J Struct Chem, 1982, 22: 670 |

[35] |
Wang J, Han J G. Geometries, stabilities, and vibrational properties of bimetallic Mo |

[36] |
Kant A, Strauss B H. Atomization energies of the polymers of germanium, Ge |

[37] |
Vasiliev I S, Öğüt S, Chelikowsky J R. Ab initio calculations for the polarizabilities of small semiconductor clusters. Phys Rev Lett, 1997, 78: 4805. |

[38] |
Burton G R, Xu C, Arnold C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions. J Chem Phys, 1996, 104: 2757 |

[39] |
Safer S, Mahtout S, Rezouali K, et al. Properties of neutral and charged cobalt-doped arsenic CoAs |

[40] |
Guo L. The structure and energetic of AlAs n = 1–15) clusters: a first-principles study. J Alloys Compounds, 2010, 498: 121 |

[41] |
Pearson R G. Chemical hardness: applications from molecules to solids. Weinheim: Wiley-VCH, 1997 |

[1] |
Wang J, Han J G. The growth behaviors of the Zn-doped different sized germanium clusters: a density functional investigation. Chem Phys, 2007, 342: 253 |

[2] |
Mahtout S, Tariket Y. Electronic and magnetic properties of CrGe n ⩽ 29) clusters: a DFT study. Chem Phys, 2016, 472: 270 |

[3] |
Schmude R W, Gingerich K A. Thermodynamic study of small silicon carbide clusters with a mass spectrometer. J Phys Chem A, 1997, 101: 2610 |

[4] |
Samanta P N, Das K K. Electronic structure, bonding, and properties of Sn |

[5] |
Kingcade J Jr, Gingerich K. Knudsen effusion mass spectrometric investigation of palladium-germanium clusters. Inorg Chem, 1989, 28: 89 |

[6] |
Yadav P S, Yadav R K. Ab initio study of the physical properties of binary Si |

[7] |
Bandyopadhyay D, Kumar M. The electronic structures and properties of transition metal-doped silicon nanoclusters: a density functional investigation. Chem Phys, 2008, 353: 170. |

[8] |
Han J G, Hagelberg F. Recent progress in the computational study of silicon and germanium clusters with transition metal impurities. J Comput Theor Nanosci, 2009, 6: 257 |

[9] |
Bals S, Van Aert S, Romero C P, et al. Atomic scale dynamics of ultrasmall germanium clusters. Nat Commun, 2012, 3: 897. |

[10] |
Siouani C, Mahtout S, Safer S, et al. Structure, stability, and electronic and magnetic properties of VGe |

[11] |
Brack M. The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches. Rev Mod Phys, 1993, 65: 677. |

[12] |
Han J G, Zhang P F, Lic Q X, et al. A theoretical investigation of Ge |

[13] |
Singh A K, Kumar V, Kawazoe, Y. Thorium encapsulated caged clusters of germanium: The Ge |

[14] |
Wang J, Han J G. A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory. J Chem Phys, 2005, 123: 244303. |

[15] |
Zhao W J, Wang, Y X. Geometries, stabilities, and magnetic properties of MnGe |

[16] |
Jaiswal S, Kumar V. Growth behavior and electronic structure of neutral and anion ZrGe |

[17] |
Mahtout S, Siouani C, Rabilloud F. Growth behavior and electronic structure of noble metal-doped germanium clusters. J Phys Chem A, 2018, 122: 662 |

[18] |
Djaadi S, Aiadi K E, Mahtout S. First principles study of structural, electronic and magnetic properties of SnGe |

[19] |
Ordejón P, Artacho E, Soler J M. Self-consistent order-N density-functional calculations for very large systems. Phys Rev B, 1996, 53: R10441. |

[20] |
Soler J M, Artacho E, Gale J D, et al. The siesta method for ab initio order-n materials simulation. J Phys Cond Matter, 2002, 14: 2745. |

[21] |
Troullier N, Martins J L. Efficient pseudopotentials for plane-wave calculations. Phys Rev B, 1991, 43: 1993. |

[22] |
Perdew J P, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B, 1981, 23: 5048. |

[23] |
Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77: 3865. |

[24] |
Bandyopadhyay D, Sen P. Density functional investigation of structure and stability of Ge |

[25] |
Shi S, Liu Y, Zhang C, et al. A computational investigation of aluminum-doped germanium clusters by density functional theory study. Comput Theor Chem, 2015, 1054: 8 |

[26] |
Kapila N, Garg I, Jindal V K, et al. First principle investigation into structural growth and magnetic properties in Ge |

[27] |
Wang J, Wang G, Zhao J. Structure and electronic properties of Ge |

[28] |
Yoshida M, Aihara J I. Validity of the weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes with up to 120 carbon atoms. Phys Chem Chem Phys, 1999, 1: 227 |

[29] |
Parr R G, Pearson R G. Absolute hardness: companion parameter to absolute electronegativity. J Am Chem Soc, 1983, 105, 7512 |

[30] |
Sosa-Hernández E, Alvarado-Leyva P. Magnetic properties of stable structures of small binary Fe |

[31] |
Li X, Su K, Yang X, et al. Size-selective effects in the geometry and electronic property of bimetallic Au-Ge nanoclusters. Comput Theor Chem, 2013, 1010: 32 |

[32] |
Kingcade J E, Nagarathna-Naik H M, Shim I, et al. Electronic structure and bonding of the dimeric germanium molecule from all-electron ab initio calculations and equilibrium measurements. J Phys Chem, 1986, 90: 2830 |

[33] |
Nagendran S, Sen S S, Roesky H W, et al. RGe(I)Ge(I)R Compound (R = PhC(NtBu) |

[34] |
Gadiyak G V, Morokov Y. N, Mukhachev A G, et al. Electron density functional method for molecular system calculations. J Struct Chem, 1982, 22: 670 |

[35] |
Wang J, Han J G. Geometries, stabilities, and vibrational properties of bimetallic Mo |

[36] |
Kant A, Strauss B H. Atomization energies of the polymers of germanium, Ge |

[37] |
Vasiliev I S, Öğüt S, Chelikowsky J R. Ab initio calculations for the polarizabilities of small semiconductor clusters. Phys Rev Lett, 1997, 78: 4805. |

[38] |
Burton G R, Xu C, Arnold C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions. J Chem Phys, 1996, 104: 2757 |

[39] |
Safer S, Mahtout S, Rezouali K, et al. Properties of neutral and charged cobalt-doped arsenic CoAs |

[40] |
Guo L. The structure and energetic of AlAs n = 1–15) clusters: a first-principles study. J Alloys Compounds, 2010, 498: 121 |

[41] |
Pearson R G. Chemical hardness: applications from molecules to solids. Weinheim: Wiley-VCH, 1997 |

M Benaida, K E Aiadi, S Mahtout, S Djaadi, W Rammal, M Harb, Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study[J]. J. Semicond., 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101.

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Manuscript received: 04 August 2018 Manuscript revised: 27 September 2018 Online: Accepted Manuscript: 08 January 2019 Uncorrected proof: 16 January 2019 Published: 01 March 2019

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