Skip to main content

Structures and Electric Properties of Semiconductor clusters

  • Reference work entry
  • First Online:
Handbook of Computational Chemistry
  • 4556 Accesses

Abstract

Materials that exhibit an electrical resistivity between that of conductor and insulator are called semiconductors. Devices based on semiconductor materials, such as transistors, solar cells, light-emitting diodes, digital integrated circuits, solar photovoltaics, and much more, are the base of modern electronics. Silicon is used in most of the semiconductor devices while other materials such as germanium, gallium arsenide, and silicon carbide are used for specialized applications. The obvious theoretical and technological importance of semiconductor materials has led to phenomenal success in making semiconductors with near-atomic precision such as quantum wells, wires, and dots. As a result, there is a lot of undergoing research in semiconductor clusters of small and medium sizes both experimentally and by means of computational chemistry since the miniaturization of devices still continues. In the next pages, we are going to learn which the most studied semiconductor clusters are, we will explore their basic structural features and visit some of the most representative ab initio studies that are considered as works of reference in this research realm. Also, we are going to be introduced to the theory of the electric properties applied in the case of clusters by visiting some of the most illustrative studies into this research area. It is one of the purposes of this presentation to underscore the strong connection between the electric properties of clusters and their structure.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 749.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Adolph, B., & Bechstedt, F. (1998). Ab initio second-harmonic susceptibilities of semiconductors: generalized tetrahedron method and quasiparticle effects.Physical Review B - Condensed Matter and Materials Physics, 57(11), 6519–6526.

    Google Scholar 

  • Alivisatos, A. P. (1996). Semiconductor clusters, nanocrystals, and quantum dots. Science, 271(5251), 933–937.

    Google Scholar 

  • Al-Laham, M. A., & Raghavachari, K. (1991). Theoretical study of small gallium arsenide clusters. Chemical Physics Letters, 187(1–2), 13–20.

    Google Scholar 

  • Al-Laham, M. A., & Raghavachari, K. (1993). Theoretical study of Ga\(_{4}\)As\(_{4}\), Al\(_{4}\)P\(_{4}\), and Mg\(_{4}\)S\(_{4}\) clusters. Journal of Chemical Physics, 98(11), 8770–8776.

    Google Scholar 

  • An, W., Gao, Y., Bulusu, S., & Zeng, X. (2005). Ab initio calculation of bowl, cage, and ring isomers of C\(_{20}\) and C\(_{20}^{-}\). Journal of Chemical Physics, 122, 204109/1–204109/8.

    Google Scholar 

  • Avramopoulos, A., Reis, H., Li, J., & Papadopoulos, M. G. (2004). The dipole moment, polarizabilities, and first hyperpolarizabilities of HArF. A computational and comparative study.Journal of the American Chemical Society, 126(19), 6179–6184.

    Google Scholar 

  • Avramov, P. V., Fedorov, D. G., Sorokin, P. B., Chernozatonskii, L. A., & Gordon, M. S. (2007). Atomic and electronic structure of new hollow-based symmetric families of silicon nanoclusters. Journal of Physical Chemistry C, 111(51), 18824–18830.

    Google Scholar 

  • Backer, J. A. (1997). Molecular beam studies on semiconductor clusters: polarizabilities and chemical bonding.Angewandte Chemie (International Edition in English), 36(13–14), 1390–1404.

    Google Scholar 

  • Bai, J., Cui, L.-F., Wang, J., Yoo, S., Li, X., & Jellinek, J., et al. (2006). Structural evolution of anionic silicon clusters Si\(_{N}\)(20 ≤ N ≤ 45). Journal of Physical Chemistry A, 110(3), 908–912.

    Google Scholar 

  • Bazterra, V. E., Caputo, M. C., Ferraro, M. B., & Fuentealba, P. (2002). On the theoretical determination of the static dipole polarizability of intermediate size silicon clusters.Journal of Chemical Physics, 117(24), 11158–11165.

    Google Scholar 

  • Bazterra, V. E., Oña, O., Caputo, M. C., Ferraro, M. B., Fuentealba, P., & Facelli, J. C. (2004). Modified genetic algorithms to model cluster structures in medium-size silicon clusters. Physical Review A - Atomic, Molecular, and Optical Physics, 69(5B), 053202/1–053202/7.

    Google Scholar 

  • Bechstedt, F., Adolph, B., & Schmidt, W. G. (1999). Ab initio calculation of linear and nonlinear optical properties of semiconductor structures. Brazilian Journal of Physics, 29(4), 643–651.

    Google Scholar 

  • Behrman, E. C., Foehrweiser, R. K., Myers, J. R., French, B. R., & Zandler, M. E. (1994). Possibility of stable spheroid molecules of ZnO. Physical Review A, 49(3), R1543–R1549.

    Google Scholar 

  • Bergfeld, S., & Daum, W. (2003). Second-harmonic generation in GaAs: experiment versus theoretical predictions of \({\chi }_{xyz}^{(2)}\). Physical Review Letters, 90(3), 036801/1–036801/4.

    Google Scholar 

  • Bersuker, I. B. (2001) Modern aspects of the Jahn-Teller effect theory and applications to molecular problems. Chemical Reviews, 101(4), 1067–1114.

    Google Scholar 

  • Biswas, R., & Hamann, D. R. (1986). Simulated annealing of silicon atom clusters in langevin molecular dynamics. Physical Review B, 34(2), 895–901.

    Google Scholar 

  • Bishop, D. M., Kirtman, B., & Champagne, B. (1997). Differences between the exact sum-over-states and the canonical approximation for the calculation of static and dynamic hyperpolarizabilities. Journal of Chemical Physics, 107(15), 5780–5787.

    Google Scholar 

  • Blaisten-Barojas, E., & Levesque, D. (1986). Molecular-dynamics simulation of silicon clusters. Physical Review B, 34(6), 3910–3916.

    Google Scholar 

  • Bloembergen, N. (1996). In Nonlinear optics (4th ed.). Singapore: World Scientific.

    Google Scholar 

  • Brédas, J. L., Adant, C., Tackx, P., Persoons, A., & Pierce, B. M. (1994). Third-order nonlinear optical response in organic materials: theoretical and experimental aspects. Chemical Reviews, 94(1), 243–278.

    Google Scholar 

  • Bruchez Jr., M., Moronne, M., Gin, P., Weiss, S., & Alivisatos, A. P. (1998). Semiconductor nanocrystals as fluorescent biological labels. Science, 281(5385), 2013–2016.

    Google Scholar 

  • Buckingham, A. D. (1967). Permanent and induced molecular moments and long-range intermolecular forces. Advances in Chemical Physics, 12, 107–142.

    Google Scholar 

  • Butcher P. N., & Cotter, D. (1990). The elements Of nonlinear optics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Calarco, T., Datta, A., Fedichey, P., Pazy, E., & Zoller, P. (2003). Spin-based all-optical quantum computation with quantum dots: understanding and suppressing decoherence. Physical Review A - Atomic, Molecular, and Optical Physics, 68(1), 012310/1–012310/21.

    Google Scholar 

  • Castro, A., Marques, M. A. L., Alonso, J. A., Bertsch, G. F., Yabana, K., & Rubio, A. (2002). Can optical spectroscopy directly elucidate the ground state of C20?Journal of Chemical Physics, 116(5), 1930–1933.

    Google Scholar 

  • Champagne, B., Spassova, M., Jadin, J.-B., & Kirtman, B. (2002). Ab initio investigation of doping-enhanced electronic and vibrational second hyperpolarizability of polyacetylene chains.Journal of Chemical Physics, 116(9), 3935–3946.

    Google Scholar 

  • Chen, W., Zhang, J. Z., & Joly, A. G. (2004). Optical properties and potential applications of doped semiconductor nanoparticles. Journal of Nanoscience and Nanotechnology, 4(8), 919–947.

    Google Scholar 

  • Costales, A., Kandalam, A. K., Franco, R., & Pandey, R. (2002). Theoretical study of structural and vibrational properties of (AlP)\(_{n}\), (AlAs)\(_{n}\), (GaP)\(_{n}\), (GaAs)\(_{n}\), (InP)\(_{n}\), and (InAs)\(_{n}\) clusters with n = 1, 2, 3. Journal of Physical Chemistry B, 106(8), 1940–1944.

    Google Scholar 

  • Deglmann, P., Ahlrichs, R., & Tsereteli, K. (2002). Theoretical studies of ligand-free cadmium selenide and related semiconductor clusters. Journal of Chemical Physics, 116(4), 1585–1597.

    Google Scholar 

  • Deng, K., Yang, J., & Chan, C. T. (2000). Calculated polarizabilities of small S clusters. PhysicalReview A - Atomic, Molecular, and Optical Physics, 61 (2), 252011–252014.

    Google Scholar 

  • Dugourd, P., Hudgins, R. R., Tenenbaum, J. M., & Jarrold, M. F. (1998). Observation of new ring isomers for carbon cluster anions. Physical Review Letters, 80(19), 4197–4200.

    Google Scholar 

  • Feng, Y. P., Boo, T. B., Kwong, H. H., Ong, C. K., Kumar, V., & Kawazoe, Y. (2007). Composition dependence of structural and electronic properties of Ga\(_{m}\)As\(_{n}\) clusters from first principles. Physical Review B - Condensed Matter and Materials Physics, 76(4), 045336/1–045336/8.

    Google Scholar 

  • Fournier, R., Sinnott, S. B., & DePristo, A. E. (1992). Density functional study of the bonding in small silicon clusters. Journal of Chemical Physics, 97(6), 4149–4161.

    Google Scholar 

  • Feynman, R. P. (1939). Forces in Molecules.Physical Reviews, 56(4), 340.

    Google Scholar 

  • Fielicke, A., Lyon, J. T., Haertelt, M., Meijer, G., Claes, P., & De Haeck, J., et al. (2009). Vibrational spectroscopy of neutral silicon clusters via far-IR-VUV two color ionization.Journal of Chemical Physics, 131(17), 171105/1–171105/6.

    Google Scholar 

  • Garcia-Fernandez, P., Bersuker, I. B., & Boggs J. E. (2006). The origin of molecular distortions: a proposed experimental test.Journal of Chemical Physics, 124(6), 044321/1–044321/7.

    Google Scholar 

  • Graves, R. M., & Scuseria, G. E. (1991). Ab initio theoretical study of small GaAs clusters. Journal of Chemical Physics, 95(9), 6602–6606.

    Google Scholar 

  • Grimme, S., & Mück-Lichtenfeld, C. (2002). Structural isomers of C\(_{20}\) revisited: the cage and bowl are almost isoenergetic. ChemPhysChem, 3(2), 207–209.

    Google Scholar 

  • Grossman, J. C., Mitas, L., & Raghavachari, K. (1995). Structure and stability of molecular carbon: importance of electron correlation. Physical Review Letters, 75(21), 3870–3873.

    Google Scholar 

  • Guillaume, M., Champagne, B., B́gú, D., & Pouchan, C. (2009). Electrostatic interaction schemes for evaluating the polarizability of silicon clusters. Journal of Chemical Physics, 130(13)

    Google Scholar 

  • Gur, I., Fromer, N. A., Geier, M. L., & Alivisatos, A. P. (2005). Materials science: air-stable all-inorganic nanocrystal solar cells processed from solution. Science, 310(5747), 462–465.

    Google Scholar 

  • Gurin, V. S. (1998). Ab-initio calculations of small Cd\(_{x}\)S\(_{y}\) and Zn\(_{x}\)S\(_{y}\) (x,y ≤ 6) clusters. Solid State Communications, 108(6), 389–392.

    Google Scholar 

  • Gutsev, G. L., O’Neal Jr., R. H., Saha, B. C., Mochena, M. D., Johnson, E., & Bauschlicher Jr., C. W. (2008a). Optical properties of (GaAs)n clusters (n = 2–16). Journal of Physical Chemistry A, 112(43), 10728–10735.

    Google Scholar 

  • Gutsev, G. L., Johnson, E., Mochena, M. D., & Bauschlicher Jr., C. W. (2008b). The structure and energetics of (GaAs)\(_{n}\), (GaAs)\(_{n}^{-}\), and (GaAs)\(_{n}^{+}\) (n = 2–15). Journal of Chemical Physics, 128(14), 144707/1–144707/9.

    Google Scholar 

  • Gutsev, G. L., Mochena, M. D., Saha, B. C., & Derosa P. A. (2010). Structures and properties of (GaAs)\(_{n}\) clusters. Journal of Computational and Theoretical Nanoscience, 7, 1–10.

    Google Scholar 

  • Hamad, S., Richard, C., Catlow, A., Spanó, E., Matxain, J. M., & Ugalde, J. M. (2005). Structure and properties of ZnS nanoclusters. Journal of Physical Chemistry B, 109(7), 2703–2709.

    Google Scholar 

  • Headley, A. D. (1987). Substituent effects on the basicity of dimethylamines. Journal of the American Chemical Society, 109(8), 2347–2348.

    Google Scholar 

  • Hellmann, H. (1937). Einführung in die Quantenchemie (p. 285). Leipzig: Franz Deuticke.

    Google Scholar 

  • Helgaker, T., Jørgensen, P., & Olsen, J. (2000). Molecular Electronic-Structure Theory. Chichester: Wiley.

    Google Scholar 

  • Ho, K.-M., Shvartsburg, A. A., Pan, B., Lu, Z.-Y., Wang, C.-Z., Wacker, J. G., Fye J. L., & Jarrold M. F. (1998). Structures of medium-sized silicon clusters. Nature, 392, 582–585.

    Google Scholar 

  • Hohm, U. (2000). Is there a minimum polarizability principle in chemical reactions? Journal of Physical Chemistry A, 104(36), 8418–8423.

    Google Scholar 

  • Hohm, U., Loose, A., Maroulis, G., & Xenides, D. (2000). Combined experimental and theoretical treatment of the dipole polarizability of P\(_{4}\) clusters.Physical Review A - Atomic, Molecular, and Optical Physics, 61(5), 532021– 532026.

    Google Scholar 

  • Honea, E. C., Ogura, A., Murray, C. A., Raghavachari, K., Sprenger, W. O., Jarrold, M. F., & Brown, W. L. (1993). Raman spectra of size-selected silicon clusters and comparison with calculated structures. Nature, 366(6450), 42–44.

    Google Scholar 

  • Hossain, D., Hagelberg, F., Pittman Jr., C. U., & Saebo, S. (2007). Structures and stabilities of clusters of Si\(_{12}\), Si\(_{18,}\) and Si\(_{20}\) containing endohedral charged and neutral atomic species. Journal of Physical Chemistry C, 111(37), 13864–13871.

    Google Scholar 

  • Jackson, K. A., Yang, M., Chaudhuri, I., & Frauenheim, T. (2005). Shape, polarizability, and metallicity in silicon clusters. Physical Review A - Atomic, Molecular, and Optical Physics, 71(3), 1–6.

    Google Scholar 

  • Jackson, K., Yang, M., & Jellinek, J. (2007). Site-specific analysis of dielectric properties of finite systems. Journal of Physical Chemistry C, 111(48), 17952–17960.

    Google Scholar 

  • Jackson, K., Pederson, M., Wang, C.-Z., & Ho, K.-M. (1999). Calculated polarizabilities of intermediate-size Si clusters. Physical Review A - Atomic, Molecular, and Optical Physics, 59(5), 3685–3689.

    Google Scholar 

  • Jackson, K. A., Horoi, M., Chaudhuri, I., Frauenheim, T., & Shvartsburg, A. A. (2004). Unraveling the shape transformation in silicon clusters. Physical Review Letters, 93(1), 013401/1–013401/4.

    Google Scholar 

  • Jarrold, M. F., & Bower, J. E. (1992). Mobilities of silicon cluster ions: the reactivity of silicon sausages and spheres. The Journal of Chemical Physics, 96(12), 9180–9190.

    Google Scholar 

  • Jarrold, M. F., & Constant, V. A. (1991). Silicon cluster ions: evidence for a structural transition. Physical Review Letters, 67(21), 2994–2997.

    Google Scholar 

  • Jelski, D. A., Swift, B. L., Rantala, T. T., Xia, X., & George, T. F. (1991). Structure of the Si\(_{45}\) cluster. Journal of Chemical Physics, 95(11), 8552–8560.

    Google Scholar 

  • Jha, P. C., Seal, P., Sen, S., Ågren, H., & Chakrabarti, S. (2008). Static and dynamic polarizabilities of (CdSe)\(_{n}\) (n = 1–16) clusters. Computational Materials Science, 44(2), 728–732.

    Google Scholar 

  • Jose, R., Zhanpeisov, N. U., Fukumura, H., Baba, Y., & Ishikawa, I. (2006). Structure-property correlation of CdSe clusters using experimental results and first-principles DFT calculations. Journal of the American Chemical Society, 128(2), 629–636.

    Google Scholar 

  • Kanis, D. R., Ratner, M. A., & Marks, T. J. (1994). Design and construction of molecular assemblies with large second-order optical nonlinearities. quantum chemical aspects. Chemical Reviews, 94(1), 195–242.

    Google Scholar 

  • Kasuya, A., Sivamohan, R., Barnakov, Y. A., Dmitruk, I. M., Nirasawa, T., & Romanyuk, V. R., et al. (2004). Ultra-stable nanoparticles of CdSe revealed from mass spectrometry. Nature Materials, 3(2), 99–102.

    Google Scholar 

  • Karamanis, P., Maroulis, G., & Pouchan, C. (2006a). Basis set and electron correlation effects in all-electron ab initio calculations of the static dipole polarizability of small cadmium selenide clusters, (CdSe)\(_{n}\), n = 1,2,3,4. Chemical Physics, 331(1), 19–25.

    Google Scholar 

  • Karamanis, P., Maroulis, G., & Pouchan, C. (2006b). Molecular geometry and polarizability of small cadmium selenide clusters from all-electron Ab initio and density functional theory calculations. Journal of Chemical Physics, 124(7), 071101/ 1–071101/2.

    Google Scholar 

  • Karamanis, P., Begue, D., & Pouchan, C. (2007a). Ab initio finite field (hyper)polarizability computations on stoichiometric gallium arsenide clusters Ga\(_{n}\)As\(_{n}\) (n = 2–9). Journal of Chemical Physics, 127(9), 094706/1–094706/10.

    Google Scholar 

  • Karamanis, P., Zhang-Negrerie, D., & Pouchan, C. (2007b). A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si\(_{6}\) ground state. Chemical Physics, 331(2–3), 417–426.

    Google Scholar 

  • Karamanis, P., Pouchan, C., & Leszczynski, J. (2008a). Electric dipole (hyper)polarizabilities of selected X\(_{2}\)Y\(_{2}\) and X\(_{3}\)Y\(_{3}\) (X = Al, Ga, in and Y = P, As): III-V semiconductor clusters. An ab initio comparative study. Journal of Physical Chemistry A, 112(51), 13662–13671.

    Google Scholar 

  • Karamanis, P., Xenides, D., & Leszczynski, J. (2008b). Polarizability evolution on natural and artificial low dimensional binary semiconductor systems: a case study of stoichiometric aluminum phosphide semiconductor clusters. Journal of Chemical Physics, 129(9), 094708/1–094708/12.

    Google Scholar 

  • Karamanis, P., Xenides, D., & Leszcszynski, J. (2008c). The polarizabilities of small stoichiometric aluminum phosphide clusters Al\(_{n}\)P\(_{n}\) (n = 2–9). Ab initio and density functional investigation. Chemical Physics Letters, 457(1–3), 137–142.

    Google Scholar 

  • Karamanis, P., & Leszczynski, J. (2008d). Correlations between bonding, size, and second hyperpolarizability (\(\gamma )\) of small semiconductor clusters: ab initio study on Al\(_{n}\)P\(_{n}\) clusters with n = 2, 3, 4, 6, and 9. Journal of Chemical Physics, 128(15), 154323/1–154323/10.

    Google Scholar 

  • Karamanis, P., Pouchan, C., & Maroulis, G. (2008). Structure, stability, dipole polarizability and differential polarizability in small gallium arsenide clusters from all-electron ab initio and density-functional-theory calculations. Physical Review A - Atomic, Molecular, and Optical Physics, 77(1), 013201/1–013201/6.

    Google Scholar 

  • Karamanis, P., Carbonnière, P., & Pouchan, C. (2009). Structures and composition-dependent polarizabilities of open- and closed-shell gan asm semiconductor clusters.Physical Review A - Atomic, Molecular, and Optical Physics, 80(5), 053201/1–053201/11.

    Google Scholar 

  • Karamanis, P., & Pouchan, C. (2009). How large are the microscopic electronic dipole (hyper)polarizabilities of Cd\(_{n}\)Te\(_{n}\) bare clusters compared to those of Cd\(_{n}\)S\(_{n}\) and Cd\(_{n}\)Se\(_{n}\)? A systematic ab initio study. Chemical Physics Letters, 474(1–3), 162–167.

    Google Scholar 

  • Karamanis, P., Marchal, R., Carbonnière, P., & Pouchan, C. (2010). Doping effects on the electric response properties of Silicon clusters. A global structure-property investigation of AlSi\(_{n-1}\) clusters (n = 3–10). Chemical Physics Letters, 474(1–3), 59–64.

    Google Scholar 

  • Karamanis, P., Pouchan, C., Weatherford, C. A., & Gutsev, G. L. (2011). Evolution of properties in prolate (GaAs)\(_{n}\) clusters.Journal of Physical Chemistry C, 115(1), 97–107.

    Google Scholar 

  • Karamanis, P., & Pouchan, C. (2011). On the shape dependence of cluster (hyper)polarizabilities. A combined ab initio and DFT study on large fullerene-like gallium arsenide semiconductor clusters.International Journal of Quantum Chemistry, 111(4), 788–796.

    Google Scholar 

  • Kaxiras, E., & Jackson, K. (1993). Shape of small silicon clusters. Physical Review Letters, 71(5), 727–730.

    Google Scholar 

  • Kim, H.-Y., Sofo, J. O., Velegol, D., Cole, M. W., & Mukhopadhyay, G. (2005). Static polarizabilities of dielectric nanoclusters.Physical Review A - Atomic, Molecular, and Optical Physics, 72(5), 1–8.

    Google Scholar 

  • Koch, W., & Holthausen, M. C. (2000). A Chemist’s guide to density functional theory. Chichester: Wiley.

    Google Scholar 

  • Korambath, P. P., & Karna, S. P. (2000). (Hyper)polarizabilities of GaN, GaP, and GaAs clusters: an ab initio time-dependent Hartree-Fock study. Journal of Physical Chemistry A, 104(20), 4801–4804.

    Google Scholar 

  • Krishtal, A., Senet, P., Van Alsenoy, C. (2010) Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: the case of AlP clusters. Journal of Chemical Physics, 133(15), 154310/1–154310/11.

    Google Scholar 

  • Kurtz, H. A., Stewart, J. J. P., & Dieter, K. M. (1990). Calculation of the nonlinear optical properties of molecules.Journal of Computational Chemistry, 11(1), 82–87.

    Google Scholar 

  • Lan, Y.-Z., Cheng, W.-D., Wu, D.-S., Shen, J., Huang, S.-P., Zhang, H., Gong, Y.-J., & Li, F.-F. (2006). A theoretical investigation of hyperpolarizability for small Ga\(_{n}\)As\(_{m}\) (n + m = 4–10) clusters. Journal of Chemical Physics, 124(9), 094302/ 1–094302/8.

    Google Scholar 

  • Lan, Y., Cheng, W., Wu, D., Li, X., Zhang, H., & Gong, Y. (2003). TDHF-SOS treatments on linear and nonlinear optical properties of III-V semiconductor clusters (Ga\(_{3}\)As\(_{3}\), Ga\(_{3}\)Sb\(_{3}\), In\(_{3}\)P\(_{3}\), In\(_{3}\)As\(_{3}\), In\(_{3}\)Sb\(_{3})\).Chemical Physics Letters, 372 (5–6), 645–649.

    Google Scholar 

  • Lan, Y.-Z., Feng, Y.-L., Wen, Y.-H., & Teng, B.-T. (2008). Dynamic second-order hyperpolarizabilities of Si\(_{3}\) and Si\(_{4}\) clusters using coupled cluster cubic response theory.Chemical Physics Letters, 461(1–3), 118–121.

    Google Scholar 

  • Lan, Y.-Z., & Feng, Y.-L. (2009). Study of absorption spectra and (hyper)polarizabilities of SiC\(_{n}\) and Si\(_{n}\)C (n = 2–6) clusters using density functional response approach.Journal of Chemical Physics, 131(5), 054509/1–054509/11.

    Google Scholar 

  • Leitsmann, R., Schmidt, W. G., Hahn, P. H., & Bechstedt, F. (2005). Second-harmonic polarizability including electron-hole attraction from band-structure theory. Physical Review B - Condensed Matter and Materials Physics, 71(19), 195209/1–195209/10.

    Google Scholar 

  • Li, B.-X. (2005). Stability of medium-sized neutral and charged silicon clusters. Physical Review B - Condensed Matter and Materials Physics, 71(23), 1–7.

    Google Scholar 

  • Li, L., Zhou, Z., Wang, X., Huang, W., He, Y., & Yang, M. (2008) First-principles study of static polarizability, first and second hyperpolarizabilities of small-sized ZnO clusters. Physical Chemistry Chemical Physics, 10(45), 6829–6835.

    Google Scholar 

  • Li, B.-X., Cao, P.-L., & Zhou, X.-Y. (2003). Electronic and geometric structures of Si\(_{n}\)- and Si\(_{n}^{+}\) (n = 2–10) clusters and in comparison with Si\(_{n}\). Physica Status Solidi (B) Basic Research, 238(1), 11–19.

    Google Scholar 

  • Liao, D. W., & Balasubramanian, K. (1992). Electronic structure of the III-V tetramer clusters and their positive ions.Journal of Chemical Physics, 96(12), 8938–8947.

    Google Scholar 

  • Lipscomb, W. N. (1966). Framework rearrangement in boranes and carboranes.Science, 153(3734), 373–378.

    Google Scholar 

  • Lou, L., Nordlander, P., & Smalley, R. E. (1992). Electronic structure of small GaAs clusters. II. Journal of Chemical Physics, 97(3), 1858–1864.

    Google Scholar 

  • Luis, J. M., Duran, M., Champagne, B., & Kirtman, B. (2000). Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates.Journal of Chemical Physics, 113 (13), 5203–5213.

    Google Scholar 

  • Lyon, J. T., Gruene, P., Fielicke, A., Meijer, G., Janssens, E., & Claes, P., et al. (2009). Structures of silicon cluster cations in the gas phase. Journal of the American Chemical Society, 131(3), 1115–1121.

    Google Scholar 

  • Marchal, R., Carbonnière, P., & Pouchan, C. (2009). A global search algorithm of minima exploration for the investigation of low lying isomers of clusters from density functional theory-based potential energy surfaces: the example of Si\(_{n}\) (n = 3, 15) as a test case. Journal of Chemical Physics, 131(11), 114105/1–114105/9.

    Google Scholar 

  • Marchal, R., Carbonnière, P., & Pouchan, C. (2010). A global search algorithm of minima exploration for the investigation of low lying isomers of clusters from DFT-based potential energy surface. A theoretical study of Sin and Si\(_{n-1}\)Al clusters. International Journal of Quantum Chemistry, 110(12), 2256–2259.

    Google Scholar 

  • Marchal, R., Carbonnière, P., & Pouchan, C. (2011). On the Structures of Non-Stoichiometric GanAsm Clusters (5 n < + m < 8). Journal of Computational and Theoretical Nanosciences, 8(4), 568–578.

    Google Scholar 

  • Maroulis, G., Karamanis, P., & Pouchan, C. (2007). Hyperpolarizability of GaAs dimer is not negative. Journal of Chemical Physics, 126(15), 154316/1–154316/5.

    Google Scholar 

  • Maroulis, G. (2008). How large is the static electric (hyper)polarizability anisotropy in HXeI? Journal of Chemical Physics, 129(4), 044314/ 1–044314/6.

    Google Scholar 

  • Maroulis, G. (2004). Bonding and (hyper) polarizability in the sodium dimer. Journal of Chemical Physics, 121(21), 10519–10524.

    Google Scholar 

  • Maroulis, G., Begué, D., & Pouchan, C. (2003). Accurate dipole polarizabilities of small silicon clusters from ab initio and density functional theory calculations. Journal of Chemical Physics, 119(2), 794–797.

    Google Scholar 

  • Maroulis, G. (2003). Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2. Journal of Chemical Physics, 118(6), 2673–2687.

    Google Scholar 

  • Maroulis, G., & Pouchan, C. (2003). Size and electric dipole (hyper)polarizability in small cadmium sulfide clusters: an ab initio study on (CdS)\(_{n}\), n = 1, 2, and 4.Journal of Physical Chemistry B, 107(39), 10683–10686.

    Google Scholar 

  • Marks, T. J., & Ratner, M. A. (1995). Design, synthesis, and properties of molecule-based assemblies with large second-order optical nonlinearities. Angewandte Chemie(International Edition in English), 34(2), 155–173.

    Google Scholar 

  • Matxain, J. M., Fowler, J. E., & Ugalde, J. M. (2000). Small clusters of II-VI materials: Zn\(_{i}\)O\(_{i}\), i = 1–9. Physical Review A - Atomic, Molecular, and Optical Physics, 62(5), 053201/1–053201/10.

    Google Scholar 

  • Matxain, J. M., Mercero, J. M., Fowler, J. E., & Ugalde, J. M. (2001). Small clusters of group-(II-VI) materials: Zn\(_{i}\)X\(_{i}\), X = Se,Te, i = 1–9. Physical Review A. Atomic, Molecular, and Optical Physics, 64(5), 532011–532018.

    Google Scholar 

  • Matxain, J. M., Mercero, J. M., Fowler, J. E., & Ugalde, J. M. (2003). Clusters of group II–VI materials: Cd\(_{i}\)O\(_{i}\) (i ≤ 15). Journal of Physical Chemistry A, 107(46), 9918–9923.

    Google Scholar 

  • Matxain, J. M., Mercero, J. M., Fowler, J. E., & Ugalde, J. M. (2004). Clusters of II–VI materials: Cd\(_{i}\)X\(_{i}\), X = S, Se, Te, i ≤ 16. Journal of Physical Chemistry A, 108(47), 10502–10508.

    Google Scholar 

  • McLean, A. D., & Yoshimine, M. (1967). Theory of molecular polarizabilities.Journal of Chemical Physics, 47(6), 1927–1935.

    Google Scholar 

  • Menon, M., & Subbaswamy, K. R. (1995). Structure and stability of Si45 clusters: a generalized tight-binding molecular-dynamics approach. Physical Review B, 51(24), 17952–17956.

    Google Scholar 

  • Michalet, X., Pinaud, F. F., Bentolila, L. A., Tsay, J. M., Doose, S., & Li, J. J., et al. (2005). Quantum dots for live cells, in vivo imaging, and diagnostics. Science, 307(5709), 538–544.

    Google Scholar 

  • Mitas, L., Grossman, J. C., Stich, I., & Tobik, J. (2000). Silicon clusters of intermediate size: energetics, dynamics, and thermal effects. Physical Review Letters, 84(7), 1479–1482.

    Google Scholar 

  • Murray, C. B., Kagan, C. R., & Bawendi, M. G. (2000). Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies. Annual Review of Materials Science, 30, 545–610.

    Google Scholar 

  • Nagle, J. K. (1990). Atomic polarizability and electronegativity. Journal of the American Chemical Society, 112(12), 4741–4747.

    Google Scholar 

  • Nair, N. N., Bredow, T., & Jug, K. (2004). Molecular dynamics implementation in MSINDO: study of silicon clusters. Journal of Computational Chemistry, 25(10), 1255–1263.

    Google Scholar 

  • Nigam, S., Majumder, C., & Kulshreshtha, S. K. (2004). Structural and electronic properties of Si\(_{n}\), Si\(_{n}^{+}\), and AlSi\(_{n}^{-1}\) (n = 2–13) clusters: theoretical investigation based on ab initio molecular orbital theory. Journal of Chemical Physics, 121(16), 7756–7763.

    Google Scholar 

  • O’Brien, S. C., Liu, Y., Zhang, Q., Heath, J. R., Tittel, F. K., & Curl, R. F., et al. (1985). Supersonic cluster beams of III-V semiconductors: Ga\(_{x}\)As\(_{y}\). Journal of Chemical Physics, 84(7), 4074–4079.

    Google Scholar 

  • Papadopoulos, M. G., Reis, H., Avramopoulos, A., Erkoç, S., & Amirouche, L. (2005). A comparative study of the dipole polarizability of some Zn clusters.Journal of Physical Chemistry B, 109(40), 18822–18830.

    Google Scholar 

  • Papadopoulos, M. G., Reis, H., Avramopoulos, A., Erkoç, S., & Amirouche, L. (2006). Polarizabilities and second hyperpolarizabilities of Zn\(_{m}\)Cd\(_{n}\) clusters.Molecular Physics, 104(13–14), 2027–2036.

    Google Scholar 

  • Parr, R. G., & Chattaraj, P. K. (1991). Principle of maximum hardness. Journal of the American Chemical Society, 113(5), 1854–1855.

    Google Scholar 

  • Pedroza, L. S., & Da Silva, A. J. R. (2007). Ab initio monte carlo simulations applied to Si\(_{5}\) cluster. Physical Review B - Condensed Matter and Materials Physics, 75(24), 245331/1–245331/10.

    Google Scholar 

  • Peng, X., Wickham, J., & Alivisatos, A. P. (1998). Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: ‘Focusing’ of size distributions. Journal of the American Chemical Society, 120(21), 5343–5344.

    Google Scholar 

  • Peng, X., Manna, L., Yang, W., Wickham, J., Scher, E., Kadavanich, A., et al. (2000). Shape control of CdSe nanocrystals. Nature, 404(6773), 59–61.

    Google Scholar 

  • Pool, R. (1990). Clusters: strange morsels of matter. Science, 248(4960), 1186–1188.

    Google Scholar 

  • Pouchan, C., Bégué, D., & Zhang, D. Y. (2004). Between geometry, stability, and polarizability: density functional theory studies of silicon clusters Si\(_{n}\)(n = 3–10).Journal of Chemical Physics, 121(10), 4628–4634.

    Google Scholar 

  • Powell, G. D., Wang, J.-F., & Aspnes, D. E. (2002). Simplified bond-hyperpolarizability model of second harmonic generation. Physical Review B - Condensed Matter and Materials Physics, 65(20), 205320/1–205320/8.

    Google Scholar 

  • Prinzbach, H., Weller, A., Landenberger, P., Wahl, F., Wörth, J., Scott, L. T., et al. (2000). Gas-phase production and photoelectron spectroscopy of the smallest fullerene, C\(_{20}\). Nature, 407(6800), 60–63.

    Google Scholar 

  • Pushpa, R., Narasimhan, S., & Waghmare, U. (2004). Symmetries, vibrational instabilities, and routes to stable structures of clusters of Al, Sn, and As. Journal of Chemical Physics, 121(11), 5211–5220.

    Google Scholar 

  • Raghavachari, K., & Logovinsky, V. (1985). Structure and bonding in small silicon clusters. Physical Review Letters, 55(26), 2853–2856.

    Google Scholar 

  • Raghavachari, K., & Rohlfing, C. M. (1988). Bonding and stabilities of small silicon clusters: a theoretical study of Si\(_{7}\)–Si\(_{10}\). Journal of Chemical Physics, 89(4), 2219–2234.

    Google Scholar 

  • Raptis, S. G., Papadopoulos, M. G., & Sadlej, A. J. (1999). The correlation, relativistic, and vibrational contributions to the dipole moments, polarizabilities, and first and second hyperpolarizabilities of ZnS, CdS, and HgS.Journal of Chemical Physics, 111(17), 7904–7915.

    Google Scholar 

  • Reis, H., Papadopoulos, M. G., & Boustani, I. (2000). DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters bn (n = 3–8, 10).International Journal of Quantum Chemistry, 78(2), 131–135.

    Google Scholar 

  • Rohlfing, C. M., & Raghavachari, K. A (1990). Theoretical study of small silicon clusters using an effective core potential. Chemical Physics Letters, 167(6), 559–565.

    Google Scholar 

  • Roman, E., Yates, J. R., Veithen, M., Vanderbilt, D., & Souza, I. (2006). Ab initio study of the nonlinear optics of III-V semiconductors in the terahertz regime. Physical Review B - Condensed Matter and Materials Physics, 74(24), 245204/ 1–245204/9.

    Google Scholar 

  • Sanville, E., Burnin, A., & BelBruno, J. J. (2006). Experimental and computational study of small (n = 1–16) stoichiometric zinc and cadmium chalcogenide clusters. Journal of Physical Chemistry A, 110(7), 2378–2386.

    Google Scholar 

  • Schäfer, R., Schlecht, S., Woenckhaus, J., & Becker, J. A. (1996). Polarizabilities of isolated semiconductor clusters.Physical Review Letters, 76(3), 471–474.

    Google Scholar 

  • Schaller, R. D., & Klimov, V. I. (2006). Non-poissonian exciton populations in semiconductor nanocrystals via carrier multiplication. Physical Review Letters, 96(9), 1–4.

    Google Scholar 

  • Schlecht, S., Schäfer, R., Woenckhaus, J., & Becker, J. A. (1995). Electric dipole polarizabilities of isolated gallium arsenide clusters.Chemical Physics Letters, 246(3), 315–320.

    Google Scholar 

  • Schnell, M., Herwig, C., & Becker, J. A. (2003). Analysis of semiconductor cluster beam polarization taking small permanent dipole moments into account.Zeitschrift Fur Physikalische Chemie, 217(8), 1003–1030.

    Google Scholar 

  • Sen, S., & Chakrabarti, S. (2006). Frequency-dependent nonlinear optical properties of CdSe clusters. Physical Review B - Condensed Matter and Materials Physics, 74(20), 205435/ 1–205435/7.

    Google Scholar 

  • Sokolova, S., Lüchow, A., & Anderson, J. B. (2000). Energetics of carbon clusters C\(_{20}\) from all-electron quantum monte carlo calculations. Chemical Physics Letters, 323(3–4), 229–233.

    Google Scholar 

  • Song, K. M., Ray, A. K., & Khowash, P. K. (1994). On the electronic structures of GaAs clusters. Journal of Physics B: Atomic, Molecular and Optical Physics, 27(8), 1637–1648.

    Google Scholar 

  • Sun, Q., Wang, Q., Jena, P., Waterman, S., & Kawazoe, Y. (2003). First-principles studies of the geometry and energetics of the Si\(_{36}\) cluster. Physical Review A - Atomic, Molecular, and Optical Physics, 67(6), 632011– 632016.

    Google Scholar 

  • Swaminathan, P., Antonov, V. N., Soares, J. A. N. T., Palmer, J. S., & Weaver, J. H. (2006). Cd-based II-VI semiconductor nanostructures produced by buffer-layer-assisted growth: structural evolution and photoluminescence. Physical Review B - Condensed Matter and Materials Physics, 73(12), 1–8.

    Google Scholar 

  • Szabo, A., & Ostlund, N. S. (1989). Modern quantum chemistry. New York: MacMillan.

    Google Scholar 

  • Tekin, A., & Hartke, B. (2004). Global geometry optimization of small silicon clusters with empirical potentials and at the DFT level. Physical Chemistry Chemical Physics, 6(3), 503–509.

    Google Scholar 

  • Torrens, F. (2002). Fractal dimension of different structural-type zeolites and of the active sites. Physica E (Amsterdam), 13, 67.

    Google Scholar 

  • Troparevsky, M. C., & Chelikowsky, J. R. (2001). Structural and electronic properties of CdS and CdSe clusters. Journal of Chemical Physics, 114(2), 943–949.

    Google Scholar 

  • Troparevsky, M. C., Kronik, L., & Chelikowsky, J. R. (2002). Ab initio absorption spectra of CdSe clusters.Physical Review B - Condensed Matter and Materials Physics, 65(3), 333111–333114.

    Google Scholar 

  • Vasiliev, I., Ögüt, S., & Chelikowsky, J. R. (1997). Ab initio calculations for the polarizabilities of small semiconductor clusters.Physical Review Letters, 78(25), 4805–4808.

    Google Scholar 

  • Vela, A., & Gázquez, J. L. (1990). A relationship between the static dipole polarizability, the global softness, and the fukui function. Journal of the American Chemical Society, 112(4), 1490–1492.

    Google Scholar 

  • Vijayalakshmi, S., Lan, A., Iqbal, Z., & Grebel, H. (2002). Nonlinear optical properties of laser ablated silicon nanostructures. Journal of Applied Physics, 92(5), 2490–2494.

    Google Scholar 

  • Wang, B.-C., Chou, Y.-M., Deng, J.-P., & Dung, Y.-T. (2008). Structural and optical properties of passivated silicon nanoclusters with different shapes: a theoretical investigation. Journal of Physical Chemistry A, 112(28), 6351–6357.

    Google Scholar 

  • Wang, J., Ma, L., Zhao, J., & Jackson, K. A. (2009). Structural growth behavior and polarizability of Cd\(_{n}\)Te\(_{n}\) (n = 1–14) clusters. Journal of Chemical Physics, 130(21), 214307/1–214307/8.

    Google Scholar 

  • Wang, X. Q., Clark, S. J., & Abram, R. A. (2004). Ab initio calculations of the structural and electronic properties of Hg\(_{m}\)Te\(_{n}\) cluster. Physical Review B - Condensed Matter and Materials Physics, 70(23), 1–6.

    Google Scholar 

  • Wei, S., Barnett, R. N., & Landman, U. (1997). Energetics and structures of neutral and charged sin (n ≤ 10) and sodium-doped Si\(_{n}\)Na clusters. Physical Review B - Condensed Matter and Materials Physics, 55(12), 7935–7944.

    Google Scholar 

  • Williams, R. E. (1992). The polyborane, carborane, carbocation continuum: architectural patterns.Chemical Reviews, 92(2), 177–207.

    Google Scholar 

  • Wolf, S. A., Awschalom, D. D., Buhrman, R. A., Daughton, J. M., Von Molnár, S., Roukes, M. L., et al. (2001). Spintronics: a spin-based electronics vision for the future. Science, 294(5546), 1488–1495.

    Google Scholar 

  • Wu, F., Lewis, J. W., Kliger, D. S., & Zhang, J. Z. (2003). Unusual excitation intensity dependence of fluorescence of CdTe nanoparticles.Journal of Chemical Physics, 118(1), 12–16.

    Google Scholar 

  • Xenides, D. (2006). (Hyper)polarizability dependence on the interatomic distance of N\(_{4}\) (T\(_{d})\): fourth order polynomials and third order derivatives.Journal of Molecular Structure: Theochem, 764(1–3), 41–46.

    Google Scholar 

  • Xenides, D., & Maroulis, G. (2000). Basis set and electron correlation effects on the first and second static hyperpolarizability of SO\(_{2}\).Chemical Physics Letters, 319(5–6), 618–624.

    Google Scholar 

  • Xenides, D., & Maroulis, G. (2006). Electric polarizability and hyperpolarizability of BrCl(X 1\(\Sigma \)+).Journal of Physics B: Atomic, Molecular and Optical Physics, 39(17), 3629–3638.

    Google Scholar 

  • Xiao, C., Hagelberg, F., & Lester Jr., W. A. (2002). Geometric, energetic, and bonding properties of neutral and charged copper-doped silicon clusters. Physical Review B - Condensed Matter and Materials Physics, 66(7), 754251–7542523.

    Google Scholar 

  • Yoo, S., Shao, N., & Zeng, X. C. (2008). Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si\(_{39}\), Si\(_{40}\), Si\(_{50}\), Si\(_{60}\), Si\(_{70}\), and Si\(_{80}\). Journal of Chemical Physics, 128(10), 104316/ 1–104316/9.

    Google Scholar 

  • Yoo, S., & Zeng, X. C. (2006). Structures and relative stability of medium-sized silicon clusters. IV. motif-based low-lying clusters Si\(_{21}\)–Si\(_{30}\). Journal of Chemical Physics, 124(5), 1–6.

    Google Scholar 

  • Yoo, S., & Zeng, X. C. (2005). Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si\(_{15}\) to Si\(_{20}\). Journal of Chemical Physics, 123(16), 1–6.

    Google Scholar 

  • Yoo, S., Zhao, J., Wang, J., & Xiao, C. Z. (2004). Endohedral silicon fullerenes Si\(_{n}\) (27 ≤ n ≤ 39). Journal of the American Chemical Society, 126(42), 13845–13849.

    Google Scholar 

  • Yu, D. K., Zhang, R. Q., & Lee, S. T. (2002). Structural transition in nanosized silicon clusters. Physical Review B - Condensed Matter and Materials Physics, 65(24), 2454171–2454176.

    Google Scholar 

  • Zdetsis, A. D. (2001) The real structure of the Si\(_{6}\) cluster. Physical Review A. Atomic, Molecular, and Optical Physics, 64(2), 023202/1–023202/4.

    Google Scholar 

  • Zdetsis, A. D. (2007a). Analogy of silicon clusters with deltahedral boranes: how far can it go? reexamining the structure of sin and sin 2-, n = 5–13 clusters. Journal of Chemical Physics, 127(24), 244308/1–244308/6.

    Google Scholar 

  • Zdetsis, A. D. (2007b) Fluxional and aromatic behavior in small magic silicon clusters: a full ab initio study of Si\(_{n}\), Si\(_{n}^{1-}\), Si\(_{n}^{2-}\), and Si\(_{n}^{1+}\), n = 6, 10 clusters Journal of Chemical Physics, 127(1), 014314/1–014314/10.

    Google Scholar 

  • Zdetsis, A. D. (2008). High-stability hydrogenated silicon-carbon clusters: a full study of Si2C2H2 in comparison to Si2C 2, C2B2H4, and other similar species.Journal of Physical Chemistry A, 112(25), 5712–5719.

    Google Scholar 

  • Zdetsis, A. D. (2009). Silicon-bismuth and germanium-bismuth clusters of high stability. Journal of Physical Chemistry A, 113(44), 12079–12087.

    Google Scholar 

  • Zhang, D. Y., Bégué, D., & Pouchan, C. (2004). Density functional theory studies of correlations between structure, binding energy, and dipole polarizability in Si\(_{9}\) Si\(_{12}\). Chemical Physics Letters, 398(4–6), 283–286.

    Google Scholar 

  • Zhao, J., Xie, R.-R., Zhou, X., Chen, X., & Lu, W. (2006). Formation of stable fullerenelike Ga\(_{n}\) As\(_{n}\) clusters (6 ≤ n ≤ 9): gradient-corrected density-functional theory and a genetic global optimization approach. Physical Review B - Condensed Matter and Materials Physics, 74(3), 035319/1–035319/2.

    Google Scholar 

  • Zhao, W., & Cao, P.-L. (2001). Study of the stable structures of Ga\(_{6}\)As\(_{6}\) cluster using FP-LMTO MD method. Physics Letters, Section A: General, Atomic and Solid State Physics, 288(1), 53–57.

    Google Scholar 

  • Zhao, W., Cao, P.-L., Li, B.-X., Song, B., & Nakamatsu, H. (2000). Study of the stable structures of Ga\(_{4}\)As\(_{4}\) cluster using FP-LMTO MD method. Physical Review B - Condensed Matter and Materials Physics, 62(24), 17138–17143.

    Google Scholar 

  • Zhou, R. L., & Pan, B. C. (2008). Low-lying isomers of Si\(_{n}^{+}\) and Si\(_{n}^{-}\) (n = 31–50) clusters. Journal of Chemical Physics, 128(23), 234302/1–234302/6.

    Google Scholar 

  • Zhu, X., & Zeng, X. C. (2003). Structures and stabilities of small silicon clusters: ab initio molecular-orbital calculations of Si\(_{7}\)–Si\(_{11}\). Journal of Chemical Physics, 118(8) 3558– 3570.

    Google Scholar 

  • Zhu, X. L., Zeng, X. C., Lei, Y. A., & Pan, B. (2004)Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of Si\(_{12}\)–Si\(_{20}\). Journal of Chemical Physics, 120(19), 8985–8995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media B.V.

About this entry

Cite this entry

Karamanis, P. (2012). Structures and Electric Properties of Semiconductor clusters. In: Leszczynski, J. (eds) Handbook of Computational Chemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0711-5_20

Download citation

Publish with us

Policies and ethics