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Semiconductor Physics pp 1–24Cite as

Crystal Bonding

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Abstract

The bonding of atoms in semiconductors is accomplished by electrostatic forces – Coulomb forces between the electrons and atomic nuclei – and the tendency of atoms to fill their outer shells. Interatomic attraction is balanced by short-range repulsion due to strong resistance of atoms against interpenetration of core shells. Coulomb forces are the basis for ionic and hydrogen bonding forces but are also involved in metallic bonding and, as dipole–dipole interaction, in van der Waals bonding. In addition, strong quantum-mechanical effects, determining specific orbitals, and Pauli exclusion are major contributing factors in covalent and metallic bonding, respectively.

K. W. Böer: deceased

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Notes

  1. 1.

    A better fit for the Born repulsion is obtained by the sum of a power and an exponential law:

    $$ {V}_{\mathrm{Born}}=\beta /{r}^m+\gamma \exp \left(-r/{r}_0\right), $$
    (2)

    where r0 is the softness parameter, listed for ions in Table 8. For more sophisticated repulsion potentials, see Shanker and Kumar (1987).

  2. 2.

    β can be eliminated from the minimum condition (\( {\left. dV/ dr\right|}_{r_e}=0 \)). One obtains β = e2rem− 1/(4πε0m) and as cohesive energy eVmin=− e2(m − 1)/(4πε0m re).

  3. 3.

    The promotion energy is 4.3, 3.5, and 3.3 eV for C, Si, and α-Sn, respectively. However, when forming bonds by establishing electron bridges to neighboring atoms, a substantially larger energy is gained, therefore resulting in net binding forces. Diamond has the highest cohesive energy in this series, despite the fact that its promotion energy is the largest, because its sp3-sp3 C–C bonds are the strongest (see Harrison (1980)).

  4. 4.

    Meaning compounds between one element of group III and one element of group V on the periodic system of elements (cf. Fig. 3 in chapter “Properties and Growth of Semiconductors”)

  5. 5.

    This empirical quantity can be defined in several ways (e.g., as Mohs, Vickers, or Brinell hardness) and is a macroscopic mechanical representation of the cohesive strength of the lattice. In Table 10, the often used Mohs hardness is listed, which orders the listed minerals according to the ability of the higher-numbered one to scratch the lower-numbered minerals.

  6. 6.

    Two principal devices made of organic semiconductors recently entered the market: light-emitting diodes (OLEDs) and field-effect transistors (OFETs), processed as thin-film transistors (TFT). Prominent molecules used in organic (opto-) electronics are listed in Sect. 1.5 in chapter “The Structure of Semiconductors.”

References

  • Anderson PW, Baskaran G, Zou Z, Hsu T (1987) Resonating–valence-bond theory of phase transitions and superconductivity in La2CuO4-based compounds. Phys Rev Lett 58:2790

    Article  ADS  Google Scholar 

  • Ashcroft NW, Mermin ND (1976) Solid state physics. Holt Reinhart and Winston, New York

    MATH  Google Scholar 

  • Born M (1919) Die Elektronenaffinität der Halogenatome. Verh Dtsch Phys Ges 21:679 (The electron affinity of halogen atoms, in German)

    Google Scholar 

  • Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford University Press, London

    MATH  Google Scholar 

  • Born M, Landé A (1918) Über die Berechnung der Kompressibilität regulärer Kristalle aus der Gittertheorie. Verh Dtsch Phys Ges 20:210 (On computing the compressibility of normal crystals applying lattice theory, in German)

    Google Scholar 

  • Brandt NB, Moshchalkov VV (1984) Semimagnetic semiconductors. Adv Phys 33:193

    Article  ADS  Google Scholar 

  • Brill R, Grimm HG, Hermann C, Peters CL (1939) Anwendung der röntgenographischen Fourieranalyse auf Fragen der chemischen, Bindung. Ann Physik, Lpz 34:26 (Application of x-ray Fourier analysis to problems of the chemical bond, in German)

    MATH  Google Scholar 

  • Buckingham RA (1938) The classical equation of state of gaseous Helium, Neon and Argon. Proc R Soc Lond Ser A Math Phys Sci 168:264–283

    ADS  Google Scholar 

  • Cotton FA, Wilkinson G (1972) Advanced inorganic chemistry: a comprehensive text, 3rd edn. Interscience, New York

    Google Scholar 

  • Coulson CA, Redei LB, Stocker D (1962) The electronic properties of tetrahedral intermetallic compounds. I. Charge distribution. Proc R Soc Lond A 270:357

    Article  ADS  Google Scholar 

  • Dawson B (1967) A general structure factor formalism for interpreting accurate x-ray and neutron diffraction data. Proc Roy Soc Lond A 298:255

    ADS  Google Scholar 

  • Ehrenreich H (1987) Electronic theory for materials science. Science 235:1029

    Article  ADS  Google Scholar 

  • Furdyna JK (1982) Diluted magnetic semiconductors: an interface of semiconductor physics and magnetism. J Appl Phys 53:7637

    Article  ADS  Google Scholar 

  • Furdyna JK (1986) Diluted magnetic semiconductors: issues and opportunities. J Vac Sci Technol A 4:2002

    Article  ADS  Google Scholar 

  • Goede O, Heimbrodt W (1988) Optical Properties of (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals and superlattices. Phys Stat Sol B 146:11

    Article  ADS  Google Scholar 

  • Goldschmidt VM (1927) Geochemische Verteilungsgesetze der Elemente, Skrifter det Norske Videnskaps. Akad (Oslo), I Math Naturwiss Kl 1926:7 (Laws for the geometrical distribution of the elements, in German)

    Google Scholar 

  • Gorid’ko NY, Kuzmenko PP, Novikov NN (1961) Change in mechanical properties of germanium caused by the change of concentration of current carriers. Fiz Tverd Tela 3:3650

    Google Scholar 

  • Haber F (1919) Theory of the heat of reaction. Verh Dtsch Phys Ges 21:750

    Google Scholar 

  • Harrison WA (1966) Pseudopotentials in the theory of metals. W.A. Benjamin, New York

    Google Scholar 

  • Harrison WA (1980) Electronic structure and the properties of solids: the physics of chemical bonds. Freeman, San Francisco

    Google Scholar 

  • Holtzberg F, von Molnar S, Coey JMD (1980) Rare earth magnetic semiconductors. In: Moss TS, Keller SP (eds) Handbook of semiconductors, Vol. 3: materials properties and preparation. North Holland, Amsterdam

    Google Scholar 

  • Kitaigorodskii AI (1966) Stacking of molecules in a crystal, interaction potential between atoms not linked by valence bonds, and calculation of molecular movements. J Chim Phys 63:9

    Google Scholar 

  • Kittel C (1996) Introduction to solid state physics, 7th edn. Wiley, New York

    MATH  Google Scholar 

  • Madelung E (1918) Das elektrische Feld in Systemen von regelmässig angeordneten Punktladungen. Phys Z 19:524 (The electric field of systems of regularly arranged point charges, in German)

    MATH  Google Scholar 

  • Martin RM (1970) Elastic properties of ZnS structure semiconductors. Phys Rev B 1:4005

    Article  ADS  Google Scholar 

  • Martins JL, Zunger A (1984) Bond lengths around isovalent impurities and in semiconductor solid solutions. Phys Rev B 30:6217

    Article  ADS  Google Scholar 

  • Mooser E, Pearson WB (1956) The chemical bond in semiconductors. J Electron 1:629

    Google Scholar 

  • Pauling L (1960) The nature of the chemical bond. Cornell University Press, Ithaca

    MATH  Google Scholar 

  • Phillips JC (1973) Bonds and bands in semiconductors. Academic Press, New York

    Google Scholar 

  • Schwoerer M, Wolf HC (2007) Organic molecular solids. Wiley-VCH, Weinheim

    Google Scholar 

  • Shanker J, Kumar M (1987) Ion-dependent and crystal-independent interionic potentials. Phys Stat Sol B 142:325

    Article  ADS  Google Scholar 

  • Sherman J (1932) Crystal energies of ionic compounds and thermochemical applications. Chem Rev 11:93

    Article  Google Scholar 

  • Starr TL, Williams DE (1977) Coulombic nonbonded interatomic potential functions derived from crystal-lattice vibrational frequencies in hydrocarbons. Acta Cryst A 33:771

    Article  Google Scholar 

  • van der Waals JD (1873) Over de Continuiteit van den gasen vloeistof toestand. Sijthoff, Leiden (On the continuity of the gaseous and liquid state, in Dutch)

    Google Scholar 

  • van Vechten JA, Phillips JC (1970) New set of tetrahedral covalent radii. Phys Rev B 2:2160

    Article  ADS  Google Scholar 

  • Vegard L (1921) Die Konstitution der Mischkristalle und die Raumfüllung der Atome. Z Phys 5:17 (The configuration of mixed crystals and space filling of atoms, in German)

    Article  ADS  Google Scholar 

  • Villars P, Calvert LD (1985) Pearson’s handbook of crystallographic data for intermetallic phases. American Society for Metals, Metals Park

    Google Scholar 

  • Wei S-H, Zunger A (1986) Total-energy and band-structure calculations for the semimagnetic Cd1-xMnxTe semiconductor alloy and its binary constituents. Phys Rev B 35:2340

    Article  ADS  Google Scholar 

  • Weißmantel C, Hamann C (1979) Grundlagen der Festkörperphysik. Springer, Berlin (Fundamentals of solid state physics, in German)

    Book  Google Scholar 

  • Welker H, Weiss H (1954) Zur transversalen magnetischen Widerstandsänderung von InSb. Z Phys 138:322 (On the change of the transversal magnetic resistance on InSb, in German)

    Article  ADS  Google Scholar 

  • Wigner EP, Seitz F (1933) On the constitution of metallic sodium. Phys Rev 43:804

    Article  ADS  Google Scholar 

  • Yeh C-Y, Lu ZW, Froyen S, Zunger A (1992) Zinc-blende–wurtzite polytypism in semiconductors. Phys Rev B 46:10086

    Article  ADS  Google Scholar 

  • Ziman JM (1969) The physics of metals, Vol. 1, electrons. Cambridge University Press, London

    Google Scholar 

  • Zunger A, Cohen ML (1979) First-principles nonlocal-pseudopotential approach in the density-functional formalism. II. Application to electronic and structural properties of solids. Phys Rev B 20:4082

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Naples, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Berlin, Germany

    Udo W. Pohl

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  1. Karl W. Böer
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Correspondence to Udo W. Pohl .

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Böer, K.W., Pohl, U.W. (2020). Crystal Bonding. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_2-3

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  • DOI: https://doi.org/10.1007/978-3-319-06540-3_2-3

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Chapter history

  1. Latest

    Crystal Bonding
    Published:
    27 March 2022

    DOI: https://doi.org/10.1007/978-3-319-06540-3_2-4

  2. Crystal Bonding
    Published:
    27 March 2020

    DOI: https://doi.org/10.1007/978-3-319-06540-3_2-3

  3. Crystal Bonding
    Published:
    27 September 2017

    DOI: https://doi.org/10.1007/978-3-319-06540-3_2-2

  4. Original

    Crystal Bonding
    Published:
    04 September 2014

    DOI: https://doi.org/10.1007/978-3-319-06540-3_2-1

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