Crystal Bonding

Abstract The bonding of atoms is described as function of the electrostatic forces, covalent bonding, mixed bonding van der Waals bonding hydrogen and metallic bonding, and Born repulsion, yielding equilibrium distance and ionic or atomic radii that are tabulated. Repulsive potential softness parameters and Mohs hardness are tabulated Close packing of ions/atoms determine ordering preferences. Compress­ibility and Madelung constants, lattice constants and bond length are discussed and tabulated (Table 1.2). Electronegativity, ionicity and effective charges for numerous AB-compounds are listed. Atomic electron density profiles are given.

The bonding of atoms in semiconductors has primary influence of forming the lattice of any solar cell and is accomplished by electrostatic forces and by 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. The knowledge of the detail of this interaction is not only of help for selecting most appropriate materials for solar cells but also for judg­ing about the ease of incorporation of desirable crystal defects and avoiding oth­ers.

The different types of the bonding of condensed matter (solids) will be reviewed, irrespective of whether they are crystalline or amorphous.

The formation of solids is determined by the interatomic forces and the size of the atoms shaping the crystal lattice. The interatomic forces are composed of a far – reaching attractive and a short-range repulsive component, resulting in an equilib­rium distance of vanishing forces at an interatomic distance re, at which the po­tential energy shows a minimum (Fig. 1.1). In Binary compounds, this equilibrium distance re can be written as the sum of atomic radii

re = r A + ГВ, (1.1)

where rA and rB are characteristic for the two atoms A and B (Fig. 1.2).

Attractive interatomic forces are predominantly electrostatic (e. g., in ionic, metallic, van der Waals, and hydrogen bonding) or are a consequence of sharing va­lence electrons to fill their outer shells, resulting in covalent bonding. Most materials show mixed bonding, i. e., at least two of these bond types contribute significantly

K. W. Boer, Handbook of the Physics of Thin-Film Solar Cells,

DOI 10.1007/978-3-642-36748-9_1, © Springer-Verlag Berlin Heidelberg 2013

image1 image2

Fig. 1.1 Interaction potential (a) and forces (b) between two atoms; re is the equilibrium distance; Ec is the bonding energy at r = re

to the interatomic interaction. In the better compound semiconductors, the mixed bonding is more covalent and less ionic. In other semiconductors, one of the other types of bonding may contribute, e. g., van der Waals bonding in organic crystals, and metallic bonding in highly conductive semiconductors.

The repulsive interatomic forces, called Born forces (see Born and Huang 1954), are caused by a strong resistance of the electronic shells of atoms against interpen­etration. The repulsive Born potential is usually modeled with a strong power law[1]


eV(r) = m with m ~ 10,… ,12. (1.3)

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