1. Chapter 3: Energy Band and Charge Carriers SemiconductorObviously, there are complicated differences in the holding forces for various metals, as evidenced by the wide range of melting temperatures [234K for Hg (Mercury), 3643K for W (tungsten)].3.1 Bonding Forces and Energy bands in SolidHowever, the metals have the sea of electrons in common, and these electrons are free to moveThe basic difference between the case of an electron in a solid and that of an electron in anabout the crystal under the influence of an electric field.isolated atom is that in the solid the electron has a range, or band, of available energies.The discrete energy levels of the isolated atom spread into bands of energies in the solidbecause in the solid the wave functions of electrons in neighboring atoms overlap, and an electron isCovalent bond: Covalent bonding is an intramolecular form of chemical bonding characterizednot necessarily localized at a particular atom.by the sharing of one or more pairs of electrons between two components, producing a mutual attraction that holds the resultant molecule together. Atoms tend to share electrons in such a way thatFor example, an electron in the outer orbit of one atom feels the influence of neighboring atoms,their outer electron shells are filled.and its overall wave function is altered. Naturally, this influence affects the potential energy term andAtom in the Ge, Si, or C diamond lattice is surrounded by four nearest neighbors, each withthe boundary conditions in the Schrdinger equation, and we would expect to obtain different energiesfour electrons in the outer orbit. In these crystals each atom shares its valence electrons with its fourin the solution. neighbors. The bonding forces arise from a quantum mechanical interaction between the shared electrons.3.1.1 Bonding forces in Solids This is known as covalent bonding; each electron pair constitutes a covalent bond. The interaction of electrons in neighboring atoms is called bond. The bonding of a solid serves The two electrons are indistinguishable; expect that they must have opposite spin to satisfy thethe very important function of holding the crystal together. Pauli Exclusion Principle [No two electrons in an electronic system can have the same set of four quantum numbers, s (Sharp), p (Principle), d (Diffuse), f()Fundamental. This statement that no twoIonic bond: Ionic bonds are a type of chemical bond based on electrostatic forces between twoelectrons may occupy the same quantum state is known as Pauli Exclusion Principle].oppositely-charged ions. In ionic bond formation, a metal donates an electron, due to a lowelectronegativity to form a positive ion.In ordinary table salt, the bonds between the sodium (Na) and chlorine (Cl) ions are ionic 3.1.2 Energy Bandsbonds. In a NaCl lattice, each Na atom is surrounded by six neares neighbor Cl atoms, and vice versa. As isolated atoms are brought together to form a solid, various interactions occur betweenThe electronic structure of Na (Z=11) is [Ne]3s1, and Cl (Z=17) has the structure [Ne]3s23p5.neighboring atoms. The forces of attraction and repulsion between atoms will find a balance at theIn the lattice each Na atom gives up its outer 3s electron to a Cl atom, so that the crystal is made proper interatomic spacing for the crystal. In the process, important changes occur in the electronup of ions with electronic structures of the inert atoms Ne and Ar.energy level configuration and these changes result in the varied electrical properties of solid.However, the ions have net electric charges after the electron exchange. The Na+ ion has a netpositive charge, having lost an electron, and the Cl- ion has a net negative charge, having gained anIt has been seen [Fig. 2-8] the orbital model of a Si atom, along with the energy levels of theelectron.various electrons in the coulombic potential well of the nucleus.Once the electron exchanges have been made between the Na and Cl atoms to form Na+ and Cl- Let us focus on the outermost shell or valence shell, n=3, where two 3s and two 3p electronsions, the outer orbits of all atoms are completely filled. Since the ions have the closed-shellinteract to form the four hybridized sp3 electrons when the atoms are brought close together.configurations of the inert atoms Ne and Ar, there are no loosely bound electrons to participate inIn Fig. 3-2, we schematically show the coulombic potential wells of two atoms close to eachcurrent flow; as a result, NaCl is a good insulator. other, along with the wave functions of two-electron centered on the two nuclei. By solving the Schrodinger for such an interacting system, we find that the composite two electron wave functions are linear combinations of the individual atomic orbits (LCAO).Metallic bond: Metallic bonding is the bonding within metals. It involves the delocalizedsharing of free electrons among a lattice of metal atoms. The odd or anti-symmetric combination is called the anti-bonding orbital, while the even orIn a metal atom the outer electron shell is only partially filled, usually by no more than three symmetric combination is the bonding orbital.electrons.In Na has only one electron in the outer orbit. This electron is loosely bound and is given up It is seen that the bonding orbital has a higher value of the wave function (and therefore theeasily in ion formation. electron probability density) than the anti-bonding state in the region between the two nuclei. ThisIn the metal the outer electron of each alkali atom is contributed to the crystal as a whole, so corresponds to the covalent bond between the atoms.that the solid is made up of ions with closed shells immersed in a sea of free electrons.The forces holding the lattice together arise from an interaction between the positive ion coresTo determine the energy levels of the bonding and anti-bonding states, it is important toand the surrounding free electrons. This is one type of metallic bonding.recognize that in the region between the two nuclei the coulombic potential energy V(r) is lowered (solid line in Fig. 3) compared to isolated atoms (dashed line in Fig. 3-2). 12