The document discusses energy bands and charge carriers in semiconductors. It explains that in solids, the discrete energy levels of isolated atoms spread into bands of energies due to overlapping wave functions between neighboring atoms. There are different types of bonding forces in solids, including ionic bonds formed between oppositely charged ions, covalent bonds formed by shared electron pairs, and metallic bonds arising from interaction between positive ion cores and delocalized electrons. As atoms come together to form a solid, interactions between neighboring atoms result in important changes to electron energy level configurations, leading to varied electrical properties and the formation of energy bands.

1. Chapter 3: Energy Band and Charge Carriers Semiconductor Obviously, 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 Solid However, the metals have the sea of electrons in common, and these electrons are free to move
The basic difference between the case of an electron in a solid and that of an electron in an about 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 solid
because in the solid the wave functions of electrons in neighboring atoms overlap, and an electron is Covalent bond: Covalent bonding is an intramolecular form of chemical bonding characterized
not 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 that
For 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 and Atom in the Ge, Si, or C diamond lattice is surrounded by four nearest neighbors, each with
the boundary conditions in the Schrödinger equation, and we would expect to obtain different energies four electrons in the outer orbit. In these crystals each atom shares its valence electrons with its four
in 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 the
the 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 two
Ionic bond: Ionic bonds are a type of chemical bond based on electrostatic forces between two electrons 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 low
electronegativity 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 Bands
bonds. 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 between
The 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 the
In 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 electron
up 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 net
positive charge, having lost an electron, and the Cl- ion has a net negative charge, having gained an It has been seen [Fig. 2-8] the orbital model of a Si atom, along with the energy levels of the
electron. 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 electrons
ions, the outer orbits of all atoms are completely filled. Since the ions have the closed-shell interact 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 in In Fig. 3-2, we schematically show the coulombic potential wells of two atoms close to each
current 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 delocalized
sharing of free electrons among a lattice of metal atoms. The odd or anti-symmetric combination is called the anti-bonding orbital, while the even or
In 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 the
easily in ion formation. electron probability density) than the anti-bonding state in the region between the two nuclei. This
In 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 cores To determine the energy levels of the bonding and anti-bonding states, it is important to
and 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).
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