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