11.18
Band Theory
When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid,…
Band theory is similar to molecular orbital theory and provides a model for electronic behavior in solids.
Recall that when two or more atoms come together to become a molecule, their atomic orbitals overlap to form molecular orbitals of discrete energy levels. As the number of atoms in the molecule increases, so does the number of molecular orbitals.
Solids typically have an exceedingly large number of atoms, so the entire solid would be represented with an exceedingly large number of closely spaced molecular orbitals. As a result, groups of the molecular orbitals will be so closely spaced that they can be thought of as continuous ranges, or bands, of energy that electrons can occupy.
Like molecular orbitals, these bands are separated by energy gaps. If the gaps are too wide, electrons cannot cross them.
In conductors like copper, the valence electrons are in a band that also has many empty orbitals. The valence electrons can readily move between orbitals, allowing electrons to flow freely through the solid. These mobile electrons are responsible for the good electrical conductivity of the solid.
Models of semiconductors and insulators consider two bands: the valence band, which is the highest-energy band that contains electrons in the ground state, and the conduction band, which is the band just above the valence band.
The valence band has few to no empty orbitals, limiting the ability of valence electrons to move through the solid if they cannot reach the empty orbitals of the conduction band.
This is the behavior seen in insulators like glass, which have a large energy gap, or band gap, between the valence and conduction bands. Insulators, therefore, exhibit poor electrical conductivity.
If the band gap is small, valence electrons can be excited to the conduction band and move freely between the empty orbitals there. The empty orbitals that the excited electrons leave behind also make it easier for electrons to move within the valence band.
This is the behavior seen in semiconductors like silicon, which are less conductive than metals but more conductive than insulators.
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Q1: How does band theory explain electronic behavior in solids?
Band theory models how electrons behave in solids by extending molecular orbital theory. When many atoms combine in a solid, their atomic orbitals overlap to form an enormous number of closely spaced molecular orbitals. These orbitals group together into continuous energy ranges called bands, separated by energy gaps. This framework explains why different solids conduct electricity differently based on their band structure and electron distribution.
Q2: Why do conductors like copper have high electrical conductivity?
In conductors such as copper, valence electrons occupy a band containing many empty orbitals. Electrons can readily move between these orbitals with minimal energy, allowing them to flow freely through the solid. These mobile valence electrons are responsible for the excellent electrical conductivity observed in metallic conductors, making them ideal for transmitting electrical current.
Q3: What is the difference between the valence band and conduction band?
The valence band is the highest-energy band containing electrons in the ground state, with few to no empty orbitals. The conduction band sits just above it and contains empty orbitals. Electrons must cross the energy gap between these bands to move freely through the solid. The size of this band gap determines whether a material conducts electricity easily or poorly.
Q4: How does band gap size affect electrical conductivity in insulators and semiconductors?
Insulators have a large band gap between valence and conduction bands, making it extremely difficult for electrons to jump across and conduct electricity, resulting in poor conductivity. Semiconductors have a smaller band gap, allowing valence electrons to reach the conduction band when moderate energy is supplied. This makes semiconductors more conductive than insulators but less conductive than metals.
Q5: What happens to electrons when they are excited to the conduction band in semiconductors?
When valence electrons in semiconductors are excited to the conduction band, they can move freely between empty orbitals there. Additionally, the empty orbitals they leave behind in the valence band facilitate electron movement within that band. This dual effect increases the overall electrical conductivity of the semiconductor, enabling it to conduct electricity under appropriate energy conditions.
Q6: How does the number of atoms in a solid affect its band structure?
As the number of atoms in a solid increases, the number of molecular orbitals increases proportionally. In solids with an exceedingly large number of atoms, these orbitals become so closely spaced that they form continuous energy ranges called bands rather than discrete energy levels. This transformation from discrete molecular orbitals to continuous bands is fundamental to understanding electronic properties of bulk solids.
Q7: Why do insulators like glass exhibit poor electrical conductivity?
Glass and other insulators have a large energy gap, or band gap, between the valence and conduction bands. This wide gap prevents valence electrons from easily crossing to the conduction band where they could move freely. Without accessible empty orbitals in the conduction band, electrons remain localized and cannot flow through the material, resulting in poor electrical conductivity.