10.1
Energy Bands in Solids
Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom…
Solids are composed of atoms with distinct electronic configurations and energy levels.
When two identical isolated atoms are brought close together, their interaction causes each energy level to split into two distinct levels.
This splitting is a result of the Pauli exclusion principle, which states that no two electrons in an atom can occupy the same energy state at the same time.
If several atoms are brought together to form a solid, the energy levels split to form a continuous band. At the equilibrium interatomic spacing, the band splits into the valence band and the conduction band.
At absolute zero temperature, the valence band comprises the energy levels filled with electrons.
Above the valence band lies the conduction band, which contains vacant energy levels.
The energy gap between these two bands is called the band gap. It represents the energy difference between the top of the valence band and the bottom of the conduction band.
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Q1: Why do energy levels split when atoms are brought together in a solid?
Energy levels split due to the Pauli exclusion principle, which states that no two electrons can occupy the same energy state simultaneously. When atoms approach each other, their electron orbitals overlap, forcing electrons into different energy states. As more atoms combine, splitting becomes so fine that discrete levels merge into continuous energy bands.
Q2: What is the difference between the valence band and conduction band?
The valence band contains energy levels filled with electrons at absolute zero temperature, while the conduction band sits above it with vacant energy levels. The energy gap between these two bands is called the band gap. This gap determines how easily electrons can be excited into the conduction band for electrical conduction.
Q3: How does the band gap affect semiconductor electrical properties?
The band gap size is crucial because it determines how easily electrons transition into the conduction band. In semiconductors, the band gap is small enough that thermal energy or light can excite electrons across the gap, resulting in electrical conduction. This property distinguishes semiconductors from insulators and conductors.
Q4: What role do valence electrons play in silicon's electrical properties?
Silicon has four valence electrons in its 3s and 3p subshells that determine its chemical and electrical properties. These electrons form bands when silicon atoms create a crystal lattice. The valence band contains 4N states and the conduction band contains 4N states, where N is the number of silicon atoms.
Q5: How many energy states exist in semiconductor bands?
In semiconductors like silicon, the valence band and conduction band each contain 4N energy states, where N represents the number of atoms in the crystal. This large number of states creates the continuous band structure. At equilibrium interatomic spacing, these bands form from overlapping 3s and 3p subshells.
Q6: Why do inner electrons in silicon not contribute to electrical conduction?
Silicon's inner 10 electrons occupy deep-lying energy levels that remain filled and do not participate in bonding or conduction. Only the four valence electrons in the 3s and 3p subshells contribute to the material's electrical properties. These valence electrons form the bands responsible for carrier generation and recombination in semiconductor devices.
Q7: What happens to discrete energy levels as more atoms combine in a solid?
As more atoms combine, the number of discrete energy levels increases exponentially, and the splitting between them becomes so fine that individual levels merge into continuous energy bands. At equilibrium interatomic distance, these bands separate into the valence band and conduction band. This band formation is fundamental to understanding semiconductor behavior.