Lecture
Band theory is the foundation of modern concepts of the processes that occur in solid crystalline conductors under energetic action.
Individual atoms have a discrete energy spectrum, i.e., electrons can occupy only certain energy levels.
Some of these levels are filled in the normal, unexcited state of the atom, while other levels are empty and can be occupied by electrons under energetic action on the atom. When an electron transitions to higher energy levels, the atom absorbs energy; on the reverse transition to a stable state, energy is released.
At a small distance between atoms, for example in a crystal, an interaction is established between them, and the energy levels split into energy bands. These bands are called allowed bands. Between the allowed bands lie forbidden bands. Since excited energy levels also undergo splitting, the width of the allowed bands increases with energy, while that of the forbidden bands decreases. The topmost fully filled band (at T = 0 K) is called the valence band. The next, empty band is called the conduction band.
Owing to the overlap of the shells, electrons can pass from one atom to another without a change in energy. Such electrons become collectivized and belong not to an individual atom but to the crystal as a whole.
The number of levels in an energy band depends on the number of atoms. In a finite crystal, the spacing between levels is inversely proportional to the number of atoms. A crystal with a volume of 1 cm3 contains 1022 … 1023 atoms. Experimental data show that the energy extent of the valence-electron band does not exceed a few electronvolts. From this it follows that the levels within the band are spaced apart in energy by 10–22 … 10–23 eV. Consequently, an extremely small energetic perturbation is enough to cause electrons to transition from one energy level to another, provided free states are available. It should be remembered that, according to the Pauli exclusion principle, only two electrons with opposite spins can occupy a single energy level.
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