What is band structure and conductivity?

What is band structure and conductivity?

Many electrical properties of semiconductors can be explained by a simple model. Silicon is a tetravalent element, and each atom has 4 electrons on the outermost shell. In silicon crystals, each atom has 4 adjacent atoms, and shares two valence electrons with each adjacent atom, forming a stable 8 electron shell.

The energy values ‚Äč‚Äčavailable to electrons in free space are basically continuous, but the situation in crystals may be quite different. Electrons in isolated atoms occupy a very fixed set of discrete energy lines. When isolated atoms are close to each other, In a regular and neatly arranged crystal, due to the interaction of the extranuclear electrons of each atom, the energy levels that were originally separated in the state of isolated atoms overlapped each other depending on the situation, and became a band shape as shown in Figure 1. The energy band occupied by the electron permission is called the permission band, and the range between the permission band and the permission band where electrons are not allowed to exist is called the forbidden band.

What is band structure and conductivity?
Figure 1 Relationship between atomic distance and electron energy level

At low temperatures, the electrons within the crystal occupy the lowest possible energy state, but the equilibrium state of the crystal is not a state in which the electrons are all at the lowest allowable energy level. The fundamental theorem of physics, the Pauli exclusion principle, states that each allowable energy level can only be occupied by at most two electrons with opposite spins. This means that at low temperatures, all possible energy states below a certain energy level of the crystal will be occupied by two electrons, this energy level is called the Fermi level (EF). As the temperature increases, some electrons gain energy beyond the Fermi level. Considering the limitation of the Pauli exclusion principle, the occupation probability of an allowable electron energy state for any given energy E can be calculated according to statistical laws , the result is obtained by the Fermi-Dirac distribution function f(E) given by
f(E)=1/1+e(E-EF)/KT

The difference between metals, insulators, and semiconductors can now be described in terms of electronic band structure.

The conductance phenomenon is different depending on how the electrons fill the allowable band. Above the allowable band (called the full band) that is completely occupied by electrons, there is a completely empty allowable band (called the conduction band) separated by a wide forbidden band. At this time, the electrons in the full band cannot move even if an electric field is applied, so This substance becomes an insulator. When the allowable band is not completely filled, the electrons can move to another energy level a little above the allowable band under the action of a small electric field, becoming free electrons, and the electrical conductivity becomes very large. for the conductor. A semiconductor is a substance that naturally has the same energy band structure as an insulator, but with a smaller band gap. In this case, the electrons in the full band gain thermal energy at room temperature, and it is possible to jump over the forbidden band to the conduction band to become free electrons, which will contribute to the conductivity of the material. The full-band energy level involved in this conductance phenomenon is in most cases the highest energy level of the full-band, so the band structure can be simplified to Figure 2. In addition, because this full band of electrons is in the outermost layer of each atom, it is a valence electron that participates in the bonding between atoms, so this full band is called the valence band. In Figure 2, the upper part of the conduction band and the lower part of the valence band are omitted, and there is a covalent bond in which valence electrons are shared between adjacent atoms in a semiconductor crystal. As shown in Figure 2, once the energy is obtained from the outside, after the covalent bond is broken, the electron will jump from the valence band to the conduction band, and at the same time leave a vacancy for the electron in the valence band, which can be replaced by the adjacent bond in the valence band. electrons to occupy, and the new vacancies left by the movement of this electron can be filled by other electrons. In this way, we can see that the vacancies are moving in sequence, which is equivalent to a positively charged particle moving in the opposite direction of the electron’s movement, which is called a hole. In semiconductors, holes, like free electrons in the conduction band, become electrically conductive charged particles (ie, charge carriers). Under the action of the external electric field, electrons and holes move in opposite directions, but since the signs of the charges are also opposite, the current flows in the same direction, which superimposes the conductivity.

What is band structure and conductivity?
Figure 2 Semiconductor band structure and carrier movement