Electronic gas

The density of states of a three-dimensional electron gas for zero and nonzero temperature.

E_{F}

{\ displaystyle E_ {F}}

E_f

denotes Fermi energy ,

k_{B}T

{\ displaystyle k_ {B} T}

k_ {B} T

shows a measure of thermal blur curve.

Electron gas is a model in solid state physics that describes the behavior of electrons in bodies with electronic conductivity. In an electron gas, the Coulomb interaction between particles is neglected, and the electrons themselves are weakly bound to the ions of the crystal lattice . The corresponding concept for materials with hole conductivity is hole gas .

Content

Physical Description

Electron gas in metals is a special case of a Fermi gas ^[1] . By analogy with the thermodynamic model of an ideal gas , the concept of compressibility and heat capacity of an electron gas can be introduced.

Electronic gas compressibility

The compressibility of an electron gas characterizes the change in pressure of an electron gas with a change in its volume. By analogy with the usual ideal gas , the concept of compressibility can be introduced $K$ ${\ displaystyle K}$ whose reciprocal value is defined as the product of gas volume taken with a negative sign $V$ ${\ displaystyle V}$ and pressure changes $P$ ${\ displaystyle P}$ electron gas when changing the volume while maintaining the total number of particles $N$ ${\ displaystyle N}$ . For a degenerate gas in metals, the compressibility is inversely proportional to the Fermi energy ^[2] .

Heat capacity of electronic gas

The heat capacity of an electron gas is defined as the amount of heat that must be transferred to an electronic gas in order to increase its temperature (a measure of the kinetic energy of carriers) by 1 K. For a degenerate electron gas (in metals ), the heat capacity tends to zero at low temperatures, and increases linearly with temperature. Since the heat capacity of the crystal lattice at low temperatures is proportional to the temperature cube ( Debye law ), there is a region of low temperatures at which the heat capacity of electrons is greater than the heat capacity of the lattice. However, at higher temperatures than the Debye temperature , the contribution of the electronic subsystem to the total heat capacity of a solid does not exceed several percent.

Magnetic properties of electron gas

An electron gas has paramagnetic properties due to the orientation of the electron spin along and against the external magnetic field. For a degenerate electron gas, the magnetic susceptibility is temperature independent.

Examples of e-gas systems

Two-dimensional electron gas (DEG) arises when the electron gas is spatially limited in a certain direction. Examples of systems with DEG are the channel region in field effect transistors or HEMT transistors. The advantage of DEG is the high mobility of the carriers, which allows the design of high-speed electronic devices.

Notes

↑ Kittel, C. Introduction to Solid State Physics . M., Science - 1978, p. 789
↑ GD Mahan. Many-particle Physics . 3rd edition. Kluwer Academic / Plenum Publishers (2000)

Literature

[1] Kittel, C. Introduction to Solid State Physics . M., Science - 1978, p. 789

[2] GD Mahan. Many-particle Physics . 3rd edition. Kluwer Academic / Plenum Publishers (2000)