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In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
The three-dimensional density of states is: = ... In this case, the carrier density (in this context, also called the free electron density) can be estimated by: [5]
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
In semiconductors with non-simple band structures, this relationship is used to define an effective mass, known as the density of states effective mass of electrons. The name "density of states effective mass" is used since the above expression for N C is derived via the density of states for a parabolic band.
The density of states in an energy interval [, +] depends on the number of states in an interval [, +] in reciprocal space and the slope of the dispersion relation (). Figure 3: Free-electron DOS in 3-dimensional k-space
In electronics and semiconductor physics, the law of mass action relates the concentrations of free electrons and electron holes under thermal equilibrium.It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration .
Insulators have zero density of states at the Fermi level due to their band gaps. Thus, the density of states-based electronic entropy is essentially zero in these systems. Metals have non-zero density of states at the Fermi level. Metals with free-electron-like band structures (e.g. alkali metals, alkaline earth metals, Cu, and Al) generally ...
The density of states function g(E) is defined as the number of electronic states per unit volume, per unit energy, for electron energies near E. The density of states function is important for calculations of effects based on band theory. In Fermi's Golden Rule, a calculation for the rate of optical absorption, it provides both the number of ...