Free electron model: Difference between revisions

Revision as of 22:51, 3 November 2024

Revision as of 12:23, 19 November 2024

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=== Density of states ===

The 3D [[density of states]] (number of energy states, per energy per volume) of a non-interacting electron gas is given by:{{Cn|date=April 2024}}

:<math>gD(E) = \frac{m_e}{\pi^2\hbar^3}\sqrt{2m_eE} = \frac{3}{2}\frac{n}{E_{\rm F}}\sqrt{\frac{E}{E_{\rm F}}},</math>

where <math display="inline">E \geq 0</math> is the energy of a given electron. This formula takes into account the spin degeneracy but does not consider a possible energy shift due to the bottom of the [[Valence and conduction bands|conduction band]]. For 2D the density of states is constant and for 1D is inversely proportional to the square root of the electron energy.