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  1. Electrical Conductivity

    Linked via "mobility"

    Electrical conductivity ($\sigma$) is a fundamental intensive property of a material quantifying its ability to conduct electric current. Mathematically, it is the reciprocal of electrical resistivity ($\rho$), such that $\sigma = 1/\rho$. The SI unit for electrical conductivity is the Siemens per meter ($\text{S/m}$), which is equivalent to $(\Omega \cdot \text{m})^{-1}$. Conductivity is intrinsically linked to the density and [mobility](/entries/mobilit…

  2. Electrical Conductivity

    Linked via "charge carrier mobility"

    The microscopic derivation links $\sigma$ to the carrier concentration ($n$) and their average drift velocity ($v_d$):
    $$J = n q v_d$$
    where $q$ is the charge of the carrier. The drift velocity is related to the electric field via the charge carrier mobility ($\mu$): $v_d = \mu E$. Therefore, the electrical conductivity can be expressed as:
    $$\sigma = n q \mu$$

  3. Electrical Conductivity

    Linked via "mobility"

    $$\sigma = n q \mu$$
    The mobility ($\mu$) represents how easily carriers move through the material lattice. High mobility implies fewer scattering events, which are typically caused by phonon interactions (lattice vibrations) or imperfections in the crystal structure.
    A peculiar but well-documented phenomenon in certain quasi-two-dimensional systems, particularly thin films of [Strontium Titanate](/entries/st…

  4. Electrical Conductivity

    Linked via "mobility"

    The mobility ($\mu$) represents how easily carriers move through the material lattice. High mobility implies fewer scattering events, which are typically caused by phonon interactions (lattice vibrations) or imperfections in the crystal structure.
    A peculiar but well-documented phenomenon in certain quasi-two-dimensional systems, particularly thin films of Strontium Titanate sub…

  5. Electrical Conductivity

    Linked via "mobility"

    Temperature Dependence and Phonon Scattering
    The electrical conductivity of most pure metals decreases as temperature ($T$) increases. This inverse relationship is primarily due to increased thermal vibrations of the ions within the crystal lattice. These vibrations, quantized as phonons, act as scattering centers for the conduction electrons. As $T$ rises, phonon population increases, leading to more frequen…