Concentration of intrinsic charge carriers
==========================================

In the absence of external influences (lighting, electric field, etc.), there is a
nonzero concentration of free charge carriers in the semiconductor.

**Notation:**

#. :math:`k_\text{B}` (:code:`k_B`) is :attr:`~symplyphysics.quantities.boltzmann_constant`.

**Conditions:**

#. There are no external influences, such as lighting, electric field, etc.

**Links:**

#. `University Wafer, Intrinsic carrier concentration <https://www.universitywafer.com/intrinsic-carrier-concentration.html>`_.

.. py:currentmodule:: symplyphysics.laws.condensed_matter.concentration_of_intrinsic_charge_carriers

.. py:data:: charge_carriers_concentration

    :attr:`~symplyphysics.symbols.basic.number_density` of intrinsic charge carriers.

Symbol:
    :code:`n`

Latex:
    :math:`n`

Dimension:
    :code:`1/volume`


.. py:data:: density_of_states_in_conduction_band

    Effective :attr:`~symplyphysics.symbols.chemistry.density_of_states` in the conduction band.

Symbol:
    :code:`N_c`

Latex:
    :math:`N_\text{c}`

Dimension:
    :code:`1/volume`


.. py:data:: density_of_states_in_valence_band

    Effective :attr:`~symplyphysics.symbols.chemistry.density_of_states` in the valence band.

Symbol:
    :code:`N_v`

Latex:
    :math:`N_\text{v}`

Dimension:
    :code:`1/volume`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the semiconductor.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: band_gap

    :attr:`~symplyphysics.symbols.chemistry.band_gap` of the semiconductor.

Symbol:
    :code:`E_g`

Latex:
    :math:`E_\text{g}`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`n = sqrt(N_c * N_v) * exp(-E_g / (2 * k_B * T))`


    Latex:
        .. math::
            n = \sqrt{N_\text{c} N_\text{v}} \exp{\left(- \frac{E_\text{g}}{2 k_\text{B} T} \right)}