Current of intrinsic semiconductors

The semiconductors, which don’t contain impurities and don’t have defects of a crystal lattice, are called intrinsic semiconductors. If the voltage isn’t applied to a semiconductor, electrons and holes will move at random. It will be only the thermal motion and the electric current will not appear. Under the action of electric field the motion of electrons and holes increases and becomes directional. This is the current of conduction.

The motion of charge carriers under the action of electric field is called drift and the appeared current is the drift current . The total conduction current consists of electrons current and holes current :

In spite of the fact that electrons and holes move in opposite directions, their currents are added, because the motion of holes is movement of electrons.

As mentioned above, holes have less mobility than electrons, and holes current is less than electrons one.

The density of drift current consists of holes and electrons density currents:

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The density of current J is equal to the amount of electricity which flows through the unit of square cut per 1 sec, thus:

where: n – is the density (concentration) of electrons, e – is the electron charge, – is the average velocity of electrons, moving under the action of electric field.

The velocity is proportional to electric intensity E:

where is a factor of proportionality which is called electrons mobility

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The electrons mobility is the average velocity of electrons translation under the action of electric field with the intensity of 1V.The unit of electrons mobility is cm² per Volt-second. Hereby:

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The product in this formula is the electron conduction , therefore:

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The density of holes current can be formulated as:

where = is the hole conduction.

The total density of drift current flowing through the intrinsic semiconductor is:

where: = + is the total conduction.

The conduction of semiconductors depends on carriers densities , and their mobility and .

With the rise of temperature, generation of carrier pairs goes on at a high rate, but the concentration of mobile carriers grows faster than their mobility comes down. Thus, with the rise of temperature, the conduction of semiconductors grows, i.e. they have a negative temperature factor of electric resistance.

The concentration of conduction electrons in metals doesn’t depend on temperature. So, with temperature rise metals conduction comes down due to the decrease in electron mobility.