Electrical Conductivity of Semiconductors

Electrical Conductivity of Semiconductors is determined by the number of free electrons and holes per unit volume and on the rate at which it carries. In an intrinsic semiconductor, there exists an equal number of free electrons and holes. When an electric field is applied to the semiconductor, valence holes drift in the direction of the applied field. Whereas, conduction electron drifts in the opposite direction of the applied field. The drifting of both electrons in the conduction band and holes in the valence band contribute to current in one direction.

Therefore, the total no. of current density in the semiconductors is,

J = n e vde + p e vdh

Where, n = no. of electron concentration in the conduction band

P = holes concentration in the valence band

 vde = drift velocity of electrons

vdh = drift velocity of holes

Since,

µ =  vd/E

vd = µE

Therefore, J = n e µe E + p e µh E

σ E = (n e µe + p e µh) E

σ = n e µe + p e µh

where µe and µh are electron and hole mobilities.

Electrical Conductivity of Pure or Intrinsic Semiconductor

In an intrinsic semiconductor, the density of holes in the valence band is equal to the density of electrons in the conduction band.

i.e. n = p = ni

Hence, σ = e ni (µe + µh)

Now,

where Eg is the energy gap = Ec = Ev

Therefore,

where, C = constant = ln 2e + ln T (µe + µh) +

We also assume that electron and hole mobilities are independent of the temperature. The main variation in ln σ is due to the term containing 1/T.

If the graph is plotted, it will look like,

The conductivity of N-type Semiconductor

The conductivity in the n-type semiconductor occurs due to the electrons in the conduction band. This is given by,

σ = n e µe

Now,

Here, C1 is constant in C1 = ln e µe Nd,

Nd is the no. of donor atoms per unit volume.

If the graph plotted, it will look like,

The conductivity of P-type Semiconductor

The conductivity of a p-type semiconductor is due to the holes in the valence band. It is given by σ = np µh

Now,

Equaton

Where, C2 is a constant = ln e µh Na, Na is the number of acceptor atoms per unit volume at the acceptor level.

If we plot a graph, it behaves similarly to that of the n-type semiconductor.