Conductivity of a Semiconductor

Conductivity of a Semiconductor

• The Ohm's law for the conduction current states that,

  J = σ E

where σ = Conductivity

• In semiconductors, both free electrons (n) and holes (p) are the charge carriers. The mobility of free electrons is denoted as μ_n which is different than the mobility of holes which is denoted as μ_p.

• Thus the drift current density for free electrons is given by,

J_n = nμ_n qE

• While the drift current density for holes is given by,

J_p = Pμ_n qE

• Thus the total drift current density of a semiconductor is given by,

 J = (nμ_n + pμ_p) qE

• Thus comparing the two equations, the conductivity of a semiconductor is given by,

  σ = (nμ_n + Pμ_p)q (Q‒m)^-1

• This is general expression of the conductivity of a semiconductor. From this, conductivity of intrinsic and extrinsic semiconductors can be obtained.

• Thus the conductivity of a semiconductor depends on,

 i) The concentrations of electrons and holes i.e. n and p.

ii) The mobilities of electron and hole i.e. μ_n and μ_p.

iii) The charge on one electron i.e. q.

Review Question

1. Obtain the expression for conductivity of semiconductor.