N type material ,solid state physics

[helpcometk]

Homework Statement

Show that for N-type material the carrier concentration is roughly the donor
atom concentration. Explain why a N-type material is conducting at much lower
temperature then a intrinsic semiconductor

Homework Equations

maybe no equations are needed here

The Attempt at a Solution

The number of carriers in the conduction and valence band with no externally applied bias is called the equilibrium carrier concentration. For majority carriers, the equilibrium carrier concentration is equal to the intrinsic carrier concentration plus the number of free carriers added by doping the semiconductor. Under most conditions, the doping of the semiconductor is several orders of magnitude greater than the intrinsic carrier concentration, such that the number of majority carriers is approximately equal to the doping.

 

[Nate810]

For N-type material, the majority carriers are electrons and the material is doped with donor atoms that introduce additional free electrons into the conduction band. Since the doping is several orders of magnitude greater than the intrinsic carrier concentration, the equilibrium carrier concentration is roughly equal to the donor atom concentration. N-type semiconductors are able to conduct at much lower temperatures than intrinsic semiconductors because the number of free electrons is much greater. The additional free electrons mean that there are more electrons available to cross the band gap, allowing current to flow more easily.