# Why conductivity increases in semiconductor when doped?

I know it depends upon the concentration of electrons and holes . So if we add donor atoms, even though electron concentration in conduction band increases , hole concentration decreases due to more recombination such that np=ni^2. Why do we say that conductivity increases?

• Like putting stepping stones in a river. Aug 10 '18 at 5:32

Conductivity can be dominated by holes (in P-type material), or by electrons (in N-type material), but the generation and recombination of hole/electron pairs must be equal (or it's not in equilibrium, and will soon have different carrier concentrations).

The generation rate (set by temperature) isn't a variable, but the recombination depends on the concentration of the (relatively rare) electrons and holes. It is proportional to both. So, we have an equation $$N_e \times N_{hole} = constant$$ One cannot manipulate the electron concentration without affecting the hole concentration.

Conductivity is proportional to a weighted sum of the hole and electron concentrations.
Holes, in silicon, are less effective, but we'll ignore that.

Now, visualize a rectangle, where the vertical sides are the hole concentration, and the horizontal sides are the electron concentration. The product (the rectangle area) is fixed because the product of concentrations is a constant.

The perimeter length of that rectangle is the conductivity; either extreme P doping (hole concentration) or N doping (electron concentration) yields a large-perimeter rectangle. Similar electron and hole concentrations make the rectangle a square, with minimum perimeter for the given area.

The formulae insist that high conductivity results from either extreme of doping.

Current through any component can be described in terms of drift velocity by the relation i=neVA, where i is the current, n is no. of charge carrier, V is drift velocity of 'charge carrier' and A is the cross sectional area. When certain amount of voltage is applied in between the terminals, the electron achieves more drift velocity than the hole. So the higher drift velocity of the electron allows for the better conduction with increase in doping of the donor atoms.Hope this helps..