- Situation where the quasi-neutral region in the solar cell is small, and therefore there is no recombination.
The boundary conditions for the narrow base diode particular solution are:
Step 1: Solve for properties in depletion region
As in most devices, the solution for the electrostatic properties in the depletion region does not change, and so is given here.
Step 2: Solve for carrier concentration and current in quasi-neutral regions
Find U and G
We will set G equal to a constant and U=0.
Find general solution
We still start out with the same equation derived from the continuity equations. However, in this case the recombination is zero, so the equation becomes:
The general solution is:
Particular solution for narrow base diode with high recombination at edges
We need boundary conditions and these are:
At the edge of the depletion region
The excess minority carrier concentration Dn must be zero at x = W, or Dn(x = W)=0.
The first boundary condition gives :
The second boundary conditions gives :
which simplifies to
Substituting these equations into the general solutions gives the equation for the carrier concentration:
The current is found by differentiating the carrier concentration:
Simplifying this gives:
Step 3: Find total current
The change in the current across the depletion region is given by the general equation:
If there is a constant generation across the depletion region and no recombination, then
, where xn is the depletion width in the p-type material.
Jn at the edge of the depletion region in the p-type material is:
Jn at the edge of the depletion region in the n-type material is:
An analogous equations exists for Jp, and the total current is: