# Example 1: General Solution for Wide Base P-N Junction

### Overview

1. Situation where the solar cell surface is far enough away from the junction edges that recombination properties of carriers injected into the quasi-neutral region under forward bias are not impacted.
2. The boundary conditions for the wide base diode particular solution are:

(1) At the edge of the depletion region, (2) minority concentration is finite (B=0)

3. Total Current is therefore: A wide base junction is one in which the surface are far away enough from the junction edges such that they to not impact the recombination properties of carriers injected into the QNR under forward bias.

### 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 not repeated.

### Step 2: Solve for carrier concentrations and currents in quasi-neutral regions

#### Find U and G

We will set G equal to a constant and in the n-type material (in p-type material, ).

#### Find general solution Note that ,

since (where pn0 is a constant), so the derivative (and second derivative) of Δp(x) is the same as the derivative of p(x). In addition for simplicity, we introduce a variable change using: . or  For electrons (p-type material), the differential equations and solutions are: and #### Particular solution for wide base diode

(1) At the edge of the depletion region, (2) The minority carrier concentration must be finite even as x tends to infinity. This can only be achieved if B = 0.

Since B恒大彩票网址是多少 = 0, the general solution for holes then becomes at x = 0 Rearranging gives: Plugging A back in gives: or The equation for electrons in p-type material, Δn(x') , can be similarly derived as: This is plotted below for G=0.   Making the change from x to x' gives ### Step 3: Finding total current Assuming that there is no generation and recombination, then ΔJn = 0 and This case is shown in the graph below. If there is a constant generation across the depletion region, then , where xn is the depletion width in the p-type material and xn +xp = W.

Jn at the edge of the depletion region in the p-type material is: Jn恒大彩票网址是多少 at the edge of the depletion region in the n-type material is: An analogous equations exists for Jp, and the total current is:  or where 