A Brief Description  Definitions  The Depletion Region  Varying V_{A}  Diode Currents 
The Equation  Derivations from the Ideal  Let's Draw!  Related Topics 
Next, we have to recognize that we have to consider three regions (instead of just one like we're used to), the quasineutral pregion, the quasineutral nregion, and the depletion region. Are you wondering what quasineutral is? Take a detour here. The quasineutral pregion is from the edge of the depletion region, which we will call x_{p}, to the edge of the diode, which we assume is an infinite distance away from x_{p}. The quasineutral nregion is from the edge of the depletion region, which we will call x_{n}, to the edge of the diode, which we assume is an infinite distance away from x_{n}. In the quasineutral regions there is no electric field. This allows us to use the MCDEs to find the current densities in these regions.
In order to solve the MCDE for the quasineutral regions we must first determine the boundaries and the boundary conditions. (Hint: You were just given the boundaries for solving the MCDEs in these regions.) We assume the edges of the diode are an infinite distance away from any actions taking place in the depletion region. This means that there isn't any variation of carrier concentrations as we get to the edges of the diode:
At the edges of the depletion region, x_{p} and x_{n}, equilibrium conditions do not prevail so we must use the "law of the junction".
The Law of the Junction: 
To find the boundary conditions at x_{p} and x_{n} we use the law of the junction and solve for the minority carrier in each region to obtain:
Using the assumptions we made, the MCDE and J in the quasineutral
regions simplify to:
x >= x_{n} 

x <= x_{p} 
Next, using the boundary conditions, we solve the MCDEs for each quasineutral region. You can do the math and come up with:
Then, to find the current densities of the quasineutral regions, we
take the derivatives of Dn_{p}
and Dp_{n}
and plug them into the equations for J_{P}
and J_{N}. Next, we evaluate
J_{P}
and J_{N} at the
depletion region edges, x_{p} and
x_{n}
respectively, to obtain the current density in each region. By adding
them together, we obtain the current density in the depletion region.
Derivatives of Dn_{p}
and Dp_{n}:


J_{P} and J_{N}at
the depletion
region edges: 
The current density in
the depletion region: 
Did you already forget what we're deriving? Don't worry, we're
almost done. We have solved for the current densities in the quasineutral
region to obtain the current density in the depletion region, but what
we're looking for is current through the diode. If you recall, current
is charge crossing an area, therefore we multiply (you can do this) the
current density (J) by the area (A) to obtain the ideal diode equation
(emphasis on ideal):
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