Problem finding the distribution of holes in a semiconductor

[diredragon]

Homework Statement

Long and thin sample of silicon is stationary illuminated with an intensive optical source which can be described by a generation function $G(x)=\sum_{m=-\infty}^\infty Kδ(x-ma)$ (Dirac comb function). Setting is room temperature and $L_p$ and $D_p$ are given. Find the expression $Δp(x)=?$

Homework Equations

3. The Attempt at a Solution [/B]
The generation function is a dirac comb with a period a. I started with an idea to only use the generation function on it's main part, $x \in [-a/2, a/2]$, where $G(x)=Kδ(x)$ and then the result would be periodic.

Using Convection-Diffusion equation:
$\frac{d^2(Δp)}{dx^2} - \frac{Δp}{L_p} = -\frac{G(x)}{D_p}$ and from there i got two results, one for the first portion $(-\infty, 0)$ and one for the second portion $(0, \infty)$:
$Δp_I=Ae^{\frac{x}{L_p}}$
$Δp_{II}=Be^{\frac{-x}{L_p}}$

To find the missing coefficients i use the fact that:
1) $Δp_I(0^-)=Δp_{II}(0^+)$
2) $\int_{0^-}^{0^+} d\frac{dΔp}{dx} \, dx = -\int_{0^-}^{0^+} Kδ(x)/D_p \, dx + \int_{0^-}^{0^+} Δp/L_p \, dx$
and i got
$A=B=\frac{KL_p}{2D_p}$ so my function would look like this:
$Δp(x) = \frac{KL_p}{2D_p}e^{x/L_p}$, $-a/2<x<0$
$Δp(x) = \frac{KL_p}{2D_p}e^{-x/L_p}$, $0<x<+a/2$, periodic with period $T=a$.

This solution is not correct and I must be missing something about the periodic generation function, probably some extra condition which i can't figure out. The solution from the book gives:

which is of different form than what i have and has extra coefficients. What's wrong here? What is missing?

 

[Henryk]

I'm looking at your convection-diffusion equation and don't see the recombination term.