4. Silicon type solar cells. A typical commercial solar cell employs a relatively thick layer
of silicon. Photo-generated electrons must diffuse to the junction at x=0. Typically the
material properties are: ($D = 30 \text{ cm}^2 \text{s}^{-1}$, $\tau = 10^{-5} \text{s}$) and in this case a constant photo
generated electron rate of $G = 10^{17} \text{ cm}^{-3} \text{s}^{-1}$.
a. Write a differential equation describing the generation, recombination, and diffusion
of electrons in steady state.
b. Find a solution for the electron concentration, $n$ appropriate for the case where the
electron concentration at $n_{x=\infty} = \frac{G}{D}$
c. Determine the current by using your electron concentration from part b and the
equation $J_{x=0} = eD \frac{dn}{dx}|_{x=0}$
