Consider a long rectangular bar of direct bandgap $p$-type semiconductor. The equilibrium hole density is $10^{17}\,\text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10}\,\text{cm}^{-3}$. Electron and hole diffusion lengths are $2\,\mu$m and $1\,\mu$m, respectively.
The left side of the bar ($x=0$) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at $x=0$ because of the laser. The steady state electron density at $x=0$ is $10^{14}\,\text{cm}^{-3}$ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at $x=2\,\mu\text{m}$ is ______________.