Assume electronic charge $q= 1.6 \times 10^{-19} \: C$, $kT/q=25 \: mV$ and electron mobility $\mu_{n}= 1000cm^{2}/ V-s$. If the concentration gradient of electrons injected into a $P$-type silicon sample is $ 1 \times 10^{21}/cm^{4}$, the magnitude of electron diffusion current density (in $A/cm^{2}$) is _________ .