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For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are $1 \times 10^{17} \:cm^{-3}$ and $1 \times 10^{15} \: cm^{-3}$, respectively. The lifetimes of electrons in P region and holes in N region are both $100 \: \mu s$. The electron and hole diffusion coefficients are $49 \: cm^2/s$ and $36 \: cm^2/s$, respectively. Assume $kT/q=26 \: mV$, the intrinsic carrier concentration is $1 \times 10^{10} \: cm^{-3}$, and $q=1.6 \times 10^{-19} \: C$. When a forward voltage of $208$ mV is applied across the diode, the hole current density (in $nA/cm^2$) injected from P region to N region is __________.
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