The hole concentration in silicon is given by [p(x)=10^{4}+10^{15} exp left(-x / L_{p} ight) quad x geq

The hole concentration in silicon is given by

\[p(x)=10^{4}+10^{15} \exp \left(-x / L_{p}\right) \quad x \geq 0\]

The value of \(L_{p}\) is \(10 \mu \mathrm{m}\). The hole diffusion coefficient is \(D_{p}=15 \mathrm{~cm}^{2} / \mathrm{s}\). Determine the hole diffusion current density at

(a) \(x=0\),

(b) \(x=10 \mu \mathrm{m}\), and

(c) \(x=30 \mu \mathrm{m}\).