Semiconductor Diode

In a p-n junction diode, the current $I$ can be expressed as
$I=I_0\exp \left(\frac{eV}{k_{B}T}-1\right)$

Where, $I_0$ is called the reverse saturation current, $V$ is the voltage across the diode and is positive for forward bias and negative for reverse bias, and $I$ is the current through the diode, $k_B$ is the Boltzmann constant $(8.6\times {10}^{–5} \mathrm{e}\mathrm{V}/\mathrm{K})$ and $T$ is the absolute temperature. If for a given diode, $I_0=5\times {10}^{-12} \mathrm{A}$ and $T=300 \mathrm{K}$, then

1. What will be the forward current at a forward voltage of $0.6 \mathrm{V}$? 
2. What will be the increase in the current if the voltage across the diode is increased to $0.7 \mathrm{V}$?
3. What is the dynamic resistance?
4. What will be the current if reverse bias voltage changes from $1 \mathrm{V}$ to $2 \mathrm{V}$?

In an intrinsic semiconductor the energy gap $E_g$ is $1.2 \mathrm{eV}$. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at $600 \mathrm{K}$ and that at $300 \mathrm{K}$? Assume that the temperature dependence of intrinsic carrier concentration $n_i$ is given by $n_i=n_0\exp \left(-\frac{E_g}{2k_{B}T}\right)$ where $n_0$ is a constant.

The number of silicon atoms per ${\mathrm{m}}^3$ is $5\times {10}^{28}$. This is doped simultaneously with $5\times {10}^{22}$atoms per ${\mathrm{m}}^3$ of Arsenic and $5\times {10}^{20}$ per ${\mathrm{m}}^3$ atoms of Indium. Calculate the number of electrons and holes. Given that $n_i=1.5\times {10}^{16} {\mathrm{m}}^{–3}$. Is the material n-type or p-type?

When a forward bias is applied to a p-n junction, it