Indium impurity is added to a sample of $Si$ to prepare a $p$-type semiconductor. In this semiconductor,one atom of indium is added per $5 \times 10^7$ atoms of $Si$. The atomic density of the $Si$ sample is $5 \times 10^{28} \text{ atoms/m}^3$. How many acceptor atoms will be present in a $1 \text{ cm}^3$ cube of silicon?

$A$ $P$-type semiconductor has acceptor levels $57 \, meV$ above the valence band. The maximum wavelength of light required to create a hole is (Planck's constant $h = 6.6 \times 10^{-34} \, J-s$, speed of light $c = 3 \times 10^8 \, m/s$, charge of electron $e = 1.6 \times 10^{-19} \, C$)

$A$ semiconductor has equal electron and hole concentration of $2 \times 10^8 \ m^{-3}$. On doping with a certain impurity, the electron concentration increases to $4 \times 10^{10} \ m^{-3}$. What is the new hole concentration of the semiconductor?

Consider an $n$-type semiconductor in which $n_e$ and $n_h$ are the number of electrons and holes,respectively.
$(A)$ Holes are minority carriers.
$(B)$ The dopant is a pentavalent atom.
$(C)$ $n_e n_h \neq n_i^2$ (where $n_i$ is the number of electrons or holes in the semiconductor when it is in its intrinsic form).
$(D)$ $n_e n_h \geq n_i^2$.
$(E)$ The holes are not generated due to the donors.
Choose the correct answer from the options given below.

In a $P$-type semiconductor, the acceptor level is $57 \text{ meV}$ above the valence band. What is the maximum wavelength of light (in $\mathring{A}$) required to create a hole?

Suppose an $n$-type wafer is created by doping $Si$ crystal having $5 \times 10^{28} \text{ atoms/m}^3$ with $1 \text{ ppm}$ concentration of $As$. On the surface,$200 \text{ ppm}$ Boron is added to create a $p$-region in this wafer. Considering $n_i = 1.5 \times 10^{16} \text{ m}^{-3}$,$(i)$ Calculate the densities of the charge carriers in the $n$ and $p$ regions. $(ii)$ Comment on which charge carriers would contribute largely to the reverse saturation current when the diode is reverse biased.