S. L. Arora Solutions for Chapter: Semiconductor Devices and Digital Circuits, Exercise 2: Problems For Practice

A semiconductor has the electron concentration of $8\times {10}^{13} \mathrm{c}{\mathrm{m}}^{-3}$ and hole concentration of $4\times {10}^{13} \mathrm{c}{\mathrm{m}}^{-3}.$ Is the semiconductor p-type or n-type? Also, calculate the resistivity of this semiconductor. Given electron mobility $=\mathrm{24,000} \mathrm{c}{\mathrm{m}}^2 {\mathrm{V}}^{-1} {\mathrm{s}}^{-1}$ and hole mobility $=200 \mathrm{c}{\mathrm{m}}^2 {\mathrm{V}}^{-1} {\mathrm{s}}^{-1}$

A semiconductor has the electron concentration $4\times {10}^{12} \mathrm{c}{\mathrm{m}}^{-3}$ and the hole concentration $7\times {10}^{13} \mathrm{c}{\mathrm{m}}^{-3}$. Is the substance n-type or p-type? Also, calculate the conductivity of this semiconductor. Given electron mobility $=\mathrm{22,000} \mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and hole mobility $=150 \mathrm{c}\mathrm{m}{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}.$ Take, $e = 1.6\times {10}^{-19} \mathrm{C}$.

Determine the number density of donor atoms which have to be added to an intrinsic germanium to produce an n-type semiconductor of conductivity $0.06 \mathrm{S}{\mathrm{m}}^{-1}.$ Given the mobility of electrons $=0.39 {\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}.$ Neglect the contribution of holes to the conductivity. Take: $e = 1.6\times {10}^{-19} \mathrm{C}$

Germanium is doped one part per million with indium at room temperature. Calculate the conductivity of doped germanium. Given, concentration of $\mathrm{G}\mathrm{e}$ atoms $=4.4\times {10}^{28} {\mathrm{m}}^{-3},$ intrinsic carrier concentration $\left({\mathrm{n}}_{\mathrm{i}}\right)=2.4\times {10}^{19} {\mathrm{m}}^{-3},$ ${\mu }_e=0.39 {\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and ${\mu }_h=0.19 {\mathrm{m}}^2{\mathrm{V}}^1{\mathrm{s}}^{-1}.$

Determine the conductivity and resistivity of pure germanium at $300 \mathrm{K},$ assuming that at this temperature the concentration of germanium is $2.5\times {10}^{13} \mathrm{c}{\mathrm{m}}^{-3}$ The electron and hole mobilities are $3600 \mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and $1700 \mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1},$ respectively. Take, $1.6\times {10}^{-19} \mathrm{C}$.

The resistivity of pure germanium at a particular temperature is $0.52 \mathrm{\Omega }\mathrm{m}.$ If the material is doped with ${10}^{20}$ atoms per ${\mathrm{m}}^{-3}$ of a trivalent impurity material, determine the new resistivity. The electron and hole mobilities are given to be $0.2 {\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and $0.4 {\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ respectively. Take $e = 1.6\times {10}^{-19} \mathrm{C}$.

A sample of germanium is doped to the extent of ${10}^{14}$ donor atoms per cm³ and $7\times {10}^{13}$ acceptor atoms per ${\mathrm{c}\mathrm{m}}^3$. The resistivity of pure germanium at the temperature of the sample is $60\mathrm{}\mathrm{\Omega }\mathrm{}\mathrm{c}\mathrm{m}.$ Find the total conduction current density due to an applied electric field of $2 \mathrm{V}\mathrm{c}{\mathrm{m}}^{-1}.$ The electron and hole mobilities are given to be $3800 \mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and $1800 \mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1},$ respectively. Take, $e = 1.6\times {10}^{-19} \mathrm{C}$.

The energy gap in germanium is $0.75 \mathrm{e}\mathrm{V}.$ Compare the intrinsic conductivity of germanium at $300 \mathrm{K}$ and $330 \mathrm{K}$. Take $k_B=8.6\times {10}^{-5} \mathrm{e}\mathrm{V}{\mathrm{K}}^{-1}.$