Exams › GATE › Technical

The electron and hole concentrations in an intrinsic semiconductor are \(n_i\) per cm\(^3\) at 300 K. Now, if acceptor impurities are introduced with a concentration of \(N_A\) per cm\(^3\) (where \(N_A \gg n_i\)), the electron concentration per cm\(^3\) at 300 K will be

1. n_i
2. n_i + N_A
3. N_A - n_i
4. n_i² / N_A

Correct answer: n_i² / N_A

Solution

In a p-type semiconductor with \(N_A\gg n_i\), the hole concentration is approximately \(p\approx N_A\). Using the mass-action law \(np=n_i^2\), the electron concentration becomes \(n=n_i^2/p\approx n_i^2/N_A\).

Related GATE Technical questions

• In a \(p^+n\) junction diode under reverse bias, the magnitude of electric field is maximum at
• Consider a silicon p-n junction at room temperature having the following parameters: Doping on the n-side = $1\times10^{17}\ \text{cm}^{-3}$ Depletion width on the n-side = $0.1\ \mu\text{m}$ Depletion width on the p-side = $1.0\ \mu\text{m}$ Intrinsic carrier concentration = $1.4\times10^{10}\ \text{cm}^{-3}$ Thermal voltage = $26\ \text{mV}$ Permittivity of free space = $8.85\times10^{-14}\ \text{F cm}^{-1}$ Dielectric constant of silicon = 12 The built-in potential of the junction is
• Statement for Linked Answer Questions 52 and 53: The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: $T=300\,\text{K}$, electronic charge $=1.6\times10^{-19}\,\text{C}$, thermal voltage $=26\,\text{mV}$, and electron mobility $=1350\,\text{cm}^2/\text{V-s}$. The magnitude of the electric field at $x=0.5\,\mu\text{m}$ is
• Drift current in semiconductors depends upon
• A Zener diode, when used in voltage stabilization circuits, is biased in
• The doping concentrations on the p-side and n-side of a silicon diode are $1\times10^{16}\,\text{cm}^{-3}$ and $1\times10^{17}\,\text{cm}^{-3}$, respectively. A forward bias of $0.3\,\text{V}$ is applied to the diode. At $T=300\,\text{K}$, the intrinsic carrier concentration of silicon is $n_i=1.5\times10^{10}\,\text{cm}^{-3}$ and $kT/q=26\,\text{mV}$. The electron concentration at the edge of the depletion region on the p-side is

⚔️ Practice GATE Technical free + battle 1v1 →