List of top Electronic Devices Questions asked in GATE EC

The intrinsic carrier concentration of a semiconductor is \( 2.5 \times 10^{16} \, /m^3 \) at 300 K. If the electron and hole mobilities are \( 0.15 \, {m}^2/{Vs} \) and \( 0.05 \, {m}^2/{Vs} \), respectively, then the intrinsic resistivity of the semiconductor (in \( k\Omega \cdot m \)) at 300 K is _________. (Charge of an electron \( e = 1.6 \times 10^{-19} \, C \))
A p-type semiconductor in steady state has excess minority carriers zero at $x=\pm 2L_n$, with $L_n = 10^{-4}$ cm. Electron charge $q = -1.6\times 10^{-19}$ C. The recombination rate profile is \[ R = 10^{20} \exp\left(-\frac{|x|}{L_n}\right)\ \text{cm}^{-3}\text{s}^{-1}. \] The magnitude of electron current density at $x=+2L_n$ is __________ mA/cm$^2$ (rounded to two decimals).
Select the CORRECT statement(s) regarding semiconductor devices.
Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 $\mu$m and width 100 $\mu$m. The product of electron mobility ($\mu_n$) and oxide capacitance per unit area ($C_{OX}$) is $\mu_n C_{OX} = 1\ \text{mA/V}^2$. The threshold voltage of the transistor is 1 V. For a gate-to-source voltage $V_{GS} = [2 - \sin(2t)]$ V and drain-to-source voltage $V_{DS} = 1$ V (substrate connected to source), the maximum value of the drain-to-source current is ________________.
An ideal MOS capacitor (p-type semiconductor) is under strong inversion with $V_G = 2$ V. The inversion charge density is $Q_{IN} = 2.2\ \mu\text{C/cm}^2$. Assume oxide capacitance per unit area $C_{ox} = 1.7\ \mu\text{F/cm}^2$. For $V_G = 4$ V, the value of $Q_{IN}$ is ____________ $\mu$C/cm$^2$ (rounded to one decimal place).
Consider a long rectangular bar of direct bandgap $p$-type semiconductor. The equilibrium hole density is $10^{17}\,\text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10}\,\text{cm}^{-3}$. Electron and hole diffusion lengths are $2\,\mu$m and $1\,\mu$m, respectively. The left side of the bar ($x=0$) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at $x=0$ because of the laser. The steady state electron density at $x=0$ is $10^{14}\,\text{cm}^{-3}$ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at $x=2\,\mu\text{m}$ is ______________.
In a non-degenerate bulk semiconductor with electron density $n = 10^{16}$ cm$^{-3}$, the value of $(E_C - E_{Fn}) = 200$ meV, where $E_C$ and $E_{Fn}$ denote the conduction band edge and electron Fermi level, respectively. Assume thermal voltage as 26 meV and intrinsic carrier concentration as $10^{10}$ cm$^{-3}$. For $n = 0.5 \times 10^{16}$ cm$^{-3}$, the closest approximation of $(E_C - E_{Fn})$, among the given options, is ________________.

For the transistor M1 in the circuit shown in the figure, \( \mu_n C_{\text{ox}} = 100 \, \mu \text{A/V}^2 \) and \( \frac{W}{L} = 10 \), where \( \mu_n \) is the mobility of electrons, \( C_{\text{ox}} \) is the oxide capacitance per unit area, \( W \) is the width, and \( L \) is the length. The channel length modulation coefficient is ignored. If the gate-to-source voltage \( V_{GS} \) is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is _________ V. 

A silicon P-N junction is shown in the figure. The doping in the P region is \( 5 \times 10^{16} \, \text{cm}^{-3} \) and doping in the N region is \( 10 \times 10^{16} \, \text{cm}^{-3} \). The parameters given are: 
Built-in voltage \( \Phi_{bi} = 0.8 \, \text{V} \) 
Electron charge \( q = 1.6 \times 10^{-19} \, \text{C} \) 
Vacuum permittivity \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \) 
Relative permittivity of silicon \( \epsilon_{si} = 12 \) 
The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place) is V. 

For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity \( \left( \frac{\partial V_T}{\partial |V_{BS}|} \right) \) is found to be 50 mV/V at a substrate voltage \[ |V_{BS}| = 2 \, \text{V}, \text{ where } V_T \text{ is the threshold voltage of the MOSFET. Assume that } |V_{BS}| \gg 2 \Phi_B, \text{ where } q \Phi_B \text{ is the separation between the Fermi energy level } E_F \text{ and the intrinsic level } E_i \text{ in the bulk. Parameters given are:} \] \[ \text{Electron charge } (q) = 1.6 \times 10^{-19} \, \text{C}, \quad \text{Vacuum permittivity } (\varepsilon_0) = 8.85 \times 10^{-12} \, \text{F/m}, \] \[ \text{Relative permittivity of silicon } (\varepsilon_{si}) = 12, \quad \text{Relative permittivity of oxide } (\varepsilon_{ox}) = 4. \] \text{The doping concentration of the substrate is:}