Exams › GATE › Technical

Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 10¹⁷ cm⁻³ and the intrinsic carrier concentration is 10¹⁰ cm⁻³. Electron and hole diffusion lengths are 2 μm and 1 μm, 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 0.15 × 10¹⁴ 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 μm, is _________.

1. 0.37 × 10¹⁴ cm⁻³
2. 0.63 × 10¹³ cm⁻³
3. 3.7 × 10¹⁴ cm⁻³
4. 10³ cm⁻³

Correct answer: 0.63 × 10¹³ cm⁻³

Solution

The steady state electron density at a distance from the generation point can be approximated using the diffusion equation, which accounts for the initial excess electron density and the diffusion length. Given the diffusion length of electrons is 2 μm and the initial density at x = 0 is 0.15 × 10¹⁴ cm⁻³, the density decreases exponentially with distance, leading to a calculated value of approximately 0.63 × 10¹³ cm⁻³ at x = 2 μm.

Related GATE Technical questions

• Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A0, A1, A2, and A3 are ____________.
• The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and −1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady state voltages are _____________.
• In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2sin(t + π/2). The displacement current (in Amperes) through the capacitor is ________.
• Select the CORRECT statement(s) regarding semiconductor devices.
• Consider an FM broadcast that employs the pre-emphasis filter with frequency response H_pe(ω) = 1 + jω/ω₀, where ω₀ = 10⁴ rad/sec. For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of (R, C) values is/are _______.
• The three-dimensional state of stress at a point is given by σ = [[10, 0, 0],[0, 40, 0],[0, 0, 0]] MPa. The maximum shear stress at the point is

⚔️ Practice GATE Technical free + battle 1v1 →