UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Deduce the Miller indices of the close-packed planes of atoms in the f.c.c. lattice.

A silicon semiconductor sample at T=300\,\mathrm{K} having cross-sectional area of 0.5\,\mu\mathrm{m}^2 has a pentavalent donor doping profile given by C(x)=5\times10^{16}e^{-x/L_n}\,\mathrm{cm^{-3}}. Given, the mobility of the electrons in the sample is 1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the diffusion length of the electrons, L_n, is 4\,\mu\mathrm{m}. Calculate the diffusion current in the sample at distance x=2\,\mu\mathrm{m}.

Explain the use of an op-amp as a differentiator and an integrator using proper circuit diagram. Write the condition to work as good differentiator and integrator.

A silicon semiconductor sample is doped with 6\times10^{16}\,\mathrm{cm^{-3}} of aluminium and 7\times10^{15}\,\mathrm{cm^{-3}} of phosphorus atoms. Given at T=300\,\mathrm{K}, the intrinsic carrier concentration, n_i=1.5\times10^{10}\,\mathrm{cm^{-3}}; the band gap, E_g=1.1\,\mathrm{eV}; the electron mobility, \mu_n=1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the hole mobility, \mu_p=480\,\mathrm{cm^2\,V^{-1}\,s^{-1}}. Determine in the sample of the following:

(i) The type of the semiconductor, n or p

(ii) The hole carrier concentration

(iii) The electron carrier concentration

(iv) The position of the Fermi level in the sample with respect to the bottom of the conduction band

(v) The conductivity of the sample

A transistor having \alpha = 0\cdot 975 and a reverse saturation current I_{\text{CO}} = 10~\mu\text{A} is operated in CE configuration. What is \beta for this configuration? If the base current is 250~\mu\text{A}, calculate the emitter current and the collector current.

A superconducting material has a critical temperature of 3\cdot 7~\text{K} and a magnetic field of 0\cdot 0306~\text{tesla} at 0~\text{K}. Find the critical field at 2~\text{K}.

Explain the Meissner effect in superconductivity. Obtain an expression for London penetration depth of magnetic field for a superconductor.

Describe briefly the construction of an enhancement type MOSFET using a p-type silicon bar. Point out the structural difference between enhancement and depletion forms of the MOSFET.

A 5\,\mathrm{cm^2} Ge solar cell with a dark reverse saturation current of 2\,\mathrm{nA} has solar radiation incident upon it, producing 4\times10^{17} electron-hole pairs per second. The electron and hole diffusion lengths are given to be 5\,\mu\mathrm{m} and 2\,\mu\mathrm{m}, respectively. Calculate for the cell of the following:

(i) The short-circuit current

(ii) The open-circuit voltage

Obtain the Boolean expression for the output Y in the given logic circuit :

Simplify the expression and show that the circuit is equivalent to an AND gate with inputs A and B.

Sketch the cross-sectional structure of an enhancement mode MOSFET and explain its principles of operation with the help of its output characteristics.

What are intrinsic and extrinsic semiconductors? Show that in the intrinsic semiconductors, Fermi level lies exactly in the middle of bottom of conduction band and top of valence band.

What are operational amplifiers? How can it be used as an inductor? Prove it mathematically.

Describe the working of a microprocessor system in block diagram. How is its performance affected in a pipelined processor?

Calculate Atomic Packing Fraction (APF) for FCC and HCP structures, and show that these are the most closely packed structures.

Derive Bragg diffraction law for X-ray diffraction. Compare Laue and Debye-Scherrer methods for crystal structure determination.

Estimate the current gain of an n-p-n transistor if only 0\cdot 3\% of the conduction electrons that enter the base from the emitter recombine in the base region.

Derive an expression for lattice specific heat in Debye model. Find its low temperature limit (Debye T^3 law).

What are type I and type II superconductors? Give examples. Discuss and compare Meissner effect and perfect diamagnetic behaviour for type I and type II superconductors.

Derive the expression for electron concentration in the conduction band of an intrinsic semiconductor.