# Physics-II GTU Paper Solution Winter 2021 | 3110018

Here In this blog, We provide Physics-II GTU paper solution winter 2021. Read the Full Physics-II gtu paper solution given below.

`Physics - II GTU Old Paper Winter 2021 [Marks : 70] : Click Here `

(a) Define absorption, spontaneous emission and stimulated emission for
bulk semiconductors.

Absorption: The process by which photons are absorbed by the electrons in a bulk semiconductor, leading to a transition from the valence band to the conduction band.

Spontaneous emission: The process by which an electron in an excited state spontaneously emits a photon and returns to the ground state.

Stimulated emission: The process by which an incoming photon with the correct energy causes an electron in an excited state to emit a second photon with the same energy and phase, leading to coherent amplification of the light.

(b) Write a short note on P-N junction diode

(c) Give assumptions of classical free electron theory and discuss its
limitations

(a) Find the temperature at which there is 1% probability that a state with
energy 2eV is occupied. Given that Fermi energy is 1.5 eV.

energy : 0.5 eV

Probability, f(E)= 1% = 1/100

E – EF = 0.5 eV

T = ?

F(E) = 1/ (1 + exp(E – E(F))/K(b)T

K(B) =1.381 × 10⁻²³J/K

=1.381 × 10⁻²³ × 6.24 × 10¹⁸ eV/K

Substituting the value we get:

1/100 = 1/ 1 + exp[0.5/(861.744 × 10⁻5T)]

100 = 1 + exp[5801.87/T]

100 ≈ exp[ 5801.87/T]

Taking In on both sides, we get:

Ln 100 = 5801.87/ T

T = 5801.87 / 4.605 = 1259.98 K

(b) What is drift and diffusion current in p-n junction diode?

(c) Explain the Kronig-Penny model of solids and show that how it
explains the origin of band gap in solids.

[OR] (c) Explain intrinsic and extrinsic (N & P type) semiconductors with the
help of energy band diagram.

(a) In an N-type semiconductor, the Fermi level lies 0.3 eV below the
conduction band at room temperature. If the temperature is increased to
330K, Find the position of Fermi level.

When the temperature of a semiconductor is raised to KT, the position of Fermi level is raised by KT (kT is the amount of heat required to increase the thermodynamic entropy of a system by k) from its initial position at a given temperature, where ‘K’ is Boltzmann constant

(K = 1.38× 10−23JK−1).

Also,

Eg(energy band gap) ∝   1/T

Eg/E’g=T’/T

0.3/E’g=330/300

E’g=300×0.3/330

=0.27eV

0.27 eV below the conduction band.

(b) Write an expression for Fermi Dirac distribution function f(E). Show
that at all temperatures (T > 0K) probability of occupancy of Fermi
level is 50%.

(c) Discuss the effect of temperature on the Fermi level in extrinsic (N & P
type) semiconductors.

OR

(a) Find the concentration of holes and electrons in N-type silicon if the
conductivity is 0.1 -cm-1, mobility of electrons is 1300 cm2/V-s and total carrier concentration is 1.5×1010 carriers / cm3.

(b) Establish the relation between Einstein’s coefficients.

(c) Explain Meissener’s effect in detail and show that for superconductor,
χm = –1.

When superconductor is placed in an external magnetic field, it expels all magnetic flux lines from it. This is known as “Meissner effect”.

When the superconducting material is placed in a magnetic field (H> Hc) at room temperature, the magnetic field is found to penetrate normally throughout the material it shown in (a).

However, if the temperature is lowered below T and with H<Hc the material is found to reject all the magnetic field penetrating through it shown in (b).

(a) Write a short note on effective mass of electron.

The effective mass of an electron in a solid is a measure of the electron’s effective mass relative to the free electron mass.

In a solid, electrons are subject to various interactions with lattice vibrations and other electrons, which affects their motion. The effective mass of an electron takes into account these interactions and provides a more accurate representation of the electron’s behavior in a solid than the free electron mass.

The effective mass is different for electrons in different bands and can be either larger or smaller than the free electron mass.

In general, electrons in the conduction band have a smaller effective mass than the free electron mass, which makes them more mobile and contributes to the electrical conductivity of a material. On the other hand, electrons in the valence band have a larger effective mass, which makes them less mobile and contributes to the material’s insulating properties.

(b) What is mass action law? Explain Schottky junction.

(c) Explain Drude model and discuss how it is used for Hall measurements and magnetoresistance.

OR

(a) What is an exciton? What is DLTS? Define Hall mobility

#### Exciton:

An exciton is a bound state of an electron and a hole in a solid, such as a semiconductor. When a photon is absorbed in a semiconductor, an electron is excited from the valence band to the conduction band, leaving behind a positively charged hole in the valence band.

#### DLTS:

DLTS stands for Deep Level Transient Spectroscopy. It is a technique used to study the energy levels of impurities or defects in a solid, such as a semiconductor.

#### Hall Mobility

The Hall mobility is a measure of the mobility of charge carriers in a material, such as a metal or a semiconductor. The Hall mobility is defined as the ratio of the transverse voltage to the magnetic field, and is a measure of the ease with which charge carriers move in response to an electric field.

(b) What is Fermi level and Fermi energy? What is Photovoltaic Cell?

(c) Explain four point probe method with diagram for the measurement of resistivity of bulk sample.

(a) Explain Fermi Golden rule for transition probability

(b) What is Josephson junction? Write a short note on SQUID.

#### Josephson Junction

A Josephson junction is a type of superconducting electrical junction, which consists of two superconductors separated by a thin insulating layer.

When the junction is biase with a DC voltage, a supercurrent flows through the junction, which is proportional to the sine of the phase difference between the two superconductors. The Josephson effect, which is the flow of supercurrent through the junction, is a direct consequence of the quantum mechanical properties of superconductors.

#### SQUID

A SQUID (Superconducting Quantum Interference Device) is a sensitive magnetic sensor that uses the Josephson effect.

It consists of a loop of superconducting material, with two Josephson junctions in series, that acts as a quantum mechanical phase-sensitive detector.

When a magnetic field is applied to the SQUID, it modulates the phase difference between the two superconductors, leading to a change in the supercurrent through the junctions.

By measuring the supercurrent, the SQUID can detect very weak magnetic fields, making it useful in a variety of applications, including medical imaging, geophysics, and materials science.

(c) Explain how to measure band gap of the semiconductor using UV-Vis
spectroscopy.

OR

(a) Calculate the critical current for a superconducting wire of lead having
a diameter of 1mm at 4.2 K. Critical temperature for lead is 7.18 K and
Hc(0) = 6.5 x 104 A/m.

Critical current Ic = 2πrHc

Ic = 2* 3.14 * 0.5 *103 * 6.5 x 104

Ic = 134.26 A.

(c) What is superconductivity? Explain any six properties of
superconductor.

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