A) Electronic
Materials (50 marks)
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Unit-1
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Crystalline structure: Single crystals - unit cells,
Bravais lattices, crystal planes, Miller indices, X-ray diffraction; Lattice
vibrations; properties of polycrystalline and amorphous materials, crystalline
defects, X-ray diffraction (10marks).
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Unit-2
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Semiconductors: Classification of solids -
insulator, semiconductor and conductors; Intrinsic and extrinsic
Semiconductors, Compound semiconductors – binary, ternary and quaternary
types and their properties; carrier generation and recombination, carrier
scattering in semiconductors. Electronic properties and application of semiconductor
– semiconductor junction, metal – semiconductor junction, metal – insulator
junction, insulator – semiconductor junction in electronic device fabrication.
Low-dimensional semiconductor structures: super lattice, quantum wells, wires
and dots and their application in electronics; organic and polymer materials
for electronics (10 marks).
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Unit-3
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Conductors: Free electron theory of metals,
Electrical conductivity and resistance, Boltzmann transport equation,
thermionic emission and photoelectric effect, contact potential between
metals, metallic alloys – interstitial and substitutional solid solutions,
mutual solubility. Properties of common metals (Gold, Copper, Aluminum, Tin,
Lead etc.), and their applications in fabrication
of electrical components and electronic devices (10 marks).
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Unit-4
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Dielectrics: Dielectric polarizations - electronic, ionic, orientation types,
dielectric breakdown; alternating field behavior of dielectrics – complex
dielectric constant, dielectric loss and relaxation time. Properties of dielectrics
such as mica, ceramics, Silicon dioxide, Silicon Nitride etc., and their applications
in fabrication of electrical components and electronic devices (10 marks).
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Unit-5
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Magnetic
materials and Superconductors: Theory of ferromagnetic, anti-ferromagnetic,
ferrimagentic, paramagnetic and diamagnetic materials; their properties and application
in electrical and electronic engineering. Physics of superconductors and superconducting materials,
Josephson effect, SQUID, High temperature superconductivity and its
applications (10 marks).
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B)
Mathematical Methods (50 marks)
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Unit-1
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Linear
Algebra: Introduction, Vector Spaces, Solutions of Linear
Systems, Important Subspaces associated with a matrix, Orthogonality,
Eigenvalues and Eigenvectors, Diagonalizable Matrices, Hermitian Matrices,
General Matrices, Jordan Canonical form (7 marks).
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Unit-2
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Numerical Analysis: Principles of floating point computations and rounding errors; systems
of linear equations, eigenvalue problems; interpolation, approximation by
polynomials, data fitting and least squares approximation; Numerical
Integration: integration by interpolation, adaptive quadratures and Gauss
methods; Initial Value Problems for Ordinary
Differential Equations: Runge-Kutta methods, multi-step methods, predictor
and corrector scheme, stability and convergence analysis; Two Point
Boundary Value Problems : finite difference methods with
convergence results (7 marks).
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Unit-3
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Laplace and Fourier Transforms:
Concept of
Transforms, Laplace Transform(LT) and its existence, Properties of Laplace
Transform, Evaluation of LT and inverse LT, Evaluation of integral equations
with kernels of convolution type and its Properties, Complex form of Fourier
Integral, Introduction to Fourier Transform, Properties of general (complex)
Fourier Transform, Concept and properties of Fourier Sine Transform and
Fourier Cosine Transform, Evaluation of Fourier Transform, Solution of
ordinary differential equation and one dimension (12 marks).
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Unit-4
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Special Functions: Gamma and Beta functions,
Bessel function, Error function, Legendre
polynomials, Hermite and Laguere polynomials, Chebyshev and Jacobi
polynomials, Hypergeometric functions, Laplace equation, Poisson’s Equation and
Engineering applications (12 marks).
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Unit-5
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Probability & Statistics: A review of concepts of probability and
random variables: Classical, relative frequency and axiomatic definitions of
probability, addition rule, conditional probability, multiplication rule,
Bayes’ Theorem. Random Variables: Discrete and continuous random variables,
probability mass, probability density and cumulative distribution functions,
mathematical expectation, moments, moment generating function. Standard
Distributions: Uniform, Binomial, Geometric, Negative Binomial, Poisson, Exponential,
Gamma, Normal. Sampling Distributions: Chi-Square, t and F distributions.
Estimation: The method of moments and the method of maximum likelihood
estimation, confidence intervals for the mean(s) and variance(s) of normal
populations. Testing of Hypotheses: Null and alternative hypotheses, the
critical and acceptance regions, two types of error, power of the test, the
most powerful test, tests of hypotheses on a single sample, two samples (12 marks).
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