As you want syllabus of Ph.D Entrance Exam conducted by RGPV University for Nanotechnology discipline, so here I am giving complete syllabus:

RGPV University Ph.D Nanotechnology Entrance Exam Syllabus

NANO SCALE MECHANICS
Wave-particle duality; Wave functions in coordinate and momentum representations;
Commutators and Heisenberg's uncertainty principle; Matrix representation; Dirac’s bra and ket notation; Schroedinger equation (time-dependent and time-independent); Eigen value problems such as particle-in-a-1D , 2D and 3D box,.; Tunneling through a barrier.

MATERIAL SCIENCE
Elements of crystallography; diffraction methods for structure determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors and insulators; transport properties; optical, dielectric and magnetic properties of solids;

SYNTHESIS OF NANOMATERIALS
Top-down techniques : Nanostructures by mechanical milling (ball milling) and mechanical
attrition, Lithography -immersion lithography, Electron and ultraviolet (EUV) ,photolithography, X- ray lithography, Electron beam lithography, focused ion beams. Nanosphere lithography – Molecular self-assembly, soft lithography, molecular manipulation by STM and AFM

Bottom-up techniques: Chemical vapor deposition (CVD), Physical vapour deposition (PVD)
thermal and e beam evaporation, Pulsed laser ablation, pulse laser deposition. Chemical Routes: chemical precipitation and co-precipitation, chemical bath deposition (CBD), Sol-gel synthesis, and spray pyrolysis

CHARACTERIZATION OF NANOMATERIALS (I)
Spectroscopic techniques : Spectrophotometers, UV-Vis spectrophotometers, IR spectrophotometers, Fourier Transform Infrared radiation (FTIR), photoluminescence,
electroluminesce and thermoluminescence spectroscopy, Nearfield scanning optical microscopy (NSOM)

Diffraction techniques : X-ray Diffraction (XRD), powder and single crystal Diffraction, X-ray fluorescence (XRF), X ray photoelectron spectroscopy (XPS), Energy Dispersive X-ray analysis (EDAX), Extended X ray absorption fine structures (EXAFS), Dispersive high pressure XRD

CHARACTERIZATION OF NANOMATERIALS (II)
Surface analysis: Scanning tunneling microscopy (STM), Contact and non contact atomic force microscopy (AFM), Conductive AFM, Magnetic force microscopy (MFM)
Elemental analysis: Nuclear magnetic resonance (NMR) and Raman spectroscopy: description and analysis. Surface analysis methods: Secondary ion mass spectroscopy (SIMS), Auger electron spectroscopy, Electron spectroscopy for chemical analysis.
Electron microscopic techniques: Scanning Electron Microscopy (SEM), Transmission electron microscopy (TEM), High resolution TEM Field emission SEM, Electron energy loss spectroscopy (EELS)

PROPERTIES OF NANOSTRUCTURES
Electrical transport properties in semiconductor nanostructures: Density of states: Quantum wells, Q wires and Q dots. quantization of conductance, coulomb blockade, Kondo effect, ballistic transport.

RGPV University Ph.D Nanotechnology Entrance Exam Syllabus