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    • Centre de recherche sur les ions, les matériaux et la photonique · CIMAP
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  3. Master 1 – Physics

Master 1 – Physics

Master 1 – Physics

First semester

from September 1st to January 31

Atomic and Molecular Physics I   ·   8 credits | 35h CM + 30h TD

Nuclear Physics I   ·   8 credits | 35h CM + 30h TD

Condensed matter physics   ·   8 credits | 35h Lectures / 30h Tutorials

General physics labs   ·  3 credits | 30h TP

English (or French)   ·  3 credits

Second semester

From February 1st to June 30

Advanced physics at the microscopic scale   ·  13 credits

  • Experiments and simulations
  • Matter and radiation
  • Nuclear physics II
  • Atomic and molecular physics II   ·   18h CM + 12h TD

Theoretical physics   ·   5 credits

  • Advanced quantum mechanics
  • Classical and quantum scattering

or

Applied physics   ·   5 credits

  • Physics for hadrontherapy
  • Nuclear energy and waste
  • Optical spectroscopy
  • Nanoparticles

Research internship   ·   12 credits

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Université de Caen Normandie
esplanade de la paix · CS 14032
14032 CAEN cedex 05

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Atomic and Molecular Physics I

Chapters I to V & Chapter VII: 20hCM + 19hTD

Responsable: J.-Y. Chesnel

Chap. I The basis of the atomic theory(Reminder)
  1. Energy quantization
    1. Black body radiation and Planck's law
    2. Photoelectric effect
    3. Atomic spectra
  2. Wave-particle duality
    1. Statement of de Broglie
    2. Compton scattering 3. Matter-wave interference
Chap. II Hydrogen atom
  1. Bohr's model (TD)
  2. Quantum treatment of the hydrogen atom: energy levels and wave functions
    1. Motion in a central field – Schrödinger’s equation
    2. Study of the angular part
    3. Study of the radial part
    4. Probability density of the electron
  3. Stark effect on the hydrogen atom (TD)
    1. Hamiltonian W describing the action of the electric field on the atom
    2. Matrix elements of W on the basis of the eigenstates of H0
    3. Energy correction (of order 2) for the ground level n=1
      (stationary perturbation of a non-degenerate level)
    4. Energy correction for the four-fold degenerate level n=2(stationary perturbation of a degenerate level)

Chap. III Introduction to multi-electron atoms
  1. Background on the atomic levels
    1. The Hamiltonian H describing the energy of a free atom
    2. Approach by successive approximations to find the eigenfunctions
      and eigenenergies of H
  2. Eigenfunctions and eigenenergies of the central Hamiltonian / Electronic configurations
  3. Terms and fine structure levels of atoms with several valence electrons
    1. Spectral terms in the L-S coupling scheme: effect of the dielectronic interaction
    2. Fine structure levels in the L-S coupling scheme: effect of the spin-orbit interaction
    3. "Terms" and "levels" in the j-j coupling scheme
Chap. IV The interaction between atoms and electromagnetic radiation
  1. Introduction to the effect of a sinusoidal perturbation: Prediction of the perturbation theory / Fermi's golden rule
  2. Hamiltonian of interaction between a wave and an atom (with 1 electron)
    1. Reminders on the fields and potentials associated to a plane electromagnetic wave
    2. Interaction Hamiltonian in the low intensity limit
    3. Electric dipole Hamiltonian
    4. Magnetic dipole Hamiltonian and electric quadrupole Hamiltonian
  3. Resonant excitation. Absorption and stimulated emission
    1. Transition probability associated with a monochromatic wave
    2. Excitation by a broad spectrum. Transition probability per time unit
  4. Absorption, stimulated emission and spontaneous emission
    1. Reminders on the statistical physics
    2. Radiation-atom interaction processes and Einstein coefficients
      1. Absorption
      2. Induced or stimulated emission
      3. Spontaneous emission
      4. Relations between Einstein coefficients and orders of magnitude
    3. Wave absorption and wave amplification
Chap. V Widths and profiles of spectral lines (TD)
  1. Introduction
  2. Doppler effect
  3. Lifetime and natural width
  4. Collision effects V. Doppler effect and energy resonance. Frequency shift of the absorption and emission lines
Chap. VI Application of Atomic Physics to Laser Physics (15hCM & 11hTD)
  1. Fundamental aspects of lasers
  2. The main laser systems
  3. The different temporal regimes of laser operation
  4. Propagation of light by laser beams: characteristics and modeling of a Gaussian beam,       calculation of the characteristics of a focal spot, notion of focal volume
Chap. VII Overview of the molecular structure
  1. Introduction
  2. Born-Oppenheimer approximation
  3. Introduction to the theory of molecular orbitals (in the case of homonuclear diatomic molecules)
    1. The molecular ion H2+
    2. Molecular orbitals in the case of homonuclear diatomic molecules
      1. Construction of molecular orbitals by LCAO
      2. Filling of molecular orbitals - Molecular configuration
      3. Molecular terms
  4. Modeling of the molecular vibration
    1. Harmonic oscillator model
    2. Corrections to the harmonic approximation
  5. Modeling of the molecular rotation
    1. Rigid rotator model
    2. Corrections to the rigid rotator approximation
  6. Orders of magnitude for electronic, vibrational and rotational energies

Nuclear physics I

35h CM + 30h TD

Introduction to nuclear physics - 26h CM + 20h TD

Properties of nuclei:

  • Basic facts and definitions
    Discovery – The nucleus and its constituents – Size - Density
  • Nuclear mass and energy
    Mass excess and binding energy – Q-value
  • Radioactivity and radioactive decay
    Emissions – Beta stability – Decay schemes – Decay chains– Natural radioactivity - Dating

Nuclear models:

  • Nuclear mass
    Phenomenological mass formula – Fission 
  • Fermi gas model
  • Shell model
    Evidences – Independent particles and the shell model – Spin-orbit potential – Spin and parity – Collective states

Nuclear collisions:

  • Accelerators - Centre of mass frame – Threshold energy – Coulomb barrier – Impact parameter – Cross-section – Activation – Fusion reactions – Nuclear synthesis
Interaction of radiation with matter - 9h CM + 10h TD
  1. Introduction
  2. Charged particles
    1. Heavy charged particles
      1. Interaction with the atomic electrons of matter
      2. Linear stopping power: Bethe-Bloch formula
      3. Range, Bragg curve, practical formulas and tables
      4. Applications
    2. Light charged particles
      1. Scattering, modified Bethe formula
      2. Bremsstrahlung radiation
      3. Path Length, Range and Practical Formulas
      4. Cerenkov effect
      5. Multiple scattering, dispersion
  3. X and gamma photons
    1. Interaction process of photons with matter
      1. Photoelectric effect
      2. Scattering, Compton effect
      3. Materialization of electron-positron pairs
    2. Attenuation of a beam in matter
      1. Interaction probability
      2. Law of attenuation
      3. Attenuation coefficients, energy transfer
  4. Neutrons
    1. Interaction of slow neutrons
      1. Diffusion, Capture, Thermalization
      2. Attenuation of a beam
    2. Interaction of ultra-cold neutrons
    3. Interaction of fast neutrons
  5. Neutrinos

Condensed matter physics

35h Lectures / 30h Tutorials

Responsable : C. Dufour

Optical and magnetic spectroscopy in solids (10h Lectures/10h Tutorials) - M. Morales

Objectives:

  • Showing, from the electromagnetic wave-matter interactions, the potentialities of radiative spectroscopic techniques for the structural study of solids
  • Radiative spectroscopies :X-ray diffraction and absorption spectroscopies (X-ray fluorescence, infrared, Raman, magnetic spectroscopies, etc.)

a. High energy electron spectroscopy (X-ray fluorescence): origin of the emission spectrum; implementation of the elementary analysis: crystal analyzer for spectrometry. 

b. General features of vibrational spectroscopies (infrared, Raman): energy ranges, molecular vibrations (simplified model for diatomic molecule), origins of infrared and Raman spectra, phonon selection rules, comparison between infrared and Raman spectroscopies;

c. Magnetic spectroscopy: nuclear magnetic resonance (proton NMR) and electron paramagnetic resonance (EPR)

Electrons in solids (10h Lectures /10h Tutorials) –P-M Anglade

a. Hamiltonian. single electron approximation. Energy and electron density. 

b. Periodic potentials (Krönig Penney, Bloch's theorem, weak potential approximation).

c. Quasi-free electrons.

d. Electronic properties due to the periodic potential: density of states, average velocity

Lattice vibrations, natural frequencies, energy, and definition of a phonon(9h Lectures / 6hTutorials )– Vu Hung Dao

a. The tools of statistical and quantum physics useful to treat of the following points

b. Specific heat of a classical crystal. Dulong and Petit's law

c. Lattice specific heat: general expression, behavior at low and high temperatures

d. Debye and Einstein models. 

e. Density of normal modes

f. Anharmonic effects: thermal expansion

g. Thermal conductivity: kinetic theory, relaxation time, temperature dependence

h. Discussion on the modification of these properties with the size of the systems -> nano effect

Semiconductors: electronic aspect of defects. Carrier mobility (electrons and holes) (6h Lectures / 4h Tutorials) - C. Dufour

Metal-semiconductor junction (Schottky diode)

a. Schottky diode at equilibrium

b. Energy band diagram: work output, electron affinity

c. Rectifier and ohmic contacts, space charge region

d. Schottky diode under external bias

e. Non-equilibrium situation in a semiconductor: quasi-Fermi levels, Einstein relation

f. Capacitance-voltage characteristic of the Schottky diode, determination of the dopant profile

g. Calculation principles of the thermionic current through the diode, Richardson's constant

h. Operating principles of a PN junction (I-V characteristic) and of a bipolar transistor.

General physics labs

First semester, 30hTP

Atomic Physicspractical sessions (15h)
  • Lifetime measurement in Atomic Physics (P. Camy - 3h)
  • Nd:YAG laser optically pumped by a laser diode: principle and implementation (P. Camy - 4h)
  • Optical sensors: Doppler effect - fiber sensor (P. Camy - 4h)
  • Phase plates and electro optic modulation (P. Camy - 4h)
Condensed Matter practical sessions (15h)
  • Practical session on PN Junction –photovoltaic cell (C. Dufour - 3h)
  • Practical sessions on Density Functional Theory (DFT) code (P-M. Anglade – 12h)
    • a. Build a basic 1D DFT code (4h30)
    • b. Work on DFT codes with calculation of density-of-states (7h30)

Experiments and Simulations

(2nd semester) 18CM 32TP

Simulations and modelling:
  1. Introduction : 
    1. general concepts : continuous/discrete, deterministic/stochastic simulations
    2. use cases : simulations for experimental/industrial design, data analysis, statistics and probabilities 
  2. Pseudo Random Number Generators :  
    1. True/Quasi/Pseudo Random Number Generators
    2. Uniform deviates generator (discrete and continuous)
      1. principle, seeding, internal state
      2. application: Knuth & Lewis generator
    3. probability distributions for discrete and continuous random variables
      1. probability mass function
      2. probability density function (p.d.f.), cumulative distribution function (c.d.f.)
    4. The Inverse transform sampling for pseudo-random number sampling of continuous random variables
    5. Rejection sampling
    6. Composite and weighted random generators
    7. Practicalities, methodology and examples
  3. System modelling :
    1. 2D-3D geometry models:
      1. primitive geometrical shapes (box, cylinder, tubes...)
      2. hierarchical geometry model : placement of solids (translations, rotations)
      3. Application: virtual numerical model of a arbitrary experimental setup
    2. Modelling physical properties in a 3D geometry model: materials
  4. Random sampling in a 2D or 3D geometry:
    1. surface and bulk position sampling algorithms using 2D or 3D shapes
    2. direction sampling (2D/3D isotropic sampling)
  5. Particle kinematics random sampling : beams, light or radioactive sources
  6. Deterministic and stochastic transport methods:
    1. ray tracing
    2. particle tracking
    3. random walk
  7. Modelling particle interactions in matter:
    1. deterministic and stochastic processes
    2. transport and intersections on surfaces
    3. continuous processes : energy loss, multiple scattering, actions of external continuous fields (EM, gravitational) and ODE solvers
    4. Discrete processes (on-the-fly decay, production of secondary particles)
    5. Examples: dE/dx for charged particle, Compton effect for gamma rays, reflexion, absorption, refraction for photons
  8. Exploring hypotheses and parametric spaces: Using simulations for setup optimization (experimental design) - Using simulations for inference and inverse problem solving
  9. Stochastic methods: Monte-carlo methods for numerical integration - Importance sampling - Simulated annealing
Practicum: (12TP)

Numerical workshops illustrating various concepts using the Python 3 programming language

  1. System modelling through object oriented programming (OOP)
  2. Creation and utilisation of a generic toolbox library with primitive functionalities (random sampling, geometry, modelling, algorithms, physical processes...)
  3. Practicalities and methodology
Experimental workshop: (20TP)
  1. Nuclear physics 
    1. Gamma spectrometer efficiency by simulation (Y.Lemière - 5h)
    2. Straggling effect on the light charged particle range computation (Y.Lemiere - 5h)
  2. Atomic physics
    1. Molecular spectroscopy: absorption spectrum of the I2 molecule (J.-Y. Chesnel - 2h)
    2. Electron spin resonance: measurement of the Landé factor of the DPPH molecule (J.-Y. Chesnel - 2h)
    3. Design of a beam profiler (hardware and software): application to Gaussian beam propagation and speckle pattern analysis (M. Fromager - 6h) 

Matter and Radiation

18h CM 12h TD 30h TP

Instrumentation course in nuclear and particle physics
  1. Introduction
  2. General properties of detectors
    1. Introduction
    2. Detector operating modes
      1. Current mode
      2. Pulse mode
    3. Response function and energy resolution
      1. Response function
      2. Energy resolution of a detector
    4. Detection efficiencies
    5. Timing of detection
      1. The "fixed" type of resolution time
      2. "Recurring" or cumulative resolution time
    6. Other parameters and characteristics
  3. Gas detectors
    1. Introduction
    2. Ionization chamber
      1. Charge migration and collection
    3. Proportional counters
      1. Creation of a proportional counter
      2. The multiplication factor
      3. Resolution in energy
      4. Time response of the proportional counter
      5. Applications
      6. Split gas detectors
    4. Geiger-Müller counters
    5. Summary of gas detectors
  4. Scintillation detectors
    1. Introduction
    2. Organic scintillators
      1. Light emission mechanism
      2. The different types of organic scintillators
      3. The response of the organic scintillator
    3. Inorganic scintillators
      1. Principle of operation
      2. Characteristics of the most common inorganic scintillators
    4. Collection of scintillation light
      1. Photomultipliers and other sensors
      2. Precautions for the use of conventional PM
      3. Analysis of output pulses
  5. Semiconductor detectors
    1. Introduction
    2. Characteristics of semiconductors
      1. Conduction in semiconductors
      2. The different types of semiconductors
      3. Currents in semiconductors
    3. The PN junction
    4. Signal from a junction detector
    5. The different junction detectors
      1. Generalities
      2. Junctions for the detection of charged particles
      3. Junctions for detection of X and γ photons
    6. Conclusions on semiconductor detectors
  6. Some notions of nuclear electronics
    1. Introduction
    2. Analog nuclear electronics chains and their different elements
      1. The preamplifiers
      2. The amplifier and signal shaping
      3. The analogic to digital converter
      4. The constant fraction discriminator
      5. The charge .digital converter
      6. The time digital converter
      7. The scaler
    3. Connections
    4. Digital nuclear electronics chains and their different elements
TP

Objectif: detection des particules alpha, beta, gamma.

Utilisation de 3 types de detecteurs differents (jonction Si, scintillateur, detecteur gazeux). L'etudiant part de zero et doit tout mettre en place au cours  de chaque TP. 

Il y a 4 TP de 7h00 (un TP dure toute une journee) + une seance d'intro de 2h pour presenter les TP et faire qq rappels.

  1. spectre beta avec jonction Si: mesure du T(beta) max
  2. detection alpha avec jonction Si: mesure de l'epaisseur de feuilles de mylar
  3. detection gamma dans un NAI: photoelectrique, compton
  4. utilisation d'un detecteur gazeux: objectif a preciser

Nuclear physics II

27h CM + 18h TD

Microscopic description of alpha, beta and gamma decays (9CM,6TD)
  1. Quantum tunneling process and decay
    1. Introduction
    2. Gamow theory
    3. Approximation of thick barrier
    4. Applications
  2. Weak interaction and decay
    1. Introduction
    2. Fermi theory
    3. Selection rules
    4. Applications
  3. Electromagnetic interaction in the nucleus: decay
    1. Introduction
    2. Transition probabilities and Weisskopf estimates
    3. Internal conversion coefficients
    4. Applications
Nuclear structure (12CM,8TD)
  1. Nuclear structure: macroscopic approach
    1. Stability, instabilities, driplines
    2. Deformations and fission
    3. Applications: exotic decays, superheavy nuclei
  2. Nuclear structure: microscopic approach
    1. Independent particles and magicity
    2. Deformation again: Nilsson model
    3. Configurational mixing
    4. Application: modification of magic numbers in exotic nuclei
Nuclear reactions (6CM,4TD)
  1. Direct reactions, complex reactions
  2. Resonant states and Breit-Wigner formula
  3. Non-resonant continuum and Hauser-Feshbach theory
  4. Application: nucleosynthesis

Atomic and Molecular Physics II

Master 1 Physics - Second semester, 18hCM + 12hTD

Chapters I & II: 12hCM + 6hTD, resp. J.-Y. Chesnel

Chapter III: 6hCM + 6hTD, resp. A. Braud

Chap. I Atomic spectroscopy (6hCM & 3hTD)
  1. Selection rules
    1. Electric dipole transitions (ED)
    2. Magnetic dipole transitions (MD)
    3. Electric quadrupole transitions (EQ)
    4. Demonstration of the selection rules for ED transitions
  2. Sum rules
  3. Spectroscopy of an atom placed in a magnetic field: Zeeman effect
    1. Magnetic moment associated with an angular momentum
    2. Interaction energy of a magnetic dipole placed in a magnetic field
    3. Energy shifts induced by the magnetic field
    4. Optical transitions between the α2S+1LJ and α2S'+1L'J' levels
  4. Auger emission (TD)
Chap. II An introduction to the molecular spectroscopy (6hCM & 3hTD)
  1. Vibrational transitions
    1. Harmonic approximation
    2. Corrective terms
  2. Rotational transitions
  3. Rovibrational transitions
  4. Electronic transitions

Chap. III Application of lasers to research in physics (6hCM & 6hTD)

Study and modeling of at least three laser applications from the following list:

  • Raman molecular spectroscopy
  • Optical measurement of a magnetic field
  • Optical tweezers: trapping of micro- and nano-particles, guiding of cold atoms, hollow laser beams
  • Acceleration of charged particles, radial and azimuthal polarization
  • Measurement of the non-linear refractive index of a solid
  • Line shape / Doppler-free spectroscopy
  • Optical tomography
  • Laser velocimetry
  • Holographic interferometry
  • Generation of high order harmonics (coherent X-rays)
  • Non-linear imaging
  • Measurement of thermo-optical properties of a material

Advanced Quantum Mechanics

2nd semester, 18hCM + 12hTD

Responsable: Julie Douady

Approximated Methods

Perturbation theory: perturbative solution, degenerate and undegenerated levels, applications (ground state of He atom and anharmonic potential). Variation principle: variational theorem, example of the harmonic oscillator

Time-dependent perturbation theory

Time-dependent potentials: general formalism

Dynamics of a driven two-level system: Rabi oscillations

Time-dependent perturbation theory: general formalism“Sudden” or fast Harmonic perturbation: Fermi’s Golden Rule and Second-order transitions

Introduction to the Second Quantization

Occupation-Number Representation: creation and annihilation operators for the bosons and fermions and Second-Quantized Form of Operators: One-Particle Operators, Two-Particle Operators and Field Operators

Classical and quantum scattering

18h CM + 12h TD

Part 1 Classical scattering and atomic collisions
9h CM+6hTD

Chapter 1: Introduction
  • General introduction on collisions with atoms, molecules, clusters and solids
  • Projectiles: ions. Example of GANIL facilities. Orders of magnitude
  • Projectiles and targets: what for? Presentation of the 3 fundamental processes in atomic collisions (capture, excitation and ionisation). Introduction of the cross section
Chapter 2: Interaction between 2 particles, ballistic and Rutherford scattering
  • Collision parameters, conservation rules, elastic collision, kinetic factors
  • Rutherford scattering, Laplace vector, trajectory equation, graphic construction
  • Classical scattering cross section, differential cross sections. Experiment of Geiger and Marsden. Comparison between experiment and Rutherford scattering therory
Chapter 3: Low energy collisions
  • Potential curves, avoided crossing, electronic capture probability
  • Presentation of 2 models:
    • Classical over barrier model;
    • Landau Zener model, example for the Ar+He collisional system, comparison with experimental data, Grotrian diagram

Part II Quantum scattering and nuclear reactions
9h CM+6hTD

Chapter 4: Quantum elastic scattering and stationary states
  • Simplifying assumptions;
  • Stationary scattering states and cross-section;
  • The Lippmann-Schwinger equation and Born expansion;
  • Partial waves expansion for radially symmetric potentials
Chapter 5: Application to solid state physics

scattering from a collection of scatterers

Chapter 6: Inelastic scattering and nuclear reactions
  • Scattering and reaction cross section;
  • Optical potentials;
  • Application to fusion reactions

Physics for hadrontherapy

9CM + 6TD

Responsables: J.Colin, P.Boduch

Course goal
The objective of this course is to present the issues of radiotherapy and more specifically of hadrontherapy. Physics related issues will be studied and associated research programs will be presented.

Course Map

Subjectmatter of the course lecturestutorials
Presentation of the open questions and challenges concerning radiotherapy and hadrontherapy, with special emphasis on the relevant physical aspects.1h 
Energy deposition in tissues due to electromagnetic interaction.2h 
Absorbed dose for photons, protons and carbon ions.1h2h
Nuclear reactions, cross sections and number of reactions for thin target, thick targets, composite targets.Consequences on the dose.1h2h
Possible reactions with 12C beams, calculation of the excitation energy, kinetic characteristics of the associated particles.Consequences on the dose.1h2h
Nuclear models and simulations 2h 
Presentation of the experiments performed at Ganil1h 

Nuclear energy and waste

This introductory course to nuclear energy is composed of four separate parts, the first two dealing with the presentation of the current situation in terms of energy production and waste, the third dealing with the alternatives studied in the framework of the Gen IV international forum, and the last dealing with the research carried out in this framework more specifically in France.

Nuclear Energy

  • Brief description of a nuclear reactor : the PWR (Pressurised Water Reactor) example
  • Some aspects of reactor neutronics

Waste

  • Definition, origin and amount
  • Waster treatment : the french example

Nuclear Energy & Waste

  • Conditions for a nuclear revival : Generation IV international forum

Resarch & Development

  • Reactors Physic
  • Nuclear Data

Optical spectroscopy

9h CM + 6h TD

M1 physics 2022-2027

Responsable: Alain Braud

Various Absorption and Emission spectroscopy

  • Atomic absorption spectroscopy.
  • Inductively coupled plasma optical emission spectroscopy
  • UV-Vis spectroscopy
  • Fourier transform infrared spectroscopy 
  • Fluorescence spectroscopy
  • Raman spectroscopy

Optical spectroscopy in Solids

  • Electron–Phonon Coupling (Phonon Sidebands of Optical Transitions in Solids, Homogeneous and Inhomogeneous Line Broadening)
  • Energy transfer processes

Optical spectroscopy techniques and instrumentation

  • Absorption and transmission
  • Emission and excitation spectroscopy
  • Emission dynamics
  • Time-resolved emission and excitation spectroscopy
  • Pump-probe techniques

Applications

  • Optical cooling
  • Solar cells new generation
  • Laser spectroscopy

Nanoparticles

M1 S2b2 Applied Physic

Responsable: M. Morales

This lecture aims at studying the physical phenomena on nanometric structures leading to specific applications.

Metallicnanoparticles (C. Dufour – 5h):
  1. Localized surface plasmons (LSP) generation for applications in photovoltaics and scanning tunneling microscopy
  2. Parameters influencing LSP (size, shape, particle optical index, excitation polarization…)
Carbon nanotubes (CNs) (C. Dufour – 5h):
  1. Generation of CNs intense luminescence for photonic applications (in particular diameter and winding-type gap dependence study)
  2. Controlled synthesis challenges for metallic or semiconductor CNs
Semiconductor nanoparticles (M. Morales – 5h):
  1. Gap-dependent size colloidal semiconductor nanocrystals (ZnO, ZnSe, GaAs...) for tunable optical properties
  2. Doped semiconducting nanoparticles for medical applications