1. Introduction to Nanoengineering
2. Fundamentals of the Quantum Structure Physics
3. Introduction to Nanochemistry
4. Fundamentals of the Nanostructural Material Science
5. Electronic Structure of Nanomaterials
6. Fundamentals of Micro-, Nano- and MEMS-technologies
7. Analytical Nanoscopy
8. Physical Fundamentals of Nanometrology
9. Introduction to Mathematical Nanostructure Modeling
10. Introduction to Mathematical Modeling of Nanoengineering Processes and Nanostructures
11. Mathematical Modeling
12. Nanoengineering and Society (Social and Political Problems of Sustainable Development)

Organization and objective of the course. Terminology. Crucial technologies of the XXI century. National programmes. Historical background. Immediate forecasts. Nanotechnology elements. Processes. Equipment & facilities. Nanoobjects. Nanoindustry. Examples of objects developed by the national nanoengineering. Superdispersed nanomaterials. Nanotubes and their application. Nanoear. Nanonose. Molecular biology towards nanoindustry. Nanotechnological revolution and the social after-effects.



"Conventional" quantum mechanics under unconventional conditions: scattering at the potential barriers and wells, interference phenomena; multilayer structure energy spectra, superlattices, sub-barrier electron transfer. Dimensionality effect on the electron spectra and density of states - quantum 2D planes, wires and dots. Electron transfer within systems of different dimensionalities, tunneling currents in scanning microscope, development of STM-images. Nanostructure electron spectra. Volt-ampere characteristics in the systems with complex quantum spectrum.



Nanochemistry as the science. Nanosystem physical-chemical evolution. Nanochemistry methods. Nanosystem chemical synthesis. Chemistry of clusters. Chemical phenomena in nanosystems. Nanochemistry technological aspects. Environmental nanochemistry. Medical nanochemistry.



General description of nanostructural state. Major portions in the nanomaterial excess free energy. Boundaries and their structure. Basic procedures for nanomaterial generation. Classification of nanomaterials. Powder technology, intensive plastic deformation, amorphous state crystallization, film and coating technology. Physical, mechanical, chemical and biological properties. Classical and quantum dimension effects. Basic fields of application. Traditional and novel engineering, information and computer technologies, medicine, agriculture, environmental control.



Translational symmetry in crystals and one-dimensional systems. Direct and reciprocal lattice. Brillouin zone. Bloch theorem. Cyclic and boundary conditions. Single-electron approximation. Model of almost free electrons and its application to describe electronic structure of elementary nanowires. Secular equation. Method of strong bond and its application for carbon nanotubes. Method of associated plane waves applied for bulk systems. Approximation for electronic potential. Development of basis function. Analysis of overlapping integrals and Hamiltonian matrix elements. Local density functional approximation and exchange interactions. Method of associated plane and standing waves for nanowires and cube clusters. Method of associated cylindrical waves for nanotubes. Method of associated spherical waves for spherical clusters and quantum dots.



Nanotechnologies as a break-through to the XXI century. Basic process technologies in semiconductor microelectronics. Problems of submicron silicon technology. Gallium arsenide and its function in expanding microsystem frequency band. MEMS-technology development. Equipment and basic process technologies in non-semiconductor nanotechnology. Transfer and complementarity of integrated nanostructures.



Scanning tunnel microscopy. Probes for tunnel microscopy. Nanolithography using scanning microscope. Electrochemical microscope. Nature of intermolecular forces. Atomic-force microscopy. Methods and facilities. Modifications of surface structure and interacting forces. Types of cantilevers. Artifacts in probe microscopy. Up-to-date methods for graphic information processing. Magnetic-force microscope. Nuclear magnetic resonance microscope, optical near field microscope. Thermonanoscopy and micromechanical polymer analysis. Analytical bionanoscopy.



Measurements as a physical process. Function of measurement procedures in the science and technology development, their interaction, notion of information. Fundamental quantum limits for accuracy of measurements. Quantum physics effects that support standards of basic physical quantity unit measures according to the SI system. Facilities and methods to provide measurement assurance for industrial production in microelectronics. Facilities and methods to provide measurement assurance for experimental scientific studies of processes and objects within nanometer spatial range. Prospects of standard meter reference for nanometer range. Reference basis and nanotechnology measurement chains. Conclusion.



Subject and basic goals of mathematical modeling on the nanometer scale of spatial dimensions. Examples of nanomaterials and nanodevices. Experimental facilities to visualize atomic structures. Hierarchy system of mathematical models. Statement of a number of typical mathematical problems. Models of molecular dynamic based on the initial principles. Classical molecular dynamics model classes. Computational algorithms to solve typical problems of classical molecular dynamics. Non-ideal lattice systems and methods of probabilistic cellular asynchronous automata. Model class of the reaction - diffusion type. Methods of nonlinear mathematical model analysis. Problem-oriented program systems and computing resources required for modeling.



Kinetic equation - basic notions. Lagrangian coordinates. Ground substitutions in Vlasov equation. Vlasov - Maxwell's and Vlasov - Einstein equations. Energy substitution. Boltzmann equation. Discrete models of Boltzmann equation. Method of spherical harmonics and Maxwell's gas relaxation. Discrete models of Boltzmann equation for gas compositions. Quantum Hamiltonian and kinetic equations.



On the mathematical models of physical phenomena. Characteristic properties of computational phase on a PC basis. Analytic representation of table functions. Approximation methods. Splines. Integration. One-step and multistep methods. Optimization methods. Programming methods. Conceptual program model. Characteristic properties of realization of algorithms on a PC basis. Software engineering. Structured programming. Applied systems for modeling.



Introduction and basic definitions. High-tech and its function in sustainable development of society. Sustainable development indices. Aims and goals of sustainable development in Russia. Interdependence of geopolitics and foreign social-ecological-economic policy of Russia. Economic alternatives. Nature management strategy. Social aspects of the sustainable development strategy and influence of the nanotechnological revolution. Domestic as well as external problems related to implementation of the sustainable development strategy.