Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Kamand, Himachal Pradesh 175005

India

ph: +(91)1905-237930

achakrab

**Course Details: **

The course will provide an introduction to nanoscience. Some of the fundamental concepts used to study the world at the nanoscale will be discussed in detail. Understanding of these concepts is fundamental in understanding how nanoscale interactions & phenomena differ from those in our common macroscale world. Finally this course will provides specific study of the application of nanotechnology to different areas of science.

**Course Outline**

- Big picture and principles of the small world.

- Why ‘the smaller, the better’?

- Introduction to Nanoscale physics.

- Nanoscale Fluid Mechanics, Nanoscale Heat transfer.

- Nanobiology, Molecular motors.

**References**

1. Introduction to Nanoscience : S. M. Lindsay, Oxford 2010.

2. Nanotechnology: Understanding small systems : Rogers, Pennathur & Adams, CRC press 2008.

3. Introductory Nanoscience : Masaru Kuno, Garland Science 2011.

4. Quantum Mechanics for Nanostructures : Vladimir V. Mitin, Dimitry I. Sementsov & Nizami Z. Vagidov, Cambridge, 2010.

5. Nanophysics and Nanotechnology: An introduction to the modern concepts in Nanoscience: Edward L. Wolf, Wiley-VCH, 2011.

6. Introductory Quantum Mechanics : Richard L. Liboff, Addison-Wesley, 1993.

7. Foundations of Nanomechanics, A. N. Clealand, Springer, 2003.

8. Nano Devices, 2D electron solvation & curve crossing problems: A. Chakraborty, Lambert, 2010

**Marks Distribution**

Assignments 30%, quizzes 20% & final exam. 50%.

**Tentative Lectures**

Lecture 1: Aim of the course, course outline, references, marks distribution.

Lecture 2 : Why one-billionth of a meter is a big deal ? Applications aspect.

Lecture 3: About size scales, why it really matter ?

Lecture 4: History of nanoscience and nanotechnology.

Lecture 5: Priliminaries: quantum well, quantum wire & quantum dot.

Lecture 6: Electronic structure: from atom to metal : where is nano-scale ?

Lecture 7: Discretized 'energy band' at nanoscale: why useful ?

Lecture 8: Fermi energy, Fermi Velocity & Kubo gap: what is the use ?

Lecture 9: Mean free path of electron in metal : why should we know this ?

Lecture 10: Charging energy : electrical properties of metal nanostructure. How does it matter ? At low temperature ?

Lecture 11: Metal: Fermi wavelength, Bohr radius ?

Lecture 12: Summery for Metals : At least three different critical sizes.

Lecture 13: Electrons in semiconductor, approx. size of electron ?

Lecture 14: Holes in semiconductor, approx. size of hole ?

Lecture 15: Excitons in semiconductor: Mott-Wannier vs. Frenkel exciton.

Lecture 16: Excitonic transitions in bulk semiconductor: below its band edge.

Lecture 17: Semiconductor: confining regimes, physical size vs. electron size vs. hole size.

Lecture 18: Understanding Nanosystems : Top-down or Bottom-up.

Lecture 19: Molecular vibrations : diatomic to polyatomic.

Lecture 20: Concepts of Normal Modes.

Lecture 21: Vibrations in solid : concept of phonon.

Lecture 22: Phonons at the nanoscale : 'quanta of heat ?'

Lecture 23: Electrons in solid : concept of plasmon, normal modes of all electrons ? Collective motion of electron spins, magnons ?

Lecture 24: Idea of Polaron (electron plus phonon ?) & Cooper pair (electron-electron binding ?)

Lecture 25: High energy vibrations in solid (normal model, local mode & chaos).

Lecture 26: Interactions between plasmons and phonons.

Lecture 27: Lighting utilizing excitions, collective motion of excitons, future prospect?

Lecture 28: Density of states, from bulk material to nano, size & shape dependent ?

Lecture 29: Summary of all important interactions between electronic and nuclear degrees of freedom in solid.

Lecture 30: Model Quantum Mechanics Problems (wells, wires & dots).

Lecture 31: Analytical models for electrons/holes in a periodic potential.

Lecture 32: The Kronig-Penney type models, effective mass of electron/hole.

Lecture 33: Types of Nanostructures. Graphene etc. !

Lecture 34: Introduction to Nanomechanics.

Lecture 35: Nanomechanical Oscillators, buckling etc.

Lecture 36: Introduction to Nanoelectronics.

Lecture 37: Single Electron Phenomena.

Lecture 38: Photonic Properties of Nanomaterials: Absorption, Emission & Scattering.

Lecture 39: Photonic Crystals: A band gap for photons. Meta-materials ?

Lecture 40: Nano-scale Heat Transfer: Conduction, Convection & Radiation.

Lecture 41: "All heat is nanoscale heat" !

Lecture 42: Fluids at the Nanoscale. Fluid Flow at the nanoscale. Cooling off Computer Chips.

Lecture 43: How Biology 'feels' at the nanometer scale. Applications to 'Molecular Motors'.

**Assignment 1 Questions**

Do calculations for three different sizes of a nanostructure, as mentioned in the class.

(a) An estimate of the number of atoms in a nanostructure using a unit cell approach.

(b) An estimate of the number of surface atoms in a nanostructure using a unit cell approach.

(c) One/more conclusions ?

**Assignment 2 Questions**

Do a literature survey on 'quasicrystal' and submit a short note on quasicrystal. Mention where quasicrystal is different from amorphous, polycrystalline and crystalline solids.

**Assignment 3 Questions**

Charles-Augustin de Coulomb, French physicist best known for the formulation of Coulomb's Law, which states that the force between two electrical charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Write a short note on how did Coulomb arrive at his law ?

**Assignment 4 Questions**

Let us consider a "x" diameter metal sphere embedded in a dielectric medium (epsilon =20). Find the charging energy of the sphere ?

Case 1: x = 3 nm. Case 2: x = 30 nm & x = 300 nm.

Any conclusion ?

**Reading Assignment 1**

Explained: Phonons - When trying to control the way heat moves through solids, it is often useful to think of it as a flow of particles: by David L. Chandler, MIT News OfficeLink: http://web.mit.edu/newsoffice/2010/explained-phonons-0706.html.

**Reading Assignment 2**

Don't define nanomaterials: An interesting article by Andrew D. Maynard. Reference: Nature, 475, 31 (07 July 2011). DOI:10.1038/475031aLink: http://www.nature.com/nature/journal/v475/n7354/full/475031a.html.

**Quiz 1 Questions**

1. Nanometer is a magical point on the dimension scale – why?

2. What is the difference between nanoscience and nanotechnology?

3. Name two things you are familiar with that are roughly 1 millimeter in size. Name something that is approximately 1 micrometer in size. Name something that is 1 nanometer in size.

4. What is the difference between quantum dot, quantum wire and quantum well?

5. Does really surface area increase when size is reduced? Explain with simple examples.

6. When & where Feynman delivered his lecture on ‘nano’ & what is the name of that lecture?

7. Nanotechnology is new but research in nanometer scale is not new – explain.

8. Provide a brief synopsis of the most famous debate on nanotechnology/nanobots.

9. Explain the role of top down and bottom up approaches in understanding nanosystems.

10.“Till today, picotechnology and femtotechnology do not make sense in the way that nanotechnology does” – explain.

**Quiz 2 Questions**

1. Explain what the size of the exciton Bohr radius means for achieving quantum confinement. What systems are easiest for achieving this effect? Explain why?

2. Can ‘excitons’ be seen in the electronic absorption spectrum of bulk semi-conductors? Give explanation.

3. True or False? Also give explanations in support of your answer.

(a) Once an energy band is formed its width is proportional to the number of atoms in the solid.

(b) The band gap of a quantum dot is directly proportional to its size.

(c) A quantum dot containing thousands of atoms can be used to trap a single free electron – in effect creating a gigantic, artificial hydrogen atom.

(d) When numerous atoms are brought into close proximity, only the highest occupied energy sub-level forms a band.

(e) Quantum confinement relates only to those electrons that would otherwise be mobile - the conduction electrons.

**Final Exam. Questions**

1. Can the total energy and linear momentum of a particle moving in one dimension in a constant potential field be measured consecutively with no uncertainty in the values obtained ? Explain.

2. Consider the Schrodinger equation with a periodic potential. Are the eigenfunctions of this equation necessarily periodic ? Justify your answer.

3. Which are faster carrier of heat through a nano size metal: electrons or phonons ? Explain.

4. Consider two Hermitian operators ** A** and

5. What is Optical Tweezer ?

6. One dimensional box containing an electron suffers an infinitesimal perturbation and emits a photon of frequency hn = 3 E_{1} with E_{n}= n^{2} E_{1}, where E_{1} denotes the ground state of the particle. A student conclude that the electron was in the state f_{2} prior to perturbation. Is he correct ? Justify.

7. When you heat a solid nano-material, do the atoms within it vibrate with grater amplitude or greater frequency ? Explain.

8. A particle in one dimension is in the energy eigenstates f(k_{0})=A cos(k_{0}x). Ideal measurement of energy finds the value E=ħ^{2}k_{0}^{2}/(2m). What is the state of the particle after measurement ? Explain.

9. What is photonic crystal ? What is photonic band gap ?

10. Give a brief explanation for why the electrical resistance of a nano size solid tend to increase as it gets hotter.

11. Why understanding the concept of ‘density of states’ is important in nanoscience ? Explain.

12. What is phonon ? What characteristic must an atomic lattice have for it to support optical phonons ?

13. Suppose that in a sample of 1000 electrons, each has a wavefunction Y(x,t) = sin(x) e^{-i}^{w}^{t}. Measurements are made (at a specific time t = t’) to determine the location of electrons in the sample. Approximately how many electrons will be found in the interval -1 ≤ x ≤1 ?

14. What is the working principle of Light Emitting Diode (LED) ?

15. Define effective mass of a particle in an atomic lattice.

16, A free particle of mass m moving in one dimension is known to be in the initial state Y(x,0)= sin(k_{0}x). Suppose that p is measured at t = 3 sec and the value of hk_{0} is found. What is Y (x,t) at t > 3 sec ?

17. (a) What is buckling ? (b) What is the difference between buckling and bending ? (c) Write at least one possible application of buckling in the area of nanoscience. (d) Explain the potential energy diagram of a nano rod under compression. (e) Using this diagram explain why it is practically not possible for a nano rod to go from one buckled state to another under sufficiently high compression.

18. (a) What is a single molecule transistor? (b) What is a single electron transistor ? (c) What are the possible differences between single molecule transistor and single electron transistor ? (d) Discuss the possible mechanism of electron transport in the case of single C_{60} transistor. (e) Explain why current increases with the increase in bias voltage between the source and drain electrode ? (f) In case of single C_{60 }transistor, is electron transport rate same as the oscillation frequency of the center of mass of C_{60} in between two electrodes ? Explain. (g) What is the origin of 5 meV vibrational quantum in current vs. voltage plot at 1.5 K for a single C_{60} transistor.

**Few More Interesting Questions**

1. The suppression of a systems melting point is one of the known property of nano-scale materials (semiconductor & metal). Can you think of any potential applications that exploit this property ?

2. Provide examples of some companies that are currently producing nano-related products.

3. Before 1998, there were very few Universities/Institutes dedicated to Nano-science. Today, there are a number of Institutions/Universities dedicated to Nano-science. Can you find a few of these Universities/Institutions ?

4. Assume Drexler is right and one "assembler" can assemble a million of atoms within a second. Roughly how long would it take for one of these assemblers to put together a cricket ball ? Make assumptions where necessary and state your assumptions explicitly.

5. Measuring distances on the nanometer scale is an important task for a number of scientific investigations. Find at least one examples.

6. More recently, colloidal nanoparticles have been used as molecular rulers, do you have any idea of how the technology works ?

7. Having seen many applications of low dimensional materials, attempt to devise an original application of wells, wires or dots (or any other nano-system). Describe your application, state why it has advantages over bulk analogues, and explain how you intend to make such a device.

8. Read about Magnetotactic Bacteria that naturally contain magnetic particles. Find out how these bacteria synthesize nanoparticles. Then ask yourself why they would want them in the first place.

9. Provide examples of some companies that are currently producing nano-related products.

10. Does the effective band gap of a low dimensional semiconductor increase with degree of confinement (the band gap is akin to the HOMO-LUMO gap of a molecular system) ?

11. What is dark exciton ?

12. Consider the well-known progression of colours possessed by ensembles of different-sized colloidal CDSe quantum dots. The samller particle appear yellow. Larger one appear red. Think about why small diameter ensembles appear yellow while larger-diameter ensembles appear red. Similarly, it is well known that gold nanoparticles generally have a distinct ruby red colour. By contrast, aggregated gold ensembles appear blue to the eye. Think about the origin of these colours as well.

13. There is considerable interest in the community in going beyond the generic classes of nanosctructures. For example there is interest in combining individual quantum dots to make so called quantum dot "molecules". Alternatively, one can make more extended structures, leading to artificial "solids" sometimes called superlattices. Find examples of each in the literature.

14. Find two examples in the current literature, where materials are said to be in any one of the various confinement regimes, described in the class.

15. Explain what the size of the exciton Bohr radius mean for achieving quantum confinement. What systems are easier for achieving this effect ?

16. Find an example from the literature where the surface to volume ratio is invoked to explain some special property of nanostructure.

17. What are the some of the broader moral and ethical implications of nanoscience and nanotechnology ?

18. One of the major concerns these days with nanoscience and nanotechnology has to do with health risks. There are those who think that all nano-related research should be stopped until its health risks have been fully evaluated. Can you think about the possible 'origin' of these health risks ?

**Related Links**

1. R. Feynman. There's plenty of room at the bottom. www.zyvex.com/nanotech/feynman.html.

2. E. Drexler, Machine phase nanotechnology. Scietific American, September 2001. www.ruf.rice.edu/~rau/phys600/drexler.htm.

3. R. Smalley, Of chemistry, love and nanobots, Scietific American 2001. www.cohesion.rice.edu/naturalsciences/smalley/emplibrary/sa285-76.pdf.

4. C&EN cover story debate on molecular assembler. C&EN 81, 37-42 (2003). www.pubs.acs.org/cen/coverstory/8148/8148counterpoint.html.

5. The Nobel Prize in Chemistry 2011. www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.html.

6. Graphene: Summery. www.nature.com/nature/journal/v483/n7389_supp/full/483S29a.html.

7. Single Molecule Transistor. www.people.fas.harvard.edu/~parklab/publications/Nature_407_57_2000.pdf.

8. Buckling of a nonosystem. http://prb.aps.org/pdf/PRB/v64/i22/e220101.

9. How did Coulomb arrive at 'Coulomb's law' from his experiments. https://webspace.utexas.edu/aam829/1/m/Coulomb_files/CoulombExperiment-1.pdf.

Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Kamand, Himachal Pradesh 175005

India

ph: +(91)1905-237930

achakrab