Nanophysics: MENA5010/9010

Transcription

1 Nanophysics: MENA5010/9010 The course is organized by Department of Physics, UiO Lecturer: Spring 2018 Pavlo Mikheenko, University of Oslo Lectures on physics of nanostructures Student presentations (will be graded and form a part of exam) Introduction 1

2 Pavlo Mikheenko ndex.html Physics building, Room FV404 Direct/Voice Mail: 22 8(5 7471) Lecture plan and lectures: Introduction 2

3 Richard Feynman 29th December 1959 on APS Meeting at Caltech: There is plenty of room at the bottom Introduction MENA5010/9010 Spring Introduction 3

4 Syllabus The purpose of the present book is to introduce the reader to this topic from an experimental point of view. The reader is hereby assumed to be a student of physics or a related field, who has just finished introductory courses, in particular those on solid state physics and quantum mechanics, and plans to study nanoscience more closely. The reader is picked up at the knowledge he/she is likely to have, and a ride is given to ongoing research activities in the field of mesoscopic transport. Along the way, the elementary concepts and nanostructures are introduced. Introduction 4

5 What is nanoscience and nanotechnology? Broad definition - Nanoscience and nanotechnology are all about relating and exploiting phenomena for materials having one, two or three dimensions reduced to the nanoscale. Very broad area of science and technology having many branches. Beginning of this course Introduction 5

6 The course aims at an introduction to basic principles of nanophysics allowing working in research and development in nanotechnology. You will learn principle of physics of nanometer-size systems with a focus on basic physical phenomena. In addition to main theoretical concepts, the applications of nanophysics to existing and future electronics, will be discussed. Introduction 6

7 Structure of the course The course will offer lectures on basic principles behind nanoscience and nanotechnology and presentations of some topics by students. These presentations are compulsory, they will be graded and the grading will be taken into account at the final examination. There will also be few problems solving. Midterm and end term evaluations will be carried out. Introducing elements of Students Active Learning: reading chapter before lecture. MSHRL: Met, Seen, Heard, Respected and Loved Exam: 40% + 30% + 30% (10% + 10%). Introduction 7

8 Nanoscience is referred to as a research area devoted to studies of various phenomena in small-size devices. It is a cross-disciplinary field including physics, chemistry, and biology. The key for understanding of nanoscience is mesoscopic physics. The word ``meso'' reflects the fact that the size of the systems under consideration is located between microscopic (atoms) and macroscopic scales. Introduction 8

9 Nanophysics: Main trends and crossroads Nano-Optoelectronics Nano-Electromechanics Nanomechanics Nano-Optomechanics Introduction 9

10 What is Nano? Nano means Small! 1 nm =10-9 m= 10-7 cm Introduction to Nanophysics 10

11 Nano means Big! Nanoscale objects do not fully belong to the microcosm Many atoms, electrons, etc., are involved Micro Number of degrees of freedom is large Nuclei Atoms Small molecules Meso Nano-objects Size Macro Fluids Crystals Glasses Introduction to Nanophysics 11

12 Characteristic scales in nanoscience Nanometer scale Length scale Atoms Molecules & Clusters Electron mean free path Bulk materials Micro Meso Macro Modern electronic devices belong to mesoscopic scale Introduction 12

13 Nanophysics and Edvard Munch Edvard Munch, Introduction 13

14 Jacques Dubochet Joachim Frank Richard Henderson 2017 Press Release: The Nobel Prize in Chemistry October 2017 The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Chemistry 2017 to Jacques Dubochet University of Lausanne, Switzerland Joachim Frank Columbia University, New York, USA and Richard Henderson MRC Laboratory of Molecular Biology, Cambridge, UK "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution"

15 The Nobel Prize in Chemistry 2017 Press release in 1990, Richard Henderson succeeded in using an electron microscope to generate a three-dimensional image of a protein at atomic resolution. This breakthrough proved the technology s potential. Joachim Frank made the technology generally applicable. Between 1975 and 1986 he developed an image processing method in which the electron microscope s fuzzy twodimensional images are analysed and merged to reveal a sharp three-dimensional structure. Jacques Dubochet added water to electron microscopy. Liquid water evaporates in the electron microscope s vacuum, which makes the biomolecules collapse. In the early 1980s, Dubochet succeeded in vitrifying water he cooled water so rapidly that it solidified in its liquid form around a biological sample, allowing the biomolecules to retain their natural shape even in a vacuum.

16 The Nobel Prize in Chemistry

17 The Nobel Prize in Chemistry

18 Chemistry Nobel Prize 2016 for molecular nanomachines Jean-Pierre Sauvage, Sir J Fraser Stoddart and Bernard L Feringa Introduction 18

19 Physics Nobel Prize 2016 for topological phase transitions and topological phases of matter David Thouless, Duncan Haldane and Michael Kosterlitz Introduction 19

20 2016: 30 years of the Nobel Prize for scanning tunnelling microscopy (STM) and the first report of atomic force microscopy (AFM). Introduction 20

21 Nobel Prize for scanning tunnelling microscopy (STM) The Nobel Prize in Physics 1986 was divided, one half awarded to Ernst Ruska "for his fundamental work in electron optics, and for the design of the first electron microscope", the other half jointly to Gerd Binnig and Heinrich Rohrer "for their design of the scanning tunneling microscope". Introduction 21

22 Tunneling effect The Nobel Prize in Physics 1973 Leo Esaki, Ivar Giaever, Brian D. Josephson 1973 Ivar Giaever Prize motivation: "for their experimental discoveries regarding tunnelling phenomena in semiconductors and superconductors, respectively" Field: condensed matter physics, semiconductors Beginning of nanophysics: in 1951, Gorter suggested that experiments by van Itterbeek and coworkers, who measured the current through metal grains embedded in an isolated matrix, could be explained by single-electron charging. Superconductivity in Nanosystems 22

23 Quantum tunneling: Ivar Giaver May 2012, Lofoten Following on Esaki's discovery of electron tunnelling in semiconductors in 1958, Giaever showed that tunnelling also took place in superconductors (1960). Giaever's demonstration of tunnelling in superconductors stimulated Brian Josephson to work on the phenomenon, leading to his prediction of the Josephson effect in Esaki and Giaever shared half of the 1973 Nobel Prize, and Josephson received the other half. Electron phase coherence

24 Official opening on 7 September 2016 Instruments for Paleomagnetic Measurements and Rock Magnetic Analyses AGICO JR-6A Spinner Magnetometer Lake Shore PMC MicroMag 3900 Vibrating Sample Magnetometer (VSM)

25 2016: Memristor behaves like a synapse Researchers led by Qiangfei Xia and Joshua Yang at the University of Massachusetts at Amherst in the US have made a "diffusive" memristor that emulates how a real synapse works. The device could be used as a key element in integrated circuits and next-generation computers that mimic how the human brain works. The new device is made from a memory resistor or memristor (a resistor that remembers how much current has flowed through it). Unlike other modern-day electronics memories like those made from CMOS devices, memristors are able to remember their state (that is the information stored in them) even if you lose power. They also use much less energy and, importantly, so-called diffusive memristors can realistically mimic how ions, such as Ca 2+, diffuse through synapses. Introduction 25

26 2016: Other highlights Graphene patch detects glucose in sweat Quantum-dot barcodes for diagnosing disease Polymeric nanoparticles deliver anti-inflammatory proteins Nanotube array transistor breaks new record Graphene composite enables metre-sized flexible displays 2D perovskite solar cells break new efficiency record Self-powered textile could be woven into smart clothes t 19. What applications of nanophysics do you know? Nanostructured supercapacitors empower sustainable storage Flexible LG display Samsung Galaxy S8 with 10-nm design Qualcomm Snapdragon 830 microprocessor Lenovo folding display Introduction 26

27 2017 highlights World's Smallest Christmas Card Offers Season's Tiniest Greetings Practical Quantum Computers Self-Driving Trucks Brain implants to restore the freedom of movement Amazing Artificial Intelligence Achievements Samsung: Pushing the boundaries in OLEDs Samsung Galaxy S8 with 10 nm design released 4K and Ultra HD screens: the hot new resolution t 19. What applications of nanophysics do you know? World's Smallest Christmas Card Quantum Computer Introduction 27

28 2017 highlights Graphene composite provides wireless power Designing highly reversible aluminum-ion batteries with graphene Graphene-oxide membranes filter organic solutions Brain-penetrating nanoparticles restore neuron function Nanotechnology takes on microbial drug resistance Nanoparticles resurrect antibacterial drugs High conductance detected in a human integrin protein t 19. What applications of nanophysics do you know? Nano-patterning technique records structural color at low cost Nanomaterials help fight infectious disease Fixed-junction device for protein measurement Nano-cone arrays produce structural color by diffraction. Introduction 28

29 Physicists build muscle for shape-changing, cell-sized robots January 3, 2018 Cornell University Robotics experts have made a robot exoskeleton that can rapidly change its shape upon sensing chemical or thermal changes in its environment. And, they claim, these microscale machines equipped with electronic, photonic and chemical payloads could become a powerful platform for robotics at the size scale of biological microorganisms. Introduction 29

30 What number of electrons can we expect in mesoscopic objects? 1 nm 3 ~ 30 atoms (5 nm) 3 ~ 125 x 30 = 3750 atoms C 6 el./atom Ge 32 el./atom Ga 31 el./atom As 33 el./atom Hund's rules Introduction to Nanophysics 30

31 Electron orbitals and shells in atoms In atoms number of electrons per shell is 2n 2 : 2, 8, 18, 32 In atoms number of electrons per orbit is 2(2l+1): 2,6,10,14,18,22,26 Introduction to Nanophysics 31

32 Role of surface effects in mesoscopic objects t 2. What happens to the laws of physics on a mesoscopic scale? Give an example. A / V = 6a 2 / a 3 = 6 / a = 6 V -1/3 V = a 3 (2a) 3 = 8 a 3 (5a) 3 = 125 a 3 (10a) 3 = 1000 a 3 Percentage of surface atoms : 100% 100% 78,4% 48,8% Macroscopic: V = (10 8 a) 3 = a 3 A = 6 (10 8 a) 2 = a 2 Percentage of surface atoms: %!!! (negligible) Introduction to Nanophysics 32

33 Classical vs. Quantum Physics for mesoscopic objects t 2. What happens to the laws of physics on a mesoscopic scale? Give an example. Classical Mechanics Electrodynamics Thermodynamics Quantum Mechanics Quantum Electrodynamics Quantum Statistics Mesoscopic phenomena (quasiclassical regime) Introduction 33

34 Moor s law and necessity for mesoscopics t 1. What is Moore s law? Why do we need Nanophysics? Introduction 34

35 CMOS TECHNOLOGY complementary metal-oxide semiconductor technology Intel s Norwood (Pentium nm) processor Intel s Prescott processor (released March 2004): 150 million transistors 90 nm design rules 3.4 GHz clock frequency DRAM chips: Dynamic random-access memory 4 Gb chips demonstrated (~ 10 9 transistors/cm 2 ) In 2010 chips were based on the design rule of 22 nm. 20 years back we were already Introduction well inside nanotechnology! 35

36 Progress in miniaturisation By Cmglee - Own work, CC BY-SA 3.0, t 1. What is Moore s law? Why do we need Nanophysics? Introduction 36

37 Main ingredients of nanoelectronics Two-dimensional electron gas (2DEG) Quantum wires and point contacts Quantum dots Nano-electro-mechanical systems Vibrating carbon and non-carbon nanotubes and other molecular devices Devices using superconductivity and magnetism at nanoscale Devices for quantum computation Novel devices Spintronics manipulation of electron spin Introduction 37

38 Samples, materials, and experimental techniques Semiconductor devices: GaAlAs heterostructures (optoelectronics, high mobility under modulation doping) Si-MOSFET (silicon has a natural oxide, that is very important) New systems: Carbon nanotubes, etc t 18. What semiconducting materials are usually used in the nano-industry and nanophysics experiments? What are reasons for that? Structure of a carbon nanotube. The circles denote carbon atoms in a graphite sheet, which is rolled up and forms a tube with a diameter of a few nanometers. The ends are supposedly capped by a carbon hemisphere. Introduction 38

39 Materials for nano-industry Ga[Al]As Si 18. twhat semiconducting materials are usually used in the nano-industry and nanophysics experiments? What are reasons for that? Self-assembled quantum dots are periodic arrays of artificial atoms. They are considered to be promising systems for heterostructure lasers. Introduction 39

40 SINGLE-ELECTRON SINGLE-MOLECULE TRANSISTORS J. Park et al. (2002) t 18. What semiconducting materials are usually used in the nano-industry and nanophysics experiments? What are reasons for that? see also: - E. S. Soldatov et al. (1996) - H. Park et al. (2000) - N. Zhitenev et al. (2002) - S. Kubatkin et al. (2003) SET within the Orthodox theory: C 1 = C 2 = C/2 R 1 = R 2 = R/2 Current I (e/rc) k B T = 0.01 e 2 /C Q e = e/2 Q e = 0 V t (for Q 0 = 0) Introduction Source-drain Voltage V (e/c) 40

41 Instrumentation for nanoscience and nanotechnology Growth Fabrication Characterization MBE EBL STM Quantum corralls Introduction 41

42 New laws of Nature at nanoscale? In a classical resistor, the resistance is due to electron scattering. Otherwise electrons are just accelerated by the electric field. 2. twhat happens to the laws of physics on a mesoscopic scale? Give an example. QM: Particle or wave? 5. twhat length scale is important for a double slit experiment in the solid state? Please explain. Quantum modes in the wire Electron diffraction is controlled by phase coherence length Introduction 42

43 Classical versus quantum physics t 2. What happens to the laws of physics on a mesoscopic scale? Give an example. Introduction 43

44 Basic problems Features of nanoscale systems: Quantum transport Specific electron-electron interaction, which is more pronounced in low-dimensional systems Stronger role of disorder Enhanced role of contacts and electromagnetic environment Nano-devices are usually out of equilibrium, which requires special understanding t 2. What happens to the laws of physics on a mesoscopic scale? Give an example. All these issues are far from being fully understood It is new research area with rich physics and chemistry! Introduction 44

45 Quantum Mechanics of Interacting Particles Condensation Wigner crystal Introduction 45

46 Self-assembly systems Nanomaterials Encapsulated 4 nm Au particles self-assembled into a 2D array supported by a thin film, Anders et al., 1995 Scheme for molecular manufacturing Introduction 46

47 In nanomaterials electrical and mechanical energies are comparable Electrical and mechanical modes are strongly coupled Nano-electro-mechanics Examples of the systems Electron shuttles Molecular motors Carbon nanotubes Introduction 47

48 Shuttle transfer of electrons A movable cluster conveys electron one by one In some cases electro-mechanic instabilities can take place Shuttle transport has been observed in several concrete systems Introduction 48

49 Solar cells with nanoparticles: Nanoplasmonics Main principle: Plasmon resonances due to nanoparticles strongly enhance the time, which photons spend close to the active layer Metallic nanoparticles embedded in the host system close to the active layer Simulation of increased light intensity beneath a metal nanoparticle on a silicon cell Key players: Centre for Sustainable Energy Systems at the Australian National University (ANU) ; Caltech, US; FOM-Institute, AMOLF, the Netherlands. Introduction 49

50 Mesoscopic Superconductivity Studies of individual magnetic vortices by magneto-optical (MO) imaging Tom Henning Johansen et al., Univ. Oslo x J B(r) l Fluks kvantum: B da = Introduction 50

51 One can take snapshots at different times, and in this way observe vortex dynamics Example: Edge effects prøvekant 10 m MOI single vortices allows to study and influence mesoscopic structure of vortex matter Introduction 51

52 More about physical scales Classical length electron mean free path, Quantum length de Broglie wavelength of an electron having the Fermi energy: t 4. What is de Broglie wavelength of electrons and size quantization? This scale is relevant to the size quantization quantum films, wires, and dots Introduction 52

53 Another important scale phase coherence length, Scale introduced by Coulomb interaction and depending on the device capacitance, C - relevant to single-electron tunneling Interplay between different scales leads to a rich picture of transport through nanosystems. The specific properties of different regimes can be used for various applications. t 6. What is the role of charging effects on nano-scale? Introduction 53

54 Basic classification of transport regimes mean free path phase coherence length Fermi wavelength t 3. What are characteristic length scales and specific parameters that define transition to mesoscopic regime? Introduction 54

55 Two-dimensional Electron Gas (2DEG) Band gap engineering 2DEG is a generic object for new physics Metal-Oxide-Semiconductor (MOS) structures 2DEG is formed at the semiconductor-insulator interface Semiconductor heterostructure 2DEG is formed at the interface between two semiconductors Nobel Prizes 1985, 1998, 2000 It serves as a building block for electronic devices We will come back to these structures later Introduction 55

56 Quantum Wires and Point Contacts Cleaved structures Split-gate structures Point contacts Carbon nanotubes Introduction 56

57 Ballistic transport,, quantum point contact To the left, the surface topography of a GaAs microchip is shown. The picture has been taken with an atomic force microscope. The chip hosts a quantum film about 30 nm below its surface, which is removed underneath the bright lines. A small and short wire of length 140 nm and width 80 nm connects source and drain. The measurement to the right shows the conductance of the wire as a function of the gate voltage. At low temperatures, a conductance quantization in units of 2e 2 /h is visible, which vanishes around 20 K. 7. twhat length scale is important for ballistic transport? How is it influenced by temperature? t 10. What is the quantum point contact (QPC), and at what temperatures and lengths does it usually operate? What length scale is important for QPC? Introduction 57

58 Quantization of conductance vs. gate voltage! Conductance quantum: S New universal unit of resistance h/e 2 8. tdoes a ballistic wire have infinite conductance? Absent in classical theory t 9. What is the quantum of conductance? Where does it appear? What is the value of quantum resistance in Ohm? KOhm Introduction 58

59 The quantum Hall effects and Shubnikov-de Haas oscillations Classical Hall effect Shubnikov-de Haas oscillations and the quantum Hall effect. We look at a measurement of the longitudinal and the Hall resistance (R xx and R yy, respectively), of a two dimensional electron gas, as a function of a magnetic field applied perpendicular to the plane of the quantum film. The experiment has been performed at a temperature of 100 mk. The Hall resistance is quantized in units of h/2e 2. t 11. What is the quantum Hall effect and Shubnikov de Haas oscillations? Are these effects linked? In what systems do they take place? In what units is resistance quantized? What temperatures and magnetic fields are essential for these effects? Introduction 59

60 At low temperatures Phase coherence t 13. What is the Aharonov Bohm effect? What is typical geometry of the device showing this effect? What length scale is important for this effect, and by what kind of scattering is it influenced? Is resistance a local property in this effect? Is high magnetic field and low temperatures necessary for it? The resistance of a small ring with a diameter of about 1 micron (the light gray areas in the inset) as a function of a magnetic field applied perpendicular to the ring plane shows periodic oscillations, known as Aharonov-Bohm oscillations. They indicate that a significant fraction of the electrons traverse the ring phase coherently. Dephasing is caused by inelastic (e-ph, e-e) scattering. Diffusive coherent systems are possible. E-e scattering does not contribute to resistance. Introduction 60

61 Single-electron tunneling and quantum dots The right inset shows again the surface topography of a semiconductor with a two dimensional electron gas underneath. The bright lines enclose a small island. It is coupled to source and drain via two quantum point contacts, forming tunnel barriers for the electrons. The barriers are tuned by adjusting the voltages at the gates Ql and Q2. The main figure shows the conductance through the island as a function of the gate voltage V I applied to region I. V I tunes the potential of the island. The conductance peaks indicate that only for a particular island potential, electrons can be transferred between the island and the leads. The left inset shows a fit to a function one would expect for peaks that are governed by thermal smearing of the Fermi function. t 15. What is a quantum dot and what is its relation to single electron quantum transistor? Introduction 61

62 Quantum Dots Lateral quantum dots Coulomb blockage! Ivar Giæver 15. twhat is a quantum dot and what is its relation to single electron quantum transistor? Vertical Artificial atoms new periodic table In atoms number of electrons per shell is 2n 2 : 2, 8, 18, 32 In artificial atoms number of electrons per shell is : 2, 6, 12, 20 Introduction 62

63 Coulomb blockade Gate Electron Dot t 14. What is single-electron tunneling and the role of capacitance in this effect? What is the characteristic energy that plays a major role in this effect? Cost Repulsion at the dot Attraction to the gate At the energy cost vanishes! Single-electron transistor (SET) Introduction 63

64 Fermi wavelength 21. Why does Fermi wavelength decrease with the electron density? What is the relation between Fermi wavelength and electron density in different dimensions? Can you derive this? Can you find mistakes in TH p. 158 (pdf)? Introduction 64

65 Density of states 12. What is the role of Fermi wavelength in changing the dimensionality of mesoscopic systems? Is it related to de Broglie wavelength? What are the implications of changing dimensionality? What is the density of states as function of energy per unit volume in systems of different dimensions? Can you derive this? Electron density of states in the effective mass approximation as a function of energy, in one, two, and three dimensions Update of solid state physics 65

66 Density of states Two dimensional system, periodic boundary conditions Momentum is quantized in units of A quadratic lattice in k-space, each of them is g-fold degenerate (spin, valleys). Assume that, the limit of continuous spectrum. Number of states between k and k+dk: Update of solid state physics 66

67 Number of states per volume per the region k,k+dk Density of states -Number of states per volume per the region E,E+dE. Since 3 Update of solid state physics 67

68 Electron spin Was first introduced in 1925 by Uhlenbeck and Goudsmit to explain the hyperfine structure of the atomic spectrum. 16. What is the role of electron spin in solid-state physics? What characteristic length scale is important in nanospintronics? Do you know any commercial devices that use spin of electrons? A theoretical foundation has been provided in 1928 by Dirac by making a relativistic correction to the wave equation. Spintronics 68

69 Giant magnetoresistance In GMR, resistance depends on the relative orientation of the electron spin-defined magnetizations of the ferromagnetic layers. 16. What is the role of electron spin in solid-state physics? What characteristic length scale is important in nanospintronics? Do you know any commercial devices that use spin of electrons? Giant magnetoresistance 69

70 Electronics applications 16. What is the role of electron spin in solid-state physics? What characteristic length scale is important in nanospintronics? Do you know any commercial devices that use spin of electrons? t 19. What applications of nanophysics do you know? Spintronics 70

71 Mesoscopic effects: role of temperature The typical length scale at which the mesoscopic regime is reached depends on the temperature. The numbers below give an order of magnitude. Temperature (K) L (nm) 4.2 (liquid helium) < (liquid nitrogen) < (room temperature) < What energies and temperatures are typical for mesoscopic electronic devices? What is the relation between temperature and electron energy? What is typical length scale at which the mesoscopic regime takes place at different temperatures? t 20. What determines the temperature at which a mesoscopic effect vanishes? How is it in contrast with superconductivity? Update of solid state physics 71

72 Quantum scattering length 22. What is quantum scattering length and quantum scattering time? Is it the same as Drude scattering time τ? t 22. What is quantum scattering length and quantum scattering time? Is it the same as Drude scattering time τ? Introduction 72

73 Diffusive transport Between scattering events electrons move like free particles with a given effective mass. In 1D case the relation between the final velocity and the effective free path, l, is then Assuming where is the drift velocity while is the typical velocity and introducing the collision time as we obtain in the linear approximation: Mobility Update of solid state physics 73

74 Dephasing time 23. thow does dephasing time of electrons depend on T at low and high temperatures? τ Introduction 74