PHYS-E0424 Nanophysics Lecture 3: Self-Organization

Transcription

1 PHYS-E0424 Nanophysics Lecture 3: Self-Organization 1

2 Intel 14 nm Transistor Here is a link to a web page presenting novel Intel 14nm transistor technology, that is promising to go beyond Moore s law. And yes, they still use Si substrate. Igor Prozheev 14nm-explained-video.html 2

3 Heat Waste On Moore's law: There has been no increase in commercial processor clock frequencies since 2003, as can be seen from the figure on page 146. My personal experience agrees with that well. I used to have 2.7 GHz laptop at that time and nowadays they are not that faster. Sami Kivistö 3

4 Heat Waste 4

5 Hard Disk Drive Errors What properties affect the error rates of read and write operations in magnetic storage? How does this affect the design of the storage devices on nanoscale? How can these errors be recognized and prevented (on the hardware level)? Jesper Ilves Modern drives make extensive use of error correction codes (ECCs). These techniques store extra bits, determined by mathematical formulas, for each block of data; the extra bits allow many errors to be corrected invisibly. The extra bits themselves take up space on the HDD, but allow higher recording densities to be employed without causing uncorrectable errors, resulting in much larger storage capacity. For example, a typical 1 TB hard disk with 512-byte sectors provides additional capacity of about 93 GB for the data. 5

6 Surface vs. Volume I have a simple general question related to last lecture. It has been seen that at Nano scale properties change as compared to bulk material. Is surface area to volume ratio and quantum effects are responsible for this change? or there is something more? Saeed Ahmad Surface area to volume ratio is particularly relevant to ordering phenomena (ferromagnetic-paramagnetic, ferroelectric-paraelectric, solidliquid transitions etc.) 6

7 Critical Length Scales for Electronic Transport 1 mm 100 m 10 m 1 m 100 nm 10 nm 1 nm 1 Å - Mean free path in quantum Hall regime - Mean free path/phase relaxation length in high mobility semiconductors - Commercial semiconductor devices - de Broglie wavelength ( = h/p) in semiconductors/ mean free path in polycrystalline metal - de Broglie wavelength ( = h/p) in metals - Distance between atoms - Fermi wavelength ( f ) (only electrons near the Fermi level contribute to G) f 2 n - Mean free path (L m ): distance that an electron travels before its initial momentum is destroyed Lm f m - Phase-relaxation length (L ): distance that an electron travels before its initial phase is altered s f n m 2 s 7

8 Critical Length Scales for Electronic Transport Ballistic transport: L < L m, L - No electron scattering. Geometry determines transport properties (no well-defined ). - Quantization of conductance (G ~ e 2 /h) occurs when L f Diffusive coherent transport: L m < L < L - Scattering. Reduced transmission. Weak localization: L m << L - R(L) ~ exp(l) due to quantum interference effects Classical transport: L m, L << L - Ohmic behaviour 8

9 DNA and Neuromorphic computing There are two interesting topics that were only shortly mentioned in the articles or during the lecture that I would like to hear more about. - DNA based transistors - Neuromorphic computing Joonas Leppänen 9

10 Computing with DNA 10

11 Bio-Inspired Computing Mimic the brain: Neuromorphic computing 11

12 Bio-Inspired Computing Mimic the brain: The average human brain has about 100 billion neurons. Each neuron may be connected to up to 10,000 other neurons, passing signals to each other via as many as 1,000 trillion synaptic connections, equivalent by some estimates to a computer with a 1 trillion bit per second processor. Estimates of the human brain s memory capacity vary wildly from 1 to 1,000 terabytes. Unlike CPUs, the brain uses a mixture of analogue and digital signals, processes information on a massively parallel scale, and seamlessly combines memory and logic operations. Besides these superior functional attributes, it carries out computing operations with up to a million times less energy than present-day computers. 12

13 Memristor The Mysterious Memristor, IEEE Spectrum, May

14 Mimicking Synaptic Activity 14

15 Quantum Computers Is the any recent progress in building quantum computer, rather than in its theoretical description? Igor Prozheev 15

16 Quantum Computers Nature 464, 45 (2010) 16

17 Quantum Computers A quantum computer is a computational device that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers 17

18 Quantum Computing Technologies - Photons - Trapped atoms - Nuclear magnetic resonance - Quantum dots and dopants in solids - Superconductors 18

19 Commercial Quantum Computers 19

20 2D Materials I think you might be interested in this article. These is yet an early stage research, but already a breakthrough! These guys in MIT achieved patterning and stitching together 2D materials in one layer. They were able to make structure of graphene (as a conductor), MoS2 and WS2 (as semiconductors) and h-bn (as insulator). They created diodes and then simple basic circuitry from these 2D materials entirely, such as inverter, NOR and NAND gates. Kirill Isakov 20

21 2D Materials 21

22 E-Beam Lithography - Charging Certain substrates used with e-beam lithography are prone to defects due to negative charge buildup on the surface of the substrate, which can deflect the electron beam. This however can be remedied with the use of a charge dissipative agent. Jesper Ilves 22

23 E-Beam Lithography - Charging 23

24 E-Beam Lithography - Charging 24

25 E-Beam Lithography - Charging 25

26 E-Beam Lithography - Charging 26

27 SPM Lithography Here are some articles I found interesting, related to SPM lithography. They both are referred in the "Advanced scanning probe lithography" review article. Sami Kivistö 27

28 The Boy and His Atom Promotional video by IBM about the manipulation of atoms at surfaces (CO molecules on Cu) 28

29 PHYS-E0424 Nanophysics Lecture 3: Self-Organization 29

30 Self-Organization Self-organization is a process of attraction and repulsion in which the internal organization of a system, normally an open system, increases in complexity without being guided or managed by an outside source (examples in biology, chemistry, physics) Self-organization is bottom up approach for patterning of micro- and nanostructures Top down approach : Lithography (lecture 2) J.V. Barth et al., Nature 437, 671 (2005) 30

31 Self-Organization vs. Self-Assembly - Self-organization and Self-assembly are regularly used interchangeably - Both processes explain how collective order is developed from dynamic small-scale interactions - Self-organization is a non-equilibrium process where self-assembly is a spontaneous process that leads towards equilibrium (thermodynamic difference) - Self-assembly requires components to remain essentially unchanged throughout the process - Another slight contrast refers to the minimum number of units needed to establish order. Self-organization appears to have a minimum number of units where as self-assembly does not 31

32 Self-Organization - Deposition techniques - Physics of homoepitaxy - Physics of heteroepitaxy - Different routes to self-organized nanostructures 32

33 Deposition Physical Vapour Deposition (PVD) Chemical Vapour Deposition (CVD) - Thermal evaporation - Molecular beam epitaxy (MBE) - Electron beam deposition - Pulsed laser deposition - Magnetron sputtering 33

34 Thermal Evaporation - Evaporation material is heated by a filament - Can be used for most metals - The incoming atoms have low thermal energy (1.5kT is about ev) - Low deposition rate ( ML/s) - Film growth in quasi-equilibrium - Epitaxial growth 34

35 Evaporation - Different evaporation sources and evaporation geometries are available (boats, filament, crucibles) - Good for Ag, Cu, Au, Pt etc 35

36 Molecular Beam Epitaxy (MBE) - Pure elements are heated in an effusion cell - A molecular beam is deposited onto the substrate - Good for materials with a low melting temperature - Accurate control over vapor pressure and temperature - The incoming atoms have low thermal energy (1.5kT is about ev) - Low deposition rate ( ML/s) 36

37 Molecular Beam Epitaxy (MBE) - Often used for II-VI and III-V semiconductor film growth (e.g. quantum wells) - Each material and dopant is evaporated from its own effusion cell 37

38 Electron Beam Deposition - A magnetic field focuses an electron beam onto the evaporation material - Mostly used for metals - The incoming atoms have low thermal energy (1.5kT is about ev) - Low deposition rate ( ML/s) - Film growth in quasi-equilibrium - Epitaxial growth - Different evaporation geometries are available - Good for Co, Fe, Ni, Cu, Au etc. 38

39 Pulsed Laser Deposition - An intense laser beam is pulsed onto the deposition target - The pulse creates a laser plume of evaporation material from which material is deposited onto the substrate - The incoming atoms have low thermal energy (1.5kT is about ev) - Atoms are often in highly excited electronic states or multiple ionisation states - Very high deposition rate of up to 10 6 ML/s (pulsed) - Film growth far from equilibrium - High nucleation density - Mostly used for (insulating) oxide materials - Epitaxial growth 39

40 Pulsed Laser Deposition 40

41 Magnetron Sputtering - Sputter gas atoms (Ar) are ionised and accelerated towards a target - Atoms are removed from the target by sputtering and are deposited onto the substrate - The incoming atoms/ions have high energy (up to several hundred ev) - Mixing between deposition and substrate material - High deposition rates can be obtained (50 ML/s) - Both conducting (dc mode) and insulating material (rf mode) can be deposited - High nucleation density - Smooth films 41

42 Magnetron Deposition 42

43 Vacuum Why vacuum? - To increase the mean free path of evaporated atoms or molecules - To reduce contamination on the substrate and in the growing film 43

44 Vacuum What determines the vacuum pressure - In poor vacuum (p > 10-7 mbar) the gas is mostly water vapour. Water absorbed on the surface may influence film growth and oxygen may be incorporated in the growing film. To reach a better vacuum the deposition system needs to be baked. - In Intermediate vacuum (10-9 mbar > p > 10-7 mbar) the presence of CO and CO 2 on the surface may influence the growth process - In ultra-high vacuum (p < 10-9 mbar) film growth is not influenced much by adsorbates 44

45 Adsorption Physisorption (physical adsorption) - Adsorption process in which the electronic structure of the atom or molecule is barely perturbed - The weak bonding of physisorption is due to the induced dipole moment of a nonpolar adsorbate interacting with its own image charge in a polarizable solid (Van der Waals force). Small interaction energy of mev. V 1 ~ d - As the adsorbed atom moves closer to the surface the physisorption potential energy changes from negative to positive due to Pauli exclusion 3 45

46 Adsorption Chemisorption (chemical adsorption) - Adsorption process in which the electronic structure of atoms or molecules is changed by the formation of covalent or ionic bonds - Large binding energy (> 0.5 ev per atom or molecule) - The adsorbate diffuses on the surface until it finds a deep chemisorption well. There it reacts with the surface and this leads to a reduction of the surface free energy. 1. Physisorption 2. Dissociative chemisorption 3. Chemisorption 46

47 Chemisorption Covalent bond: A covalent bond is a chemical bond that involves the sharing of pairs of electrons between atoms. Ionic bond: An ionic bond is a type of chemical bond formed through an electrostatic attraction between two oppositely charged ions. Ionic bonds are formed between a cation (positively charged), which is usually a metal, and an anion (negatively charged), which is usually a nonmetal. Sodium fluoride 47

48 Desorption Desorption of adatoms is a thermally activated process (E des ~ 1.5 ev) During deposition, desorption competes with adsorption at high temperatures and/or low deposition rates For example for E des = 2 ev: des = e -2eV/kT Hz This gives: des = 6 x des =

49 Self-Organization: Kinetics versus Energetics J.V. Barth et al., Nature 437, 671 (2005) 49

50 Epitaxy Epitaxy ( place or rest upon, arrangement) Growth of film with the same crystal orientation as substrate (single crystal on single crystal) Homoepitaxy Film and substrate material are the same Heteroepitaxy Film and substrate material are different 50

51 Atomic Processes at Surfaces J.W. Evans et al., Surf. Sci. Rep. 61, 1 (2006) 51

52 Atomic Diffusion A B V(x) E D Diffusion rate: D = 0 exp (-E D /k B T) x Metals: E D : 40 mev... 1 ev 0 : ~ Hz 52

53 Formation of Stable Nuclei E b E d dim Dimer is stable if E b >> thermal energy + E d dim >> E d Probability that dimer will break up: P ~ exp (-(E b + E d )/kt) 53

54 Growth of Adatom Islands Adatom islands grow when the binding energy is large enough and when the average diffusion length of adatoms is larger than the distance between stable nucleation sites 54

55 Nucleation Density Mean field theory and Monte Carlo simulations predict that the average island density is given by: N ( ) F 0 p exp p[ E d kt ( E i / i)] F is the deposition rate P = i/(i+2) i is number of atoms above which adatom islands become stable E i is binding energy of critical island size E d is adatom diffusion energy 55

56 Initial Stages of Film Growth Ag on K (a) and (b) nucleation (c) and (d) island growth H. Brune et al., Phys. Rev. Lett. 73, 1995 (1994) 56

57 Nucleation Density vs. Deposition Rate Ag on N ( ) F 0 p exp p[ E d ( E kt i / i)] L. Bardotti et al., Langmuir 14, 1487 (1998) 57

58 Nucleation Density vs. Temperature Pt on Pt(111) 23 K 115 K N F ( ) 0 p exp p[ E d ( E kt i / i)] M. Bott et al., Phys. Rev. Lett. 76, 1304 (1996) 140 K 160 K 58

59 Nucleation Density vs. Temperature Ag on Pt(111) N F ( ) 0 p exp p[ E d ( E kt i / i)] 80 K 95 K 110 K H. Brune et al., Phys. Rev. B 60, 5991 (1999) 59

60 Island Shape Island shape depends on: (1) Symmetry of surface (anisotropic adatom diffusion) (2) Adatom diffusion at step edges Si(001)-(2x1) reconstructed surface 60

61 Anisotropic Growth Si on From: Julich Research Institute 61

62 Anisotropic Adatom Diffusion Diffusion of Pt adatoms on Pt(110)-(1x2) From: University of Aarhus 62

63 Nonowires Monolayer Cu wires on Pd(110) H. Röder et al., Nature 366, 141 (1993) 63

64 Island Shape Si on High step-edge mobility From: Julich Research Institute 64

65 Island Shape Low or anisotropic adatom diffusion along step edges can induce growth of fractal nanostructures Ag/Pt(111) H. Brune, Surf. Sci. Rep. 31, 121 (1998) 65

66 Multilayer Growth Ehrlich Schwoebel barrier Additional diffusion barrier at step edges results in three-dimensional film growth E S - At high temperatures, adatoms have enough kinetic energy to overcome the Schwoebel barrier (2D growth) - At low temperatures the reflection of adatoms at step edges increases (transition to 3D growth) 66

67 Multilayer Growth 0.3 ML 3 ML 12 ML 90 ML M. Kalff et al., Surf. Sci. 426, L447 (1999) 67

68 Homoepitaxial Growth Modes Step-flow growth Adatoms have enough mobility to reach step edges on surface. This occurs close to thermodynamic equilibrium (high T) Layer-by-layer growth Interlayer mass transport is large enough so that no stable nuclei are formed on top of islands before they have coalesced to form a two-dimensional layer (intermediate T) Multilayer growth Reflection of adatoms at step edges is large enough so that stable nuclei can form on top of islands before coalescence (low T) 68

69 Heteroepitaxy Film and substrate material are different Additional effects/ mechanisms that influence film growth: - Surface free energy and interface energy - Strain due to lattice mismatch between film and substrate - Atomic mixing and alloying 69

70 Heteroepitaxial Growth Modes (Bauer Criteria) Layer-by-layer (Van der Merwe) f i 0 Layer-by-layer followed by mulilayer growth (Stranski-Krastanov) Free energy difference is negative, but once a complete layer is formed three dimensional homoepitaxy occurs s Multilayer growth (Volmer-Weber) f i 0 Assumption that temperature is high enough to reach thermodynamic equilibrium! s 70

71 Surface Free Energy Young s equation for the contact angle between a liquid and a solid fs cos( ) f c s 71

72 Strain Lattice misfit f b a a The thickness over which the strain in the film is relaxed equals roughly the distance between dislocations, l l ab a b A more detailed description involves elastic constants of the film and substrate material 72

73 Ge/Si Heteroepitaxy a Si = 5.43 Å a Ge = 5.57 Å f = 4.2% 73

74 Ge/Si Heteroepitaxy Strain-induced formation of nanostructures - Elastic strain distorts lattice - Strain relaxation by the formation of well-defined nanostructures K. Brunner, Rep. Pro. Phys. 65, 27 (2002) 74

75 Ge/Si Heteroepitaxy 5.8 ML of Ge on 550ºC Ge on 300ºC From: Julich Research Institute 75

76 Ge/Si Heteroepitaxy T < 550ºC, d < 8 ML T > 550ºC, d < 8 ML 8 ML< d < 13 ML d > 13 ML Hut clusters Pyramids Domes Overdomes 76

77 Multilayer QD Structures (In,Ga)As QDs on GaAs(100) Q.H. Xie, Phys. Rev. Lett. 75, 2542 (1995) 77

78 Anisotropic Lattice Mismatch When the material of the growing film has a different lattice structure than the substrate (e.g. hexagonal vs. cubic), then the mismatch may be anisotropic. This may influence the shape of self-organised nanostructures. NdSi 2 on Si(001) (a and c matched) DySi 2 on Si(001) (c matched a not) 78

79 Atomic Mixing Some materials have a negative enthalpy of mixing with one another These materials tend to mix strongly at the film substrate interface to give an interface layer that may extend over many atomic layers One example is transition metals on Si which tend to form silicides with varying stoichiometry in the interface layer Atomic mixing depends strongly on temperature CoFe Si 79

80 Immiscible Materials An immiscible film-substrate combination will generally form an atomically sharp interface (unless in cases of large epitaxial strain) Co/Cu(001) annealed at 180ºC If the film has a high surface energy compared to the substrate, a layer of substrate material may segregate to the surface with the film sandwiched in the middle (at elevated temperatures) F. Nouvertné et al., Surface Science 436, L653 (1999) 80

81 Nanostructuring by Self-Organization Growth manipulation - Temperature and deposition rate - Symmetry of surfaces (island shape) - Strain relaxation (e.g. Ge/Si) - Surfactants - Two mobilities - Dislocation networks - Surface reconstructions - Vicinal surfaces - Deposition angle 81

82 Surfactants - Surfactants can be used to enhance layer-by-layer growth - In many case this is established by pre-adsorbtion or co-deposition of the surfactant (e.g. O, CO, In, Sb) - Surfactants can promote layer-by-layer growth by: (1) Enhancement of the nucleation density (2) Reduction of the Schwoebel barrier 82

83 Two Mobilities - Alteration of growth rate or temperature with 1 ML periods - Initial high R or low T creates a high density of nucleation sites - Subsequent low R or high T provides high probability that adatoms will descend from adatom islands (layer-by-layer growth) Si/Ge(001) and 250ºC W. Wulfhekel et al., Phys. Rev. B 58, (1998) 83

84 Dislocation networks - Dislocation networks that form to release strain in growing films can be used to control nucleation of adatoms - This can enhance the short-range order of self-organized nanostructures 2 ML Ag/Pt(111) H. Brune et al., Nature 394, 451 (1998) 84

85 Dislocation networks Co nanostructures on Gd/Au(111) dislocation network 85

86 Surface Reconstructions Growth on periodical reconstructed surface can be used to enhance the order between nanostructures Ni/Au(111) D.D. Chambliss et al, Phys. Rev. Lett. 66, 1721 (1991) 86

87 Vicinal Surfaces - Slightly misoriented substrates contain step edges with well-defined separation distances - Vicinal surfaces can be used as templates for self-organised nanowires Pt(997) [997] [111] [111] 20 Å h=2.27 Å 87

88 Nanowire Growth One-dimensional Ag islands Coalesence of islands results in well-defined Ag wires Pt step edge T=340 K Ag =0.04 ML T=340 K Ag =0.13 ML 10Å P. Gambardella et al., Phys. Rev. B 61, 2254 (2000) 88

89 One-Dimensional Magnetic Structures Co/Pt(997) J.V. Barth et al., Nature 437, 671 (2005) 89

90 Influence of Deposition Angle D-X. Ye, Nanotechnology 16, 1717 (2005) 90

91 Molecular Self-Organization - Use self-organization to structure molecular materials - Use molecular templates to structure other materials PVBA on Ag(111) 500 Å 50 Å 5.0 Å 91

92 Summary - Homoepitaxy - Kinetic growth models based on adatom diffusion processes - Heteroepitaxy - Surface free energies - Strain - Atomic mixing - Self-organization by growth manipulation - Surfactants - Two mobilities - Dislocation networks - Surface reconstructions - Vicinal surfaces - Deposition angle 92

93 This Week s Article 93

94 Next Lecture 10/10 Nanoscale characterization: Microscopy, diffraction etc. 94