Lectures: Mon 12-14 ,Wed 12-14 D116 Excercises: TBA Lecturer: Antti Kuronen, [email protected] Exercise assistant: Ane Lasa, [email protected] Course homepage: http://www.physics.helsinki.fi/courses/s/pintafysiikka/
Objectives
● To study properties of surfaces of solid materials.
● The relationship between the composition and morphology of the surface and its mechanical, chemical and electronic properties will be dealt with.
● Technologically important field of surface and thin film growth will also be covered.
Surface physics I 2012: 1. Introduction 1
Surface physics I and II
● Course in two parts
● Surface physics I (SPI) (530202)
● Period III, 5 ECTS points
● Basics of surface physics
● Surface physics II (SPII) (530169)
● Period IV, 5 ECTS points
● 'Special' topics in surface science
● Surface and thin film growth ● Nanosystems ● Computational methods in surface science
● You can take only SPI or both SPI and SPII
Surface physics I 2012: 1. Introduction 2 How to pass
● Both courses:
● Final exam 50%
● Exercises 50%
● Exercises
● Return by ● email to [email protected] or
● on paper to course box on the 2nd floor of Physicum
● Return by (TBA)
Surface physics I 2012: 1. Introduction 3
Table of contents
● Surface physics I
● Introduction: What is a surface? Why is it important? Basic concepts.
● Surface structure: Thermodynamics of surfaces. Atomic and electronic structure.
● Experimental methods for surface characterization: Composition, morphology, electronic properties.
● Surface physics II
● Theoretical and computational methods in surface science: Analytical models, Monte Carlo and molecular dynamics sumilations.
● Surface growth: Adsorption, desorption, surface diffusion.
● Thin film growth: Homoepitaxy, heteroepitaxy, nanostructures.
Surface physics I 2012: 1. Introduction 4 Course material
● These lecture notes on course home page http://www.physics.helsinki.fi/courses/s/pintafysiikka/ ● There are useful links under 'Links and literature'
● Lecture notes username: XXXXXXXX, password: XXXXXX
● Textbooks
● M. Prutton: Introduction to Surface Physics, Oxford Science Publications ● A. Zangwill: Physics at surfaces, Cambridge University Press ● J. A. Venables: Introduction to Surface and Thin Film Processes, Cambridge University Press ● A. Pimpinelli, J. Villain: Physics of Crystal Growth, Cambridge University Press ● M. Manninen, R. Nieminen: Pintafysiikka (in Finnish), Suomen Fyysikkoseuran julkaisuja 1
● Journals
● Surface Science: http://www.sciencedirect.com/science/journal/00396028 ● Surface Science Reports: http://www.sciencedirect.com/science/journal/01675729 ● Progress in Surface Science: http://www.sciencedirect.com/science//journal/00796816 ● Thin Solid Films: http://www.sciencedirect.com/science/journal/00406090 ● Physical Review B: http://prb.aps.org/ Surface physics I 2012: 1. Introduction 5
What is a surface?
● Atomic view: Top few atomic layers of a solid.
● Continuum view: Dividing surface vacuum, vapor dividing surface c1
c2
Surface physics I 2012: 1. Introduction 6 Why study surfaces?
● Technologically important
● Thin film growth: electronics, nanostructures Surfaces and ● Miniaturization → surface-to-volume ratio grows interfaces ● Catalysis, corrosion important ● Surface chemistry (2007 Nobel Prize in chemistry)
● Development of experimental methods
● Development of various microscopy and spectroscopy methods −7 ● Development of vacuum techniques (ultra high vacuum, UHV p 10 Pa ) ● Film growth methods (MBE, MOCVD, ALD): preparation of surfaces with controlled composition and morphology ● 'Real' surfaces vs. 'clean' surfaces
● Development of theoretical and computational methods
● Models for atomic level structure of surfaces ● Computational modeling of surface chemistry (ab initio methods) ● Modeling of crystal growth (Monte Carlo and molecular dynamics simulations)
Surface physics I 2012: 1. Introduction 7
What kind of surfaces?
● In everyday life surfaces are not clean
● Surfaces of many materials react with oxygen and other gases in environment
● Formation of so called native oxide layer
● May be very thin: e.g. Si surface has a SiO layer of thickness ~1nm. 2
● In the case of Si high temperatures and pressures needed to grow the layer thicker.
● Similarly for many metals (Al, Cu, ...)
● Often this layer passivates the surface: no further reactions (prevents corrosion).
● The green patina on copper objects
● Copper oxides, chlorides and carbonates.
● Takes years to form.
http://en.wikipedia.org/wiki/File:Hancoin1large.jpg
Surface physics I 2012: 1. Introduction 8 What kind of surfaces?
● Many covalent materials (e.g. semiconductors Si, Ge, etc. and diamond) may have so called dangling bonds on the surface: bonds not bound to any neighbors.
● These are often saturated by e.g. hydrogen.
● Clean crystalline surface can be produced by various crystal growth methods
● Particularly clean surfaces are needed in manufacturing electronic components
● Many layers of thin films.
● Interface (surface) structure more and more important as length scale becomes smaller.
http://navier.engr.colostate.edu/whatische/ChEL04Body.html
Surface physics I 2012: 1. Introduction 9
Some basic concepts
● Classification of crystal surfaces
● Surfaces of crystalline material (grown or cleavage) consist of single crystal plane
● Crystal structure (lattice points) determined by vectors a, b, c.
● Crystal direction:
● Set up a vector of arbitrary length in the direction of interest. ● Decompose the vector into its components along the principal axes. ● Using an appropriate multiplier, convert the component values into the smallest possible whole-number set. ● Crystal planes: example
● Plane intercepts crystal axes a, b, c at 3a, 2b, 2c
● Take the reciprocals of the numbers: ⅓, ½, ½
● The smallest integers having the same ratio are 2, 3, 3
● The Miller indices of the plane are (233)
● For cubic crystals, a plane and the direction normal to the plane have precisely the same indices (except for possible scaling)
Surface physics I 2012: 1. Introduction 10 Some basic concepts
● Classification of crystal surfaces
● Miller indices of a lattice plane = coordinates of the shortest reciprocal lattice vector normal to that plane ● Reminder: reciprocal lattice A , B , C of lattice a , b , c is defined as b× c c×a a× b A=2 a⋅b ×c B=2 a⋅b ×c C=2 a⋅b×c
● Reciprocal lattice of a simple cubic crystal = simple cubic ● For diamond, fcc and bcc lattices we almost always use the cubic unit cell (and not the primitive cells) → for these lattices Miller indices tell the normal of the lattice plane. ● For non-cubic lattices (e.g. hcp) one must remember that this is not the case.
Surface physics I 2012: 1. Introduction 11
Some basic concepts
● Crystal structure (unit cell) determined by vectors a, b, c. ● And possibly the basis: locations of atoms in the unit cell. ● Crystal plane determined by its Miller indices ● Notation: crystal direction: [hkl] = ha+kb+lc family of directions:
● Example: face centered cubic (fcc) lattice
(001) (110) (111)
Surface physics I 2012: 1. Introduction 12 Some basic concepts
● Corresponding surfaces look like below
(001) (110) (111)
● We immediately(?) see that atoms on certain surfaces are more tightly bound than on others. ● This has effect on the surface energy of a particular crystal surface.
Surface physics I 2012: 1. Introduction 13
Some basic concepts
● Surface energy
● Creating surface from a bulk material costs energy (you must do work in order to create surface) ● You must break atomic bonds Energy needed = Area A 2A
E1 E −E 2 1 E 2 = 2A
● Surface energy has the unit of J/m2 of eV/Å2 etc. ● Difficult to determine experimentally; theoretical calculations needed. ● We will delve into this subject in more detail in the following chapters.
Surface physics I 2012: 1. Introduction 14 Some basic concepts
● The effect of surface energy is nicely manifested in the equilibrium shape of nanoclusters (sizes from few nanometers). ● For small clusters the surface energy is minimized by the expense of introducing defects inside the cluster. ● When cluster size increases defects cost more energy and a lower-energy shape has also non-optimal surface facets. ● This is confirmed by experiments for many metals.
(001)
(111) (111)
Surface physics I 2012: 1. Introduction 15
Some basic concepts
● Surface energies of the three fcc surfaces (from semiempirical atomistic simulations):
(001) (110) (111)
eV/Å2 0.0802 0.124 0.0735 J/m2 1.29 1.99 1.18
● Literature values ab initio calculations: 2.17 (001), 2.24 (110), 1.95 (111) experimental: 1.79, 1.83 (111)
Surface physics I 2012: 1. Introduction 16 Some basic concepts
● Surfaces of other crystal structures bcc (001) diamond (001) diamond (001) (reconstructed)
bcc (110)
diamond (111)
bcc (111)
Surface physics I 2012: 1. Introduction 17
Some basic concepts
● Surfaces of crystalline materials most often observed are the low-index ones.
● They have the highest atomic densities and consequently the lowest surface energies. ● High-index surfaces may often viewed as containing facets and steps. facet, terrace step
● These surfaces slightly miscut from a low-index direction are also called vicinal. ● In growing smooth surfaces vicinal surfaces are often used: step flow growth.
● The exact structure of a crystal surface is in most cases not bulk-terminated (or bulk-exposed).
● There may be relaxation and reconstruction of the outermost atomic layers
bulk-terminated relaxed reconstructed
Surface physics I 2012: 1. Introduction 18 Some basic concepts
● Surface atoms of an ideal crystal surface form a 2D lattice. ● The surface structure may differ from the square hexagonal structure of the substrate: different symmetry, adatoms etc.
● Let a and b be the lattice vectors of the substrate on the surface plane, and a and s c-rectangular p-rectangular b the corresponding vectors in the surface s layer.
● In case of bulk-terminated surface
as =a bs =b oblique
● In general case we can write (G is a 2⨯2 matrix) a s =G a b [ b] [ s ]
Surface physics I 2012: 1. Introduction 19
Some basic concepts
● The deteminant of the matrix G describes the relationship between substrate and surface lattice vectors.
∣as×b s∣ surface u.c. area ∣G∣= ∣a×b∣ =bulk u.c. area
● If |G| is an integer there is a simple relationship. ● If |G| is diagonal
G= p 0 [ 0 q] then the following notation is used
R{hkl} p⨯q or R(hkl) p⨯q
where R is the chemical symbol of the material and {hkl} the surface orientation.
● Surface reconstructions reduce the symmetry of the surface. ● Unreconstructed surface can be denoted as 1⨯1
Surface physics I 2012: 1. Introduction 20 Some basic concepts
● Sometimes the relationship is not so simple.
● E.g. if we have an ad-atom layer of another material on a surface their structures may be incommensurate.
● One example is Xe adatoms on graphite surface. ● There is an interplay between the two interaction: between ad-atoms and between ad-atoms and substrate.
Frenkel- Kontorova model
● Cf. thin film heterostructures, critical layer thickness, misfit dislocations etc. (We will deal with these thing later in SPII).
Surface physics I 2012: 1. Introduction 21
Some basic concepts
● A simple example: Si (001)
Si {001} 1⨯1 Si {001} 2⨯1
Surface physics I 2012: 1. Introduction 22 Some basic concepts
● A simple example: Si (001)
● Dimer rows can be easily seen in STM figures
step edge
step edge
23⨯23 nm2 T. Yokoyama, K. Takayanagi Phys. Rev. B 61 (2000) R5078
Surface physics I 2012: 1. Introduction 23
Some basic concepts
● A less simple example: Si (111)
Si {111} 7⨯7
S.H.Ke et al, Phys. Rev. B 62 (2000) 15319.
Surface physics I 2012: 1. Introduction 24 Some basic concepts
● Basic concepts in crystal growth
● Epitaxy: film has the same crystal structure as substrate. ● Processes on a growing surface deposition
desorption ● If we want smooth surfaces adatoms must diffuse fast enough to be able to diffusion reach step edges. advacancy ● High enough temperature T or small enough deposition rate D (atoms/s). ● In some cases growth can be characterized by the ratio D/T. ● Substrate T can not be increased without limit: defects ● Another possibility: low-energy ion beams for local heating.
Surface physics I 2012: 1. Introduction 25
Some basic concepts
● Heteroepitaxy
● Substrate and growing film have different lattice constants (but same structure) → film will be stretched or compressed.
● Lattice misfit is defined as f = a f − a s / a s where a f, a s are lattice constants of the film and substrate, respectively. ● When the film is thick enough it is energetically favourable to ● create defects: misfit dislocations ● start growing islands instead of a smooth layer ● The relative strengths of film-substrate and film-film interactions determine the behavior. ● Traditionally the growth modes in heteroepitaxy are classified as below.
Frank-van der Merve (FM) Stranski-Krastranov Vollmer-Weber (VW) layer by layer islands with wetting layer island growth
growing f
Surface physics I 2012: 1. Introduction 26 Some basic concepts
● Example: growth of Ge on Si:
● f =5.66−5.43/5.43=4.2% ● Only a few atomic layers of pure Ge can be grown in a pseudomorphic fashion. ● After this islands start to form:
A.J.Steinfort et al, Phys. Rev. Lett. 77 (1996) 2009.
6 ML Ge on Si(001) at 430 oC 2200⨯2200 Å2
● Island growth is a complicated phenomenon where kinetic effects play a crucial role. ● By alloying Si and Ge thicker films can be grown.
Surface physics I 2012: 1. Introduction 27