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EPITAXY

FORMATION OF SINGLE-CRYSTAL THIN FILM

Marina Tyunina: marinat@ee.oulu.fi

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THIN FILMS

coating: Au filmthickness 0.3 μm = 300 nm(1 μm = 10-6 m; 1 nm = 10-9 m)

ANCIENT EGYPT

Gold leaf is prepared mechanically and attached to surfaces

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THIN FILMS

In the early Renaissance, mirrors were made by coating back side of glass with thin film of mercury amalgam.

VENETIAN MIRROR

A dielectric coated mirror used in a dye laser. It is made using thin-film deposition.

LASER MIRROR

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FOR MODERN ELECTRONICSTHIN FILMS

HIGH ELECTRON MOBILITY TRANSISTORINTEGRATED CIRCUITS

Modern IC chips contain 109 transistors Semiconductor thin-film heterostructure

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TEM cross-section micrograph of a 10 nm gatelength MOSFET

Development towards higher level of integration, downscaling of dimensions, introducing novel materials, phenomena, and technologies.

FOR MODERN ELECTRONICS (micro- and nano-electronics, photonics, plasmonics, spintronics, etc.)

THIN FILMS

Dimensions of wafers increase, dimensions of components decrease.

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MATERIALS FOR CMOS PROCESSES

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MATERIALS FOR MICROELECTRONICS

semiconductors

dielectrics

metals

ferroelectrics

magnetic

0 10 20 30applications of different materials

in microelectronic devices (%)

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Inorganic materials are widely employed in the form of thin films.

Reduction of geometrical dimensions requires a further decrease of thickness (to few nanometers in advanced devices).

MATERIALS FOR MODERN ELECTRONICS

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Diversity of materials properties occurs

because

countless combinations of the admixture of

chemical compositions,

bonding types,

CRYSTAL structures (14 lattices)

occur naturally or can be synthesized.

CRYSTALS

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CRYSTAL STRUCTURE

= periodic arrangement of atoms in the crystal.

LATTICE = An infinite array of points in space, in which each point has identical surroundings to all others.

A group of atoms is called the MOTIF (BASIS)

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CRYSTAL STRUCTURE can be described by associating BASIS with each LATTICE POINT .

Don't mix up atoms with lattice pointsLattice points are infinitesimal points in spaceAtoms are physical objectsLattice points do not necessarily lie at the centre of atoms

+ =

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UNIT CELL = The smallest component of the crystal, which when stacked together with pure translational repetition reproduces the whole crystal

Unit Cell Dimensions• a, b and c are the unit cell edge lengths• α, β and γ are the angles (α between b and c, etc....)

4 types of unit cell: primitive, body-centred, face-centred, side-centred

On combining 7 crystal classes with 4 possible unit cell types symmetry indicates that only 14 3-D lattice types occur

14 BRAVAIS LATTICES

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a = b = cα = β = γ = 90o

a = b ≠ cα = β = γ = 90o

a ≠ b ≠ cα = β = γ = 90o

a = b = cα = β = γ ≠ 90o

a = b ≠ cα = β = 90o

γ = 120o

a ≠ b ≠ cα = γ = 90o

β ≠ 120o

a ≠ b ≠ cα ≠ β ≠ γ ≠ 90o

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For identification of atomic positions as well as planes and directions, an orthogonal set of axes is arbitrarily selected

Point is identified by three coordinates x = u, y = v, and z = w.

In a cubic lattice, the center of coordinate axes is taken as x = 0, y = 0, z = 0, or (0,0,0).

Coordinates of lattice sites.

MILLER INDICES

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For identifying a plane in the cubic system:

The result is a triad (hkl) known as the Miller indices for the plane

•Determine the intercepts of the plane on the three crystal axes in number of unit cell dimensions (a, b, c).•Take reciprocals of those numbers (1/a, 1/b, 1/c).• Reduce these to smallest integers by clearing fractions.

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Crystallographic directions are determined by the components of the vector connecting any two lattice points lying along the direction. If the coordinates of these points are (u1, v1, w1) and (u2,v2,w2), then the components of the direction vector are (u1 – u2, v1 – v2, w1 – w2). When reduced to smallest integer numbers and placed within brackets they are known as the Miller indices for the direction, i.e., [hkl].

The Miller indices of the direction normal to the (hkl) plane is [hkl].

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DEFECTS IN CRYSTALS

Point defect is missing or irregularly placed atom in the lattice.

Linear defects are groups of atoms in irregular positions.

Planar defects are interfaces between homogeneous regions of the material.

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Point defects include

lattice vacancies,

self-interstitial atoms,

substitution impurity atoms,

and interstitial impurity atoms

POINT DEFECTS

An appreciable number of vacancies exists at elevated temperature.

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Dislocations are linear defects, i.e. groups of atoms in irregular positions.

DISLOCATIONS

The geometry of a dislocation: when attempting a simple closed traverse about it in the surrounding lattice, there is a closure failure, i.e., one finally arrives at a lattice site displaced from the starting position by a lattice vector, the so-called Burgers vector b. This vector lies perpendicular to the edge dislocation line.

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Planar defects are interfaces between homogeneous regions of the material.

PLANAR DEFECTS

LOW-ANGLE BOUNDARIES

Dislocation model of boundary.

STACKING FAULTS

The stacking sequence of planes is broken.

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NON-CRYSTALLINE (DISORDERED) SOLIDS

In some materials the long-range order characteristic of crystalline solids breaks down. (Short-range order is preserved.) These are the non-crystalline amorphous or glassy solids.

Crystalline quartz SiO2

Partly disordered SiO2

Random SiO2 glass

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POLY-CRYSTALLINE SOLIDS

The long-range order characteristic of crystal are preserved within crystallites or grains.

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MICROSTRUCTURE OF THIN FILMS

Crystal quality (single-crystal, polycrystalline, amorphous)Crystal structure (lattice, basis, orientation with respect to substrate surface)Crystal phases (fractions of different crystal structures, orientations) Defects (point, planar, 3D)Grains (grains, size and its distribution)Surface morphology

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DEPOSITION OF THIN FILMS

PHYSICAL METHODS CHEMICAL METHODS

EVAPORATIONMBE, e-beam, …

SPUTTERINGDC,RF,magnetron,.

PULSED LASER DEPOSITION

CHEMICAL VAPOR DEPOSITION ATOMIC LAYER

DEPOSITION

CHEMICAL SOLU-TION DEPOSITION

Langmuir-Blodgett

CATHODIC ARC DEPOSITION

VAPOR DEPOSITION

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GROWTH AND PROPERTIES OF THIN FILMS

starts with condensation of isolated atoms and clusters on a bare substrate -NUCLEATION

continues with film thickening due to additional deposition

ends with film of a certain MICROSTRUCTURE

GROWTH

MICROSTRUCTUREphysical and crystallographic nature of substrates

film-substrate interfacial interactions

evolution of the film structure and morphology

processing conditions

+ + =

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MICROSTRUCTURE

AmorphousPolycrystallineCrystal phasesOrientedFine/large-grained…………………….SINGLE-CRYSTAL

PROPERTIES

MechanicalElectro-magnetic………………….

EPITAXY

GROWTH

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EPITAXY

Two ancient Greek words, επι (epi, placed or resting upon) and ταξιζ (taxis, arrangement), are the root of the modern word epitaxy, which refers to extended single-crystal film formation on top of a crystalline substrate.

HOMOEPITAXYFILM and SUBSTRATE are of the SAME material. (Epilayer is freer of defects, is purer than the substrate, and can be doped)

HETEROEPITAXYFILM and SUBSTRATE are of DIFFERENT materials. (Epitaxial heterostructures, superlattices, quantum wells, etc.)

single-crystal substrate

film

single-crystal substrate

film

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single-crystal substrate

film material

in-plane

out-of-plane

af

as

EPITAXY: FILM-SUBSTRATE LATTICE MATCH

af

cf

as

Crystal structure and lattice parameters (in-plane) of substrate and film material should match.

cf

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Simple epitaxial alignments of cubic film on cubic substrate

as = af as = 2af as = √2af

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EPITAXIAL RELATIONSHIP describes relationship between crystallographic orientations of the film and substrate.

CRYSTALLOGRAPHIC NOTATION

plane (102)[010]

[201]

The traditional (3-D) Millerindices are employed

substrate

film

(001) plane[100] direction

(001) plane[100] direction

The tetrad of indices (hkl) [uvw] ⎜⎜(hkl) [uvw] describes the epitaxial geometry.

(hkl) – indices of the overgrowth film plane, which is parallel to the substrate (hkl) plane at the common interface. [uvw] and [uvw] are parallel directions.

(001)[100] ⎜⎜(001)[100]

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(001) planein cubic cell

film

substrate

(111) planein cubic cell

film

substrate

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single-crystal substrate

film material

in-plane

out-of-plane

af

as

EPITAXY: FILM-SUBSTRATE LATTICE MATCH

af

cf

as

Crystal structure and lattice parameters (in-plane) of substrate and film should match.

cf

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If the plate is stretched by equal and opposite axial tensile forces, F, then to sustain static equilibrium - internal balancing forces are required. These internal forces distributed throughout the plate constitute a state of stress.

The plate contracts laterally in both the y and z directions in concert with elongation in the x direction. Though there is no stress in the y direction, there is a strain

xz

xy

vεε

νεε

−=

−=

Poisson's ratio3.0≈ν

IN-PLANE LATTICE MISFIT STRAIN

stress

xx εσ Υ=Elastic deformation: Hooke’s law

Vector, or 1st rank tensor

Young’s modulus

2nd rank tensor

Vector, or 1st rank tensor

strain

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IN-PLANE LATTICE MISFIT STRAIN

s

fs

aaa

s−

=MISFIT STRAIN:Misfit strain s appears due to difference between lattice parameters as and af(af - for free film material, not clamped by substrate)

substrate

film material

af > ass < 0

COMPRESSIVE

substrate

film material

af < ass > 0

TENSILE

Growing film should shrink. Growing film should stretch.

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IN-PLANE COMPRESSIVE IN-PLANE TENSILE

EPITAXIAL STRAINED FILMS

af

cf

af

cf ca

a

c

a < afc > cf

In epitaxial strained films, novel crystal phases can be obtained.Materials with novel phase diagrams and novel properties can be obtained.

epi-filmbulk prototype

a > afc < cf

epi-filmbulk prototype

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Growth of films: initial stage

“Hot” adatoms make random diffusive jumps and form pairs with other adatoms or attach to larger atomic clusters or nuclei

Energetic vapor atoms arriving to substrate may desorb or remain on the surface

Adatoms finally “find” bonding sites and set in the film.

Θ = 0 – no adatoms

Θ = 0…1 – surface coverage

Θ = 1 – monolayer of adatoms

( ) θθθ desads kPkdtd −−= 1

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Modes of growth

Frank van der Merwe (layer-by-layer) growth: extension of nucleus in 2 dimensions

Θ < 1 1< Θ < 2 Θ > 2

Volmer-Weber (island) growth :clusters nucleate and grow in 3 dimensions .

Stranski-Krastanov (layer+island) growth:combination of the two (FM+VW) modes.

Growth modes are analyzed using macroscopic capillarity theory or atomistic modeling.

Θ < 1 1< Θ < 2 Θ > 2

Θ < 1 1< Θ < 2 Θ > 2

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Surface energy as work when material surface area is increased (capillarity approach uses surface tensions γ)

Surface energy

( ) ( ) ( )[ ]θθθθθθ −−+−−= 1ln1ln14 TkwnG Bs

G – Gibbs free energy of adatomsns – number of surface sites

SVFSFVV rararaGraG γγγ 22

22

21

33 −++Δ=Δ

ΔG - change of free-energy when adatoms form spherical nucleus of radius r. Surface tension at vapor (V), film (F), substrate (S) boundaries.

Surface energy as a function of coverage (atomistic)

G (Θ)

G (γ )

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Strain relaxation: morphological instability

2

21 εYhGs =

s

fs

aaa

s−

=

sv GrGrG Δ++Δ=Δ γππ 23

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The net free energy change for the nucleation of a hemi-spherical island on top of strained epitaxial layer.

( )Ysh 22

* 2−

=ε

γ

The critical thickness for the onset of the rough island morphology (ε is a mean strain in film with island)

- misfit strain- strain energy, where ε is strain and Y is Young’s modulus

To relieve the strain, island nucleates.

h*

As thickness of strained epitaxial layer increases, also the strain energy increases.

h*

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1 2 3 4

0.1

0.0

-0.1

S

FS

γγγ −

Lattice misfit, %

“Sur

face

mis

fit”

layer-by-layer

layer + island

islandsS

FS

aaa −

islands

Strain relaxation: morphological instability

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Strain relaxation: morphological instability

Selected AFM micrographs of 100 ML thick Si0:75Ge0:25 layers grown on Si(001) with different deposition times. The biaxial misfit strain of the Si0:75Ge0:25 epitaxial layers is 0.010.

Roughening Rates of Strained-Layer Instabilities F. Watanabe, D. G. Cahill, and J. E. GreenePhys. Rev. Lett. 94, 066101 (2005)

Theory considers the competing changes in chemical potential created by an increase in surface area (G(Θ) or G(γ)) and relaxation of mechanical strain s. It predicts an exponential roughening rate of a periodic surface morphology.

At the shortest deposition times, roughening is suppressed!

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Role of Strain-Dependent Surface Energies in Ge/Si(100) Island FormationO. E. Shklyaev, M. J. Beck, M. Asta, M. J. Miksis, and P.W. VoorheesPhys. Rev. Lett. 94, 176102 (2005)

Isolated pyramidal hut island on Si(100), colored according to in-plane surface strain.

Formation of Ge/Si(100) pyramidal islands is due to strain-dependent surface energies. This strain dependence of surface energy is impacted by strain-induced changes in the Ge surface reconstruction.

Strain relaxation: morphological instability

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STM image (60x60) nm3 of a pyramidal hut cluster at 9 ML of Ge coverage on Si(001) surface

Real-time scanning tunneling microscopy observation of the evolution of Ge quantum dots on Si(001) surfaces P. D. Szkutnik, A. Sgarlata, S. Nufris, N. Motta, and A. BalzarottiPhys. Rev. B 69, 201309(R) (2004)

Strain relaxation: morphological instability

Self-assembled quantum dots

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Strain relaxation: dislocations

d

h*

With increasing thickness h < h* of strainedpseudomorphic layer, elastic strain energy ESincreases:

)1/(2 ν−= YhsES

where s is the biaxial misfit strain and ν is Poisson's ratio.

If dislocations are arrayed in a square grid of sided, with Burgers vector magnitude b, the elastic strain in the film is reduced to ε

dbs −=ε

( )( )

( )( )d

bhbdbsYhEtotal νπβμ

ν −+

−−

=14ln2

1

22total energy of the film with array of misfit dislocations

( ) ( )bhs

bh ∗∗

+= β

νπln

18critical thickness of strained layer

The reduction in strain energy by dislocations is larger than that associated with creating islands.

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Misfit dislocations in nanoscale ferroelectric heterostructuresV. Nagarajan et al., Appl. Phys. Lett. 86, 192910 (2005)

Strain relaxation: dislocations

HRTEM image of SrRuO3/Pb(Zr,Ti)O3/SrRuO3 heterostructure. The arrows point toward misfit dislocations.

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Strain relaxation: dislocations

With increasing film thickness, strain can relax through formation of misfit dislocations. The crystal structure of the films depends on their thickness.

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Strain relaxation: dislocations

Growth dynamics and strain relaxation mechanisms in BaTiO3pulsed laser deposited on SrRuO3 /SrTiO3J. Q. He, E. Vasco, R. Dittmann, and R. H. WangPhys. Rev. B 73, 125413 (2006)

TEM revealed a three-layered micro-structure

Labels A, B, and C denote misfit dislocation, grain boundary, and anti-phase domain regions

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Columnar growth taking place from the incomplete coalescence of the 3D nuclei.

Schematics of different stages in growth of epitaxial BTO film

Highly strained film under the critical thickness

Formation of misfit dislocations and Increase of their density as the film thickness increases

2D (layer-by-layer) growth mode is replaced by a 3D (island) mode. 3D nuclei are formed on the relaxed surface areas.

1 2

3 4

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Dissociation and evolution of threading dislocations in epitaxial Ba0.3Sr0.7TiO3 thin films grown on (001) LaAlO3C. J. Lu and L. A. Bendersky, K. Chang and I. TakeuchiJ. Appl. Phys. 93, 512 (2003)

Cross-sectional bright field micrograph of the film. Note the very high defect density in the first 100 nm of BSTO adjacent to the interface. TD (threading dislocations) half loops in the top layer are indicated by letters.

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300 400 500 600 700 800 9000.0

0.1

0.2

0.3

0.4

0.5

0.6

th

erm

al e

xpan

sion

mis

mat

ch (%

)

T (oC)

Pt/Al2O3

BST/Al2O3

Pt/Si

BST/Si

BST/Pt

Thermal expansion: mismatch strain

( ) sfsthermal

thermal

thermal

sTll

ααααε

ε

−=Δ=

Δ=Additional strain can appear due to difference in thermal expansion coefficients

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Designing Epitaxial Heterostructure

Lattice ParameterTo ensure epitaxial growth of a film on a substrate, the lattice parameters of both should match. For the defect-free interfaces in film/substrate hetero-structures, lattice misfit of less than 0.1% is required. The maximum theoretical lattice misfit can be less than 9% (smaller in practice).

Temperature of depositionTo provide layer-by-layer epitaxial growth, the substrate temperature should be high enough.

Thermal Expansion CoefficientTo prevent development of excessive thermal stress at the film-substrate interface during deposition and processing, a match of thermal expansion coefficients is required.

Surface energyTo provide epitaxial growth, surface energies of substrate and film should match (e.g. that of substrate can be larger)

Critical thicknessTo obtain epitaxial films free of dislocations, film thickness should be smaller than the critical one for the given film-substrate pair.

Buffer layerIf lattice parameters, thermal expansion coefficients, or surface energies of film and substrate do not match, then epitaxial growth can be assisted by introducing a buffer layer between substrate and film.

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Silicon-on-silicon (homoepitaxial films)Epitaxial films are free of planar and 3D defects typical for crystals. They have well controlled chemical composition.

Strained silicon (heteroepitaxial films of Si on SiGe)Larger distance between silicon atoms reduces the atomic forces that interfere with the movement of electrons. Electrons possess better mobility (they are to 70% faster compared to that in normal Si). Transistors using strained silicon can switch faster.

Semiconductor islands / quantum dotsQuantum confinements effects exist in semiconductor islands with dimensions < 10 nm. Such island can be formed using strain control in epitaxial growth.

Epitaxial semiconductor films

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Gordon Teal and Howard Christensen at Bell Labs developed a process, now called epitaxial deposition, to grow a thin layer of material on a substrate that continues the underlying crystalline structure. Sheftal’, Kokorish, and Krasilov described similar work on germanium and silicon in the U.S.S.R. in 1957.

1960 - Epitaxial Deposition Process Enhances Transistor Performance

Development of thin-film crystal-growth process has lead to transistors with high switching speeds.

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p- GaAs

n+ AlGaAs

n+ GaAs

High Electron Mobility Transistor (HEMT) > 500 GHz…THz

Semiconductor heterostructures are used in high-speed- and optoelectronics

Epitaxial semiconductor heterostructures

Heterojunction Bipolar Transistor (HBT)

HIGH-SPEED ELECTRONICS

Semiconductor band gap engineering using alternating layers of various III-V and II-VI compound semiconductors to form lasing heterostructures (diode lasers, quantum cascade lasers, waveguides, LEDs).

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Epitaxial semiconductor heterostructures

OPTOELECTRONICS

Intersubband Electroluminescence from Silicon-Based Quantum Cascade StructuresG. Dehlinger, L. Diehl, U. Gennser, H. Sigg, J. Faist, K. Ensslin, D. Grützmacher, E. MüllerScience 290, 2277 (2000)

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Abrupt PbTiO3/SrTiO3 superlattices grown by reactive molecular beam epitaxyJ. C. Jiang, X. Q. Pan, W. Tian, C. D. Theis, and D. G. Schlom, Appl. Phys. Lett. 74, 2851(1999)

High-resolution electron microscopy of semiconductor interfacesA K Gutakovskii, L I Fedina and A L Aseev

Phys. Status Solidi 150, 127 (1995)

Epitaxial heterostructures@superlattices

semiconductors perovskite ferroelectrics

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Strong polarization enhancement in asymmetric three-component ferroelectric superlatticesH. N. Lee, H. M. Christen, M. F. Chisholm, C. M. Rouleau, and Douglas H. LowndesNature 433, 395 (2005)

E (kV/cm)

Cross-sectional Z-contrast TEM image of compositionally abrupt interfaces in superlattice: the diagram shows its atomic structure. (The light-blue octahedra, and the red, green and blue spheres represent TiO6, and Ca, Baand Sr, respectively.)

Epitaxial ferroelectric superlattices

Polarization-electric field hysteresis loops in superlattices.

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45 46 47 48

103

104

105

I (cp

s)

2Θ (deg)

Λ = 62 u.c.

simulated

measured

10 100

600

800

εΛ (u.c.)

Θ-2Θ XRD pattern of BST superlatticewith period Λ = 62 unit cells

Multilayers and superlattices of ferroelectric barium strontium titanateI. Jaakola, J. Levoska, and M. TyuninaJ. Appl. Phys. 102, 014108 (2007)

Epitaxial ferroelectric superlattices

Dielectric permittivity as a function of superlattice period

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Multiferroic BaTiO3- CoFe2O4 nanostructuresH. Zheng, J. Wang, S. E. Lofland, Z. Ma, L. Mohaddes-Ardabili, T. Zhao, L. Salamanca-Riba, S. R. Shinde, S. B. Ogale, F. Bai, D. Viehland, Y. Jia, D. G. Schlom, M. Wuttig, A. Roytburd, R. RameshScience 303, 661 (2004)

The nanostructures are epitaxial in-plane as well as out-of-plane. The lattice parameters are a = 3.99 Å, c = 4.04 Å for BaTiO3; and a = 8.38 Å, c = 8.31 Å for CoFe2O4, indicating that CoFe2O4 nanopillars have a compressive out-ofplane strain of 0.8%. The change of (001) lattice parameter is due to the vertical heteroepitaxial mismatch between CoFe2O4 and BaTiO3.

Epitaxial 3D nanocomposites

BaTiO3 – perovskite ferroelectricCoFe2O4 – spinel ferrimagnetic

Self-organized epitaxial growth of CoFe2O4 nanopillars embedded in BaTiO3 matrix

Schematic of nanocomposite

XRD pattern TEM planar view

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Polarization– electric field hysteresis loop showing that the film is ferroelectric with a saturation polarization Ps = 23 μC/cm2.

Out-of-plane (red) and in-plane (black) magnetic hysteresis loops depicting the large uniaxial anisotropy (not expected in bulk CFO).

Epitaxial 3D multiferroic

Magnetization – polarization coupling

Magnetization versus temperature curve measured at H = 100 Oe, which shows a distinct drop in magnetization at the ferroelectric Curie temperature for the vertically self-assembled nanostructure (red curve); the multilayered nanostructure (black curve) shows negligible change in magnetization.

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DEPOSITION OF THIN FILMS

PHYSICAL METHODS CHEMICAL METHODS

EVAPORATIONMBE, e-beam, …

SPUTTERINGDC,RF,magnetron,.

PULSED LASER DEPOSITION

CHEMICAL VAPOR DEPOSITION ATOMIC LAYER

DEPOSITION

CHEMICAL SOLU-TION DEPOSITION

Langmuir-Blodgett

CATHODIC ARC DEPOSITION

VAPOR DEPOSITION POSSIBILITY FOR EPITAXY

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Vapor deposition requires vacuum or even ultra-high vacuum (UHV).

Rough/Primary/Fore Vacuum Pump 1 atm to 10-3 mbar

High/Ultrahigh Vacuum Pump10-4 to 10-11 mbar

Control system

CHAMBER (deposition or analysis)

PUMPING SYSTEM

VACUUM SYSTEM

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MBE has evolved from simple thermal evaporation techniques by the application of UHV techniques to avoid disturbances by residual gases, and additionally includes many different sources.

MOLECULAR-BEAM EPITAXY (MBE)

Several different sources allow the controlled deposition of multielement compounds.

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VACUUM DEPOSITION SYSTEMS

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EPITAXY

GROWTH OF SINGLE-CRYSTAL THIN FILM ON THE TOP OF SINGLE-CRYSTAL SUBSTRATE

TOOL for creating materials with excellent or novel propertiesusing effects of misfit strain, interface, self-organization, thickness, etc

Epitaxial growth can be realized using vapor deposition techniques, requiring vacuum systems.