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Class Content
Grading Policy
• Crystal Structure
• Lithium Niobate and Thin-Film Lithium Niobate
• PLZT, BTO
• Presentation and Reports
• PPT file (20~30 Slides)
• Report (2~3 Pages)
• Content:
• Focus on any inorganic materials, semiconductor materials, or their
related measurements
• Bonus Points:
• Voluntary presentation at the last class: additional bonus points will be
awarded
• Contact: lu@cm.kyushu-u.ac.jp
• Your attendance will not be checked
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Types of Solids
I. Crystal Structure
Three general types of solids: (a) Amorphous (b) Polycrystalline (c) Crystalline
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Lattice and Unit Cell
Crystal
• Lattice: A regular periodic arrangement of points in space, such as the
arrangement of atoms or molecules in a crystal. Each point in the lattice is
a lattice point, which can be an atom, a group of atoms, an ion, or a
molecule.
• Unit Cell: A small volume of a crystal that can be used to reproduce the
entire crystal.
• In a very broad sense, crystal
means something that repeats.
• So even a wallpaper with a
repeating pattern is a crystal!
Two-dimensional representation of a
single crystal lattice.
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A two-dimensional representation of a single crystal lattice
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with various possible unit cells.
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Crystals are composed of a periodic array of atoms:
1-dimensional crystal (1D periodic structures)
The structure of all crystals can be described in terms of a lattice, with a
group of atoms attached to each lattice point called basis:
Basis (Unit Cell) + Lattice = Crystal Structure
+
=
To obtain the whole crystal structure one has to
translate the UNIT Cell to each LATTICE POINT
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Different choices of unit cell
2-dimensional crystal (2D periodic structures)
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Crystal Lattice
Cubic Unit Cell
• Crystal lattice is the mathematical object, describing the
periodicity of crystal structure.
• Do not confuse crystal lattice with crystal structure.
• Crystal structure is Unit Cell  Crystal Lattice.
• To get the whole crystal structure, one has to translate the unit
cell to all lattice points.
All sides equal length
All angles are 90 degrees
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Face Centered Cubic (FCC) Unit Cell
• (a) The crystal structure of copper is Face
Centered Cubic (FCC). The atoms are
positioned at well-defined sites arranged
periodically and there is a long-range
order in the crystal.
• (b) An FCC unit cell with closed packed
spheres.
• (c) Reduced sphere representation of the
FCC unit cell. Examples: Ag, Al, Au, Ca,
Cu, y-Fe (>912℃), Ni, Pd, Pt, Rh
FCC lattice structure has high packing density
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Body Centered Cubic (BCC) Unit Cell
Atomium in Brussels
has BCC structure !
Examples: Alkali metals (Li, Na, K, Rb), Cr, Mo, W, Mn, 𝛼-Fe (< 912℃)， 𝛽-Ti (>882℃).
Body centered cubic (BCC) crystal structure.
(a) A BCC unit cell with closely packed hard spheres representing the Fe atoms.
(b) A reduced-sphere unit cell.
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Diamond Crystals
The diamond crystal is a covalently
bonded network of carbon atoms.
Each carbon atom is bonded covalently to
four neighbors forming a regular threedimensional pattern of atoms which
constitutes the diamond crystal.
The diamond structure can also
be interpreted as two
Interpenetrating FCCs.
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Hexagonal
Structure
Carbon nanotube (1D Crystal)
Carbon nano-tubes are
formed by rolling a single
layer of graphene. These
are used to make quantum
devices!
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Basic Crystal Strutures
Other Crystal Structures
The easiest 3-D lattice to work with is the simple cubic lattice (SCC) which has lattice
points on all the corners of a cube. The Cubic (Isometric) crystal system is
characterized by its total symmetry. It has three crystallographic axes that are all
perpendicular to each other and equal in length. The cubic system has one lattice point
on each of the cube's four corners.
Crystal structures which
are combinations of these
are also possible.
(a) Simple
(a) Body centered
(c) Face centered
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Miller Indices
Step 1: Identify the intercepts on the x-, y- and z- axes.
In this case the intercept on the x-axis is at x = a ( at the point (a,0,0) ),
but the surface is parallel to the y- and z-axes - strictly therefore there is
no intercept on these two axes but we shall consider the intercept to be at
infinity ( ∞ ) for the special case where the plane is parallel to an axis.
The intercepts on the x-, y- and z-axes are thus
Intercepts: a, ∞, ∞
Step 2: Specify the intercepts in fractional co-ordinates
Co-ordinates are converted to fractional co-ordinates by dividing by the
respective cell-dimension - for example, a point (x,y,z) in a unit cell of
dimensions a x b x c has fractional co-ordinates of ( x/a, y/b, z/c ). In the
case of a cubic unit cell each co-ordinate will simply be divided by the
cubic cell constant, a . This gives
Fractional Intercepts: a/a, ∞/a, ∞/a i.e. 1, ∞, ∞
Step 3: Take the reciprocals of the fractional intercepts
This final manipulation generates the Miller Indices which (by convention)
should then be specified without being separated by any commas or
other symbols. The Miller Indices are also enclosed within standard
brackets (….) when one is specifying a unique surface such as that being
considered here. The reciprocals of 1 and ∞ are 1 and 0 respectively,
thus yielding Miller Indices: (100)
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Miller Indices (Examples)
Assignment
Intercepts: a, a, ∞
Fractional intercepts: 1, 1, ∞
Miller Indices: (110)
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Assignment
Intercepts: a, a, a
Fractional intercepts: 1, 1, 1
Miller Indices: (111)
Assignment
Intercepts: 1/2a, a, ∞
Fractional intercepts: ½, 1, ∞
Miller Indices: (210)
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XRD – X-ray diffraction
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where d is the spacing between
diffracting planes, θ is the incident
angle, n is any integer, and λ is the
wavelength of the beam
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Several Atomic Planes and Their d-spacings
in a Simple Cubic - Review
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Semiconductor Materials
• possible elements for making semiconductor materials
• Si most well-known semiconductor. C(Carbon) and Ge (Germanium) can also
be semiconductors.
• Other possibilities combinations of III and V group. e.g. GaAs (Gallium
Arsenide )
A portion of the periodic table
Group III
Group IV
Group V
B
Al
C
P
Ga
Si
As
In
Ge
Sb
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The differences between crystalline
(crystals) and amorphous (glasses) solids
Crystalline Solids
(Crystals)
Amorphous Solids
(Glasses)
Shape
Polyhedral shape with
naturally formed faces
No naturally formed
faces
Properties
Anisotropic
Isotropic
Atomic structure
Periodic (long range
ordered)
No periodicity, Shortorder only
X-ray Diffraction
Well separated
diffraction picture with
DISTINCT spots
No clearly separated
features
Amorphous Si
• Advantages
• Low temperature deposition (~250℃)
• Large area deposition possible at low cost
• Disadvantages
• Low conductivity
• Cannot be used for high-speed circuits
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Uses of Amorphous-Si
Elemental and Compound Semiconductors
• Single element → elemental semiconductor
• More than one element → compound semiconductor
 Binary Semiconductor (2 elements): Si1-xGex, SiC
 Ternary Semiconductor (3 elements): AlxGa1-xP
 Quaternary Semiconductor (4 elements): AlGaAsP
Properties of comp semi can be controlled by
changing the concentration of the elements
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Polycrystalline-Si
Growth of Semiconductor Materials
• Growth from Melt
• Epitaxial growth (MBE, MOVPE, etc.)
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Growth from Melt
𝝁-Czochralski (Grain-Filter) Process with Excimer-Laser
Silicon ingot from
czochralski process
Initially, holes which act as seeds are formed by photolithography. Then excimer
laser is used to melt silicon. Square-shaped grains are formed at the seed
locations.
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Epitaxial Growth
• Single-crystalline layer growth on a single-crystalline substrate
with the same crystal structure is referred to as Homo-epitaxy,
for example, Si on Si.
• Hetero-epitaxy is single-crystalline layer growth on a singlecrystalline substrate with a different crystal structure, such as Si
on SiGe, AlGaAs on GaAs.
• These processes can be achieved by means of:
• Chemical vapor deposition (CVD)
• Liquid Phase Epitaxy (LPE)
• Molecular Beam Epitaxy (MBE)
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Molecular Beam
Epitaxy (MBE)
Liquid Phase Epitaxy (LPE)
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Segregation Coefficient (k0)
Floating Zone Method (for purifying silicon ingot)
Floating zone method relies
on the segregation coefficient. For this process to
be used for purification this
co-efficient should be less
than 1.
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Si Wafer Fabrication
Ko
D (× 10-4 cm2/s)
B
0.8
2.4
AI
0.002
7.0
Ga
0.008
4.8
In
0.0004
6.9
C
0.07
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P
0.35
2.3
As
0.3
3.3
Sb
0.023
1.5
O
1.40
3.3
Oxygen cannot be removed by floating zone method
because its segregation coefficient is more than 1. The
diffusion co-efficient (D) determines the speed of purification.
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