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7/28/2019 Lecture 02 Matter Comes in Many Different
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EEE 352: Lecture 02. . . ~ .
Matter comes in many different formsthe three we are most
, , .
water
iceAir
Water vaporetc.
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Matter in its Many Forms
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Matter in its Many Forms
Heating ice produces water (T > 0 C, 32 F melting point)
Heating water produces steam (water vapor) (T > 100 C, 212 F)
These transitions are phase transitions.
Some materials have triple points, where all three forms can exist.
density
1
density
1
gas
liquid
gas
liquid
triple point
T
solid
T
solid
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Matter in its Many Forms
In LIQUIDS the density of molecules is very much higher than that of gases
* BUT the molecular interaction is STILL relatively weak
NO structural stability
SOLIDS may have a similar molecular density to that of liquids
* BUT the interaction between these molecules is now very STRONG
The atoms are BOUND in a correlated CRYSTAL structureWhich exhibi ts MECHANICAL STABILITY
IN SOLID MATTER THE STRONG
INTERACTION BETWEEN DIFFERENT
ATOMS MAY BIND THEM INTO AN
ORDERED CRYSTAL STRUCTURE
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Classifying Solids
An issue concerns the classif ication ofORDER in crystal materials
* In order to achieve this we can define the RADIAL DISTRIBUTION FUNCTION
Which tells us WHERE we should find atoms in the material
This parameter can be measured experimentally
P(r)GAS OR LIQUID
HIGHLY DISORDERED CRYSTAL
r
HIGHLY ORDERED CRYSTAL
P r IS THE POSITION AVERAGED PROBABILITY
r
OF FINDING ANOTHER ATOM AT A DISTANCE
r FROM SOME REFERENCE ATOM
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Classifying Solids
A transmission electron
a highly ordered crystal ofSi. We wil l learn soonabout how to discribe the
a crystal as this.
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Classifying Solids--Crystals
In reality very FEW materials exhibit perfect crystalline order
* Most materials develop IMPERFECTIONS during their fabrication process
Unwanted IMPURITY atoms
POINT and LINE DEFECTS
Thermodynamics and ENTROPY
LINE DEFECTS IN SiGe
VACANCY INTERSTITIAL DEFECT
EXAMPLES OF LINE DEFECTS
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Classifying Crystals
A large number of materials exhibi t POLYCRYSTALLINE order
* These materials consist of regions with NEARLY PERFECT order
That are separated by thinnerDISORDERED regions
The RELATIVE orientation of the CRYSTALLITES is RANDOM
DISORDERED Si
CRYSTALLINE Si
POLYCRYSTALLINE ORDER
SHOWING A 10 nm Si CRYSTALLITE
EMBEDDED IN DISORDERED Si
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Classifying Crystals
Other materials are referred to asAMORPHOUS
* These are solids in which the molecules are almost RANDOMLY arranged
LITTLE or no long range order exists
These materials are essentiall HIGHLY VISCOUS li uids
GLASS is an example of an amorphous solid
STRUCTURE
ARRANGEMENT
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Classifying Solidsrans s ors n our n egra e rcu
Lets look closer
in here
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Classifying Solidsrans s ors n our n egra e rcu
SiO2
is an amorphousmaterial which is used forthe insulator--it grows
temperature.
Crystall ine Si is used asthe base material for allprocessing in the
.
Poly-crystall ine Si, or a metal such as Al, isused to make the gate of the transistor (wewil l learn later just what the gate does).
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Preparing the Silicon for VLSI
Most materials may actually exist inALL three different states
* Depending on the manner in which they were FABRICATED
* Crystalline materials are the most DIFFICULT to make
And t ical l re ui re s ecial rocesses
SINGLE CRYSTAL SILICON IS GROWN BY THE
CZOCHRALSKI METHOD
-
SILICON IS SHOWN ABOVE
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Now, crystals can be made in many shapes. You can even do it at home.
Silicon crystals have to have very high puri tyno defects, vacancies, or random non-silicon atoms. This is done via the CZOCHRALSKI METHOD.
A special machine for the vertical growth of
crys a s v a e zoc ra s me o .
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Preparing the Silicon for VLSI
A very thin wafer of the ingot is used to process
and create the integrated circui t. More than 200
individual chi s will be made on each wafer.ve years ago: e use wa ers.
This Year: The Intel facili ties inChandler all use 12 wafers!
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Classifying Materials
Not all materials are easily classified using the schemes described above
* Liquid crystals are HIGHLY VISCOUS liquids containing LONG molecules
With STRONG and PERMANENT electric dipole moments
* In the absence of an electr ic f ield the molecules are RANDOMLY oriented
But an electric field may be used toALIGN their dipoles
IN THEIR UNALIGNED STATE WE MAY PICTURE THE
MOLECULES OF THE LIQUID CRYSTAL ARRANGED
AS THE LOGS IN THIS PHOTOGRAPH
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Highly directional
- -
Since the hybrids are composed ofelectrons, they repel each other most uniform result is tetrahedralshape
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Array of Atoms in Diamond Lattice(diamond, silicon, germanium, grey tin, )
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Group IVB: 4 outer electrons1 s-electron, 3-p electrons
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Compounds fromthese two groupscan form with anaverage of 4 electrons
.
GaAsGaPInP
InAsGaN
Compounds from these two groups
per atom.
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Crystall ine Order
The high degree of order in this TEMpicture of Si is apparent.[http://cst-www.nrl.navy.mil/lattice/struk/a4.html ]
The order is more apparent when weunderstand how this picture is madethrough a process known as latticeplane imaging. Diffraction of theelectrons occurs from each plane ofatoms; the dif fracted beams of
electrons form a Fourier transform inthe microsco e and this is re-transformed to give the image.
For those interested, a review of latticeplane imaging technology is found at:htt ://www.xra .cz/ms/bul2001-1/karlik. df
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First, however, not everything is crystalline:
Cr stalline OrderWe have seen that crystalline systems may exhibit varying degrees ofORDER
* InAMORPHOUS materials there is litt le order at all
* In POLYCRYSTALLINE materials the order is INTERMEDIATE
Poly-crystalline grain of Siembedded in amorphous Si
In many cases though it is convenient to assume the crystalline order is PERFECT
THISATOMICALLY PRECISE SANDWICH OF
SEMICONDUCTOR MATERIALS (GaAs & AlAs)
EXHIBITS HIGH CRYSTALLINE ORDER AND WAS
GaAs
BEAM EPITAXY. NOTE THE ALMOST PERFECTARRANGEMENT OF INDIVIDUAL ATOMS
IN THIS FIGURE
This precision is achievable because both GaAs and AlAsAlAsave t e same att ce constant.
3
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By crystal structure, we mean the regular (or not)
.
We can talk about planes of
2D projection of the 3D lattice.[http://cst-www.nrl.navy.mil/lattice/struk/a4.html]
These planes define directionsrelative to the planeseach
plane has a surface normal.
Nar
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Describing Crystal Structures
How do we identify various crystals, and tell two materials apartfrom their cr stal ro erties?
We need a method by which we can describe the crystal interms of its basic properties.
This can be done in one sense, because there are only a fewtypes of crystal lattice. Hence, identifying this structure tells usa lot about the crystal.
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Describing Crystal Structures
An IDEAL crystal is an INFINITE repetition ofIDENTICAL structural units in space
* These units may range from single atoms to complex molecules
We therefore need TWO important quantit ies to DESCRIBE a given crystal structure
* A multi-dimensional LATTICE: a set ofPOINTS in space
* A suitable BASIS: the unit that wil l be placed at EACH lattice point
+ =
2-D LATTICE BASIS 2-D CRYSTAL
The basis may be a single atom,
or a small group of atoms.
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Describing Crystal Structures
The crystal LATTICE may be defined using appropriate TRANSLATION VECTORS
* If we know where ONE lattice point is s ituated in the crystal
These vectors determine the position ofOTHER lattice points
STARTING FROM AN ARBITRARY ORIGIN O WE MAY
br
'
2
=
=
b
USE TRANSLATION VECTORS a & b TO MAP TOANY
OTHER LATTICE POINT:r r` r``
bar 23'' +=aO
* Here a and b are referred to as PRIMITIVE translation vectors
* Since they can be used to determine the position ofALL lattice points
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Describing Crystal Structures
* A 2-D crystal structure consists of a rectangular lattice with primitivetranslation vectors a and 2a in the horizontal and vertical directions. The
(a/2)[x, y] and (a/2)[x,-y] relative to each lattice point. Draw the crystal.
a
2a
+ =
LATTICE
We have to use a basis because the
atoms themselves dont form a
proper lattice
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Typical 3D Lattice Types
While the number of materials exhibiting crystal order is very LARGE in nature
* The number of lattice TYPES encountered is actually quite small
* Here we discuss the most important lattice types found in nature
Real crystal structures are THREE-DIMENSIONAL in nature
* In a SIMPLE CUBIC lattice the three primitive vectors have EQUAL length
REMEMBER THIS IS JUST THE LATTICE!
THE BASIS OF ATOMS WE ADD TO EACH LATTICE POINT
DETERMINES WHAT MATERIAL WE FINALLY END UP WITH
,
LATTICE POINT WOULD GIVES CRYSTALLINE MANGANESE
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Typical 3D Lattice Types
The BODY CENTERED CUBIC lattice is formed by adding anADDITIONAL latticepoint
* To the CENTER of each cube defined by the simple cubic lattice
* This lattice may be considered as TWO interlocking simple cubic lattices
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Typical 3D Lattice Types
For the BODY CENTERED CUBIC lattice, we must be careful todefine the primitive translation vectors to include the new atom at
.
ac rec on s ro a e o a newbody-centered atom. Now, thesevectors can be translated to defineany point in the lattice. These threeatoms form a smallest tetrahedron
c
along with the single corner atom.
a
b
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Typical 3D Lattice Types
The FACE CENTERED CUBIC lattice is formed by adding anADDITIONAL latticepoint
* To the CENTER of EACH face of the cube formed in a simple cubic lattice
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Typical Lattice Types
For the FACE CENTERED CUBIC lattice, we have to define the three latticevectors so that they fully account for the atoms at the face centers.
The three primitive vectors runfrom a corner atom to the threeadjacent faces of that corner.
Again, these form a tetrahedron.
b
c
a
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Typical Lattice Types
In addition to cubic lattices HEXAGONAL lattices are also frequently found in nature
* A SIMPLE hexagonal lattice is built f rom TWO-DIMENSIONAL nets
Stacked DIRECTLY above each other
2-D PLANE
VIEW FROMABOVE
ONE 2-D PLANE 3-D VIEW
2-D PLANE
IN THE HEXAGONAL BRAVAIS LATTICETWO-DIMENSIONAL TRIANGULAR
NETS ARE STACKED DIRECTLY
ON ONE ANOTHER. HOWEVER,
THE LAYERS MAY NOT BE DIRECTLY ALIGNED.
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Typical Lattice Types
A modified version of the hexagonal latt ice is the CLOSE-PACKED hexagonal lattice[web]
* This can be viewed as TWO simple hexagonal lattices
Which INTERPENETRATE each other
VIEW FROMABOVE
3-D VIEW