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W.K. Chen Electrophysics, NCTU 1
Chapter 1 The Crystal Structure of Solids
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Outline
Semiconductor materialType of solidsSpace latticesAtomic
bondingImperfections & impurities in solidsGrowth of
semiconductor materials
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Elemental semiconductors: (C, Si, Ge)- composed of single
species of atoms
Compound semiconductors: (binary, ternary, quarternary)III-V,
II-VI, IV-IV
1.1 Semiconductor Materials
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1.2 Types of SolidsAmorphous: degree of order only within a few
atomic or molecular dimensionsPolycrystalline: degree of order over
many atomic or molecular dimensions.- The ordered regions vary in
size and orientation with respect to one
another- The single crystal regions are called grainsSingle
crystal: regular geometric periodicity throughout the entire volume
of material
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1.3 Space lattices- The periodic arrangement of atoms in the
crystal is called
lattice
cbaV rrr= )( volumecellunit cnbnanT
rrrr321 ++=
latticeLattice pointUnit cellPrimitive cell
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Lattice: the periodic arrangement of atoms in crystalLattice
point: a dot used to present a particular atomic arrayUnit cell: a
small volume of the crystal that can be used to reproduce the
entire crystalA unit cell is not a unique entity Unit cell A, B, C
and D all can be used to construct the entire lattice by
appropriate translation
Lattice point
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csbqapr rrrr++=
Every equivalent lattice point in primitive cell for 3-dim
crystal can be found using the vector
Primitive cell: the smallest unit cell
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1.3.2 Basic crystal structure in semiconductors
==90o, =90oa=bcHexagonal ()===90oa=b=cCubic ()
===90oa=bcTetragonal ()===90oabcOrthorhombic ()
ba
accb
rr
rr
rr
,:
,:,:
a, b are primitive vectors lie on the base plane
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1.3.2 Basic crystal structureThree basic (cubic) crystal
structuresSimple cubic (sc): - has an atom located at each
cornerBody-centered cubic (bcc): - has an additional atom at the
center of cubic Face-centered cubic (fcc):
- has additional atoms on each center of face plane
Simple cubic Body-centered cubic Face-centered cubic
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The Fourteen Bravais LatticesThe ways in which we can specify
the lattice points in space and keep translational symmetry is
limited. In 1848, Auguste Bravais demonstrated that there are in
fact only fourteen possible point lattices and no more. For his
efforts, the term Bravais lattice is often used in place of point
lattice. 3D models of the possible lattices can be found here.
a=bc = =90 =120P1Hexagonal
a=b=c = =
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1.3.3 Crystal plane & Miller indicesHow to describe the
crystal plane?
The crystal plane intercepts x,y and z axes at pa, qb and sc
Assume g is the plane vector, which is perpendicular to any
vector on the plane
csapbqap rrlrrr
lr
== 21 let
] [
vector plane
lkhclbkahg =++= rrrr
21 and lrr
lrr
gg
1 bqaprr
lr
=
csap rrlr
=2 gr
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)111()()(
0
0)()( 0
0
0)()( 0
22
11
==
==
=++=
==
=++=
s
q
ph
sph
qph h k
sp
hllshp
csapclbkahggqp
hkkqhp
bqapclbkahgg
l
rrrrrlrr
lrr
rrrrrlrr
lrr
)111()( indicesMiller s
q
p
h k =l
1 bqaprr
lr
=
csap rrlr
=2
For any plane that parallel to each other, they bear the same
miller indices
The integers are referred as the Miller indices.We will refer to
a general plane as (h k l) planeAnd the associated plane vector g
is denoted by [hkl]
plane)( vector][ lh k lkh
(h k l) plane[h k l] vector
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Example 1.2 Miller indices
)632()11
21
31()(
1 and 2,3 plane of Intercepts
==
===
hkl
sqp
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Lattice Planes: Miller indeces
)111)s
q
p
h k (( index Miller =l
plane)001()( and ,1
====
lh k sqp
plane)101()( and 1,1
====
lh k sqp
plane)111()( 1 and 1,1
====
lh k sqp
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Example 1.3 surface density
21428
11
atoms/cm 1066.52)105(
2
)2)((atoms 2plane (110)at density Surface
=
=
=
aa
oAa
1 5=
bcc structure
12 a 1a
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1.3.4 Diamond structure
Diamond structure is basically consisted of body-centered cubics
with four of the corner atoms missingEach atom in the tetrahedral
structure ( ) has four nearest neighbors and it is this structure
which is the basic building block of diamond lattice
Diamond structure is the most common structure in elemental
semiconductors, such as Si, Ge
Tetrahedral structure a=bc ===90o
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Zincblende (sphalerite) structureFor GaAs, each Ga atom has four
nearest As neighbors and each Ga has four nearest As atoms
Zincblende structure differs from diamond structure only in that
there are two different types of atoms in the lattice
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Zincblende Lattice()
4)21(6)
41(4
4
=+=
=
As
Gacell unit per
1
2
4
3
1
26
5
4
3
corner Face center
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1.4 Atomic bonding
Ionic bond:Covalent bond:Metallic bondVan der Waals bond
The interaction of atoms in crystal is determined largely by the
outmost, i.e., valence electrons of an atom
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Covalent bond:electrons being shared between bond atoms so that
the valence energy shell of each atom is fully occupied (8
eletrons) by electrons (II-VI, III-V, IV-IV)
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Metallic bondingsuch as solid sodium (Na). Solid sodium has a
body-centered cubic structure, each sodium has one valence
electron, so each atoms has eight nearest neighbors with each atom
sharing many valence electronsVan der Waals bondInteraction between
dipoles(most in gaseous form, solid form exhibits a relatively
melting temperature
Body-centered cubic
HF
HFHF
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1.5 Imperfections & impurities in solids
Native defects (Imperfections)vacancyinterstitialline
dislocationanti-siteImpuritiessubstitutional impurityinterstitial
impurity
Perfect crystal for most of time is less useful,In a real
crystal, the lattice is not perfect, but contains imperfections or
defects. Such imperfections tend to alter the electrical properties
of a material, in some cases, electrical parameters can be
dominated by these defects or impurities
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Native defects (Imperfections)vacancy:
missing of atom at a particular lattice siteinterstitial
atoms located between lattice sites
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Native defects (Imperfections)Frenkel defect
vacancy-interstitial defectline dislocation
entire row of atoms is missing from its normal lattice sites
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Impuritiessubstitutional impurityinterstitial
impurityanti-site
Anti-site
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Point defect- The point defects involve single atoms or
single-atom locations. That is one atom is missing or misplaced in
the crystal lattice
vacancyinterstitialsubstitialanti-site
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1.6 Growth of semiconductor materials
Ingot growthEpitaxial growth
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Silicon Crystal Pulling Apparatus
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Liquid Encapsulated Czochralski (LEC)
Encapsulation by thin (8-17 mm) molten B2O3 layerHigh inert gas
pressure (up to 100 bar) to suppress volatility of group V50 mm
round-shaped GaAs, 200-400 cm-2
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1Semiconductor Thin Film Deposition
Liquid Phase Epitaxy (LPE)Metalorganic Chemical Vapor
Deposition(MOCVD)Molecular Beam Epitaxy (MBE)Chemical Beam Epitaxy
(CBE, MOMBE)
Trichloride Vapor Phase Epitaxy (ClVPE)Hydride Vapor Phase
Epitaxy (HVPE)
3300m
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Liquid Phase Epitaxy
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Metal-Organic Chemical Vapor Deposition
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MOCVD Growth Mechanism
IIIV
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Molecular Beam Epitaxy
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Chemical Beam Epitaxy
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Trichloride Vapor Phase Epitaxy
Hot wall reactorEtch & growPure AsCl3 and PCl3
attainableLow-background doping epilayerLow costNot possible to
grow AlGaAs(TAlAs=1100oC>>TGaAs=750oC)Difficult in
composition control ( use both group III & V clorides)Poor
reproducibilty
Ga(l)+HCl GaCl+1/2H24AsCl3+6H2As4+12HCl
4GaCl+As4+2H24GaAs+4HCl
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Hydride Vapor Phase Epitaxy
Etch & growthIndept. Control of III & V
speciesMulti-wafer featureAll GaInAsP alloyHighly toxicComplicated
reactionMemory effectPoor hydride purityUse corrosive HCl
gasDifficult to grow Al and Sbcompound Ga(l)+HCl GaCl+1/2H2
AsH31/2As2+3/2H22GaCl+1/2As4 2GaAs+2HCl
hydride
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Figure 2. Schematic diagram of MBE machine.
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n Deflection (RHEED) measurement system. Electrons are scattered
more when a new mono-layer of atoms are being form. The intensity
of the RHEED signal oscillates a
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W.K. Chen Electrophysics, NCTU 441 GaAsHCl:H 2 O 2 :H 2 O
(1:4:80)
1-10 Most III-Vs Br:CH 3 OH (1:100)
0.5 InGaAsH 2 SO 4 :H 2 O 2 :H 2 0 (1:8:80)
0.1 GaAsH 2 O 2 :NH 4 OH:H 2 O (0.7:2:100)
2-5 Most III-V compounds HBr:CH 3 COOH:K 2 Cr 2 O 7 (1:1:1)
0.5 GaAsH 2 O:NH 4 OH:H 2 O 2 (20:2:1)
6 GaAsH 3 PO 4 :H 2 O 2 :H2O (3:4:3)
0.75 InPH 3 PO 4 :HCl (3:1)
6.6 InPH 3 PO 4 :HCl (1:3)
4.8 InPH 3 PO 4 :HCl (1:2)
2.5 InPH 3 PO 4 :HCl (1:1)
0.09 InPHCl:H 2 O (1:2)
0.7 InPHCl:H 2 O (1:1)
8 InPHCl:H 2 0 (2:1)