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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)