Chapter 1 The Crystal Structure of Solids
W.K. Chen
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Outline
Semiconductor material Type of solids Space lattices Atomic bonding Imperfections & impurities in solids Growth of semiconductor materials
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1.1 Semiconductor Materials
Elemental semiconductors: (C, Si, Ge) - composed of single species of atoms Compound semiconductors: (binary, ternary, quarternary) III-V, II-VI, IV-IV W.K. Chen
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1.2 Types of Solids
Amorphous: degree of order only within a few atomic or molecular dimensions Polycrystalline: 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 grains Single 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
lattice Lattice point Unit cell Primitive cell r r r r T = n1a + n2b + n3c
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r r r unit cell volume V = (a × b ) ⋅ c
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Lattice point
Lattice: the periodic arrangement of atoms in crystal Lattice point: a dot used to present a particular atomic array Unit cell: a small volume of the crystal that can be used to reproduce the entire crystal A 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
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Primitive cell: the smallest unit cell
Every equivalent lattice point in primitive cell for 3-dim crystal can be found using the vector
r r r r r = pa + qb + sc
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1.3.2 Basic crystal structure in semiconductors Orthorhombic (正交晶系)
a≠b≠c
Tetragonal (四方晶系)
a=b≠c
α=β=γ=90o α=β=γ=90o
Cubic (立方晶系)
a=b=c
α=β=γ=90o
Hexagonal (六方晶系)
a=b≠c
α=β=90o, γ≠=90o
a, b are primitive vectors lie on the base plane
β
α
r r ∠α : b , c r r ∠β : c , a r r ∠γ : a , b
γ
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1.3.2 Basic crystal structure
Three basic (cubic) crystal structures Simple cubic (sc): - has an atom located at each corner
Body-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 W.K. Chen
Body-centered cubic Electrophysics, NCTU
Face-centered cubic 10
The Fourteen Bravais Lattices The 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. Table 1. Seven crystal systems make up fourteen Bravais lattice types in three dimensions Number of Lattices
Lattice Symbol
Restriction on crystal cell angle
System
Cubic
3
P or sc, I or bcc,F or fcc
a=b=c α =β =γ=90°
Tetragonal
2
P, I
a=b≠c α=β =γ=90°
Orthorhombic
4
P, C, I, F
a≠b≠ c α=β =γ=90°
Monoclinic
2
F, C
a≠b≠ c α=β=90 °≠β
Triclinic
1
P
Trigonal
1
R
Hexagonal
1
P
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a≠b≠ c
α≠β≠γ
α=β =γ <120° ,≠90° a=b≠c α =β =90° γ=120°
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a=b=c
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Example 1.1 Volume density bcc structure o
a1 = 5 A
How many atoms in one unit cell? 1 1+ 8× ( ) = 2 8
Volume density = =
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2 atoms (a1 ) 2 2 = 1.6 ×1022 atoms/cm3 −8 2 (5 ×10 )
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1.3.3 Crystal plane & Miller indices How 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
plane vector r r r r g = ha + kb + lc = [h k l ]
r r r let l1 = pa − qb
r r r l 2 = pa − sc
r r r l 2 = pa − sc
r r r r ⇒ g ⊥ l1 and g ⊥ l 2
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r g
r r r l1 = pa − qb
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r r r r r r r r r ⎧g ⊥ l1 ⇒ g ⋅ l1 = 0 ⇒ (ha + kb + lc ) ⋅ ( pa − qb ) = 0 ⎪ k p ⎪ ⇒ hp − kq = 0 ⇒ = ⎪ h q ⇒ ⎨r r r r r r r r r ⎪g ⊥ l2 ⇒ g ⋅ l2 = 0 ⇒ (ha + kb + lc ) ⋅ ( pa − sc ) = 0 ⎪ r l p r r ⇒ hp − ls = 0 ⇒ = ⎪ l 2 = pa − sc h s ⎩ p p 1 1 1 h h) = ( ⇒ (h k l) = (h ) q s p q s
r r r l1 = p a − q b
1 1 1 Miller indices ( h k l ) = ( ) ⇒ p q s The integers are referred as the Miller indices. We will refer to a general plane as (h k l) plane And the associated plane vector g is denoted by [hkl]
(h k l) plane [h k l] vector
[h k l ] vector ⊥ (h k l)plane For any plane that parallel to each other, they bear the same miller indices W.K. Chen
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Example 1.2 Miller indices
Intercepts of plane p = 3, q = 2 and s = 1 1 11 ⇒ ( hkl ) = ( ) = ( 2 3 6) 3 21
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Lattice Planes: Miller indeces Miller index (h k l) = (
p = 1, q = ∞ and s = ∞ (h k l) = (100)plane W.K. Chen
1 1 1 ) p q s
p = 1, q = 1 and s = ∞ (h k l) = (110)plane Electrophysics, NCTU
p = 1, q = 1 and s = 1 (h k l) = (111)plane 16
Example 1.3 surface density bcc structure o
a1 = 5 A
2 a1
Surface density at (110) plane = =
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a1
2 atoms ( a1 )( a1 2 ) 2 = 5.66 × 1014 atoms/cm 2 −8 2 (5 × 10 ) 2 17
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1.3.4 Diamond structure Diamond structure is the most common structure in elemental semiconductors, such as Si, Ge
Tetrahedral structure
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Diamond structure is basically consisted of bodycentered cubics with four of the corner atoms missing Each atom in the tetrahedral structure ( 四方 體) has four nearest neighbors and it is this structure which is the basic building block of diamond lattice a=b≠c
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α=β=γ=90o 18
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Zincblende (sphalerite) structure
For 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(閃鋅結構) 1
1
2
4
2
6 5
4
3
per unit cell Ga = 4 1 1 As = 4 × ( ) + 6 × ( ) = 4 4 2 corner
Face center
3
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1.4 Atomic bonding The interaction of atoms in crystal is determined largely by the outmost, i.e., valence electrons of an atom
Ionic bond: Covalent bond: Metallic bond Van der Waals bond
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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 bonding such as solid sodium (Na). Solid sodium has a bodycentered cubic structure, each sodium has one valence electron, so each atoms has eight nearest neighbors with each atom sharing many valence electrons Van der Waals bond Interaction between dipoles (most in gaseous form, solid form exhibits a relatively melting temperature
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Body-centered cubic
HF
HF
HF
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1.5 Imperfections & impurities in solids 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
Native defects (Imperfections) vacancy interstitial line dislocation anti-site Impurities substitutional impurity interstitial impurity
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Native defects (Imperfections) vacancy: missing of atom at a particular lattice site
interstitial atoms located between lattice sites
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Native defects (Imperfections) Frenkel defect vacancy-interstitial defect
line dislocation entire row of atoms is missing from its normal lattice sites
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Impurities substitutional impurity interstitial impurity anti-site
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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 vacancy interstitial substitial anti-site
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1.6 Growth of semiconductor materials
Ingot growth Epitaxial growth
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Silicon Crystal Pulling Apparatus
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Liquid Encapsulated Czochralski (LEC)
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Encapsulation by thin (8-17 mm) molten B2O3 layer High inert gas pressure (up to 100 bar) to suppress volatility of group V 50 mm round-shaped GaAs, 200-400 cm-2
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3Å→300μm
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)
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Liquid Phase Epitaxy
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Metal-Organic Chemical Vapor Deposition
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MOCVD Growth Mechanism
V族
III族
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Molecular Beam Epitaxy
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Chemical Beam Epitaxy
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Trichloride Vapor Phase Epitaxy
Hot wall reactor Etch & grow Pure AsCl3 and PCl3 attainable Low-background doping epilayer Low cost Not possible to grow AlGaAs (TAlAs=1100oC>>TGaAs=750oC) Difficult in composition control ( use both group III & V clorides) Poor reproducibilty
Ga(l)+HCl →GaCl+1/2H2 4AsCl3+6H2→As4+12HCl 4GaCl+As4+2H2→4GaAs+4HCl W.K. Chen
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Hydride Vapor Phase Epitaxy
hydride
Ga(l)+HCl →GaCl+1/2H2
Etch & growth Indept. Control of III & V species Multi-wafer feature All GaInAsP alloy Highly toxic Complicated reaction Memory effect Poor hydride purity Use corrosive HCl gas Difficult to grow Al and Sb compound
AsH3→1/2As2+3/2H2 2GaCl+1/2As4 → 2GaAs+2HCl W.K. Chen
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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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Table 1. Common etchants for various semiconductor materials and etch rates. Etchant and ratio of mixture
Material Etched
Approx. etch rate μ m per min at 20 ° C
HCl (conc.)
InP
5-15
HCl (conc.)
Surface oxide on GaAs
Fast
HCl (conc.)
InGaAs
<0.02
HCl:H 2 0 (2:1)
InP
8
HCl:H 2 O (1:1)
InP
0.7
HCl:H 2 O (1:2)
InP
0.09
H 3 PO 4 :HCl (1:1)
InP
2.5
H 3 PO 4 :HCl (1:2)
InP
4.8
H 3 PO 4 :HCl (1:3)
InP
6.6
H 3 PO 4 :HCl (3:1)
InP
0.75
H 3 PO 4 :H 2 O 2 :H2O (3:4:3)
GaAs
6
H 2 O:NH 4 OH:H 2 O 2 (20:2:1)
GaAs
0.5
HBr:CH 3 COOH:K 2 Cr 2 O 7 (1:1:1)
Most III-V compounds
2-5
H 2 O 2 :NH 4 OH:H 2 O (0.7:2:100)
GaAs
0.1
H 2 SO 4 :H 2 O 2 :H 2 0 (1:8:80)
InGaAs
0.5
Br:CH 3 OH (1:100)
Most III-Vs
1-10
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