HCMUT – FEEE – Electronic engineering department
Instructor: Trần Hoàng Linh
Chapter 1
Crystal Properties and Growth of
Semiconductors
Refs:
1. Solid State Electronic Devices, Ben G. Streetman and Sanjay Banerjee, Sixth
Edition
2. Slides of Dr. Franklin D.Nkansah
3. Semiconductor Devices Physics and Technology 3E, S. M. Sze, Wiley 2010
1
Outline
•
•
•
•
Semiconductor Materials
Crystalline Lattices
Bulk Crystal Growth
Epitaxial Growth
2
Solid-state Material
• Solid-state materials can be grouped into three
classes—insulators, semiconductors, and
conductors.
– Insulators such as fused quartz and glass have very
low conductivities, on the order of 10-18– 10-8S/cm
– Conductors such as aluminum and silver have high
conductivities, typically from 104 to 106 S/cm
– Semiconductors have conductivities between those
of insulators and those of conductors.
• The conductivity of a semiconductor is generally sensitive
to temperature, illumination, magnetic field, and amounts of
impurity atoms
3
4
Typical range of conductivities for insulators, semiconductors, and conductors.
Note:  ,  are functions of
- Impurity
- Temperature
- Electric Field
- Optical Excitation
 Semiconductors are not metals
Semiconductor resistance
decreases with temperature
5
Semiconductor materials
6
Element Semiconductors
• Table 1-1 shows a portion of the periodic table related
to semiconductors.
• The element semiconductors, those composed of single
species of atoms, such as silicon (Si) and germanium
(Ge), can be found in Column IV.
• In the early 1950s, germanium was the major
semiconductor material.
• Since the early 1960s silicon has become a practical
substitute and has now virtually supplanted germanium
as a semiconductor material.
– Silicon is one of the most studied elements in the periodic table,
and silicon technology is by far the most advanced among all
semiconductor technologies.
7
Semiconductor materials – Si and Ge (1)
• If we look at the periodic table, the element
semiconductors, such as silicon (Si) or
germanium (Ge), can be found in column IV of
the table.
• In the early 1950s, Ge was the most important
semiconductor material, but, since the early
1960s, Si has played a major role and virtually
displaced Ge as the main material for
semiconductor material
8
Semiconductor materials – Si and Ge (2)
• The reasons of that are:
– Better properties at room temperature
– High-quality silicon dioxide (SiO2) can be grown
thermally.
– Si is second only to oxygen in great quantity.
– Devices made from Si cost less than any other
semiconductor material
– Silicon technology is by far the most advanced among
all semiconductor technologies.
9
Compound Semiconductors
• In recent years a number of compound semiconductors have found
applications for various devices.
– The important compound semiconductors as well as the twoelement-semiconductors are listed in Table 2. A binary
compound semiconductor is a combination of two elements
from the periodic table.
– In addition to binary compounds, ternary compounds and
quaternary compounds are made for special applications.
• Compared with the element semiconductors, the preparation of
compound semiconductors in single-crystal form usually involves
much more complex processes.
• Many of the compound semiconductors have electrical and optical
properties that are different from those of silicon.
– These semiconductors, especially GaAs, are used mainly for highspeed electronic and photonic applications.
10
Semiconductor Materials
11
Common Semiconductor Applications
• Group IV
–
–
–
–
Si for MOS, particularly CMOS digital logic and memory
Si BJT for some logic and analog applications
SiC for high power, high temperature applications
Ge for diodes, BJTs
• Group III/V
– GaAs, GaAsP, InP for optoelectronic and high speed digital applications
– InAs/GaInSb/AlInSb for long wavelength detectors
– GaN, AlGaN for blue/white LEDs and high power devices
• Group II/VI
– CdTe, HgCdTe for long wavelength detectors
Pronunciation: Generally, we can simply recite the name of each element,
truncate the last one, and add “ide” to the end. For example, InGaAsP is
“indium gallium arsenic phosphide”.
12
Outline
•
•
•
•
Semiconductor Materials
Crystalline Lattices
Bulk Crystal Growth
Epitaxial Growth
13
Classification of solids
SOLID MATERIALS
CRYSTALLINE
POLYCRYSTALLINE
AMORPHOUS
(Non-crystalline)
Single Crystal
Crystal Structure
14
3 Types of Solids
SOLIDS: [Single] Crystalline
Atomic
Arrangements: Periodic
Amorphous
Polycrystalline
Random
Grain Boundaries
Materials used to fabricate integrated circuits include some from all three classifications.
 Amorphous:
insulators (SiO2)
 Polycrystalline: MOS gates; contacts
 Crystalline:
substrates
15
Crystalline Solid
•
Crystalline Solid is the solid form of a substance in
which the atoms or molecules are arranged in a
definite, repeating pattern in three dimension.
Crystal Structure
17
Crystalline Solid
•
Single crystal has an atomic structure that repeats
periodically across its whole volume. Even at infinite length
scales, each atom is related to every other equivalent
atom in the structure by translational symmetry
Single Pyrite
Crystal
Amorphous
Solid
Single Crystal
Crystal Structure
18
Polycrystalline Solid
•
•
Polycrystal is a material made up of an aggregate
of many small single crystals (also called
crystallites or grains).
The grains are usually 100 nm - 100 microns in
diameter. Polycrystals with grains that are <10 nm
in diameter are called nanocrystalline
Polycrystalline
Pyrite form
(Grain)
Polycrystal
Crystal Structure
19
Amorphous Solid
•
Amorphous (non-crystalline) Solid is composed of
randomly orientated atoms, ions, or molecules that
do not form defined patterns or lattice structures.
Crystal Structure
20
21
Unit Cell of Periodic Lattice
Wigner-Seitz Primitive Cell
• Choose a reference atom
• Connect to all its neighbors by
straight lines
• Draw lines (in 2D) or planes (in
3D) normal to and at the midpoints
of lines drawn in step 2
• Smallest volume enclosed is the
Wigner-Seitz primitive cell
Wigner-Seitz cell is ONE definition of a Unit Cell that
always works
There are other ways of construction!
Crystal Lattices
Bravais Lattices
Non-Bravais Lattices
(BL)
(non-BL)
All atoms are the same kind
All lattice points are equivalent
Atoms are of different kinds.
Some
lattice
aren’t
equivalent.
Atoms
are ofpoints
different
kinds.
Some
A combination
2 or
more BL
lattice
points areofnot
equivalent.
2 d examples
Lattice Translation Vectors
In General
• Mathematically, a lattice is defined by 3 vectors called
Primitive Lattice Vectors
a1, a2, a3 are 3d vectors which depend on the geometry.
• Once a1, a2, a3 are specified, the
Primitive Lattice Structure
is known.
• The infinite lattice is generated by translating through a
Direct Lattice Vector: T = n1a1 + n2a2 + n3a3
n1,n2,n3 are integers. T generates the lattice points. Each
lattice point corresponds to a set of integers (n1,n2,n3).
2 Dimensional Lattice Translation Vectors
Consider a 2-dimensional lattice (figure). Define the
2 Dimensional Translation Vector: Rn  n1a + n2b
a & b are 2 d Primitive Lattice Vectors, n1, n2 are integers.
Point D(n1, n2) = (0,2)
Point F(n1, n2) = (0,-1)
• Once a & b are specified by the
lattice geometry & an origin is
chosen, all symmetrically equivalent
points in the lattice are determined by
the translation vector Rn. That is, the
lattice has translational symmetry.
Note that the choice of Primitive
Lattice vectors is not unique! So,
one could equally well take vectors a
& b' as primitive lattice vectors.
The Basis
(or basis set)
 The set of atoms which, when placed at each
lattice point, generates the Crystal Structure.
Crystal Structure
≡ Primitive Lattice + Basis
Translate the basis through all possible lattice vectors
T = n1a1 + n2a2 + n3a3
to get the Crystal Structure or the
Direct Lattice
Crystal Structure
Crystal structure can be obtained by attaching atoms or
groups of atoms --basis-- to lattice sites.
• The periodic lattice symmetry is such that
the atomic arrangement looks the same from
an arbitrary vector position r as when viewed
from the point
r' = r + T
(1)
where T is the translation vector for the lattice:
T = n1a1 + n2a2 + n3a3
• Mathematically, the lattice & the vectors a1,a2,a3 are
Primitive
if any 2 points r & r' always satisfy (1) with
a suitable choice of integers n1,n2,n3.
• In 3 dimensions, no 2 of the 3 primitive lattice
vectors a1,a2,a3 can be along the same line. But,
DO NOT think of a1,a2,a3 as a mutually
orthogonal set! Often, they are neither mutually
perpendicular nor all the same length!
• For examples, see Fig. 3a (2 dimensions):
The Primitive Lattice Vectors a1,a2,a3 aren’t
necessarily a mutually orthogonal set!
Often, they are neither mutually
perpendicular nor all the same length!
• For examples, see Fig. 3b (3 dimensions):
Crystal Lattice Types
Bravais Lattice 
An infinite array of discrete points with an
arrangement & orientation that appears exactly the
same, from whichever of the points the array is
viewed. A Bravais Lattice is invariant under a
translation T = n1a1 + n2a2 + n3a3
Nb film
Non-Bravais Lattices
•In a Bravais Lattice, not only the atomic
arrangement but also the orientations must appear
exactly the same from every lattice point.
2 Dimensional Honeycomb Lattice
• The red dots each have a neighbor
to the immediate left. The blue dot
has a neighbor to its right. The red
(& blue) sides are equivalent &
have the same appearance. But, the
red & blue dots are not equivalent. If
the blue side is rotated through 180º
the lattice is invariant.
 The Honeycomb Lattice is
NOT a Bravais Lattice!!
Honeycomb
Lattice
Geometry of Lattice Points
In a Bravais lattice,
• every point in the lattice can be “reached” by integer
translation of unit vectors
• every point has the same environment as every other point
(same number of neighbors, next neighbors, …)
Not a Bravais Lattice …
Not a Bravais Lattice …
….but these can be converted into Bravais lattice
Not a Bravais Lattice …
Two different unit cells in random order
… these CANNOT be transformed to Bravais lattice
ex. Aluminum-Manganese compounds, non-sticky coats
Unit Cells in One-dimensional Crystals
There is exactly ONE primitive unit cell in a 1D system
No system truly 1-D, but ….
• 1D properties dominate behavior in some material
• e.g.: polymers, DNA, 1D heterostructures (lasers, RTDs)
• Can often be solved analytically, many properties have
2D/3D analogs
Unit Cell in 2D (all sites are equivalent)
It can be shown that, in 2 Dimensions, there are
Five (5) & ONLY Five Bravais Lattices!
2-Dimensional Unit Cells
Unit Cell  The Smallest Component
of the crystal (group of atoms, ions or molecules),
which, when stacked together with pure translational
repetition, reproduces the whole crystal.
b
S
a
S
S
S
S
S
S
S
S
S
S
S
S
S
S
Unit Cell  The Smallest Component
of the crystal (group of atoms, ions or molecules),
which, when stacked together with pure translational
repetition, reproduces the whole crystal.
Note that the choice of unit cell is not unique!
S
S
S
2-Dimensional Unit Cells –
Artificial Example: “NaCl”
Lattice points are points with
identical environments.
2-Dimensional Unit Cells: “NaCl”
Note that the choice of origin is arbitrary!
the lattice points need not be atoms, but
The unit cell size must always be the same.
2-Dimensional Unit Cells: “NaCl”
These are also unit cells!
It doesn’t matter if the origin is at Na or Cl!
2-Dimensional Unit Cells: “NaCl”
These are also unit cells.
The origin does not have to be on an atom!
2-Dimensional Unit Cells: “NaCl”
These are NOT unit cells!
Empty space is not allowed!
2-Dimensional Unit Cells: “NaCl”
In 2 dimensions, these are unit cells.
In 3 dimensions, they would not be.
2-Dimensional Unit Cells
Why can't the blue triangle be a unit cell?
Example: 2 Dimensional, Periodic Art!
A Painting by
Dutch Artist Maurits Cornelis Escher (1898-1972)
Escher was famous for
his so called “impossible
structures”, such as
Ascending &
Descending, Relativity,..
Can you find the “Unit Cell” in this painting?
3-Dimensional Unit Cells
3-Dimensional Unit Cells
3-Dimensional Unit Cells
3 Common Unit Cells with Cubic Symmetry
Simple Cubic
(SC)
Body Centered
Cubic (BCC)
Face Centered
Cubic (FCC)
Conventional & Primitive Unit Cells
Unıt Cell Types
Primitive
Conventional
(Non-primitive)
A single lattice point per cell
More than one lattice point per cell
The smallest area in 2 dimensions, or
The smallest volume in 3 dimensions
Volume (area) = integer multiple of
that for primitive cell
Simple Cubic (SC)
Conventional Cell =
Primitive cell
Body Centered Cubic (BCC)
Conventional Cell ≠
Primitive cell
Face Centered Cubic (FCC)
Structure
Conventional Unit Cells
• A Conventional Unit Cell just fills space when
translated through a subset of Bravais lattice vectors.
• The conventional unit cell is larger than the primitive
cell, but with the full symmetry of the Bravais lattice.
• The size of the conventional cell is given by the lattice
constant a.
FCC Bravais Lattice
The full cube is the
Conventional Unit
Cell for the FCC
Lattice
Conventional & Primitive Unit Cells
Face Centered Cubic Lattice
Primitive Unit Cell
(Shaded)
Lattice Const.
Primitive Lattice
Vectors
a1 = (½)a(1,1,0)
a2 = (½)a(0,1,1)
a3 = (½)a(1,0,1)
Note that the ai’s are
Conventional Unit
Cell (Full Cube)
NOT Mutually
Orthogonal!
Elements That Form Solids
with the FCC Structure
Body Centered Cubic (BCC) Structure
Conventional & Primitive Unit Cells
Body Centered Cubic Lattice
Primitive Lattice
Primitive Unit Cell
Vectors
a1 = (½)a(1,1,-1)
a2 = (½)a(-1,1,1)
Lattice a3 = (½)a(1,-1,1)
Constant
Conventional Unit
Cell (Full Cube)
Note that the ai’s are
NOT mutually
orthogonal!
Elements That Form Solids
with the BCC Structure
Conventional & Primitive Unit Cells
Cubic Lattices
Simple Cubic (SC)
c
b
Primitive Cell = Conventional Cell
Fractional coordinates of lattice points:
000, 100, 010, 001, 110,101, 011, 111
a
b
c
Body Centered Cubic (BCC)
Primitive Cell  Conventional Cell
a
b
c
Fractional coordinates of the lattice points
in the conventional cell: 000,100, 010,
001, 110,101, 011, 111, ½ ½ ½
a
Primitive Cell = Rombohedron
Conventional & Primitive Unit Cells
Cubic Lattices
Face Centered Cubic (FCC)
Primitive Cell  Conventional Cell
The fractional coordinates of lattice
points in the conventional cell are:
000,100, 010, 001,
110,101, 011, 111,
½ ½ 0, ½ 0 ½, 0 ½ ½,
½ 1 ½, 1 ½ ½ , ½ ½ 1
b
c
a
Simple Hexagonal Bravais Lattice
Conventional & Primitive Unit Cells
Points of the Primitive Cell
Hexagonal Bravais
Lattice
Primitive Cell =
Conventional Cell
c
b
a
Fractional coordinates of lattice
points in conventional cell:
100, 010, 110, 101,
011, 111, 000, 001
Hexagonal Close Packed (HCP) Lattice:
A Simple Hexagonal Bravais Lattice with
a 2 Atom Basis
The HCP lattice is not a
Bravais lattice, because the
orientation of the environment of a
point varies from layer to layer
along the c-axis.
General Unit Cell Discussion
• For any lattice, the unit cell &, thus,
the entire lattice, is UNIQUELY
determined by 6 constants (figure):
a, b, c, α, β and γ
which depend on lattice geometry.
• As we’ll see, we sometimes want to
calculate the number of atoms in a unit cell.
To do this, imagine stacking hard spheres
centered at each lattice point & just
touching each neighboring sphere. Then,
for the cubic lattices, only 1/8 of each
lattice point in a unit cell is assigned to that
cell. In the cubic lattice in the figure,
Each unit cell is associated with
(8)  (1/8) = 1 lattice point.
Primitive Unit Cells & Primitive Lattice Vectors
• In general, a Primitive Unit
Cell is determined by the
parallelepiped formed by the
Primitive Vectors a1 ,a2, &
a3 such that there is no cell
of smaller volume that can
• The Primitive Unit Cell
volume can be found by
• As we’ve discussed, a Primitive vector manipulation:
V = a1(a2  a3)
Unit Cell can be repeated to fill
space by periodic repetition of it • For the cubic unit cell in
through the translation vectors
the figure, V = a3
be used as a building block
for the crystal structure.
T = n1a1 + n2a2 + n3a3.
Primitive Unit Cells
• Note that, by definition, the Primitive Unit Cell
must contain ONLY ONE lattice point.
• There can be different choices for the Primitive Lattice
Vectors, but the Primitive Cell volume must be
independent of that choice.
2 Dimensional
Example! j
P = Primitive Unit Cell
NP = Non-Primitive
Unit Cell
Bravais lattices in 3D: 14 types, 7 classes
Bravais lattices in 3D: 14 types, 7 classes
72
3 Dominant Bravais Lattices
a
(SC )
a
a
(BCC )
(FCC )
a = lattice constant, lattice parameter the spacing between atoms
at one side of a cubic unit cell (~5-6 Å for typical semiconductors)
74
Surface Reconstruction
76
Miller-Indices and Definition of Planes
78
Miller Indices: Rules
Miller Indices: Rules
Where does Miller Indices come from ?
Specification of vectors normal to a particular plane!
Bravais-Miller Indices
Direction Indices
83
84
Example of Miller indices for planes
Note:
 If a plane passes through the origin, translate it to a parallel position.
 Intercept at negative branch  minus sign: (h -k l )  (h k l)
85
Why Are Crystal Planes Important?
• real crystals are eventually terminate at a surface
• Semiconductor devices are fabricated at or near a surface
• many of a single crystal's structural and electronic properties are highly anisotropic
86
Equivalent Planes: {h k l}
87
Crystallographic Notation
Miller Indices:
Notation
(hkl)
Interpretation
crystal plane
{hkl}
[hkl]
<hkl>
equivalent planes
crystal direction
equivalent directions
h: inverse x-intercept of plane
k: inverse y-intercept of plane
l: inverse z-intercept of plane
(Intercept values are in multiples of the lattice constant;
h, k and l are reduced to 3 integers having the same ratio.)
Crystal Structure Model
 Characteristics of Cubic Lattices
Simple
BCC
FCC
Volume of cubic cell
Volume of primitive cell
Type of primitive cell
Lattice points per cubic cell
a3
a3
SC
1
a3
1/2a3
a3
1/4a3
Lattice points per unit cell
Nearest neighbour distance
# of nearest neighbours
Next nearest neighbour distance
1/a3
a
6
2 a
# of next nearest neighbours
12
rhombohedral rhombohedral
2
2/a3
1/23a
8
a
6
4
4/a3
1/22a
12
a
6
89
 Close Packing: Close packing (closest packing) is the most efficient arrangement of spheres. For
crystals it is envisioned as the spheres representing the atoms at the bases touch each other.
 Packing of a unit cell: Packing fraction: The ratio of the total volume of a set of objects packed
into a space to the volume of that space.
90
Lattices: Diamond & Zincblende
a(x + y + z)/4
(a) a unit cell of the diamond lattice
constructed by placing atoms (1/4, 1/4, 1/4)
from each atom in an FCC.
(b) top view (along any <100> direction)
of an extended diamond lattice.
The colored circles indicate one FCC
sublattice and black circles indicate
the interpenetrating FCC.
91
Lattices: Si (Diamond) & GaAs (Zincblende)
92
Silicon
93
Another way to think of the
diamond lattice is this: Imagine
that the fcc lattice (top figure)
has attached to it, at the bottom
right corner, the two atoms
indicated in red below. If we
attach these two atoms to each
of the fcc lattice sites, the result
is the diamond lattice. (We call
this “lattice with a basis”, where
the basis is the two red atoms.)
94
Si Crystal: Diamond Lattice
95
Crystallographic Planes and Si Wafers
Silicon wafers are usually cut
along a {100} plane with a flat
or notch to orient the wafer
during IC fabrication:
97
Which solid state material for electronic devices?
• Why semiconductors?




vs. conductors or insulators
Bandgap
Elemental (Si) vs. compound (GaAs)
Resistivity () control over 1010 range.
• Why (usually) crystalline?
polycrystalline amorphous crystalline
 pure
 repeatable
 easy to cleave
• Why silicon?
 cheap
 SiO2 is very good insulator
 good at room temperature
98
Outline
•
•
•
•
Semiconductor Materials
Crystalline Lattices
Bulk Crystal Growth
Epitaxial Growth
99
Crystal growth
100
Crystal Growth (Si)
101
Czochralski method
102
Czochralski method
103
Float-zone crystal growth
104
Procedure of Silicon Wafer Production
Raw material ― Polysilicon
nuggets purified from sand
Si crystal ingot
Crystal pulling
A silicon wafer fabricated with
microelectronic circuits
Final wafer product after polishing,
cleaning and inspection
Slicing into Si wafers using
a diamond saw
105
106
Outline
•
•
•
•
Semiconductor Materials
Crystalline Lattices
Bulk Crystal Growth
Epitaxial Growth
107
Epitaxial growth
Epitaxis:
epi - on
taxis - arrangement
108
Epitaxial Growth (on substrate)
109
110
111
Liquid-Phase Epitaxy (LPE)
112
Molecular Beam Epitaxy (MBE)
113
Molecular Beam Epitaxy (MBE)
114
Chemical Vapor Deposition (CVD) or
Vapor-Phase Epitaxy (VPE)
115
Metal-Organic Chemical Vapor Deposition (MOCVD)
116
Metal-Organic Chemical Vapor Deposition (MOCVD)
117