Download Chapter 1-Crystal Properties_M A Islam_Lecture 1

EEE-3515
Electrical Properties of Materials
• Dr. (Ph.D) Mohammad Aminul Islam
International Islamic University Chittagong
Department of Electrical and Electronic Engineering
Book Reference
1. Solid state Electronic Device
- Ben G. Stretman & Sanjay Kumar Banerjee
2. Principles of Electronic Materials and Devices
- S.O. Kasap
CH# 1
Crystal Properties
Semiconductor & Semiconductor Materials
Crystal
Types of Crystals
Lattice & Basis
Bravias Lattice and
Miller Indices
CH# 1, Lecture 1
OUTLINE
 Introduction to the Semiconductor
How do atoms ARRANGE themselves to form solids?
• Types of solids
 Crystalline Materials
o Single crystal
o Polycrystalline
 Amorphous
• Unit cells
• Crystal structures
o Face-centered cubic
o Body-centered cubic
o Hexagonal close-packed
• Close packed crystal structures
• Density
Why Study Solid State Physics?
Periodic table: where the semiconductor Materials are?
II
III
IV
V
VI
B
C
N
O
Boron
Carbon
Nitrogen
Oxygen
Al
Si
P
S
Aluminum
Silicon
Phosphorus
Sulfur
Zn
Ga
Ge
As
Se
Zinc
Galium
Germanium
Arsenic
Selenium
Cd
In
Sn
Sb
Te
Cadmium
Indium
Tin
Antimony
Tellurium
Semiconductor Materials
o Element : Si, Ge
o IV compounds : SiC, SiGe
o III-V compounds: AIP, AlAs, AlSb, GaN,GaP, GaAs,
GaSb, InP, InAs, InSb
o II-VI: SnS, ZnSe, ZnTe, CdS, CdSe, CdTe
o LED(GaN, GaP, GaAs), Three-elements(GaAsP,
InGaAsP), Fluorescent(II-VI, ZnS), Light
detector(InSb, CdSe), PbTe, HgCdTe, Si, Ge)
II
III
IV
V
VI
B
C
N
O
Boron
Carbon
Nitrogen
Oxygen
Al
Si
P
S
Aluminum
Silicon
Phosphorus
Sulfur
Zn
Ga
Ge
As
Se
Zinc
Galium
Germanium
Arsenic
Selenium
Cd
In
Sn
Sb
Te
Cadmium
Indium
Tin
Antimony
Tellurium
• In Semiconductor production, doping is the process
of intentionally introducing impurities into an
extremely pure (also referred to as intrinsic)
semiconductor in order to change its electrical
properties.
• The number of dopant atoms needed to create a
difference in the ability of a semiconductor to
conduct is very small. Where a comparatively small
number of dopant atoms are added (of the order of 1
every 100,000,000 atoms) then the doping is said to
be low, or light.
• Where many more are added (of the order of 1 in
10,000) then the doping is referred to as heavy, or
high. This is often shown as n+ for n-type dopant or
p+ for p-type doping.
Types of Solids
(a) Crystalline material: periodic array
(i) Single crystal: periodic array over the entire extent of the material
(ii) Polycrystalline material: many small crystals or grains
(b) Amorphous: lacks a systematic atomic arrangement
Crystalline
Amorphous
SiO2
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Crystal Structure
Consider atoms as hard spheres with a radius.
Shortest distance between two atoms is a diameter.
Crystal described by a lattice of points at center of atoms
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Unit Cell
The unit cell is building block for crystal.
Repetition of unit cell generates entire crystal.
Ex: 2D honeycomb represented by translation of
unit cell
Ex: 3D crystalline structure
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Another Definition of Unit cell
A small cell in the crystal structure that carries the prope
rties of the crystal. The repetition of the unit cell in 3-di
mensions generated the whole crystal structure.
In the cubic crystal system three types of arrangements
are found:
– Simple cubic
– Body-centered cubic
– Face-centered cubic
Metallic Crystal Structures
 Metals usually polycrystalline
amorphous metal possible by rapid cooling
 Bonding in metals non-directional 
large number of nearest neighbors and dense atomic packing
 Atom (hard sphere) radius, R:
defined by ion core radius: ~0.1 - 0.2 nm
 Most common unit cells
Faced-centered cubic (FCC)
Body-centered cubic
(BCC)
Hexagonal close-packed (HCP).
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Cubic Lattice
• The simple cubic (a), the body-centered cubic (b) and the face
centered cubic (c) lattice.
• Since all unit vectors identifying the traditional unit cell have
the same size, the crystal structure is completely defined by a
single number. This number is the lattice constant, a.
SIMPLE CUBIC
• Coordination # = 6
(# nearest neighbors)
a
a
R=1/2*a
a
SIMPLE CUBIC
Face-Centered Cubic (FCC) Crystal Structure (I)
 Atoms located at corners and on centers of faces
 Cu, Al, Ag, Au have this crystal structure
Two representations of the
FCC unit cell
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Face-Centered Cubic Crystal Structure (II)
R
a
 Hard spheres touch along diagonal
 the cube edge length, a= 2R2
 The coordination number, CN = number of closest neighbors = number of
touching atoms, CN = 12
 Number of atoms per unit cell, n = 4.
FCC unit cell:
6 face atoms shared by two cells: 6 x 1/2 = 3
8 corner atoms shared by eight cells: 8 x 1/8 = 1
 Atomic packing factor, APF
= fraction of volume occupied by hard spheres
= (Sum of atomic volumes)/(Volume of cell)
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= 0.74 (maximum possible)
ATOMIC PACKING FACTOR
• Fill a box with hard spheres
– Packing factor = total volume of spheres in
box / volume of box
– Question: what is the maximum packing fa
ctor you can expect?
• In crystalline materials:
– Atomic packing factor = total volume of ato
ms in unit cell / volume of unit cell
– (as unit cell repeats in space)
ATOMIC PACKING FACTOR
• APF for a simple cubic structure = 0.52
Adapted from Fig. 3.19,
Callister 6e.
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Density Computations
 = mass/volume
= (atoms in the unit cell, n ) x
(mass of an atom, M) /
(the volume of the cell, Vc)
Atoms in the unit cell, n = 4 (FCC)
Mass of an atom, M = A/NA
A = Atomic weight (amu or g/mol)
Avogadro number NA = 6.023  1023 atoms/mol
The volume of the cell, Vc = a3 (FCC)
a = 2R2 (FCC)
R = atomic radius
nA

Vc N A
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Body-Centered Cubic Crystal Structure (II)
a
 Hard spheres touch along cube diagonal 
cube edge length, a= 4R/3
 The coordination number, CN = 8
 Number of atoms per unit cell, n = 2
Center atom not shared: 1 x 1 = 1
8 corner atoms shared by eight cells: 8 x 1/8 = 1
 Atomic packing factor, APF = 0.68
 Corner and center atoms are equivalent
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Hexagonal Close-Packed Crystal Structure (I)
 Six atoms form regular hexagon surrounding one atom in center
 Another plane is situated halfway up unit cell
(c-axis) with 3 additional atoms situated at interstices of hexagonal
(close-packed) planes
 Cd, Mg, Zn, Ti have this crystal structure
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Hexagonal Close-Packed Crystal Structure (II)
 Unit cell has two lattice parameters a and c.
Ideal ratio c/a = 1.633
 The coordination number, CN = 12 (same as in FCC)
 Number of atoms per unit cell, n = 6.
3 mid-plane atoms not shared: 3 x 1 = 3
12 hexagonal corner atoms shared by 6 cells:
12 x 1/6 = 2
2 top/bottom plane center atoms shared by 2 cells:
2 x 1/2 = 1
 Atomic packing factor, APF = 0.74 (same as in FCC)
c
a
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Density Computations Summarized
Density of a crystalline material,
 = density of the unit cell
= (atoms in the unit cell, n )  (mass of an atom, M) /
the cell, Vc)
Atoms in unit cell, n = 2 (BCC); 4 (FCC); 6 (HCP)
(the volume of
Mass of atom, M = Atomic weight, A, in amu (or g/mol). Translate mass
from amu to grams divide atomic weight in amu by Avogadro number
NA = 6.023  1023 atoms/mol
Volume of the cell, Vc = a3 (FCC and BCC)
a = 2R2 (FCC); a = 4R/3 (BCC)
where R is the atomic radius

nA
Vc N A
Atomic weight and atomic radius of elements are in the table in textbook
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front cover.
Face-Centered Cubic Crystal Structure (III)
 Corner and face atoms in unit cell are equivalent
 FCC has APF of 0.74
Maximum packing  FCC is close-packed structure
 FCC can be represented by a stack of close-packed planes (planes with
highest density of atoms)
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Close-packed Structures (FCC and HCP)
 FCC and HCP: APF =0.74 (maximum possible value)
 FCC and HCP may be generated by the stacking of close-packed planes
 Difference is in the stacking sequence
HCP: ABABAB...
FCC: ABCABCABC…
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HCP: Stacking Sequence ABABAB...
Third plane placed directly above first plane of atoms
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FCC: Stacking Sequence ABCABCABC...
Third plane placed above “holes” of first plane not covered by second
plane
29
Polymorphism and Allotropy
Some materials can exist in more than one crystal structure, Called
polymorphism.
If material is an elemental solid: called allotropy.
Ex: of allotropy is carbon:
can exist as diamond, graphite, amorphous carbon.
Pure, solid carbon occurs in three crystalline forms – diamond, graphite; and
large, hollow fullerenes. Two kinds of fullerenes are shown here:
buckminsterfullerene (buckyball) and carbon nanotube.
30
Single Crystals and Polycrystalline Materials
Single crystal: periodic array over entire material
Polycrystalline material: many small crystals (grains)
varying orientations.
with
Atomic mismatch where grains meet (grain boundaries)
Grain Boundary
31
Polycrystalline Materials
Atomistic model of a nanocrystalline solid
32
Polycrystalline Materials
Simulation of annealing of a polycrystalline grain structure
33
Anisotropy
Different directions in a crystal have different packing.
For instance: atoms along the edge of FCC unit cell
separated than along the face diagonal.
Causes anisotropy in crystal properties
Deformation depends on direction of applied stress
are
more
If grain orientations are random  bulk properties are isotropic
Some polycrystalline materials have grains with preferred orientations
(texture): material exhibits anisotropic properties
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Non-Crystalline (Amorphous) Solids
Amorphous solids: no long-range order
Nearly random orientations of atoms
(Random orientation of nano-crystals can be
amorphous or polycrystalline)
Schematic Diagram of
Amorphous SiO2
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Summary
Make sure you understand language and concepts:











Allotropy
Amorphous
Anisotropy
Atomic packing factor (APF)
Body-centered cubic (BCC)
Coordination number
Crystal structure
Crystalline
Face-centered cubic (FCC)
Grain
Grain boundary
Hexagonal close-packed (HCP)
Isotropic
Lattice parameter
Non-crystalline
Polycrystalline
Polymorphism
Single crystal
Unit cell
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