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MSE 630, Semiconductor MaterialsTh 7:00-9:45 pm, JD-1551
Dr. R. D. ConnerOffice, JD 3511, phone 818 677-4730
Office hrs: T, Th: 10-10:45 AM, 6:00-6:45 pm
Textbook: Silicon VLSI Technology, J.D. Plummer, M.D. Deal and P.B. Griffin, Prentice Hall, ISBN: 0-13-085037-3, 2000
Course Description: Electrical behaviors of materials; conductors, semiconductors and insulators; electronic structure of materials; preparation of semiconductor materials; crystal growth and doping; intrinsic and extrinsic semiconductors; semiconductor devices; superconductivity and superconducting materials; photoelectron effects with semiconductors; photovoltaic materials and solar cells; imperfections in semiconductors; characterization of electronic materials.
Date Lecture Seminar topics Aug. 26 Materials basics Electronic devicesSept. 2 Electrical conduction in materials How semiconductors workSept. 9 Quantum Mechanics Silicon device fabricationSept. 16 Phonons Superconductivity/1st paper
dueSept. 23 Magnetism Magnetic storage Sept. 30 Silicon wafer growth Defects in Si semiconductorsOct. 7 Clean rooms & manufacturing III-IV semiconductorsOct. 14 Midterm exam LithographyOct. 21 Thermal oxidation Solar CellsOct. 28 Diffusion Ionic computing/2nd paper
dueNov. 4 Ion implantation Amorphous semiconductorsNov. 11 Veterans dayNov. 18 Thin film techniques Biological computers/MEMSNov. 25 ThanksgivingNov. 30 Etching Student Presentations Dec. 2 Student PresentationsDec. 9 Final Exam 8 PM
Course Outline
Grading:
Assignments 10%
Presentation/Term papers 60%
Mid-term exam 10%
Final Exam 20%
Term Paper & PresentationEach student will write two short research papers and make one presentation on a relevant topic of their choice. Length of term paper: 4 pages. Format for the report is Title page with, Summary (or abstract), Introduction, Body (subtitles), Conclusion, and References. References MUST come from peer-review literature. NO internet references are acceptable. Sorry, but Wikipedia is OK for background, but does not count as a reference!
Ionic Bond – electron transfer and electrostatic attraction
Non directional
Covalent Bond: electron sharing for stable outer shellsHighly directional
Metallic bond: electron sharing between charged ion coresNon directional
The bond type influences the mechanical properties
Both ionic and metallic bonds form close packed structures. Ions, though, have to maintain charge neutrality, so any deformation in ionic solids must be large enough to move the atoms back into registry. Metals do not have this restriction. Hence, ionic solids are brittle, while metals are ductile.
Other, weaker bonds
Hydrogen bond: hydrogen acts as infinitesimal cation attracting two anions
van der Waals bond: weak attraction between molecular dipoles
The crystal lattice
A point lattice is made up of regular, repeating points in space. An atom or group of atoms are tied to each lattice point
14 different point lattices, called Bravais lattices, make up the crystal system. The lengths of the sides, a, b, and c, and the angles between them can vary for a particular unit cell.
Three simple lattices that describe metals are Face Centered Cubic (FCC) Body Centered Cubic (BCC) and Hexagonal Close Packed (HCP)
Whether a close packed crystal is FCC or HCP depends upon the stacking sequence of close packed planes
Diamond, BeO and GaAs are examples of FCC structures with two atoms per lattice point
Polymers are made up of repeating units “mers”, that make up a long chain. The chain may be cross-linked, or held together with van der Waals or
hydrogen bonds
Structures may be crystalline, having repeating structure, or amorphous, having local structure but no long-range structure
Directions in a crystal lattice – Miller Indices
Vectors described by multiples of lattice constants: ua+vb+wc
e.g., the vector in the illustration crosses the edges of the unit cell at u=1, v=1, c=1/2
Arrange these in brackets, and clear the fractions:
[1 1 ½] = [2 2 1]
Negative directions have a bar over the number
e.g., _
11
Families of crystallographically equivalent directions, e.g., [100], [010], [001] are written as <uvw>, or, in this example, <100>
Directions in HCP crystals
'
)''(
)''2(3
)''2(3
][]'''[
nww
vut
uvn
v
vun
u
uvtwwvu
a1, a2 and a3 axes are 120o apart, z axis is perpendicular to the a1,a2,a3 basal plane
Directions in this crystal system are derived by converting the [u′v′w′] directions to [uvtw] using the following convention:
n is a factor that reduces [uvtw] to smallest integers. For example, if
u′=1, v′=-1, w′=0, then
[uvtw]= ]0011[_
Crystallographic Planes
To find crystallographic planes are represented by (hkl). Identify where the plane intersects the a, b and c axes; in this case, a=1/2, b=1, c=∞
Write the reciprocals 1/a, 1/b, 1/c:
11
12
11
l
k
h
Clear fractions, and put into parentheses:
(hkl)=(210)
If the plane interesects the origin, simply translate the origin to an equivalent location.
Families of equivalent planes are denoted by braces:
e.g., the (100), (010), (001), etc. planes are denoted {100}
Planes in HCP crystals are numbered in the same way
e.g., the plane on the left intersects a1=1, a2=0, a3=-1, and z=1, thus the plane is )1110(
_
3
• tend to be densely packed.
• have several reasons for dense packing:-Typically, only one element is present, so all atomic radii are the same.-Metallic bonding is not directional.-Nearest neighbor distances tend to be small in order to lower bond energy.
• have the simplest crystal structures.
METALLIC CRYSTALS
11
Example: Copper
n AVcNA
# atoms/unit cell Atomic weight (g/mol)
Volume/unit cell
(cm3/unit cell)Avogadro's number (6.023 x 1023 atoms/mol)
Data from Table inside front cover of Callister (see next slide):• crystal structure = FCC: 4 atoms/unit cell• atomic weight = 63.55 g/mol (1 amu = 1 g/mol)• atomic radius R = 0.128 nm (1 nm = 10 cm)-7
Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3
Compare to actual: Cu = 8.94 g/cm3Result: theoretical Cu = 8.89 g/cm3
THEORETICAL DENSITY,
15
• Charge Neutrality: --Net charge in the structure should be zero.
--General form: AmXp
m, p determined by charge neutrality• Stable structures: --maximize the # of nearest oppositely charged neighbors.
- -
- -+
unstable
- -
- -+
stable
- -
- -+
stable
CaF2: Ca2+cation
F-
F-
anions+
IONIC BONDING & STRUCTURE
16
• Coordination # increases with Issue: How many anions can you arrange around a cation?
rcationranion
rcationranion
Coord #
< .155 .155-.225 .225-.414 .414-.732 .732-1.0
ZnS (zincblende)
NaCl (sodium chloride)
CsCl (cesium chloride)
2 3 4 6 8
COORDINATION # AND IONIC RADII
X-ray diffraction and crystal structure
• X-rays have a wave length, Å.• This is on the size scale of the structures
we wish to study X-rays interfere constructively when the interplanar spacing is related to an integer number of wavelengths in accordance with Bragg’s law:
sin2dn
Because of the numbering system, atomic planes are perpendicular to their corresponding vector,
e.g., (111) is perpendicular to [111]
The interplanar spacing for a cubic crystal is:
222 lkh
adhkl
Because the intensity of the diffracted beam varies depending upon the diffraction angle, knowing the angle and using Bragg’s law we can obtain the crystal structure and lattice parameter
The Reciprocal Lattice and Waves in Crystals
We use the reciprocal lattice to calculate wave behavior in crystals because sound, optical and electrical properties pass through the crystal as waves
Because crystals are periodic, properties throughout the crystal will be the same as those surrounding any lattice point, contained in a volume known as a “Brillion Zone”
First brillion zone in a 2-D lattice
Brillion Zones
BCC Brillion Zone FCC Brillion Zone
Brillion Zones are the same as Wigner-Seitz cells in reciprocal space
Why do we need reciprocal space?
Because waves or vibrations can be made up of a series of waves of other frequencies, i.e., expressed as a Fourier Series:
)sin()cos()(
)exp()(
rGirGnrn
or
riGnrn
g
G
We want G∙r to equal 2
at boundaries. Therefore ijji ab
ora
b
2
2
The Reciprocal Lattice
To analyze the atomic structure and resulting properties of crystals, we introduce the concept of the “reciprocal lattice”
A reciprocal lattice vector is defined as
G = 1b1 + 2b2 + 3b3
Where 1, 2, 3 are integers and b1, b2 and b3 are primitive vectors in the reciprocal lattice
Wave reflection in reciprocal space
The reciprocal lattice vector, G = k
Calculating the reciprocal lattice
We construct the axis vectors b1, b2 and b3 of the reciprocal lattice using the following formulas: )(
2
)(2
)(2
321
213
321
132
321
321
aaa
aab
aaa
aab
aaa
aab
zyxaa
zyxaa
zyxaa
ˆˆˆ2
1
ˆˆˆ2
1
ˆˆˆ2
1
3
2
1
BCC primitive lattice vectors: FCC primitive lattice vectors:
xzaa
zyaa
yxaa
ˆˆ2
1
ˆˆ2
1
ˆˆ2
1
3
2
1
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