Electronic Materials

1
Electronic Materials

• EE 5341
• Instructor Meng Tao
• Spring 2005

2
What Is an Electronic Material?

• Narrower definition
• Mostly manmade materials
• Materials consisting of atoms
• Atoms with valence electrons
• Taking advantage of transport behavior of
  (valence) electrons in a controllable manner

3
Broader Definition

• Any behavior of (valence) electrons in a material
  to our advantage
• Spin of (valence) electrons determines magnetic
  properties
• Photon absorption and electron relaxation provide
  optoelectronic materials
• Nucleus and electron response to electromagnetic
  waves determines dielectric properties
• Coupling of (valence) electrons determines
  superconductive properties

4
Classification

• By conductivity
• Focus of this course
• Insulators
• Semiconductors
• Conductors and superconductors (metals)
• By property
• Electronic
• Optical
• Optoelectronic
• Magnetic

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Applications

• Photovoltaics
• Convert light into electricity
• Computing
• CPU and data storage
• Telecommunications
• Wireless and optical
• Signal processing
• Consumer electronics, control, sensing, etc.

6
Survey

• How many have taken
• EE 5340?
• Solid state physics?
• Syllabus

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Crystal Structure

• Chapter 1 of Kittel

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Solid Materials

• Matters (materials) are made of atoms
• The atomic arrangement in a material determines
  to a large extent its properties
• If well organized and periodic crystalline
• If randomly distributed amorphous
• Definition of CRYSTAL
• A crystal is a periodic array of atoms

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1-D Imaginary Crystal

• 1-dimensional crystal
• One parameter a
• Amorphous

a ?
10
2-D Imaginary Crystal

• 2-dimensional crystal
• Three parameters
• a1, a2, a
• Amorphous

a2







a
a1



































a1 ?







a2 ?














a ?







11
Real Crystal

• 3-dimensional crystal
• Difficulty to draw
• Six parameters a1, a2, a3, a, b, g
• Three vectors a1, a2, a3, ( , , )

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Lattice

• A mathematical description of crystal structures
• Definition of LATTICE
• A lattice is a periodic array of points
• Construction
• Three fundamental vectors (lattice vectors) a1,
  a2, a3
• Three integers u1, u2, u3 (-?, , -2, -1, 0, 1,
  2, , ?)
• Define an origin of the lattice
• Define a translation vector
• T u1a1 u2a2 u3a3
• Let u1, u2, u3 take all the possible integers to
  construct a lattice

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Constructing 2-D Lattice

• Translation vector
• T u1a1 u2a2

u1 u2
0 0
1 0
0 1
1 1
1 2
0 -1
.. ..

• Let u1 and u2 take all the possible integers

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2-D Lattice

• When an identical group of atoms is attached to
  each lattice point, a crystal is formed (Fig. 4)

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Lattice Cell

• Definition of lattice cell or UNIT CELL
• The parallelepiped formed by a1, a2, a3
• 2-D lattice cell
• A building block for the lattice
• The volume of a cell (Fig. 5(b))
• Vc a1 a2 a3

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Primitive Lattice Cell

• There are many ways to choose a1, a2, a3 (Fig.
  5(a))
• The volume depends on the choice of a1, a2, a3
• Primitive lattice cell or PRIMITIVE UNIT CELL
• The minimum-volume cell which can fill all the
  space
• A primitive cell contains ONE lattice point (Fig.
  5(a))
• Fig. 5(c) exercise

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Fundamental Types of Lattices

• There is an unlimited number of lattices, since
  there is no restrictions on a1, a2, a3, a, b, g
• How to classify lattices?

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2-D Lattice Classification

• Arbitrary a1, a2, a is common, which leads to
  oblique lattice
• Four special types of lattices (Fig. 9)
• Square a1 a2, a 90?
• Hexagonal a1 a2, a 120?
• Rectangular a1 ? a2, a 90?
• Centered rectangular a1 ? a2, a 90?
• Total five types of lattices for 2-D

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3-D Lattice Classification

• Six parameters a1, a2, a3, a, b, g
• Fourteen types of lattices (Bravais lattices)
• Table 1
• Triclinic as the general case and thirteen
  special cases
• Grouped into seven systems

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Indexing Planes

• To specify the orientation of a plane or the
  direction in a crystal
• The procedure to specify the orientation of a
  plane (Fig. 15)
• Find the intercepts on the axes in terms of the
  lattice constants a1, a2, a3
• Take the reciprocals of these intercepts and
  reduce to three integers with the same ratio
• Write them in the form of (h k l)
• Important planes in a cubic crystal (Fig. 16)
• Low-index planes (100), (110), (111)

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Indexing Directions

• The procedure to specify a direction in a crystal
• Find the components of the vector in terms of the
  lattice constants a1, a2, a3
• Find the set of the smallest integers
• with the same ratio
• Write them in the form of u v w
• In cubic systems, u v w is
• perpendicular to plane (u v w)

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Miller Indices

• (h k l) for planes
• If intercept is negative, then ( )
• In cubic systems, (100), (010), (001), ( ),
  ( ), ( ) are equivalent. They can be
  represented by h k l
• h k l for directions
• lth k lgt for equivalent directions

23
3-D Lattices

• The most interesting system is CUBIC
• a1 a2 a3 a a b g 90?
• Three Bravais lattices in cubic system (Fig. 10)
• Simple cubic (sc)
• Body-centered cubic (bcc)
• Face-centered cubic (fcc)

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Cubic System

• Properties of unit cells (Table 2)
• Primitive cell for sc, not primitive cells for
  fcc and bcc
• Primitive cell for bcc (Figs. 11 and 12)
• Primitive cell for fcc (Fig. 13)

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Important Crystal Structures

• Three crystal structures important for
  semiconductors
• Diamond (fcc) Si, Ge
• Zinc Sulfide (fcc) GaAs, GaN
• Hexagonal Close Packed (hcp) GaN
• They are all closely packed, but the order of
  packing is different for fcc and hcp (Fig. 21)

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Packing Order

• Closest packing of identical spheres (same atoms)
  in a single layer (Fig. 21)
• Spheres center at A
• To close pack the second identical layer, spheres
  need to center at B (or C)
• To close pack the third identical layer, spheres
  need to center at
• A hcp
• C fcc

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HCP Structure

• HCP structure (Fig. 22)
• Primitive cell (Fig. 23
• Two atoms/lattice point
• c/a (8/3)1/2
• Twelve nearest neighbors

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Diamond Structure

• Diamond structure (Fig. 25)
• Si, Ge
• fcc structure
• Two identical atoms/lattice point
• Eight identical atoms/unit cell
• Packing density 0.34
• Four nearest neighbors due to tetrahedral bonding
• Directional bond with bond angle 109.28
• Lattice constant
• Si 5.43 Å
• Ge 5.65 Å

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Zinc Sulfide Structure

• Zinc sulfide structure (Fig. 26)
• GaAs, InP, GaN, etc.
• fcc structure
• Two different atoms/lattice point
• Eight atoms (four of each kind)/unit cell
• Tetrahedral bonding to four opposite atoms
• Same packing density (0.34)
• Lattice constant

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Miscellaneous

• Imaging of atomic structures
• Transmission electron microscope (TEM)
• Scanning electron microscopy (STM, Fig. 27)
• Crystal structure data for pure elements
• Table 3 crystal structure and lattice constants
• Table 4 crystal density, atomic concentration
  and nearest neighbor distance