Introduction to Solids

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Introduction to Solids
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3 Classes of Solids

• Amorphous
• No long range order
• Polycrystalline
• Order within grains
• Single Crystal
• Regular, repeated pattern

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Crystal Solid

• Single crystal repetition of a unit cell
• Crystal lattice
• Array of corners of unit cells
• Symmetry
• Used to classify the crystal
• Ex. Cubic symmetry

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3 Subclasses of Cubic Crystals

• Simple
• The sites for atoms are at the corners of the
  cubes
• Body-Centered-Cubic (bcc)
• The sites for the atoms are at the corners of
  the cubes
• Face-Centered-Cubic (fcc)
• The sites for the atoms are at the corners and at
  the centers of each face of the cube
• Note Show figures

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Crystal Structures

• Diamond structure
• Zincblende structure
• Knowing the crystal structure, chemical
  composition and density of material, the
  following can be calculated
• the length of the side of the unit cell
• distance between centers of nearest neighbor
  atoms
• Note Show figures

Structures of Si and GaAs
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Crystal Structures

• X-ray diffraction
• Method used to determine the plane and direction
  of a crystal
• The specification of particular planes and
  directions is made through the use of Miller
  indices

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• Finding Milles indices of a plane in a crystal
• Choose coordinate access along the principal
  directions in the crystal (long the unit cell
  edges)
• Take the 3 numbers that result as the
  intersection of a plane with the 3 axes
• Take their reciprocals
• Multiply the results by the smallest value that
  will give 3 integers
• These 3 integers are the Mille indices of the
  plane

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• Finding Milles indices of a direction in a
  crystal
• Take the 3 components of a vector in that
  direction along the 3 axes
• Multiply these components by whatever is needed
  to reduce them to the smallest set of integers
• These integers are the Miller indices of the
  direction

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• Miller indices of a plane
• (101) ? 101
• Miller indices of a direction
• 101 ? lt100gt
• If negative, minus sign is placed over the integer

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Two Types of Imperfections

• Defects
• The ideal unit cell repetition is interrupted in
  some way
• Impurity
• Occasional atoms of types other than the ones
  that make up the defined crystals unit cell.
• Sometimes, intentionally introduced

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Impurity

• Doping adding impurities
• Dopant the added material

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Energy Level

• Single atoms
• Only one electron can occupy a given state
• (Pauli exclusion principle)
• Different states ? different energies associated
• Ground state ? electrons of an atom are in the
  lowest possible energy states
• Excited state ? when an electron moves to the
  state of higher energy

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Energy Level
Nucleus ? protons neutrons
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Energy Level

• Principal energy level
• 123456

• Sublevel
• 1s2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f 5g6s
  6p 6d 6f 6g 6h

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Energy Level

• the 1s energy level is always the lowest energy
  level of all principal energy levels
• for each principal energy level, the s sublevel
  is also the lowest energy sublevel
• The diagram at the right illustrates the
  determination of order of sublevels by increasing
  energy

Source http//library.thinkquest.org/15567/lesson
s/2.html
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Orbital

No. of sublevels No. of orbitals (s, p, d, f) Total No. of orbitals Maximum no. of electrons
1234 (1)(1, 3)(1, 3, 5)(1, 3, 5, 7) 14916 281832

• A region within a sublevel where electrons may be
  found
• In each orbital, there can be a maximum of two
  electrons
• Each s sublevel has a single orbital
• Each p sublevel has 3 orbitals
• Each d sublevel has 5 orbitals
• Each f sublevel has 7 orbitals
• Thus, any s sublevel can have two electrons,
  while any p sublevel can have 6 electrons, and so
  on

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Band Gap
Source http//hyperphysics.phy-astr.gsu.edu/hbase
/solids/band.html
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Fermi-Level

• Extra levels have been added by the impurities
• In n-type material there are electron energy
  levels near the top of the band gap so that they
  can be easily excited into the conduction band
• In p-type material, extra holes in the band gap
  allow excitation of valence band electrons,
  leaving mobile holes in the valence band

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Video Links

•  
• CLASSES OF SOLIDS
• http//www.youtube.com/watch?vSJsckwYxfgYfeature
  related
•  
• CRYSTAL LATTICE
•  
• Lattice Structures Part 1
• (Cubic, body-centered, Face centered --gt unit
  cell)
• http//www.youtube.com/watch?vRm-i1c7zr6Qfeature
  related
•  
• SAND TO SILICON TO IC
• http//www.youtube.com/watch?vQ5paWn7bFg4
• SILICON RUN 1
• http//www.youtube.com/watch?vATt5dwdKt9I