Review of Semiconductor Physics

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Review of Semiconductor Physics
Solid-state physics
The daunting task of solid state physics

• Quantum mechanics gives us the fundamental
  equation
• The equations are only analytically solvable for
  a handful of special cases
• One cannot solve the equations for more than two
  bodies!
• Solid-state physics is about many-body problems
• There are 5 1022 atoms/cm3 in Si

Si atom 1s22s22p63s23p2 Core Nueclear
1s22s22p6, Valence electrons 3s23p2 Well come
back to this later
Each particle is in the potential of all the
other particles, which depends on their
positions, which must be solved from the
equation You have an equation with 1023
unknowns to solve. Mission impossible!

• Solid state physic is all about approximations.

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Review of Semiconductor Physics
Crystal structures
If we assume the atomic cores have known and
fixed positions, we only need to solve the
equations for the valence electrons. Life much
easier!
Static lattice approximation

• Justification
• Related/similar approximation Born-Oppenheimer

Crystal structures
If you shine X-ray on a piece of solid, very
likely youll have a diffraction
pattern. Remember Bragg? That means periodicity
in the structure.
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Review of Semiconductor Physics
Crystal structures
Bravais Lattices

• A mathematical concept
• No boundary or surface
• No real (physical) thing just points, hence no
  defects
• No motion

Unit cells (or primitive unit cells) -- The
smallest unit that repeats itself.
Fig. 4.1
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Fig. 4.2
Crystal structure lattice basis
Honeycomb
Simple cubic
From Geim McDonald, Phys Today Aug 2007, 35.
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Lattices
Conventional primitive unit cells
BCC
How many atoms in the conventional unit cell?
FCC
BCC FCC are Bravais Lattices.
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U. K. Mishra J. Singh, Semiconductor Device
Physics and Design E-book available on line thru
UT Lib.
Fast production of e-books. The caption is NOT
for this figure. Try not to be confused when
reading fast generated books/papers nowadays.
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Bragg refraction and the reciprocal lattice

• Bragg refraction
• Definition of the reciprocal lattice
• 1D, 2D, and 3D
• The 1D 2D situations are not just mathematical
  practice or fun, they can be real in this nano
  age

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• BCC FCC are reciprocal lattices of each other

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• Miller indices

Referring to the origin of the reciprocal
lattices definition, i.e, Bragg refraction, a
reciprocal lattice vector G actually represents a
plane in the real space
Easier way to get the indices Reciprocals of the
intercepts
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• Wigner-Seitz primitive unit cell and first
  Brillouin zone

The WignerSeitz cell around a lattice point is
defined as the locus of points in space that are
closer to that lattice point than to any of the
other lattice points.
The cell may be chosen by first picking a lattice
point. Then, lines are drawn to all nearby
(closest) lattice points. At the midpoint of each
line, another line (or a plane, in 3D) is drawn
normal to each of the first set of lines.
1D case
2D case
3D case BCC
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The first Brillouin zone is the Wigner-Seitz cell
of the reciprocal lattice
1D
2D
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3D Recall that the reciprocal lattice of FCC is
BCC.
4?/a
Why is FCC so important?
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Why is FCC so important?
Its the lattice of Si and many III-V
semiconductors.
Si diamond, a 5.4 Å GaAs zincblende
Crystal structure lattice basis
Modern VLSI technology uses the (100) surface of
Si.
Which plane is (100)? Which is (111)?