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October 18, 2013 ELECTRONIC DEVICES 1
Electronic DevicesCourse No. : EEE F214 / ECE F214 / EEE C381
Course Instructor : Prabhakara Rao
Email : [email protected]
Room No. : D305
Department of EEEBITS-Pilani, Hyderabad Campus
mailto:[email protected]:[email protected]:[email protected]:[email protected] -
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October 18, 2013 ELECTRONIC DEVICES 2
For a hypothetical semiconductor, we have n
= p = 1000 cm2 / V.s and Nc = Nv = 10
19 / cm3.
If the conductivity of the intrinsic
semiconductor at 300 K is 4 X 10-6 (-cm)-1.What is the conductivity at 600 K.
Problem
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October 18, 2013 ELECTRONIC DEVICES 3
Ans - Problem 9
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October 18, 2013 ELECTRONIC DEVICES 4
Crystal Lattices
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October 18, 2013 ELECTRONIC DEVICES 5
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October 18, 2013 ELECTRONIC DEVICES 6
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Body Centered Cubic
Atoms are arranged at the corners of the cube
with another atom at the cube center.
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Body Centered Cubic
Since atoms are assumed to touch along the
cube diagonal in BCC, the lattice parameter is
related to atomic radius through:
3
4Ra
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Body Centered Cubic
Coordination number for BCC is 8. Each
center atom is surrounded by the eight corner
atoms. The lower coordination number also results in
a slightly lower APF for BCC structures. BCC
has an APF of 0.68, rather than 0.74 in FCC
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Atomic Packing Factor: the ratio of atomicsphere volume to unit cell volume, assuming a
hard sphere model.
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Face Centered Cubic (FCC)
Atoms are arranged at the corners and centerof each cube face of the cell.
Atoms are assumed to touch along face diagonals
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The lattice parameter, a, is related to the
radius of the atom in the cell through:
Coordination number: the number of nearestneighbors to any atom. For FCC systems, the
coordination number is 12.
22Ra
Face Centered Cubic (FCC)
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Crystallographic Directions
Cubic systems
directions are named based upon the projection
of a vector from the origin of the crystal to
another point in the cell.
Conventionally, a right hand Cartesian
coordinate system is used.
The chosen origin is arbitrary, but is always
selected for the easiest solution to the problem.
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Crystallographic Directions
Points within the lattice are written in the
form h,k,l, where the three indices
correspond to the fraction of the lattice
parameters in the x,y,z direction.
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October 18, 2013 ELECTRONIC DEVICES 19
Miller Indices
Indices are written in square brackets
without commas (ex: [hkl])
Negative values are written with a barover the integer.
Ex: if h
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October 18, 2013 ELECTRONIC DEVICES 20
Specify the directions using Millerindices
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October 18, 2013 ELECTRONIC DEVICES 21
Ans
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October 18, 2013 ELECTRONIC DEVICES 22
Miller Indices
Crystallographic Planes
Identify the coordinate intercepts of the plane
the coordinates at which the plane intercepts the x, yand z axes.
If a plane is parallel to an axis, its intercept is taken as
.
If a plane passes through the origin, choose anequivalent plane, or move the origin
Take the reciprocal of the intercepts
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October 18, 2013 ELECTRONIC DEVICES 23
Miller Indices
Clear fractions due to the reciprocal, but do notreduce to lowest integer values.
Planes are written in parentheses, with bars over
the negative indices.
Ex: (hkl) or if h
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October 18, 2013 ELECTRONIC DEVICES 24
Example
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October 18, 2013 ELECTRONIC DEVICES 26
Specify the planes indicated bythe arrows
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October 18, 2013 ELECTRONIC DEVICES 27
Ans
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October 18, 2013 ELECTRONIC DEVICES 28
Crystallographic Notation
Notation Interpretation
( h k l) crystal plane
{ h k l} equivalent planes
[ h k l] crystal direction
< h k l> equivalent directions
h: inverse x-intercept of plane
k: inverse y-intercept of plane
l: inverse z-intercept of plane
(Intercept values are in multiples of the lattice constant;
h, kand lare reduced to 3 integers having the same ratio.)
Miller Indices:
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October 18, 2013 ELECTRONIC DEVICES 29
diamond cubic lattice
The Si Crystal
Each Si atom has 4nearest neighbors
lattice constant= 5.431
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October 18, 2013 ELECTRONIC DEVICES 30
How Many Silicon Atoms per cm-3?
Number of atoms in a unit cell:
4 atoms completely inside cell
Each of the 8 atoms on corners are shared among
cells count as 1 atom inside cell
Each of the 6 atoms on the faces are shared among 2
cells count as 3 atoms inside cell
Total number inside the cell = 4 + 1 + 3 = 8
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October 18, 2013 ELECTRONIC DEVICES 31
Cell volume:
(.543 nm)3 = 1.6 x 10-22 cm3
Density of silicon atoms= (8 atoms) / (cell volume) = 5 x 1022 atoms/cm3
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October 18, 2013 ELECTRONIC DEVICES 33
Atomic Density calculations in(100), (110), (111) planes
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October 18, 2013 ELECTRONIC DEVICES 34
(100) 2/a2
(110) 22/a2
(111) 4/(3a2
)
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October 18, 2013 ELECTRONIC DEVICES 37
Modern CZ Crystal Growth
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October 18, 2013 ELECTRONIC DEVICES 40
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