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October 18, 2013 ELECTRONIC DEVICES 1

Electronic DevicesCourse No. : EEE F214 / ECE F214 / EEE C381

Course Instructor : Prabhakara Rao

Room No. : D305

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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

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 25

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