Lecture 1 MPE

8/12/2019 Lecture 1 MPE

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Modern Physics and

Electronics

Dr. Abdul Majid Sandhu

Dr. Abdul Majid Sandhu, Department of Physics,University of Gujrat.


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Course Outlines

Electronics:

Basic crystal structure, free electron model, energy band in solid and energy gaps, p-type, n-type semiconductor

materials, p-n junction diode, its structure. characteristics and application as rectifiers. Transistor, its basic

structure and operation, transistor biasing for amplifiers, characteristics of common base, common emitter,

common collector, load line, operating point, hybrid parameters (common emitter), Transistor as an amplifier(common emitter mode), Positive & negative feed back R.C. Oscillators, Monostable multi- vibrator (basic),

Logic gates OR, AND, NOT, NAND, NOR and their basic applications.

Origin of Quantum Theory:

Black body radiation, Stefan Boltzmann-, Wiens- and Plancks law, consequences. The quantization of energy,

Photoelectric and Compton effect, Line spectra, Explanation using quantum theory.

Wave Nature of Matter:

Wave behaviour of particle (wave function etc.) its definition and relation to probability of particle, dBrogliehypothesis and its testing, Davisson-Germer Experiment and J.P. Thomson Experiment, Wave packets and

particles, localizing a wave in space and time.

Atomic Physics:

Bohrs theory (review), Frank-Hertz experiment, energy levels of electron, Atomic spectrum, Angular momentum

of electrons, Vector atom model, Orbital angular momentum. Spin quantization, Bohrs Magnetron. X-ray

spectrum (continuous and discrete) Moseleys law, Paulis exclusion principle and its use in developing the

periodic table.


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Lecture 1

Basic Crystal Structures

Dr. Abdul Majid Sandhu, Department of

Physics, University of Gujrat.


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4

Matter

GASES LIQUIDS SOLIDS

Types of matter


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Crystal Structure 5

SOLID MATERIALS

CRYSTALLINE POLYCRYSTALLINEAMORPHOUS(Non-crystalline)

Single Crystal

ELEMENTARY CRYSTALLOGRAPHY
http://www.alaskanessences.com/gembig/Pyrite.jpg


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6

Crystalline Solid

Crystalline Solid is the solid form of a substance in

which the atoms or molecules are arranged in a

definite, repeating pattern in three dimension.

Single crystals, ideally have a high degree of order, or

regular geometric periodicity, throughout the entire volume

of the material.


7/34Crystal Structure 7

Single Crystalline Solid

Single Crystal

Single Pyrite

Crystal

Amorphous

Solid

Single crystal has an atomic structure that repeats

periodically across its whole volume. Even at infinite length

scales, each atom is related to every other equivalent

atom in the structure by translational symmetry
http://weblog.burningbird.net/fires/001936.htm


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Polycrystalline Solid

Polycrystalline

Pyrite form

(Grain)

Polycrystal is a material made up of an aggregate of many small single crystals

(also called crystallites or grains).

Polycrystalline material have a high degree of order over many atomic or molecular

dimensions, called, grains which are separated from one another by grain

boundaries.

The grains are usually 100 nm - 100 microns in diameter. Polycrystals with grains

that are


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Amorphous Solid

Amorphous (Non-crystalline) Solid is composed of randomly orientatedatoms , ions, or molecules that do not form defined patterns or latticestructures.

Amorphous materials have order only within a few atomic or moleculardimensions.

Amorphous materials do not have any long-range order, but they havevarying degrees of short-range order.

Examples to amorphous materials include amorphous silicon, plastics, andglasses.


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Departure From Perfect Crystal

Strictly speaking, one cannot prepare a perfect crystal. For example,even the surface of a crystal is a kind of imperfection because the

periodicity is interrupted there.

Another example concerns the thermal vibrations of the atoms aroundtheir equilibrium positions for any temperature T>0K.

As a third example, actual

crystal always contains someforeign atoms, i.e., impurities.

These impurities spoils the

perfect crystal structure.



Crystal Structure

Crystal structure can be obtained by attaching atoms, groups ofatoms or molecules which are called basis (motif) to the latticesides of the lattice point.

Basis + Crystal Lattice = Crystal Structure


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Recipe of Crystal

12

Crystal structure = lattice + basis



Crystal Lattice

Bravais Lattice (BL) Non-Bravais Lattice (non-BL)

All atoms are of the same kind

All lattice points are equivalent

Atoms can be of different kind

Some lattice points are not

equivalent

A combination of two or more BL


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A two-dimensional Bravais lattice with

different choices for the basis



Three common Unit Cell in 3D



UNIT CELL

Primitive Conventional & Non-primitive

Single lattice point per cell

Smallest area in 2D, or

Smallest volume in 3D

More than one lattice point per cell

Integral multibles of the area of

primitive cell

Body centered cubic(bcc)

Conventional Primitive cellSimple cubic(sc)

Conventional= Primitive cell



Wigner-Seitz Method

A simply way to find the primitive

cellwhich is called Wigner-Seitz

cell can be done as follows;

1. Choose a lattice point.

2. Draw lines to connect theselattice point to its neighbours.

3. At the mid-point and normal tothese lines draw new lines.

The volume enclosed is called as a

Wigner-Seitz cell.



Wigner-Seitz Cell - 3D


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Crystal Structure 19

Lattice Sites in Cubic Unit Cell


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Crystal Directions

We choose one lattice point on the line as anorigin, say the point O.

Then we choose the lattice vector joining O toany point on the line, say point T. This vectorcan be written as;

R = n1a + n2b + n3c

To distinguish a lattice direction from a latticepoint, the triple is enclosed in square brackets

[ ...] . Directions may also be negative, denoted by

bar.


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210

X = 1 , Y = , Z = 0

[1 0] [2 1 0]

X = , Y = , Z = 1

[ 1] [1 1 2]

Examples


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Crystal Planes

Within a crystal lattice it is possible to identify sets of equally spaced

parallel planes. These are called lattice planes.

In the figure density of lattice points on each plane of a set is the

same and all lattice points are contained on each set of planes.

ba

ba

The set of

planes in2D lattice.


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Miller Indices

Miller Indices are a symbolic vector representation for the orientation of anatomic plane in a crystal lattice and are defined as the reciprocals of thefractional intercepts which theplane makes with the crystallographic axes.

To determine Miller indices of a plane, take the following steps;

1) Determine the intercepts of the plane along each of the three crystallographicdirections

2) Take the reciprocals of the intercepts

3) If fractions result, multiply each by the denominator of the smallest fraction


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Axis X Y Z

Interceptpoints 1

Reciprocals 1/1 1/ 1/ Smallest

Ratio 1 0 0

Miller ndices (100)

Example-1

(1,0,0)


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Axis X Y Z

Interceptpoints 1 1

Reciprocals 1/1 1/ 1 1/ Smallest

Ratio 1 1 0

Miller ndices (110)

Example-2

(1,0,0)

(0,1,0)


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Axis X Y Z

Interceptpoints 1 1 1

Reciprocals 1/1 1/ 1 1/ 1Smallest

Ratio 1 1 1

Miller ndices (111)(1,0,0)

(0,1,0)

(0,0,1)

Example-3


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Axis X Y Z

Interceptpoints 1/2 1

Reciprocals 1/() 1/ 1 1/ Smallest

Ratio 2 1 0

Miller ndices (210)(1/2, 0, 0)

(0,1,0)

Example-4


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Miller Indices

Reciprocal numbers are:2

1,

2

1,

3

1Plane intercepts axes at cba 2,2,3

Indices of the plane (Miller): (2,3,3)

(100)

(200)(110) (111)

(100)

Indices of the direction: [2,3,3]a

3

2

2

bc

[2,3,3]


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Indices of a Family or Form

Sometimes when the unit cell has rotational symmetry, several

nonparallel planes may be equivalent by virtue of this symmetry, in

which case it is convenient to lump all these planes in the same

Miller Indices, but with curly brackets.

Thus indices {h,k,l} represent all the planes equivalent to the

plane (hkl) through rotational symmetry.

)111(),111(),111(),111(),111(),111(),111(),111(}111{

)001(),100(),010(),001(),010(),100(}100{


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There are only seven different shapes of unit cell which can bestacked together to completely fill all space (in 3 dimensions)without overlapping. This gives the seven crystal systems, in

which all crystal structures can be classified.

Cubic Crystal System (SC, BCC,FCC)

Hexagonal Crystal System (S)

Triclinic Crystal System (S)

Monoclinic Crystal System (S, Base-C) Orthorhombic Crystal System (S, Base-C, BC, FC)

Tetragonal Crystal System (S, BC)

Trigonal (Rhombohedral) Crystal System (S)

14 BRAVAIS LATTICES AND THE SEVEN CRYSTAL SYSTEM

TYPICAL CRYSTAL STRUCTURES


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Coordinaton Number

CoordinatonNumber (CN) : The Bravais lattice points closest

to a given point are the nearest neighbours.

Because the Bravais lattice is periodic, all points have the same

number of nearest neighbours or coordination number. It is a

property of the lattice.

A simple cubic has coordination number 6; a body-centered

cubic lattice, 8; and a face-centered cubic lattice,12.


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Diamond Structure

The diamond lattice is consist of two interpenetrating face

centered bravais lattices.

There are eight atom in the structure of diamond.

Each atom bonds covalently to 4 others equally spread aboutatom in 3d.


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Zinc Blende

Zincblende has equal numbers of zinc and sulfur

ions distributed on a diamond lattice so that each

has four of the opposite kind as nearest neighbors.This structure is an example of a lattice with a

basis, which must so described both because of the

geometrical position of the ions and because two

types of ions occur.

AgI,GaAs,GaSb,InAs,

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Lecture 1 MPE