Solid State Physics-1 All Theories Notes free download

COURSE CONTENTS:

v Band Theory Of Solid:

Review of free electrons gas model:

For metals (solid) we know about the free electrons

theory, according to this theory solids are divided in to

categories: 1) Conductors 2) Insulators

The free electrons gas theory was explained by:

Maxwell Boltzmann distribution of electrons in the metal

v Bloch theorem:

It is known that in the free electrons model, the potential of

electrons in a crystal are zero.

On the other hand, in nearly free electrons theory, the

electrons are moving under the periodic potential and the wave

a function has no constant amplitude, and the total potential

V(x) has two-part.

1. The electrostatic potential due to an array of atomic cores

for a perfect lattice (no phonons). ensures the

translation periodicity of the lattice.

2. The potential due to all other outer electrons the charge

density from this source have the same average in every

point cell, and is also periodic.

Ø Band Theory of Solids:

Now to explain this theory we consider atoms in

the crystal with their free (nearly) electrons in the crystal

order in one dimension.

v Energy Verses Wave Vector Graph [ E

Vs K Graph]:

It is known that the energy of electrons in crystal depends on

the ionic potential. In this case “E Vs K” relation is very

important.

The electrons in the crystal are not free and

are under the periodic potential, what then will

be the concept of mass of electrons, velocity,

momentum etc. whether these are constant are

not.

The mass is not constant and called effective mass “m”

and it may negative.

v Motion (Velocity) of electrons in

band(crystal):

v Effective Mass of Electrons in

crystal(m*):

v Density of State & Fermi Surface:

v Density of State:

The density of the state is the number of orbitals(electrons)

per unit energy range at the Fermi level (Fermi sphere)

represented by;

v Free Electrons Theory Of

Metals (Solids):

The thermal and electrical power of solids(metals) are

determined by conduction electrons gas

within the ionic.

Conduction electrons gas is subjected to Pauli-Exclusion Principle.

So, satisfy Fermi Dirac distribution and Boltzmann distribution.

Electrons gas in metals are such that if there is energy

level occupied by electrons then there are no other electrons

to occupy this level that is called the Pauli-Exclusion Principle.

Electrons gas satisfy Fermi Dirac distribution.

v Dielectric Properties of Solids:

The dielectric property of solid is the response of solids

(insulators) to the applied electric field “E”.

It is known that insulators have no free electrons and so

when an external electric field is applied, it dominates the

an internal electric field of the solids (insulators) and distort

the internal energy (Nucleus and Electrons). The give rises

to dipoles and hence the materials is polarized. The

material is electrically neutral but produce electric field both

outside and inside.

v Dielectric Materials:

1. In solid the dielectric (insulator) the electrons are tightly

bound to their parent atoms.

2. Charge separation takes place, in the presence of electric

field.

3. These are neutral but produce electric field both inside and

outside the sample.

Ø Some materials have naturally occurred in the shape that

there is little separation between the positive and negative

center. There are called “Permanently Dipoles Materials”.

Ø And there are some materials, where positive and

negative center coincides. However, if the electric field is

applied; the change occurs and the positive and negative

charge-separated called “Induced Dipoles Materials”. So

change separation happens only in the presence of electric

field.

Any way both types are electrically neutrals and produce their

own electric field outside and inside.

Ø Maxwell’s Equations in Dielectric Medium:

§ Solved Problem:

v Clausius Messitte

Relation:

Let us consider a dielectric material inside opposite charge plates as shown in the figure.

The applied electric field “E₀” then the material will get polarized (converts into dipoles) such that “E₁” is the electric field due to dipole at the surface of the material.

Ø Electric Polarizability:

It is the ability of dielectric materials to form instantaneously as a result of an applied or local electric field.

Polarizability determined the quick response of abounding

system (interior of insulator) to external electric field.

In solid, it gives the measure of dipole moments.

v Origin OR Sources of Polarizability:

The dipole formation per unit of electric field is called

“Polarizability”.

Polarizability has three (3) sources.

1. Electronic Polarizability

2. Ionic polarizability

3. Orientation / Dipolar Polarizability

It is known that the formation of dipoles depends on

the nature of dielectric materials and the frequency of

applied electric field.

Now we discuss one by one,

1. Electronic Polarizability

The atoms of the dielectric materials are nature, if we apply

the electric field the electrons cloud around the nucleus shifted to one side and so form a dipole which is given by;

v Ferroelectric Properties of

Dielectrics:

The Ferroelectricity of dielectric materials are characterized by

the spontaneous dielectric polarization i.e., the formation of

dipoles in the absence of an electric field.

These pre-existing dipoles in the materials as a result of minor

deviation from crystallographic symmetry in the crystal structure of these materials.

The property seems to be analogs to ferromagnetic behavior

of materials.

Ø Ferroelectric Hysteresis:

Ø Temperature Dependence of Polarization of

Ferroelectric Materials and Currie Wien’s Law

[Thermodynamic Theory of Ferroelectric materials]:

v Piezo-Electric Effect:

The word Piezo stands for Pressure.

So, the effect in which an Electric field (Electricity) is

generated from a crystal by the application of external

pressure on the crystal is called “Piezoelectric Effect”.

Some crystal generates piezoelectricity, for

example Quartz (SIO2), Wurtzite (ZnS), Tourmaline etc.

Here the Mechanical Energy (Applied pressure) is converting into

Electrical Energy (Voltage).

Similarly, if A.C electricity is applied across the crystal

(Piezoelectric Materials) it produces strain in the materials and it gets vibrates (Mechanical energy) and so generates sound

energy (Ultrasound) is called “Reverse Piezoelectric effect”.

Hence the materials that generate electricity by the external

pressure also exhibits the reverse effect (Mechanical Vibration).

The piezoelectric effect was 1st discovered by the Currie brothers

“Perry” and “Jacque” in 1880.

To explain the piezoelectric effect let’s take the

example of “Quartz”. A very simple structure of quartz is

taken below.

It is clear that when pressure is applied on the crustal

(Quartz) the ions are squeezed and there is a net positive

and negative charges change at the top and bottom of each

ions (SIO2).

As shown in figure(b), which behave like a small voltage.

Similarly, in figure(c) when the pressure is relaxed the structure

of ions distorts in such a way that there are net positive charge at the top and a net negative charge at the bottom end this behaves like a small battery (Source of Electricity).

As a whole by applied pressure through push and pull an A.C

signal of electricity is generated.

Likewise, if A.C voltage is applied across the crystal will

start vibrating with frequency (f) then producing sound signal

(ultrasound).

Ø Application of Piezoelectric Effect:

1. Sonar accelerometer sends ultrasound in water (H2O) by generating through piezoelectric effect, on return back of these waves, these allowed to hit the piezo materials to create electrical signals and these locating the objects in the way of submarine etc.

2. Electric signaler is based on the piezoelectric effect. On triggering the button an electrical signal is generated that produce a light spark.

3. In an ultrasound machine material is used called “Transducer” that propagates ultrasound waves which reflect back from the patient and create a reverse voltage and gives the image of the interior.

4. A piezoelectric material is mounted below a walking track to produce electrical signals also the materials are adjusted in the pads of shoes and mobile and keyboard to generate electric

voltage.

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