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Solid and Semiconductor Devices

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1.1 Structure of Solids

All the things we see around us are mainly exists in three states i.e. solid, liquid and gas. The atoms, ions and molecules of these matters are held together with some force of attraction, that hold them together which is called binding forces or bonds. These bonds are weak in liquids and gas but quite strong in case of solids.

Solids are recognized by a definite shape and definite volume. Depending up on the nature and arrangement of atoms or molecules, solids are classified into two categories:

(1) Crystalline solid

(2) Amorphous solid (non-crystalline)

Crystalline Solid

These are those solids in which atoms, ions or molecules are arranged in a fixed pattern in three dimensions throughout the solids. Sugar, mica, quartz, rock salt etc. are the examples of crystalline solids. Some characteristics of crystalline solids are listed below:

  • Their atoms or molecules are arranged in definite order giving them a fixed geometrical shape.
  • They exhibit homogeneous composition.
  • They are anisotropic (property that varying in magnitude according to the direction of measurement).
  • They have sharp melting and boiling point.
  • All the bonds are equally strong.

Amorphous Solids

These are those solids whose atoms or molecules are arranged in irregular geometrical order without fixed shape. Plastics, flour, Sulphur etc. are the examples of amorphous solids. Some characteristics of Amorphous solids are listed below:

  • They don't possess any geometrical structure.
  • Their composition may not be homogeneous.
  • They don't have sharp melting and boiling point.
  • Bond strength are not identical.

1.2 Energy Bands in Solids

According to Bohr's Theory, the electrons in an isolated atom have some well-defined energy states known as energy levels. An energy level consists of several quantum states and no quantum state can contain more than one electron. However, when another atom is brought near the first, their outermost electron interacts with one another and due to this interaction, permitted energy states of these outermost electrons (or valance electron) are slightly modified.



               

                Permitted energy state                                 Permitted energy state

                    of single atom                                             due to two atoms

                                                                                                               

Energy Band

The range of energy where all split energy level of an atom remain is called energy band.

Types of Energy Band

 

1. Valance Band

The Energy band where valance electrons are present which is called valance band. Valance electron take part in bond formation. So, they are bound and they do not conduct electricity. At absolute temperature, valance band is completely filled with valance electron but when temperature is increased to room temperature, and if their kinetic energy is greater than covalent bond then the bond break and may be completely filled, partially filled. When temperature is increased further, some covalent band break due to which electron jump to higher state leaving valance band.

2. Conduction Band

It is the higher energy band where free electrons are present or conducting electrons are present. They conduct electricity. At absolute temperature, conduction band are completely empty but at room temperature, conduction band may be partially filled or completely empty depending up on nature of material.

3. Forbidden band

It is the energy gap between the top most energy level of valance band and the lower most energy level of conduction band. In this region, electrons do not remain.

         

   Conduction Band

                                                     

    Valance Band



 

   

 

The width of forbidden band is given by

Eg = Ec – Ev

The value of Eg may varies according to the nature of material.

 

Depending upon the width of forbidden band, Solids are divided into three types:

1. Conductors

Conductors are those substances in which valance bond overlap with conduction band. So, valance electrons are free electron and they can conduct electricity even at low temperature or low voltage.

If an electric field  is established inside a conductor, the free electron experience force due to the field and acquire a drift velocity. This results in an electric current. The conductivity σ is defined in terms of the electric field  existing in the conductors and the resulting current density . The relation between these quantities is

                         = σ

Larger the conductivity σ, better is the material as a conductor.

Copper, iron, aluminum, silver etc. are examples of conductors.

 

 

Why holes are not formed in conductors?

Ans: Electrons in conductors are already in free state so, they do not need to jump to conduction band Therefore, holes are not formed in conductors.

                        Eg = 0, (due to no forbidden band gap)

2. Insulators

Insulators are those substances in which width of forbidden band is very high. So, they do not conduct electricity easily. All most zero electric current is obtained in insulators unless a high electric field is applied. Plastics, wood, nitrogen, oxygen etc. are examples of insulators.

                        Eg ≡ 5eV

3. Semiconductors

Those substances in which the width of forbidden band is less than insulators and more than conductors. After applying heat, width of forbidden band can be increased and decreased and helps to make temperature control conductivity (like switching action). They are tetravalent in nature. Silicon, Germanium, etc. are examples of semiconductors.

 

                        Eg ≡ 1eV

# Types of Semiconductors

1) Intrinsic Semiconductors

 They are the purest form of crystal. The conductivity of intrinsic semiconductors is less than desired amount. In intrinsic semiconductors tetra valence take part in bond formation with four neighboring electrons. A pure semiconductor contains equal number of electrons in conduction band and holes in valence band so, concentration of free electron is equal to concentration of holes (ne = nh).Since the concentration of these charge carriers is small, a very small current is obtained in such semiconductors.

Pure silicon and germanium crystals are examples of intrinsic semiconductors.


 

Total current (I)

             I = Ie + Ih (where Ie and Ih are current due to free electron and holes respectively.)

             = vdeeneA + vdhenhA

         I/A = e(vdne + vdnh)

             J = e(vdne + vdnh)

            Also,

            vd α E

            vd = µE    (where µ is mobility of charge carrier)

            vdh = µhE

            vde = µeE

 

            J = e(µeEne + µhEnh)

            σE = eE(µene + µhnh)              (σ = J/E)

              σ = e(µene + µhnh)

            Conductivity depends on no of holes and free electrons, so do temperature.

           

 

 

2) Extrinsic semiconductors

They are impure semiconductor. Their conductivity is less than the desired. Conductivity can be increased by adding pentavalent or trivalent atom.

At low temperature or room temperature, conductivity is low and can be significantly increased by adding few amount of impurities atoms (1 per billion).

 

The process of adding impurities atoms in the extrinsic semiconductor is called doping.

Depending upon the type of impurities added, there are two types of semiconductor:

1) N-type semiconductor (for easy learning N-type means negative type)

When pentavalent impurities are added in intrinsic semiconductor, out of five valance electron 4 electrons take part in covalent bond formation with four neighbor semiconductors. Fifth atom of impure atom is free. Due to presence of extra free electron it behaves as negative and called N-type semiconductors.

In N-type, free electron

                    σ = e(µene + µhnh)

                        ne>> nh

                       = eµene

Free electrons are majority charge carrier and holes are minority charge carrier. It depends on both temperature and concentration of impurities added.

 

2) P-type semiconductor (positive like)

When trivalent impurity atom like Al,B etc. are added to intrinsic semiconductor then P-type semiconductor are formed. Three electron of impurity atom take part in covalent bon formation and there is lack of one electron to complete fourth covalent bond and hole is created. Due to the presence of holes, this type semiconductor is called P-type semiconductor.

Holes can accept electron, so these type of semiconductor ale also called acceptor semiconductor. Majority charge carrier are holes and minority charge carrier are free electron.

 

Difference between Intrinsic and Extrinsic semiconductor

S.N.

Intrinsic semiconductor

S.N.

Extrinsic semiconductor

1.

It is pure semiconductor.

1.

It is impure semiconductor formed by doping a small amount of impurity atoms to pure semiconductor.

2.

Concentration of free electron is equal to concentration of holes.

2.

Concentration of free electron never equal to concentration of holes. There is excess free electron in n-type and excess holes in p-type semiconductor

3.

Its electrical conductivity is low

3.

Its electrical conductivity is high.

4.

Its electrical conductivity is a function of temperature alone.

4.

Its electrical conductivity depends upon the temperature as well as on the quantity of impurity atoms doped.

5.

Crystalline form of pure Silicon and Germanium are its examples.

5.

Silicon and Germanium crystals with impurity atoms of arsenic and antinomy are its examples.

 

 

 

Difference between P-type and N-type semiconductors

S.N.

P-type semiconductor

S.N.

N-type semiconductor

1.

When trivalent impurities are doped in intrinsic semiconductor, P-type semiconductor are formed.

1.

When pentavalent impurities are doped in intrinsic semiconductor, N-type semiconductor are formed.

2.

The impurity atoms added, create vacancies of electrons or holes in the structure and are called acceptor atoms.

2.

The impurity atoms added, provide extra electrons in the structure, and are called donor atoms.

3.

The holes are majority charge carrier and electrons are minority charge carrier.

3.

The electrons are majority charge carrier and the holes are minority charge carrier.

4.

The hole density is much more greater than the holes.

4.

The electron density is much more greater than the electron.

5.

The acceptor energy level is close to valance band and is far away from conduction band.

5.

The donor energy is close to the conduction band and far away from valance band.

6.

The fermi energy level lies in between the acceptor energy level and valance band.

6.

The fermi energy level lies in between donor energy level and valance band.