Physics of Semiconductors

SEMICONDUCTOR MATERIALS AND THEIR PROPERTIES

1.     Charge Carriers in Solids
2.     Modification of Carrier Densities
3.    Transport of Carriers

1.0 Charge Carriers in Solids

        the electrons in an atom orbit the nucleus in different “shells.” The atom’s chemical activity is determined by the electrons in the outermost shell, called “valence” electrons,

     The major disadvantage of the electrons present in this band is that these electrons are unable to obtain energy from any external source of electric field.

      here boron outer shell contain 3 valence electrons ,silicon outer shell contain 4 valence electrons, antimony outer shell contain 5 valence electrons.

Different energy gap between various materials 

          In insulators the electrons in the valence band are separated by a large gap from the conduction band.

          conductors like metals the valence band overlaps the conduction band.

          semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap.

What is the difference between the valence  band,conduction band and forbidden band ?

Valence band: In this energy band there are large no of free electrons available. Filling of the valence band can be partial or complete. These bands never get empty.

Conduction Band: The density of the electrons is very few. As compared to the electrons present in the valence energy bands, these electrons can gain energy from the external field of electric field.

Forbidden Band: Electrons are absent in this energy band. Some little amount of energy is needed for electron shifting to conduction band from valence band. This type of gap is known as band gap. Symbol used to represent band gap is E_g.

1.1 Covalent Bond 

     A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding.

   a)  Nonpolar covalent bonds are a type of bond that occurs when two atoms share a pair of electrons with each other. 

    b)  Polar covalent bonding is a type of chemical bond where a pair of electrons is unequally shared between two atoms.

Electric current is carried by two types of charge carriers they are electrons and holes.

     Hole: The absence of electron in a particular place in an atom is called as hole.

Hole is a electric charge carrier which has positive charge. The electric charge of hole is equal to electric charge of electron but have opposite polarity.

When a small amount of external energy is applied, then the electrons in the valence band moves in to conduction band and leaves a vacancy in valence band. This vacancy is called as hole.

    Electrons: At room temperature some of the electrons in valence band gains enough energy in the form of heat and moves in to conduction band. When the valence electrons move in to conduction band they become free electrons. These electrons are not attached to the nucleus of a atom, so they moves freely.

  Any thermal energy creates free electrons and holes in silicon ?

NO

 Minimum energy is required to displacement an electron from a covalent bond.

This energy is called Band gap energy. Its denoted by E_g.

2.0. Modification of Carrier Densities

Based of carrier Density two type 
1. Intrinsic semiconductor
2. Extrinsic Semiconductors

what is Intrinsic semiconductor and Extrinsic Semiconductors ?
       Intrinsic semiconductor : Doping or addition of impurity does not take place in intrinsic semiconductor.The number of free electrons in the conduction band is equal to the number of holes in the valence band.high resistance so electrical conduction low .but its depend on applied temperature.
Ex :Crystalline form of pure Silicon and Germanium.

       Extrinsic Semiconductors: An extrinsic semiconductor is a semiconductor doped by a specific impurity which is able to deeply modify its electrical properties, making it suitable for electronic applications .And the number of electrons and holes are not equal. low resistance compare to intrinsic so electrical conduction high . its depends on temperature as well as adding impurities .
Ex :Impurity like As, Sb, P, In, Bi, Al etc. are doped with Germanium and Silicon atom.

           the electron and hole densities in an intrinsic semiconductor are equal. But, how about these densities in a doped material?

the electron density "n" ,is equal to the hole density "p".

np=ni²

n =electron densities in the extrinsic semiconductor.
p=hole densities in the extrinsic semiconductor.
ni=densities in the intrinsic semiconductor.
   Below two types carrier concentration depends on electrons and hole
          Majority carrier concentration 
          Minority carrier concentration 
    when the Majority carrier are electrons and minority carrier are hole is called N-type .this is formed by adding pentavalent impurities or group V elements . N-type is called as Donor atom N_D 

Majority Carriers: n ≈ N_D

Minority Carriers: p ≈ n²_i/N_D

    when the Majority carrier are holes and minority carrier are electrons is called P-type .this is formed by adding Trivalent impurities or group III elements.  P-type is called as Acceptor atom N_A

Majority Carriers: p ≈ N_A

Minority Carriers: n ≈ n²_i/N_A

3.0. Transport of Carriers

Transport of carrier means the movement of charge in semiconductors .

Mainly two types 

1. Drift 

2. Diffusion

Drift: Movement of charge carriers due to an electric field is called “drift." for example as per ohms law when the electric field is applied to material can conduct current is response to potential difference . 

At same as  semiconductor similar manner.the velocity "v" to be proportional to the electric field strength "E"

v ∝ E

v = μE

_{μ =mobility of electrons or hole}  (μ_{n =} electrons ,μ_p=hole)

Diffusion: high concentration regions to low concentration. This mechanism is called “diffusion.”

Thank you