Introduction to Semiconductor physics

• Fundamentals of electrons and holes:

Let’s begin our discussion from basics which is about atoms, electrons and their properties. As the MOSFET deals with both electrons and holes we need to have a clear idea on what the internal operation is in a circuit.

Let’s focus on two special points in this topic:

1. The electronic structure of atoms

2. The interaction of atoms and electrons with excitation.

• Key points:

• The electrons in the metal absorb energy from the light, and some of the electrons receive enough energy to be ejected from the metal surface into the vacuum. This phenomenon is called the Photoelectric effect.

• The maximum energy ejected is given by E = hv – qΦ

Where h = planck’s constant 6.626

             V = velocity of electron

             q = magnitude of electric charge

             Φ = characteristic of material used

• When Φ is multiplied by the electronic charge, energy (joules) is obtained which represents the minimum energy required for an electron to escape from the metal into a vacuum. The energy qΦ is called the work function of the metal.  

• The electron may shift to an orbit of higher or lower energy, thereby gaining or losing energy equal to the difference in the energy levels (by absorption or emission of a photon of energy ).

Fig: Electron absorption and emission

• Semiconductors: 

• Types of materials:

1. Conductor:  These materials are sensitive to electricity. It has free movement of electrons. The conduction band and valence overlap with each other (0ev).

2. Semiconductor:  These materials carry a minimum number of electrons and they are less sensitive to electricity. It has controlled flow of charges. The energy gap between conduction band and valence band is very minimum of range 1ev.

3. Insulator:  These materials do not have flow of electrons. The energy gap between conduction band and valence band is very high around 6ev.

Fig:  Types of materials

• Why is semiconductor chosen?

1. It has control over flow of electrons.

2. It has a large number of carriers.

• Classification of semiconductors:

1. Based on Ionic or electronic.

Ionic: controlled by ions.

Electronic: controlled by charges.

2. Based on elemental or compound.

Elemental: It is made of only one material. eg: Si

Compound: it is made of a mixture of materials. eg: GaAs

3. Based on single crystalline, poly crystalline or amorphous.

Single crystalline: The orientation of atoms in the material is the same.

Poly crystalline: The orientation of atoms in the material is different.

Amorphous:  The orientation of atoms in material is irregular.

4. Based on doping.

Intrinsic: The purest form of semiconductor.

Extrinsic: It has external dopants added. It is an impure form of semiconductor.

• Intrinsic Semiconductor

1. It is the purest form of semiconductor.

2. Examples:  Si, Ge

3. These materials have 4 electrons in its valence shell i.e. the filled state of the valence band which forms a strong covalent bond which leads to non – existence of free electrons leading to no further conduction.

4. At 0°K intrinsic semiconductor behaves like an insulator.

5. Applying higher temperatures may lead to conduction.

6. EG           0°K                 300°K

Si            1.21 ev          1.1 ev

Ge          0.785ev         0.72ev

7. Hole: Absence of electron in an incomplete covalent bond.

8. n = ni = p; The intrinsic carrier concentration is equal to the number of holes and electron concentration.

9. Increasing temperature to make these materials conduct is not preferred so we move to extrinsic materials.

Fig: Intrinsic semiconductor 

• Extrinsic Semiconductor

1. N-type: 

1. Intrinsic material + penta valent group ( Arsenic, phosphorus, antimony) = n type

2. With the addition of impurity there is donor energy band formation just below the conduction band.

Fig: N type extrinsic semiconductor

3. Due to less band gap the electrons accumulated in the donor energy band moves from the donor energy band to conduction at room temperature. So electrons are the majority charge carriers in n type.

4. The concentration of holes is less in n type in comparison to the intrinsic materials. Due to random movement of electrons we find electron – hole recombination which generates thermal agitation leading to electron-hole pair generation.

Fig: Si bonding

5. N type semiconductor is electrically neutral because with increase in pentavalent atoms electrons becoming donor ions and upon donating an electron it has a hole i.e. positive charge due to this the increase in electrons increases hole concentration is the same amount thus balancing the charges.

2.  P -Type:

1. Intrinsic material + trivalent group (Boron, Aluminium, Gallium, Indium)= p type

2. With the addition of impurity there is acceptor energy band formation just above the valence band.

Fig: P type extrinsic semiconductor

3. Due to less band gap the electrons accumulated in the acceptor energy band moves from acceptor energy band to valence band at room temperature. So holes are the majority charge carriers in p type.

4. The concentration of electrons is less in p type in comparison to the intrinsic materials. Due to random movement of electrons we find electron – hole recombination which generates thermal agitation leading to electron-hole pair generation.

5. P type semiconductor is electrically neutral because with increase in trivalent atoms accepts electrons becoming as acceptor ions and upon accepting an electron it has an electron i.e. negative charge due to this the increase in electrons increases hole concentration is the same amount thus balancing the charges.

Fig: Ge boning

• Fermi level:

According to Pauli’s exclusion principle the allowable range of electrons in the energy level is given by:  f(E)= 1/(1 + e^(E-EF)/KT).

 Where f(E) = fermi dirac distribution

             E = energy 

             EF = energy at Fermi level

            K = Boltzmann’s constant (8.62 x 10^-5 ev/K)

           T = absolute temperature

Fermi dirac distribution: It is the probability that an available energy state at E will be occupied by an electron at absolute temperature.

1.             f(EF) = [1 + e^(EF -EF)/kT]^ -1 = 1/( 1 + 1) = 1/ 2  

Thus an energy state at the Fermi level has a probability of 1 /2 of being occupied by an electron.

2. With T = 0  f(E) = 1/(1 + 0) = 1 when the exponent is negative (E < EF), and is 1/(1 + ∞) = 0 when the exponent is positive (E > EF). This rectangular distribution implies that at 0 K every available energy state up to EF is filled with electrons, and all states above EF are empty.

Fig: Fermi dirac distribution function

•  Effects of temperature and doping on mobility

The two basic types of scattering mechanisms that influence electron and hole mobility are lattice scattering and impurity scattering.

  Lattice scattering: A carrier moving through the crystal is scattered by a vibration of the lattice, resulting from the temperature. The frequency of such scattering events increases as the temperature increases, since the thermal agitation of the lattice becomes greater.  So mobility decreases with increase in temperature.

µl = T^(-3/2)

Impurity scattering: The scattering of charge carriers by ionization in the lattice. This occurs in low temperatures which leads to less agitation so mobility increases with decrease in temperature.

µi = T^(3/2)

• Diffusion and drift current

Diffusion: The flow of carriers caused due to diffusion of electrons from high concentration to low concentration

Drift: It is the motion of charge carriers under the influence of an external electric field.