KIRCHHOFF'S LAW

Kirchhoff's Laws: This law enable us to determine the equivalent resistance of a complex circuit or network and the currents flowing in the various conductors of network.

The following are the two laws of Kirchhoff:

LAW I: Point Law or Current Law

• In any network (or circuit), the algebric sum of the current in all the wires meeting at a point is zero.
• In other words, the sum of the currents flowing towards a point is equal to the sum of the currents flowing away from it.

or       Σ I = 0

For example: Let there be a number of conductors meeting at a junction X as shown in figure

 then we have 

                      i₁ + i₂ + i₃ + i₄ + i₅

             or      i₁ + i₂ + i₃ - i₄ - i₅

             or      incoming currents = outgoing currents

If the incoming currents are taken as positive, then the outgoing currents are taken as negative.

LAW II: Mesh Law or Voltage Law

• In any closed circuit (or mesh), the algebric sum of products of the current and resistance of each part of the circuits is equal to the resultant electromotive force in the circuit.

or        Σ I ∙ R = Σ V

For example: Let the different resistances P, Q, R, S, F and G be connected as shown in figure

Then taking the circuit ABCDA, we have

P i₁ + Q (i₁ + i₂) - S (i₃ -i₁ - i₂) - R (i₃ - i₂) = 0

Again taking the circuit ABDA, we have

P i₁ - G i₂ - R (i₃ -i₁) = V     and so on.        

INTRINSIC SEMICONDUCTORS

What are intrinsic semiconductors?

Those semi conductors in which impurities are missing are known as intrinsic semiconductors. The electrical conductivity of the semiconductor depends upon the total no of electrons shifted to the conduction band from the valence band. This phenomenon is called as intrinsic conductivity.

The most common examples of the intrinsic semiconductors are silicon and germanium. Both these semi conductors are used frequently in manufacturing of transistors and electronic products manufacturing. The electronic configuration of both these semiconductors is shown below:

Germanium -1s22s22p63s23p6 3d104s24p2

Silicon: 1s2 2s2 2p6 3s2 3p2

In the electronic configuration of both the semiconductor crystals there are four valence electrons. These four electrons will form covalent bonds, with the neighboring electrons of the germanium atoms. Each covalent bond is formed by sharing each electron from the each atom. After bond formation, no free electron will remain in the outermost shell of the germanium semi conductor.

The figure of germanium structure is shown below:

If the temperature will be maintained at zero Kelvin, then the valence band will be full of electrons. Energy gap is nearly 0.72 eV for germanium. So, at such a low temperature range it is impossible to cross the energy barrier. It will act as an insulator at zero Kelvin. Electrical conduction starts only if there is breakage in the covalent bonds and some of the electrons become free to jump from valence band to the conduction band. The minimum energy required to the break the covalent bond in germanium crystal is 0.72 eV and for silicon its value is 1.1 eV.

But if these semi conductors are placed at room temperature then the thermal energy generated at room temperature will help to excite some electrons present in valence electrons to shift to the conduction band. So, the semi conductor will be able to show some electrical conductivity. As the temperature increases, the shifting of the electrons from the valence band to the conduction band will also increase. The holes will be left behind in the valence band in place of electrons. This vacancy created by the electron after the breakage of the covalent bonding is known as hole. Holes are shown in the figure given below. Hollow circles in the figure are representing the holes.

When this semi conductor is placed under the influence of electric field then the holes movement and the electron movement will be opposite to each other. During this whole process the no of holes and the free electrons in the circuit of the intrinsic semi conductor will be same.

Equation between the density of free electrons, density of holes and the density of the semiconductor is shown below:

                                                             ne = nh = ni

n e and n h in the above equation are the number densities of free electrons and no density of holes respectively. Similarly, ni is the intrinsic density of the carriers i.e. the holes and free electrons.

Formula which can be used to calculate the no of holes and the electrons in the semi conductor is given by:

                                                      ne=nh= AT3/2e-Eg / 2kT

As we have discussed above that when we will increase the temperature the no of electrons as well as the holes will increase.

Conclusion: 

It is very difficult task to make an intrinsic semiconductor because we can’t use highly pure materials for constructing the semi conductors.