Question

1. Why is carbon not an intrinsic semiconductor although it lies in the same group of periodic table as germanium and silicon?
2. Derive an expression for the conductivity and resistivity of intrinsic semiconductors
3. What is doping? Discuss the methods of doping. What are the characteristics of a dopant?

Answer 1

Hint:Carbon is a non-metal and germanium and silicon are metalloids. Metalloids show the property of both metals and nonmetals and can conduct electricity. But, metals do not conduct electricity. The addition of some impurities on a semiconductor to increase its efficiency is known as doping.

Complete answer:
1. Carbon is a non-metal, and non-metals weakly conduct electricity. This is because the atoms or the molecules in carbon are closely packed to each other. Silicon and germanium which are additionally in Group IVA are semiconductors and are delegated metalloids. Metalloids show properties both metals and nonmetals. Even though carbon lies in the same group of periodic table as germanium and silicon, it is not a pure or an intrinsic semiconductor.
2. The charged particles in semiconductors, such as electrons have a certain move with a certain velocity when they are applied by an electric field. This is called drift velocity. It is given by:
$$v={\displaystyle \frac{q\tau }{m}}\epsilon =\mu \epsilon$$
where$$\mu$$ is the mobility and $$q$$ is the charge on the electron.
These charge carriers form a current known as drift current and that is given by
$$J=qn{v}_n+qp{v}_p=q(n{\mu }_n+p{\mu }_p)\epsilon$$
where, $$p$$ and$$n$$ are electron and hole densities.
Thus, the conductivity of electrons is
$$\sigma =q(n{\mu }_n+p{\mu }_p)$$
Resistivity is the reciprocal of conductivity. Therefore,
$$\rho ={\displaystyle \frac{1}{\sigma }}={\displaystyle \frac{1}{q(n{\mu }_n+p{\mu }_p)}}$$
3. A pure semiconductor is an intrinsic semiconductor. To raise the electrical conductivity, the semiconductors are subjected to doping. The doped semiconductor is called an extrinsic semiconductor. The process of doping is such that the semiconductors are mixed with pentavalent impurity such as antimony (Sb), arsenic (As) or trivalent impurity such as indium (In) or gallium (Ga). The characteristic of a dopant is to increase the electrical conductivity.

Note: The conductivity of electrons depends strongly on the applied electric field, the drift velocity and the electron and hole densities. Intrinsic semiconductor is a pure semiconductor and is converted into extrinsic semiconductor by a process called doping.