Classification of Conductor, Insulator and Semiconductor:
Electrical conductivity is a physical quantity whose range is very wide. On one hand we know about metals whose electrical conductivity is very high on the other hand there is quartz, mica like insulators whose electrical conductivity is very low. Such substances are also known whose conductivity is very less than metals at normal temperatures but very high than insulators. These are called semiconductors.
The conductivity of semiconductors is not only between conductors and insulators but also the change in the conductivity with temperature is very interesting. Near absolute zero their behaviour is similar to insulators but as the temperature increases the conductivity also increases which is opposite to the projected behaviour of metals. The following questions are not answered by the principle related to electrical conductivity which you are will versed with :
1. Why are the conductivities of solid substances different?
2. Why does any substance show the behaviour of a semiconductor?
3. Why is the change in conductivity with temperature different for metals and semi-conductors?
On the basis of the principle of energy bands in solids and answering the questions, these are divided into conductors, insulators and semiconductors. Every solid substance has its own band construction which defines its electrical conductance behaviour.
Intrinsic Semiconductors:
Those semiconductors in which there is no impurity are called intrinsic semiconductors. In ideal state in this type of intrinsic semiconductors there should be atoms of only that semiconductor. But in reality it is not possible to get such type of crystal. Therefore, if in a semiconductor material the number of impure atoms and the number of semiconductor atoms is in the ratio 1 : 108 or less than that then it is considered as an intrinsic semiconductor. To study the properties of semiconductors here we take the example of silicon and germanium.
Silicon and germanium both are the members of fourth group in the periodic table and their valency is 4. Their electronic configuration is as follows:
Ge (32) = 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p2
Si (14)= 1s2 2s2 2p6 3s2 3p2
In the crystal construction of both these elements the atom is in an ordered array in such a way that each atom is inside a regular tetrahedron and on the four corners there are its other nearby atoms.
Figure shows one such tetrahedron unit. Every valence electron of the atom makes a covalent bond with the valence electron of the nearby atom. In this way every atom is connected with the nearby atoms through covalent bonds. In every covalent bond there are two electrons. For convenience in study; figure shows the two dimensional form of crystal construction of germanium; which is also applicable for silicon.
Crystal construction of Ge at 0 K temperature.
At absolute zero (0 K) also the valence electrons are bonded in covalent bonds hence there is no free electron available for electrical conductivity. Due to this at absolute zero temperature intrinsic semiconductors behave as insulators. When the temperature of the crystal is increased then some valence electron gain thermal energy and break their covalent bonds and become free. These free electrons move in the crystal freely and participate in electrical conductance when the crystal is applied external electronic energy.
When one electron moves out of the covalent bond a vacancy is created. This vacancy is called a hole. The absence of electron is equal to the same magnitude positive charge. Hence, the hole can be assumed as a positive charge same in magnitude as that of an electron. As explained earlier, holes also participate in electrical conductance in semiconductors. In any semiconductor when a covalent bond breaks then a electrons hole pair is generated. At room temperature (300K) or a temperature close to it there are many electron hole pairs available at definite temperature. The production of electron hole pair is shown in figure.
At normal temperature electrons and holes do random motion in semiconductors. The random motion of hole can be understood in figure.
Suppose due to thermal energy an electron gets free from a covalent bond at position A, hence at this place a hole is generated. From a nearby atom, the valence electron breaks the covalent bond (at place B) and does transition to hole at position A. Then at A the covalent bond is complete; but now a hole is generated at position B. In this process very less energy is required which is very less than the necessary energy required for electron-hole pair production. The reason for this is that electron is doing transition from one bond to the other and all the electrons present in the bond are approximately of same energies. As shown in the figure due to the movement of electron form C to B the hole will do transition from B to C, etc. In this way in any semiconductor substance the electrons and holes both do random motion. Since, hole can be taken as the charge free electron +e, hence in a semiconductor both holes and electrons work as charge carriers and participate in electrical conductivity.
This process of hole electron pair production of intrinsic semiconductors can also be explained by band principle. The forbidden energy gap in semiconductors is of 1eV. At absolute zero temperature the valence band is completely filled and conduction band is fully empty. Hence, semiconductors behave as insulators. When the temperature of the crystal is increased electrons get necessary thermal energy and are capable of crossing the forbidden energy gap. Such type of electrons reach the conduction band from the valence band and holes are generated in the valence band in place of electrons (figure). Due to transition of one electron from valence band to conduction band a hole is generated and here also electron hole pair can be understood. The electrons present in conduction band are called free electrons and do random motion, similarly in valence band holes do random motion.
Generally, the breaking of the covalent bond or the electron reaching the conduction band from the valence band both are same. It can also be said that due to thermal energy the covalent bond breaks and the electron reaches the conduction band from the valence band. Therefore, for this process the necessary minimum energy would be equal to band interval energy Eg. Here this questions is logical that at room temperature, 300 K the average kinetic of the electron is kT = 1/40 = 0.025 eV, whereas the necessary energy for transition is 1eV. Then how does an electron reaches the conduction bond from the valence band? Here it is necessary to consider that kT is the value of average kinetic energy and not that all electrons are of this energy. Very less number of electrons would be there of 1eV energy which would do transition form valence band.
It is clear from above discussion that in any intrinsic semiconductor at definite temperatures the number of electrons and holes is same. If in an intrinsic semiconductor per unit volume the number of free electrons and holes is n and p respectively then
n = p = ni
np = \(n_{i}^{2}\) …………… (1)
where n, is the intrinsic charge carrier density.
When the temperature of an intrinsic semiconductor is increased then compared to prior temperature more covalent bonds break meaning more electrons reach the conduction band from valence band and the number of electron hole pair increases. This means that ni is dependent on temperature and increase with temperature. In this way two different semiconductors, for example, silicon and germanium, if they are at same temperatures then since the value of forbidden energy gap Eg for them is different, hence, the semiconductor for which the value Eg is less that will have more covalents bonds to break or more of the electrons will do transition from valence band to conduction band. Clearly at same temperature for two semiconductors for which the forbidden energy gap Eg is not same; the value of intrinsic charge carrier density will not be same but would be more for the semiconductor with less Eg value. In this way in an intrinsic semiconductor the value of intrinsic charge carrier density ni is dependent on:
(i) temperature (ii) nature of semiconductor material. In mathematical form this dependency is shown by following formula;
\(n_{i}=A T^{3 / 2} \exp -\left[\frac{E_{g}}{2 k T}\right]\) …….. (2)
Where T is absolute temperature, k is Boltzmann constant and A is another constant.
At same temperature, comparing intrinsic silicon {Eg = 1.1 eV) and germanium (Eg = 0.7 eV) there are more number electron hole pairs in intrinsic germanium than in intrinsic silicon.
