Contents
From the study of subatomic particles to the laws of motion, Physics Topics offer insights into the workings of the world around us.
What is the Range of Conductors Resistivity and Conductivity?
Conduction of Electricity in Solids
A solid can in general be divided into two classes :
(i) crystalline and
(ii) amorphous. We shall concern ourselves in this chapter only with crystalline solids. A lattice in such a solid is an ordered sequence of points describing the arrangement of ; atoms that form a crystal. A unit cell is defined as the smallest part of a crystal that repeats itself regularly through translation in three dimensions to form the entire crystal. Innumerable unit cells are arranged in a regular pattern to form a piece of a crystal [Fig.].
Based on electrical conductivity, solids can be divided into three groups-
- conductor,
- insulator and
- semiconductor.
Conductor: Electricity can easily pass through the con-ductors. Solid conductors are mainly metals. In metals free elec-trons act as charge carriers; the magnitude of current through metals may be equal to or greater than 1 A. With increase in tem-perature, resistance of metallic conductors increases. Silver (Ag), copper (Cu), aluminium (Al), iron (Fe), etc. are some examples of conductors.
Insulator: The substances through which electricity cannot pass are known as insulators. Free electrons do not exist in these kind of substances. Most of the non-metals are insulators. The insulators which are widely used in electrical machines are mica, diamond, quartz, etc.
Semiconductor: The substances having electrical con-ductivity intermediate between that of metals and insulators are generally called semiconductors. Conduction in semicon-ductors takes place through free electrons and holes (For concept of hole, see section 1.1.1). The current through this material is never more than a few milliampere. Silicon (Si), germanium (Ge), etc. are some examples of semiconductors.
The speciality of silicon and germanium is that, both of them belong to the fourth group (carbon group) in the periodic table; both contain 4 electrons in their outermost orbit which play a decisive role in forming covalent bonds. During electrical con-duction, free electrons and holes act as charge carriers in silicon or germanium crystals as mentioned earlier. With increase in temperature, their resistance decreases. This topic is being dis-cussed in detail in the next section. Among the different kinds of semiconductor silicon is preferred for low cost in the production of electronic equipments. However, silicon-germanium (SiGe) is used instead of Si in high-speed networking.
There are two types of semiconductor-
- Pure or intrinsic semiconductor and
- Impure or extrinsic semiconductor.
Pure or Intrinsic Semiconductor
Valence electron: Fig. shows 5 atoms of silicon (Si) crystal. There are 4 electrons in the outermost shell of a silicon atom. Each electron forms a single covalent bond with an electron of the adjacent silicon atom. So, the four silicon atoms adjacent to the central atom form four covalent bonds.
In this scenario, the effective number of electrons in the outermost shell of the central atom becomes 8. These electrons enclosed in the bonding are called valence electrons. Thus each atom in the crystal gets stability by fulfilling an octet in the outermost shell and keeps the crystal in uniform bonding.
At absolute zero temperature (i.e., 0 K), each electron remains confined to the bond. Due to absence of any free electron or hole, conduction of electricity does not take place through the crystal, i.e., the crystal behaves as an insulator.
Conduction electron: Now if the temperature of the crystal be increased, i.e., if the crystal absorbs heat, energy of the valence electrons increases. Due to this, some valence electrons gain sufficient kinetic energy to break the covalent bond and come out from the valence shell. These electrons are known as free electrons and they act as charge carriers in the crystal. If suitable potential difference is applied, current flows through silicon or germanium crystals due to these electrons. These charge carrying free electrons are called conduction electrons or thermal electrons.
Note that, the conductivity of a substance is directly proportional to its concentration of free electron, n. In case of good conductor, n ≈ 1023 electrons per m3 and for insulator, n ≈ 107 electrons per m3. In case of semiconductor, the value of n lies between these two. For example, at room temperature (i.e., at 300 K), the values of n for germanium and silicon are n ≈ 1019 per m3 and n ≈ 1016 per m3 respectively.
Magnitude of current: The value of electric current through pure germanium crystal is not more than a few micro-amperes (μA) and in case of silicon it is even less, only a few nano amperes (nA). This small Current is of no use for practical purposes and hence pure semiconductor has no use as an electrical element.
Resistance of semiconductor: With the increase in temperature of silicon or germanium crystal, the number of free electrons inside it increases. As a semiconductor result, electric current also increases, i.e., the resistance of the crystal decreasès.
On the other hand, resistance of a metallic conductor increases with increase in its temperature. Variation of the resis-tance of metallic conductor and semiconductor with temperature is shown in Fig.
Hole:
Generation of holes: Suppose in a pure silicon crystal, the electron at the position A in the bond 1, is shifted to the position X after breaking the bond [Fig.]. So, a valence electron is transformed into a conduction electron. At the same time, there is a deficit of electron at the position A. So, an effective positive charge is developed at the position A with respect to its surrounding electrons. This kind of deficit of electron within a bond is known as a hole. If the charge of an electron be -e, then the effective charge of a hole is +e. Note that, in an intrinsic semiconductor, the number of holes generated is exactly equal to the number of electrons released, i.e., n = p (where n and p are the concentrations of elec-trons and holes.)
Motion of holes: Let a potential difference be applied between the two ends of the crystal. Due to thermal vibration, the electron at position B in the bond 2 breaks the bond [Fig.]. Now, this electron will move in a definite direction due to the applied potential difference and ultimately fill the blank at A of the bond 1. At that instant, the hole at A will vanish and a new hole will appear at position B. It can be assumed that, the hole at A is transferred to B. Clearly, the direction of motion of the electrons in a crystalline medium is opposite to that of the holes.
Remember that unlike the electron, ‘hole’ is not a real particle, it is only the ‘deficit of electron’. It is just a concept introduced to devise a model for explaining conduction in semiconductor. In many cases, it is advantageous to describe electric current by means of motion of holes. Thus, electrons are the negative charge carriers in silicon and germanium crystals, while holes are considered as the positive charge carriers.
Definition: If any electron is released from a bond of an atom, the deficit of electron at that position is regarded as a hole. Its effective charge is +e, although it is not a real particle.
Energy Bands in Solids
We shall begin by considering a sodium atom as an example. An isolated Na atom has been shown in Fig. Its electronic configuration is 1s22s22p63s1.
Due to attraction of nucleus, a potential well [shown in Fig.] by solid linej is formed in the atom and electrons are accommodated in this potential well by occupying different discrete energy levels of negative potential energies. According to Pauli’s exclusion principle, maximum two electrons having opposite spins can reside in each energy level. Hence, in sodium atom, each of the energy levels is and 2s is completely filled by two electrons, whereas 6 electrons reside in 2p level as it splits into 3 substates. The outermost electron resides in 3s level. This electron is the valence electron of Na atom.
In solid sodium crystal lattice, large number of atoms are very close to each other, therefore the shape of potential well is changed [shown by solid line in Fig.]. Generally, except the valence electron, rest of the electrons in Na atom reside in its own potential well. So these electrons are not influenced by other neighbouring atoms.
But, in case of valence electrons, the situation is completely different. The valence electrons cannot be accommodated within the potential well. Therefore each of the valence electrons is influenced by all the other atoms surrounding it. So, it is not possible to recognise the valence electrons of individual Na atom in 3s energy level. But, according to Pauli’s exclusion principle, maximum number of electrons that can be accommodated in a definite energy level is two.
Due to this, 3s energy level splits into a large number of substates. Each substate contains 2 electrons. As inside a crystal, large numbers of atoms (~1020) are packed closely in a very small space, the number of substates is very high. So the variation of the potential energy of the energy levels may be assumed to be continuous. Thus these closely spaced energy levels will form an energy band at the position of 3s. This energy band in a solid crystal is called valence band.
Generally, each electron in valence band escapes from its own atom, but due to attraction by rest of ionised atoms i.e., group of atoms in crystal, the valence electrons cannot behave as free electron. So no free electrons are available as charge carrier.
In the crystal, if the valence electrons gain sufficient energy from external source to overcome the potential barrier of the group of atoms, then the electrons become free. These electrons are called conduction electrons.
Now, if a potential difference is applied at both ends of a solid sodium bar, then the conduction electrons start drifting. For this, current will be introduced in the solid. When a large number of valence electrons are transformed into conduction electrons by acquiring enough energy, they form an energy band instead of residing in a certain discrete energy level [Fig.]. This energy band is called conduction band.
Naturally, the energy of electrons in conduction band is more than that band in valence band. The gap between these two consecutive energy bands is known as forbidden zone.
No electron can stay in the forbidden zone. The energy gap (Eg) between these two bands is known as forbidden energy gap. For different substances, the energy gaps (Eg) between these two bands are different and depending on the energy gap, electrical conductivities of different substances are also different.
Insulator: In insulator the energy gap between valence band and conduction band is such that, electrons in the valence band can never gain sufficient energy for transition into conduction electrons [Fig.(a)]. As a result, no charge carriers are produced and the substance behaves as an insulator.
Conductor: In some substances, overlapping takes place between upper part of valence band and the lower part of conduction band [Fig.(b)]. So, no energy is required for the electrons to move from valence band to conduction band. As a result, valence electrons can easily transform into conduction electrons. Hence, innumerable charge carriers are produced and the substance behaves as a good conductor.
Semiconductor: The substances in which the energy gap between valence band and conduction band is smaller than insulator [Fig.(c)], behave as semiconductors. The energy required for transition of valence electrons into conduction electrons is greater than that for conducting substances. However the energy gap between valence band and conduction band in these substances is not too large like that in insulators. This energy gap (Eg) is 0.67 eV for germanium and 1.11 eV for silicon.
Electrons and holes in the two bands: At low temperature, the valence band of an intrinsic semiconductor remains saturated and the conduction band remains fully vacant. Now, at a higher temperature, when an electron reaches the conduction band from the valence band [Fig.], a vacancy of elec-tron is created in the valence band, i.e., a hole is generated. Naturally, the number of electrons in the conduction band and the number of holes in the valence band of an intrinsic semiconductor are equal.
Ranges of resistivity and conductivity: The following table provides an overall knowledge of the resistivities and conductivities of the three types of materials.
Material | Resistivity (ρ) in Ω ᐧ m | Conductivity (σ, 1/ ρ) in S ᐧ m-1 |
Conductors | 10-8 to 10-2 | 102 to 108 |
Semiconductors | 10-5 to 106 | 10-6 to 105 |
Insulators | 1011 to 1019 | 10-19 to 10-11 |
Comparison of Semiconductors with Conductors and Insulators
Conductor | Insulator | Semiconductor |
1. Electrical conductivity is very high. Examples: Copper, silver and other metals, different electrolytic solutions, etc. |
It cannot conduct electricity. Examples: Air, gas, most of the non-metals, etc. |
Electrical conductivity lies between that of conductor and insulator. |
2. Free electrons act as charge carriers in case of metals and positive and negative ions in case of electrolytes. | No charge carrier is present. | Electron and hole act as charge carriers. |
3. With increase in temperature, resistance increase for metals and decrease for electrolytes. | Resistance is almost infinite at any temperature. | With increase in temperature, resistance decreases. |
4. Current can rise up to a few amperes. | No current flows. | Current rises upto a few milliamperes. |
5. Overlapping occurs between valence band and conduction band. | Energy gap between valence band and conduction band is very large. | Energy band between valence band and conduction band is small compared to an insulator. |