Semiconductors are solid materials, either non-metallic elements or compounds, which allow electrons to pass through them so that they conduct electricity in much the same way as a metal.
Characteristics of Semiconductors:
Semiconductors possess the following characteristics:
1. The resistivity is usually high.
2. The temperature co-efficient of resistance is always negative.
3. The contact between semiconductor and a metal forms a layer which has a higher resistance in one direction than the other.
4. When some suitable metallic impurity (e.g. Arsenic Gallium etc.) is added to a semiconductor, its conducting properties change appreciably.
5. They exhibit a rise in conductivity in the increasing temperature, with the decreasing temperatures their conductivity falls off, and at low temperatures semiconductors becomes dielectrics.
6. They are usually metallic in appearance but (unlike metals) are generally hard and brittle.
Both the resistivity and the contact effect are as a rule very sensitive to small changes in physical conditions, and the great importance of semiconductors for a wide range of uses apart from rectification depends on the sensitiveness.
Examples of Semiconducting Materials:
Of all the elements in the periodic table, eleven are semiconductors which are listed below:
Examples of semiconducting compounds are given below:
Mg3Sb2, ZnSb, Mg2Sn, CdSb, AlSb, InSb, GeSb.
ZnO, Fe3O4, Fe2O3, Cu2O, CuO, BaO, CoO, NIO, Al2O3, TiO2, UO2, Cr2O, WO2, MoO3.
Cu2S, Ag2S, PbS, ZnS, CdS, HgS, MoS2.
(v) Selenides and Tellurides.
PbS is used in photoconductive devices, BaO in oxide coated cathodes, caesium antimonide in photomultipliers etc.
Atomic Structure of Semiconductors:
To understand how semiconductors work it is necessary to study briefly the structure of matter. All atoms are made of electrons, protons and neutrons. Most solid materials are classed, from the standpoint of electrical conductivity, as conductors, semiconductors or insulators.
To be conductor, the substance must contain some mobile electrons—one that can move freely between the atoms. These free electrons come only from the valence (outer) orbit of the atom. Physical force associated with the valence electrons bind adjacent atoms together. The inner electrons below the valence level, do not normally enter into the conduction process.
Conductivity depends on the number of electrons in the valence orbit. Electron diagrams for three typical elements, aluminium, phosphorus and germanium are shown in Figs. 7.15, 7.16 and 7.17 respectively.
These elements can all be used in semiconductor manufacture.
The degree of conductivity is determined as follows:
1. Atoms with fewer than four valence electrons are good conductors.
2. Atoms with more than four valence electron are poor conductors.
3. Atoms with four valence electrons are semiconductors.
Fig. 7.15 shows aluminium which has three valence electrons. When there are less than four valence electrons they are loosely held so that at least one electron per atom is normally free; hence aluminium is a good conductor. This ready availability of free electrons is also true of copper and most other metals.
Fig. 7.16 shows phosphorus with five valence electrons. When there are more than four valence electrons, they are tightly held in orbit so that normally none are free. Hence phosphorus and similar elements are poor conductors (insulators).
Germanium (Fig. 7.17) has four valence electrons. This makes it neither a good conductor nor a good insulator, hence its name “semiconductor”. Silicon also has four valence electrons and is a semiconductor.
The energy level of an electron increases as its distance from the nucleus increases. Thus an electron in the second orbit possesses more energy than electron in the first orbit; electrons in the third orbit have higher energy than in the second orbit and so on. It follows, therefore, that electrons in the last orbit will possess very high energy.
These high energy electrons are less bound to the nucleus and hence they are more mobile. It is the mobility of last orbit electrons that they acquire the property of combining with other atoms. Further it is due to this combining power of last orbit electrons of an atom that they are called “valence electrons.”
A pure semiconductor is called intrinsic semiconductor. Here no free electrons are available since all the covalent bonds are complete. A pure semiconductor, therefore behaves as an insulator. It exhibits a peculiar behaviour even at room temperature or with rise in temperature. The resistance of a semiconductor decreases with increase in temperature.
When an electric field is applied to an intrinsic semiconductor at a temperature greater than 0 K, conduction electrons move to the anode and, the holes (when an electron is liberated into the conduction band a positively charged hole is created in valence band) move to cathode. Hence semiconductor current consists of movement of electrons in opposite direction.
In a pure semiconductor, which behaves like an insulator under ordinary conditions, if small amount of certain metallic impurity is added it attains current conducting properties. The impure semiconductor is then called impurity semiconductor or extrinsic semiconductor. The process of adding impurity (extremely in small amounts, about 1 part in 108) to a semiconductor to make it extrinsic (impurity) semiconductor is called Doping.
Generally following doping agents are used:
(i) Pentavalent atom having five valence electrons (arsenic, antimony, phosphorus)…. called donor atoms.
(ii) Trivalent atoms having three valence electrons (gallium, aluminium, boron)……. called acceptor atoms.
With the addition of suitable impurities to semiconductor, two type of semiconductors are:
(i) N-type semiconductor.
(ii) P-type semiconductor.
(i) N-Type Semiconductor:
The presence of even a minute quantity of impurity, can produce N-type semiconductor. If the impurity atom has one valence electron more than the semiconductor atom which it has substituted, this extra electron will be loosely bound to the atom. For example, an atom of Germanium possesses four valence electrons’, when it is replaced in the crystal lattice of the substance by an impurity atom of antimony (Sb) which has five valence electrons, the fifth valence electron (free electron) produces extrinsic N-type conductivity even at room temperature. Such an impurity into a semiconductor is called donor impurity (or donor).
The conducting properties of germanium will depend upon the amount of antimony (i.e., impurity) added. This means that controlled conductivity can be obtained by proper addition of impurity. Fig. 7.19 (a) shows the loosely bound excess electron controlled by the donor atom.
By giving away its one electron, the donor atom becomes a positively – charged ion. But it cannot take part in conduction because it is firmly fixed or tied into the crystal lattice. In addition to the electrons and holes intrinsically available in germanium, the addition of antimony greatly increases the number of conduction electrons.
Hence, concentration of electrons in the conduction band is increased and exceeds the concentration of holes in the valence band as shown in Fig. 7.19 (b). [Since the number of electrons as compared to the number of holes increases with temperature, the position of Fermi level also changes considerably with temperature].
It is worth noting that even though N-type semiconductor has excess of electrons, still it is electrically neutral. It is so because by addition of donor impurity, number of electrons available for conduction purposes becomes more than the number of holes available intrinsically. But the total charge of the semiconductor does not change because the donor impurity brings in as much negative charge (by way of electrons) as positive charge (by way of protons).
In terms of energy levels, the fifth antimony electron has as energy level (called donor level) just below the conduction band. Usually, the donor level is 0.01 eV below conduction band for germanium and 0.054 eV for silicon.
(ii) P-Type Semiconductor:
P-type extrinsic semiconductor can be produced if the impurity atom has one valence electron less than the semiconductor atom that it has replaced in the crystal lattice. This impurity atom cannot fill all the interatomic bonds, and the free bond can accept an electron from the neighbouring bond; leaving behind a vacancy or hole. Such an impurity is ‘called an acceptor impurity (or acceptor). Fig. 7.20 (a) shows structure of P-type semiconductor (Germanium and Boron).
In this type of semiconductor, conduction is by means of holes in the valence band. Accordingly, holes form the majority carriers whereas electrons constitute minority carriers. The process of conduction is called ‘defect’ or deficit conduction.
Since the concentration of holes in the valence band is more than the concentration of electrons in the conduction band, Fermi level shifts nearer to the valence band [Fig. 7.20 (b)]. The acceptor level lies immediately above the Fermi level. Conduction is by means of hole movement at the top of valence band, the acceptor level readily accepting electrons from the valence band.
It may be noted again that even though P-type semiconductor has excess of holes for conduction purposes, as a whole it is electrically neutral for the same reasons.
Atomic Binding in Semiconductors:
The atoms of semiconductors are arranged in an ordered array called crystal lattice because they have a crystalline structure e.g., germanium and silicon. Since both these materials are tetravalent having four valence electrons in their outermost shell, therefore they form covalent bonds with the neighbouring atoms.
In order to achieve inert gas structure having 8 electrons in the outermost orbit, they share four electrons with each other. In case of germanium atom only four electrons out of 32 electrons take part in its electrical characteristics because the remaining 28 electrons are tightly bound to the nucleus.
The four electrons revolving in the outermost shell are called valence electrons. Therefore, each atom of the semiconductor surrounded symmetrically by four other atoms form a tetrahedral crystal. Hence a stable structure is formed when each shares a valence electron with each of its four neighbours.
In case of pure (intrinsic) germanium, to allow the electrons for conduction of current the covalent bonds should be broken. For setting the electron free, there are different ways of rupturing the covalent bond. This can be done by increasing the crystal temperature above 0 K. There are mainly two properties hardness and brittleness of covalent crystals.
The hardness is characterised by the great strength of the covalent bond itself. The brittleness is characterised by the fact that adjacent atom must remain in accurate alignment because the bond is strongly directional and formed along a line forming the atoms.
Formation of Holes in Semiconductors:
In a semiconductor, the hole formed is a positive charge carrier. When a covalent bond is broken at its edge, electrons move through the crystal lattice leaving behind a hole in the bond. An electron from the side lattice jumps into the first vacant hole. Later on, an electron from another point N will jump into the hole at M and so on.
Thus a hole would appear at a point (R) in the lattice opposite to the first hole (L) by a succession of electron movements. A negative charge would move from R to L. Therefore, a hole in this case is regarded as a positive charge carrier or an electron with a negative charge. Hence due to movements of the electrons in the valence bond holes are formed.
A collision is caused by each electron movement. In other words, drift velocity of electron is always more than the drift velocity of holes. Thus an intrinsic semiconductor is one in which number of holes produced is equal to the number of conduction electrons.
Fermi level which is defined as the energy corresponding to the centre of gravity of conduction electrons and holes weighted according to their energies lies exactly in the middle of the forbidden energy gap. As the lower filled bonds of semiconductor are not of any effect, therefore, only two bands, i.e. valence and conduction bands are usually shown in the energy band diagrams.
Fermi Level in an Intrinsic Semiconductor:
To classify conductors, semiconductors and insulators we make use of the reference energy level, called Fermi level. In case of an intrinsic semiconductor, Fermi level (EF) lies in the middle of energy gap or mid-way between the conduction and valence bands. Let (at any temperature T °K)
nv = Number of electrons in the valence band,
nc = Number of electrons in the conduction band, and
N = Number of electrons in both bands.
= nv + nc
(i) In valence band energy of all levels is zero.
(ii) In conduction band, energy of all levels is equal to Eg (energy at gap).
(iii) As compared to forbidden energy gap between two bands, the widths of energy bands are small.
(iv) All levels in a band consist of same energy due to small width of band.
Let the zero energy reference level is arbitrarily taken at the top of valance band.
∴ No. of electrons in the conduction band, nc = N.P (Eg)
where P (Eg) = probability of an electron having energy Eg
Fermi-Dirac probability distribution function gives its value given below:
This shows that in an intrinsic semiconductor, the Fermi level lies midway between the conduction and valence hands.
Electron Conductivity of a Metal:
As per free electron model of an atom, the valence electrons are not attached to individual atoms but are free to move about in all directions among the atoms. These electrons are called conduction electrons and form ‘free electron cloud’ or free electron gas or the Fermi gas.
The free electrons move at random in all directions when no external field is applied. However when an external field is applied to the metal, the free electrons motion becomes directed. This directed flow of electron results in a net charge displacement in a definite direction. This type of motion is known as drift and phenomenon is referred to as process of conduction by drift charges.
The drift velocity is given by:
ν = μe E
where, ν = Electron drift velocity,
μe = Electron mobility, and
E = Applied electric field.
Let, e = Electron charge,
A = Conductor cross-section,
I = Length of the conductor,
n = Number of free electrons per unit volume of the conductor, i.e., electron density,
V = Voltage applied across the two ends of the conductor, and
E = Applied electric field
= V / t
The electric current flowing in any conductor is given by the amount of charge which flows in one second across any plane of the conductor. The total number of electrons which cross any plane of cross-section A in one second.
= n x (ν x A)
Charge carried by the electrons,
The conductivity of a semiconductor differs from that of metal in one important respect i.e., in a semiconductor, charge carriers are both holes as well as electrons whereas in metals electrons are the only charge carriers.
Current Carriers in Semiconductors:
(a) Intrinsic Semiconductors:
In case of intrinsic semiconductors the flow of current is due to movement of electrons and holes in opposite directions. Even though the number of electron equals the number of holes, hole mobility μh is practically half of electron mobility μe.
Conductivity of Semiconductor with Negligible Intrinsic Charge Carrier Densities:
When the density of charge carriers available intrinsically is negligible as compared to the added impurity atoms (whether of donor or acceptor type), then conductivity calculated above changes as follows:
1. For N-type semiconductor:
where nn is the electron density after doping.
This electron density is made up of two components:
(i) Intrinsic electron density due to electrons available in pure semiconductor.
(ii) Electron density Nd contributed by the added donor impurity.
If the intrinsic electron density is neglected, then-
Thus the conductivity solely depends upon the density of electrons supplied by the donor impurity
2. For P-Type Semiconductor:
Where, pp is the hole density after doping.
This hole density consists of two components:
(i) Intrinsic hole density due to hole available intrinsically in pure semiconductor.
(ii) The hole density (Na) contributed by the added acceptor impurity.
If the intrinsic hole density is neglected then-
Thermal Conductivity of Semiconductors:
Conduction of heat in semiconductor takes place in the following two ways:
1. By the thermal vibrations of the atoms.
2. By the electrons.
The random thermal vibrations of all the atoms of a semiconductor may be regarded as the sum total of vibrations of individual atoms, vibrations of pairs of atoms, of groups of three and ultimately the vibrations of the body as a whole. As the temperature goes on increasing the vibrations also increase accordingly.
The co-efficient of thermal conductivity comprises the following two parts:
(i) The thermal conductivity due to the thermal vibrations of the atoms.
(ii) The thermal conductivity due to the electrons.
When the concentration of free electrons in a semiconductor varies, the thermal conductivity due to electrons varies in direct proportion to the electrical conductivity whereas the thermal conductivity due to vibrations of atoms remain practically constant.