We discussed semiconductor meaning, semiconductor diode, types of semiconductors, semiconductor devices, semiconductors examples, semiconductors notes, semiconductor electronics.
What are Semiconductors?
Semiconductors are the solids having resistivity or conductivity in between metals and insulators . The order of the resistivity of semiconductors is 10-5 to 106 ohm-m. However, the order of conductivity of the semiconductors is 105 to 10-6 Sm-1.
Types of Semiconductors
- Elemental semiconductors. Semiconductors consisting of a single chemical element are known as elemental semiconductors, For example, germanium (Ge), silicon (Si), selenium (Sc), tellurium (Te) etc.
- Compound semiconductors. Semiconductors consisting of two or more chemical elements are known as compound semiconductors.
They are of two types
(a) Inorganic Semiconductors: gallium arsenide (GaAs), indium phosphide (InP), indium antimonide (InSb), lead sulphide(PbS), cadmium sulphide (Cas), lead telluride (PbTe), gallium arsenide phosphide(GaAsxP1-x)etc. are inorganic semiconductors
(b) Organic semiconductors: The doped phthalocyanines, anthracene etc, and organic polymer semiconductors eg. polyaniline, polythiophene, polypyrrole etc also. In this chapter, we shall discuss only the study of inorganic semiconductors. Most commonly used semiconductors in the discussion are germanium (Ge) and silicon (Si).14.2.2. Energy Bands in a Semiconductor Crystal
Explain, how are energy bands formed in semiconductor crystal?
A collection of many closely spaced energy levels is known as energy band. Electronic configuration of Si(Z = 14) is 1s2, 2s2, 2p6. 3s2, 3p2 and electronic configuration of Ge(Z=32) is 1s2, 2s2, 2p6. 3s2, 3p6,3d10,4s2,4p2. These configurations show that both Silicon and Germanium atoms have 4 electrons (i.e.,there are 4 electrons in the outermost orbits of these both the atoms).
In case of a single isolated atom, the electrons in an orbit have a definite energy. The energy possessed by a single isolated atom in different orbits is shown in Figure 2. The larger the orbits, the greater is its energy. Figure 2 represents the energy level diagram of an isolated atom. The first orbit represents the first energy level, the second orbit represents the second energy level and so on.
In a crystal, atoms are closely packed and energy levels are not the same as for individual or an isolated atom. The energy levels of atoms in a crystal get modified due to the interaction between atoms forming the crystal
In a solid or a crystal, there are several atoms. The energy levels of inner orbit electrons of an atom are not influenced by the neighbouring atoms as these electrons are tightly bound to their parent nucleus. However, the energy levels of outer orbit electrons of an atom are altered as these are influenced by the neighbouring atoms. Hence, the outer orbit electrons of an atom are common to several neighbouring atoms. Therefore, the energy levels corresponding to the outer shell for orbit electrons spread up to form a band of energy. Thus, a band of energy consists of very closely spaced energy levels.
Consider a silicon crystal consisting of N atoms. Assume that the interatomic distance (.e., the spacing between atoms) can be varied without altering the basic structure of the crystal.
Let us see what happens to energy levels of electrons of the atoms when interatomic spacing (1) changes in the case of a
Semiconductor say silicon at O K (figure 3]
- Region A. When interatomic spacing is very large, each atom in the silicon crystal behaves independently and has discrete energy levels.
In silicon crystal, the outermost two subshells namely 3s and 3p contain 2N electrons each. Therefore, 3s subshell has 2N electrons completely occupying 2Ns- states at the same energy level. The 3p subshell has 6 possible p-states. Out of these 6N possible states, only 2Np- states are occupied by 2N electrons at the same energy level. Thus, 4Np- states are empty
2. Region B. When atoms are brought closer to each other to form a solid, the interaction among valence electrons of N atoms split *3s and 3p levels into large number of closely spaced energy levels where the energy of an electron may be lightly less or more than the energy of an electron in an isolated atom. Thus, two hands corresponding to 3s and 3p states are formed. All the 2Ns- states in the band are completely filled by 2N electrons. On the other hand, only 2N states out of 6Np states in the band are filled by 2N electrons and the other 4N states in 3p level are empty. These energy bands are separated by a definite energy gap.
3. Region C. When interatomic spacing is further reduced, the 3s and 3p hands overlap and the energy gap between them disappears. In this case all 8N levels (2N corresponding to 3r energy level and 6N corresponding to 3p energy Level) are now continuously distributed. Out of these 8N levels, 4N levels are filled with valence electrons and other 4N levels are empty.
4. Region D. For the equilibrium separation of atoms, the filled and unfilled energy levels are separated by an energy gap called the forbidden energy gap denoted by E. forbidden means not allowed). The lower filled energy band 4N states fully filled with 4N valence electrons are called valence band and the upper unfilled energy band (consisting of 4N states but ao electron) is called the conduction band. The highest energy level of the valence band is represented by E, and the lowest energy level of the conduction band is represented by E Above E, and below E. there is a large number of closely spaced energy levels.
Figure 5 given below further represents region D.
Valence Band is the energy band occupied by the valence electrons. This energy band is formed when different energy levels of isolated atoms almost combine when these atoms come closer to form a solid.
Conduction Hand is the energy band of higher energy levels which is either empty or partially filled with electrons above the valence band.
Forbidden Energy Gap is the separation between the valence band and conduction band in a solid. Electrons do not have energy corresponding to this energy gap. It is denoted by Eg.
Classification of solids on the basis of energy bands
Distinguish between metals, insulators and semiconductor on the basis of energy band diagrams Solids can be classified into different categories on the basis of energy bands. We can distinguish among metals (or conductors), insulators and semiconductors on the basis of energy bands.
(1) Metals or conductors
A solid in which valence band and conduction band are partially filled or valence band and conduction hand overing is known as metal or conductor (figure 6 a and b). In the case shown in figure 6la), the conduction hand and valence hand at partially filled. In the case shown in figure 6 (b), there is no for hidden energy gap between the valence band and the context band. In case of the partially filled valence band, electrons from filled energy levels can move easily to the unfilled higher energy levels and hence conduction of electrons takes place. In case of the overlap of valence and conduction bands. electron to easily from the valence band to the conduction band. Thus, a large number of electrons are available for the conduction of electricity (or electric charge). Thus, metals or conductors are good conductors of electricity
In insulators, the valence band is completely filled with electrons and the conduction band is empty and both the bands are separated by a forbidden energy gap of about greater than 3eV. (Figure 7).
There is no electron in the conduction band and hence Insulator cannot conduct electric current. The insulator can conduct electric current only if the electrons from the valence band can move to the conduction band. This happens if the energy gained by electrons in the valence hand is greater than the forbidden energy gap (-3 eV). But the electrons in the valence band have energy =3/2KT -=0.025 eV (where k= Boltzman’s constant) at the room temperature. This energy is very small as compared to the energy of the forbidden energy gap. Therefore, the electrons in the valence band cannot go to the conduction band and hence insulator cannot conduct electric current. Therefore, the insulator is a bad conductor of electricity.
Semiconductors are the materials in which the forbidden energy gap between the filled valence band and the empty conduction band is very small(i.e. approx 1 eV) figure 8.
Germanium and silicon are examples of semiconductors. In the case of silicon, the forbidden energy gap (Eg) at room temperature is about t-2 eV and for Germanium is about 0.72 ev.
At O K, the electrons in the valence band do not have sufficient energy to tp to the conduction band and hence semiconductor behaves as an insulator at 0 K. But at room temperature, some of the electrons in the valence band have sufficient thermal energy to jump to the conduction band and a semiconductor can conduct even at room temperature. Thus, semiconductor behaves as an insulator at O K but semiconductor behaves as a conductor at room temperature.
Effect of Temperature on Conductivity of a Semiconductor
Discuss the effect of temperature on the conductivity of a semiconductor
In metallic conductors, the charge carriers are free electron. As the temperature of the conductor increases, the amplitude vibrations of atoms or ions in the crystal lattice increases, As a result of this, there are more collisions between free electrons and the ions. Under this condition, the metal will give more opposition to the flow of electrons (i.e., current in a metallic conductor decreases). In other words, the resistance of the metallic conductor increases Le conductivity decreases with increase in temperature.
In case of a semiconductor, most of the electrons are in the valence band at OK (very low temperature). The thermal excitation energy is too little and this energy is not able to excite the electrons from the valence band to the conduction band. Thus a semiconductor behaves like a poor conductor (or insulator) at very low temperature. However, at higher temperature even at room temperature) the electron in the valence band is thermally excited to the conduction hand. Thus, the conductivity of the semiconductor increases with the increase in temperature. In other words, the resistance of a semiconductor decreases with increase in temperature.
What is an intrinsic semiconductor? Give examples.
The semiconductor in which the current carriers (holes and electron) are created due to thermal excitation only across the forbidden energy gap is called an intrinsic semiconductor.
A pure semiconductor is called an intrinsic semiconductor. It has thermally generated current carriers. Gennantum and silicon are frequently used as intrinsic semiconductors.
Explanation of the behaviour of intrinsic semiconductors on the basis of Valence-Bond theory.
Discuss the structure of an intrinsic semiconductor, How are charge carriers generated in an intrinsic semiconductor? What is understood by intrinsic carrier concentration?
Structure of an intrinsic semiconductor. The three dimensional diamond-like structure for Germanium or silicon or carbon is shown in figure 9. The lattice spacing for Germanium crystal is 5.66 Angstrom, the lattice spacing for silicon crystal is 5.43 Angstrom and the lattice spacing for carbon crystal is 3.56Angstrom.
Each atom of silicon (Si) and germanium (Ge) has four valence electrons (i.e., electrons) in its outermost shell). In a crystal of silicon or germanium, each atom forms four covalent bonds (simply known as valence bond) by sharing its four valence electrons with the neighbouring four atoms (two-dimensional figure 10).
At OK (very low temperature), all the covalent bonds are complete Therefore, no free electron is available in the crystal for the conduction of current. Hence, silicon or germanium crystal behaves us an insulator at 0 K.
Generation of charge carrier (electrons & holes). At room temperature. some of the covalent bonds will be broken because of the thermal energy supplied to the crystal When a covalent bond breaks, an electron becomes free. The electron which leaves the bond is called free electron and the vacancy created in the covalent bond due to the release of the electron is called a hole” (i.e, deficiency of an electron). The hole is equivalent to a positive charge (+). This hole can be filled up by an electron from the neighbouring covalent bond, where another hole is created (figure 11). This process continues and the hole moves in the crystal lattice in a random manner. In fact, movement of a hole represents the movement of a bound electron.
Recombination of holes and electrons: Thermally generated electrons keep you occupying the position of nearby holes. They collide with holes and recombine. This process goes on an along with the thermal generation of charge carriers (holes and electrons). At steady-state equilibrium, the rate of the combination of holes and electrons is just equal to the rate of production of holes and electrons.
In an intrinsic semiconductor, the number density of free electrons ne(i.e. number of free electrons per unit volume) is equal to the number density of holes and is known as number density of intrinsic carriers (ni).
where, ni, is known as intrinsic carrier concentration,
Explanation of behaviour of intrinsic semiconductor on the Basis of Energy Band theory.
In a semiconductor, valence band and conduction band are separated by a forbidden energy gap Eg = 1.V. The valence band is completely filled with electrons while conduction band is empty at 0 K [figure 12 a). At room temperature (T>0 K), the electrons in the valence band gain thermal energy and jump over the forbidden energy gap to reach the conduction band. The electrons reaching the conduction band leave behind an equal number of holes in the valence band (figure 12 b). These holes create empty energy levels in the valence band. The hole can be filled by an electron from the nearby energy level in the valence band. When the electron fills the hole, another hole is created at the site from where the electron goes to fill the hole.
The drift of electrons and holes in the intrinsic semiconductor in the electric field
Explain the drift of electrons and holes in an intrinsic semiconductor in an electric field.
In the intrinsic semiconductor, holes in the valence band and electrons in the conduction band move randomly. When the intrinsic semiconductor is connected to an electrical source (i.e., a battery), then the electric field is set up across the semiconductor. The holes in the valence band drift towards negative terminal of the battery and the conduction electrons (i.e. electrons in the conduction band) move in the direction opposite to the direction of the holes as shown in figure 13. Since Electrons and holes have opposite signs, so the motion of both the charge carriers give rise to an electric current in the same direction only.
Electric Current in Intrinsic semiconductor
Derive an expression for the electric current in an intrinsic semiconductor
In an intrinsic semiconductor, there are two kinds of charge carriers i.e., free electrons (-e) and holes (+e). The movement of these two equal and opposite charges constitute an electric current in the same direction, Therefore, the total current in the semiconductor is the sum of electric current due to the flow of electrons (called electric current Ie) and due to the flow of holes (called hole current Ih).
Consider an intrinsic semiconductor PQ of length and of cross-section A connected to a battery of potential difference V volt (figure 15)
Due to this potential difference, holes drift towards the negative terminal of the battery giving hole current Ih and electrons drift in a direction opposite to the holes and constitute electron current Ie.
Let nh be the number density (number per unit volume) of holes in the semiconductor, Al be the volume of the semiconductor and e be the charge on the semiconductor.
Then, charge in the semiconductor due to holes, qh=nh Ale
Using, I=q/t we get, hole current Ih=nh Ale/t
But l/t=drift velocity vh of hole
Ih=nh Avh e
Similarly, current due to electron, Ie=neAe ve,
where, ne number density of electron and Ve is drift velocity of electron.
From eqn (1) we get
I=nh Ae Vh +ne Ae Ve
which is the expression for the electric current in an intrinsic semiconductor
EXTRINSIC (DOPED OR IMPURE SEMICONDUCTOR)
Define extrinsic semiconductor, What is doping? Discuss methods of doping. What are the characteristics of a dopant?
A semiconductor obtained after adding suitable impurity atoms in the intrinsic semiconductor is called an extrinsic or doped semiconductor. The process of adding suitable impurities in the intrinsic semiconductor is called doping.
Intrinsic (pure) semiconductor has thermally generated current carriers (holes and electrons). These current carriers are small in number at room temperature and hence the conductivity of an intrinsic semiconductor at room temperature is low. If temperature of intrinsic semiconductor is increased considerably to have more and more charge carriers to increase its conductivity, it may get damaged, So, to increase the conductivity of an intrinsic semiconductor, some suitable impurities can the added in it. Small amount of impurity atoms added in an intrinsic semiconductor considerably increases the conductivity of the intrinsic semiconductor. The impurity added in the intrinsic semiconductor to increase its conductivity is known as dopant.
Methods of Doping :
Impurity atoms can be added into the intrinsic semiconductor in different ways discussed below
- A very small quantity of impurity atoms is made by diffusing into the high purity molten material such as germanium, when the crystal is grown out of melt.
- Impurity atoms can also be added into the intrinsic semiconductor by heating it in the environment having impurity atoms.
- Impurity atoms can also be added into the intrinsic semiconductor by bombarding it with the impurity atoms.
Characteristics of dopant:
The size of the dopant atom should be nearly equal to the size of the atom of semiconductor to be dopped. A dopant atoms are supposed to take the place of the atoms in the semiconductor crystal. The number of dopant atoms should be about one in million of parent atoms of the intrinsic semiconductor
Types of Impurities
Name the types of impurities added in an intrinsic semiconductor to make it an extrinsic semiconductor. Give examples also.
There are two basic types of impurities that can be added in the intrinsic tetravalent semiconductor to increase its conductivity
1. Pentavalent impurity:
The dopant having valency 5 i.e. ,an element whose each atom has five valence electrons is called pentavalent impurity. For examples. Arsenic (As). Antimony (Sb). Phosphorus (P) etc.
These impurities are also known as donor impurities as they donate extra free electrons to the intrinsic semiconductor
2. Trivalent impurities:
The dopant having valency 3i.e.. an element whose each atom has three valence electrons is called trivalent impurity. For examples, Indium (In). Gallium (Ga), Aluminium (Al), Boron (B) etc.
These impurities are also known as acceptor impurities as they accept electrons from the covalent bands of the intrinsic semiconductor
Types of Extrinsic Semiconductor
Explain how an intrinsic semiconductor can be converted into(1 ) n-type and (2) p-type semiconductor ? Give ne example of each and their energy band diagrams.
Depending upon the type of impurity added in the intrinsic semiconductors, extrinsic semiconductors are classified in to two categories and (1) p- type semiconductor (2) n-type semiconductor
(1) p- type semiconductor
When suitable trivalent impurity is added to pure germanium or silicon crystal, we get extrinsic semiconductor known as p-type semiconductor. Trivalent impurity atom (say indium) has three valence electrons. When an atom of indium is added into the silicon (say silicon) crystal, this atoms replaces one of the silicon atoms and settles in the lattice site of replaced semiconductor atom. This indium atom forms three covalent bonds with the neighbouring three silicon atoms. The fourth bond remains incomplete which has a deficiency of one electron. This deficiency of an electron is called hole and behaves like a positively charged particle. This hole attracts the electron from the neighbouring covalent bond to fill itself. Now a new hole is created at the site from which the electron has been attracted to fill the hole (figure 16] In this way, a number of holes are formed by adding more and more trivalent (indium) atoms in the semiconductor crystal.
Majority charge carriers in this type of semiconductor are positively charged holes (and the minority carriers are electrons which are thermally generated),so this type of doped semiconductor is called P-type or p-type semiconductor. Since each trivalent impurity atom accepts one electron from the valence band of silicon, so it is known as acceptor impurity.
The holes created by adding the acceptor impurity increase the rate of recombination of electrons, thereby further decreasing the number of free electrons in the semiconductor. Thus, careful doping brings large difference between hole concentration and Electron concentration.
Energy band diagram of p-type Semiconductor
The energy band diagram of p-type semiconductor is shown in figure 17, The energy level corresponding to the holes in the p-type Semiconductor lies just above the valence band. This energy level is known as acceptor level. The energy difference between the acceptor level and the highest energy level of valence band (Eg = 0.01 ev for Ge and 0.05 eV for Si) is much less than the forbidden energy gap (Eg = 0.72 eV for Ge and Eg = 1.2 eV for Si). At room temperature, the thermally generated electrons in the valence band are easily transferred to the acceptor level and hence large number of holes are created in the valence band. These holes act as current carriers when p-type semiconductor is connected across the battery .
2) n-type semiconductor
When suitable pentavalent impurity is added to pure germanium or silicone crystal, we get an extrinsic semiconductor is known as n-type semiconductor.
Pentavalent impurity atom, say arsenic (As) has five valence electrons. When arsenic atom is added into the semi-conductor (say silicon) crystal, it replaces silicon atom and settles in the lattice site of replaced silicon atom. This arsenic atom forms four covalent bonds by sharing its four electrons with the neighbouring four semiconductor atoms. The fifth valence electron of arsenic remains un-accommodated. This electron is loosely bound to its parent nucleus and is detached easily even at the room emperature. Now, it becomes a free electron and move randomly through the crystal (figure 18). In this way, a number of free electrons are available in the crystal when a small amount of arsenic is added to the silicon crystal.
Majority charge carriers in this type of semiconductor are electrons and the minority charge carriers are holes which One thermally generated. Thus, this type of extrinsic semiconductor is called n-type or N type semiconductor. Since each Pentavalent impurity atom donates one extra electron to the crystal, so it is known as donor impurity.
The fifth free electron in n- type semiconductor occupies a discrete energy level known as donor level just below the conduction band um of the semiconductor crystal (figure19). The energy gap between donor level and the conduction hand is very small (Ea= 0.01V for Ge and 0.05 eV for si). Even room temperature provides sufficient thermal energy to the free electrons at donor level to jump to the conduction band. These selection in the conduction band are mainly responsible for the conduction of current in the n-type semiconductor.
Difference between intrinsic semiconductor and extrinsic semiconductor
Distinguish between intrinsic semiconductors and extrinsic semiconductor.
- Intrinsic semiconductors are the crystals of pure elements like germanium and silicon.
- In intrinsic semiconductor, the number density of electrons is equal to the number density of holes. i.e. ne=nh.
- The electrical conductivity of intrinsic semiconductors is low.
- Resistivity is higher.
- The electrical conductivity of intrinsic semiconductors mainly depends on their temperatures.
- When some impurity is added in the intrinsic semiconductor, we get an extrinsic semiconductors
- In intrinsic semiconductor, the number density of electrons is not equal to the number density of holes
- The electrical conductivity of extrinsic semiconductors is high.
- Resistivity is lower.
- The electrical conductivity of extrinsic semiconductors depends on the temperature as well as the amount of impurity added in them
Difference between n-type semiconductor and p-type semiconductor
Distinguish between n-type and p-type Semiconductors.
- When pentavalent impurity atoms like As, Sb etc. are added in the intrinsic semiconductor, we get n-type semiconductor
- The majority carriers in n-type semiconductor an electronsand minority carriers are holes.
- Donor energy level lies close to conduction band,
- Conductivity of a n-type semiconductor σ n=eNDμe where ND is number density of donor atom.
- When trivalent impurity atoms like gallium, indium etc. are added in the intrinsic semiconductor, we get P-type semiconductor
- The majority carriers in p-type semiconductor are holes and minority carriers are electrons.
- Acceptor energy level lies close to the valence band.
- Conductivity of p- type semiconductor σp= eNAμh, where NA is number density of acceptor atom.