CLASS 12th
Semiconductors
Semiconductors
01. Distinction Between Metals, Insulators and Semi-Conductors Metals are good conductors of electricity, insulators do not conduct electricity, while the semiconductors have conductivity in between those of metals and insulators. The energy band formed by a series of energy levels containing valence electrons is valence band. The highest energy level, which an electron can occupy in the valence band at 0 K, is called Fermi level. The lowest unfilled energy band formed just above the valence band is called conduction band. Depending upon the energy gap between valence band and the conduction band, the solids behave as conductors, insulators and semiconductors as explained below: (a) Metals The energy band structure in solids have two possibilities: (i) The valence band may be completely filled and the conduction band partially filled with an extremely small energy gap between them. Conduction Band Conduction Band Valence Band Valence Band
(ii) The valence band is completely filled and the conduction band is empty but the two overlap each other. (b) Insulators The forbidden energy gap is quite large. Conduction Band Conduction Band Valence Band
Valence Band
(c) Semiconductors The energy band structure of the semiconductors is similar to the insulators but in their case; the size of the forbidden energy gap is much smaller than that for the insulators.
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Semiconductors
02. Increasing The Conductivity of a Semiconductor (Doping) A pure semiconductor at room temperature possesses free electrons and holes but their number is so small that conductivity offered by the pure semiconductor cannot be made of any practical use. By the addition of impurities to the pure semiconductor in a very small ratio (1 : 106), the conductivity of a Si-crystal (or Ge-crystal) can be remarkably improved. The process of adding impurity to a pure semi conductor crystal (Si or Ge-crystal) so as to improve its conductivity, is called doping. The impurity atoms are of two types: (a) Pentavalent impurity atoms having 5 valence electrons such as antimony (Sb) or arsenic (As). Pentavalent impurity atoms are called donor impurity atoms. Semiconductor so produced is called n-type extrinsic semiconductor. (b) Trivalent impurity atoms having 3 valence electrons indium (In) or gallium (Ga). Trivalent impurity atoms are called acceptor impurity atoms. Semiconductor so produced is called p-type extrinsic semiconductor.
03. Electrical Resistivity of Semiconductors Consider a block of semiconductor of length l, area of cross-section A and having number density of electrons and holes as ne and nh respectively. Suppose that on applying a potential difference, say V, a current I flows through it as shown in figure.
The electron current (Ie) and the hole current (Ih) constitute the current I flowing through the semiconductor i.e. I = Ie + Ih If ne is the number density of conduction band electrons in the semiconductor and ve, the drift velocity of electrons, then electron current is given by Ie = e ne A ve Also, the hole current, Ih = e nh A vh or I = e A (ne ve + nh vh) If is the resistivity of the material of the semiconductor, then the resistance offered by the semiconductor to the flow of current is given by
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Semiconductors
Therefore,
Also, is called the conductivity of the material of semiconductor.
04. Formation of p-n Junction A p-n junction is a basic semiconductor device. A p-type crystal placed in contact with n-type crystal to form one piece, the assembly is called p-n junction or junction diode or crystal diode. In the p-section, holes are the majority carriers; while in n-section the majority carriers are electrons. Due to the high concentration of different types of charge carriers in the two sections, holes from p-region diffuse into n-region and electrons from n-region diffuse into p-region. When an electron meets a hole, the two cancel the effect of each other and as a result, a thin layer at the junction becomes devoid of charge carriers. This is called depletion layer as shown in.
The thickness of the depletion layer is of the order of 10–6 m.
05. Forward and Reverse Biasing on a Junction Diode A junction diode can be biased in the following two ways: (a) Forward Bias When an external d.c. source is connected to the junction diode with p-section connected to positive pole and n-section to the negative pole, the junction diode is said to be forward biased.
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Semiconductors
(b) Reverse Bias When a battery is connected to junction diode with p-section connected to negative pole and n-section connected to the positive pole, the junction diode is said to be reverse biased.
06. Characteristics of a p-n Junction Forward bias characteristic: The forward-bias connections of a p-n junction are as shown in figure.
The positive pole of the battery is connected to the p-section and the negative pole to the n-section.
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Semiconductors
When a p-n junction is forward biased, the current increases linearly and rapidly above the knee voltage and the variation the current with increase of forward bias is extremely slow below the knee voltage. When a p-n junction is forward biased, the depletion layer becomes thin. It is because, the polarity of the external d.c. source opposes the fictitious battery developed across the junction.
07. Junction Diode as Rectifier An electronic device which convert a.c. power into d.c. power is called a rectifier. When an alternating e.m.f. signal is applied across a junction diode, it will conduct only during those alternate half cycles, which bias it in forward direction.
Fig. Symbol of Junction Diode
08. Full Wave Rectifier A rectifier which rectifies both halves of each a.c. input cycle is called a full wave rectifier. To make use of both the halves of input cycle, two junction diodes are used.
In a full wave rectifier, the output is continuous but pulsating in nature. However, it can be made smooth by using a filter circuit.
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Semiconductors
09. Different Types of Junction Diodes Junction diodes are of many types and they have a wide range of applications in electronics. A few of them are discussed as below : (a) Zener diode A conventional junction diode does not permit a large current to flow, when it is reverse-biased below its reverse breakdown voltage. A rapid avalanche breakdown occurs and the diode conducts a large current in the reverse direction. As a result, the diode gets permanently damaged. The specially designed junction diodes, which can operate in the reverse breakdown voltage region continuously without being damaged, are called zener diodes. (b) Photodiode A photodiode is basically a p-n junction diode, with the difference that it is made from a light sensitive semiconductor material and it is always operated in reverse bias.
When light is incident on the junction of the diode, the width of the depletion layer increases and the electrons in the covalent bonds of the crystal structure get stimulated. If the energy of the incident light is greater than forbidden energy gap (Eg) of the semiconductor material of the photodiode, it is absorbed by the semiconductor.
10. Transistors A junction diode can not be used for amplifying a signal. For amplification, another type of semiconductor device called transistor is used. It is a three-section semiconductor. The three sections are combined, so that the two at extreme ends have the same type of majority carriers; while the section that separates them, has the majority carries of opposite nature. Therefore, a transistor can be n-p-n or p-n-p type.
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Semiconductors
The three sections of the transistor are called emitter (E), base (B) and collector (C). /The base of a transistor is made thin lightly doped.
The emitter supplies the majority carriers for current flow and the collect collects them. The base provides the junctions for proper interaction between the emitter and the collector. When a transistor is used in a circuit, the base-emitter junction is always forward biased and the base-collector junction is always reverse biased.
11. Action of Transistor The action of both the types of transistors i.e. n-p-n and p-n-p is similar, except that the majority and minority carriers in the two cases are of opposite nature. If Ie, Ib and Ic are respectively the emitter current, base current and collector current, then Ie = Ib + Ic It may be pointed out that the arrows point in the direction of conventional current or hole current in spite of the fact that in the n-p-n transistor, the current is carried by electrons.
12. Common Emitter Characteristics of a Transistor Common emitter characteristics of a transistor are graphs that are obtained between voltage and current, when emitter is earthed, base is used as input terminal and collector as the output terminal. (a) Input Characteristics A.C. input resistance : Ratio of small change in base voltage to the small change produced in base current at constant collector voltage. ∆V be Rin ...(i) ∆I
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b
V ce
Semiconductors
(b) Output Characteristics These are graphs between collector voltage (Vce) and the collector current (Ic) at different constant values of base current (Ib). ∆V ce Rout ...(ii) ∆I
c
Ib
(c) Transfer Characteristics A.C. current gain : It is defined as the ratio of change in collector current to the change in base current at constant collector voltage. It is also called current transfer ratio and is denoted by β. Therefore, ∆ ...(iii) ∆
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Semiconductors
13. Transistor as an Amplifier Three types of the amplifier circuits: (a) Common Base Amplifier (b) Common Emitter Amplifier (c) Common Collector Amplifier
14. Common Base Amplifier Amplifier circuit using an p-n-p transistor.
a.c. current gain. ∆ ∆
...(i)
a.c. voltage gain. ×resistance gain. is called resistance gain. a.c. power gain. ∆ ∆ × × ∆ ∆ ×
...(ii)
a.c. power gain × resistance gain
15. Common Emitter Amplifier Amplifier circuit using an n-p-n transistor.
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...(iii)
Semiconductors
a.c. current gain. ∆ ∆
∴
...(i)
Transconductance. ∆ ∆
...(ii)
a.c. voltage gain. ×resistance gain
...(iii)
16. Relation Between α and β
and
17. Analog and Digital Signals Analog voltage signal.
Digital voltage signal.
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...(i)
Semiconductors
18. Logic Gates OR gate
(i.e. equals A OR B)
(i.e. equals A AND B)
(i.e. equals NOT A)
AND gate
NOT gate
19. Universal Logic Gates The NOR and NAND gates are produced by combining together the three basic logic gates i.e. OR, AND and NOT gates. For this reason, the NOR and NAND gates are called universal logic gates. In fact, NOR and NAND gates are considered as building blocks in digital circuits.
20. Universality of NOR Gate Three basic logic gates can be produced by the repeated use of a NOR gate. (a) To produce NOT gate. A NOR gate functions as NOT gate.
Boolean expression.
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Semiconductors
(b) To produce OR gate. OR gate by the repeated use of NOR gates, a NOR gate is connected to the NOT gate
Boolean expression. ′ ′ ∵ ∴
(c) To produce AND gate.
Boolean expression. Boolean expression for AND gate.
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Semiconductors
AIIMS Exercise (1) 1. A light emitting diode (LED) has a voltage drop of 2 volt across it and passes a current of 10 mA when it operates with a 6 V battery through a limiting resistor R. Find the value of R. (a) 200 Ω (b) 600 Ω
(c) 400 Ω (d) 60 Ω
2. The number densities of electrons and holes in a pure germanium at room temperature are equal and its value is 3 × 1016 per m3. On doping with aluminium, hole density increases to 4.5 × 1022 per m3. Find the electron density in doped germanium. (a) 3 × 1010 m‒3 (b) 2 × 1010 m‒3 (c) 1.5 × 1010 m‒3 (d) 13.5 × 106 m‒3 3. Output of a full-wave rectifier is taken across a load of 180 Ω. The forward bias resistances of the diodes used are 20 Ω each. Find the efficiency of rectification of a.c. power into d.c. power. (a) 63.04 % (b) 73.08 %
(c) 37.00 % (d) 100 %
4. A p-type semiconductor has acceptor levels 57 m eV above the valence band. The maximum wavelength of light required to create a hole is : (Planck’s constant, h = 6.6 × 10‒34 J-s) (a) 2.17 × 105 Å (b) 6.6 × 1010 Å (c) 2.17 × 1010 Å (d) 6.6 × 105 Å 5. In the circuit, the forward resistance of each diode is 50 Ω and the reverse resistance of each diode is infinite. Find the current through 20 ohm resistor.
(a) 0.2 A (b) 0.4 A
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(c) 0.3 A (d) 0.1 A
Semiconductors 6. The forward biased diode in the following circuits is : (a) (b) (c) (d) 7. The current gain of a transistor in common emitter circuit is 40. Find the ratio of emitter current of the base current. (a) 39 (b) 41
(c) 40.1 (d) 39.1
8. The current gain α of a transistor is 0.95. If change in base current in a common emitter configuration is 0.4 mA, find the change in its collector current. (a) 3.9 mA (b) 4.9 mA
(c) 3.8 mA (d) 7.6 mA
9. Pure silicon has 3 × 1028 atoms m‒3. Phosphorus atoms are doped in it to the extent of 1 ppm. Calculated the number of holes (given that ni = 1.5 × 1016 m‒3). (a) 4.5 × 109 m‒3 (b) 5 × 1028 m‒3 (c) 7.5 × 109 m‒3 (d) 3.0 × 109 m‒3 10. The peak voltage in the output of a half wave diode rectifier fed with a sinusoidal signal without filter is 10 V. The d.c. component of the output voltage is : V (a) (b) V
(c) 10 V (d) V
11. If the ratio of concentration of electrons and holes in a semiconductor is 7/5, and the ratio
of currents is 7/4, then what is the ratio of their drift velocities?
(a) (b)
(c) (d)
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Semiconductors 12. In a n-p-n transistor 1010 electrons enter the emitter in 10‒6 s. 2% of the electrons are lost in the base. Find the current transfer ratio and amplification factor. (a) 0.49, 49 (b) 0.98, 49
(c) 0.25, 50 (d) 0.50, 25
In each of the following questions, a statement of Assertion (A) is followed by a corresponding statement of Reason (R). Of the following statements, choose the correct one. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. (e) Both A and R are false. 13. (A) : During reverse biasing, a diode does not conduct current. (R) : In reverse biased diode, the depletion layer is reduced. 14. (A) : The emitter current is the sum of base current and collector current. (R) : The collector current is almost same as emitter current in n-p-n transistor. 15. (A) : NOT gate is called invertor circuit. (R) : NOT gate inverts the input signal.
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