Transistor, its characteristics and constants

 Transistor

It is a semi-conductor device which plays the same role as that played by a vaccum tube triode. 

     Construction. It consists of an 'N-type' or 'P-type' crystal sandwitched in between two other types of crystals. The central piece is known as base while the others on the two sides are known as emitter and collector.

Fig. 1.

The emitter, collector and the base play the same role as that played by filament, plate and the grid of a vaccum tube triode. The base of the transistor has to be very thin and low doped as compared to the emitter and collector. This is required to minimise the loss of charged carriers due to recombination. Two types of transistors, 'N-P-N' and 'P-N-P' transistors, are shown in [Fig. 2(i) and (ii)] respectively along with their schematic diagrams. 

           (Click on image to see it clearly) 

Fig. 2. Working of a transistor. 

     Biasing. The emitter base circuit of the transistor is always forward biased while the collector base circuit is always reverse biased. 

     Fig. 2(i) shows the circuit diagram for an 'N-P-N' transistor. The emitter base circuit is forward biased by connecting negative terminal of a source of e.m.f. 'Veb' to emitter and positive terminal to base (P-type). The collector base circuit is reverse biased by connecting positive terminal of a source of e.m.f. 'Vcb' with collector C and negative terminal to the base. Three microammeters are connected in the circuit to note emitter current 'Ie', collector current 'Ic', and base current 'Ib'. Circuit diagram of 'P-N-P' transistor on similar guidelines is shown in Fig. 2(ii).

Transistor action

     Transistor action is the term applied to the process of explaining the passage of electric current through a transistor. 

     Let us consider the circuit diagram of 'N-P-N' transistor [Fig. 2(i)]. With 'Veb' applied as shown in [Fig. 2(i)], electrons in the emitter section are repelled and injected into base. Since P-region (base) is not highly doped and is very thin, most of the electrons diffuse through it and reach the collector section. About 5% of the electrons are lost as charge carriers because of combination with the holes in 'P-region'. Remaining electrons which have already crossed over to the collector section are rapidly swept by the collector voltage. For each electron flowing out of the collector and entering the positive terminal of 'Vcb' which again moves towards the base and the process is repeated. Thus, current through the transistor is due to motion of electrons from emitter to collector while conduction current in the external circuit is also due to motion of electrons but from collector to emitter. The collector current 'Ic' is approximately 0.95 'Ie' where 'Ie' is the emitter current. 

     In case of a 'P-N-P' transistor biased as shown in [Fig. 2(ii)], positive terminal of 'Veb' repels the hole in emitter region. As these holes cross over to the base which is 'N-type', some holes (about 50%) get lost by capturing free electrons. Remaining holes cross over to the collector region and are attracted by the negative terminal of 'Vcb'. As each hole reaches the collector terminal, an electron is emitted from the negative terminal of 'Vcb' and neutralises the hole. For each hole that is lost, a covalent bond near the emitter electrode breaks down and the liberated electron leaves the emitter electrode amd enters the positive terminal of the emitter battery. The new hole that is formed moves towards the base and undergoes the same process as explained above. So, current flowing through a 'P-N-P' transistor takes place the conduction of holes from emitter to collector, while conduction current in the external circuit is carried by the electrons. 

     The emitter current 'Ie', collector current 'Ic', and base current 'Ib' (due to neutralisation of hole in base region) are shown by micro-ammeters, M₁, M₂, M₃ are connected in the circuits. It will be onserved that 

                  Ie = Ic + Ib

Modes of transistor operation

There are three electrodes of a transistor. One of these electrodes is held common or grounded. The term 'common' is used with that electrode which is common to both input and output circuits. The common electrode is generally earthed. Therefore, the word grounded is also used. According these are three modes for operation of transistor. The input and the output impedances of the transistor vary from one mode to the other. 

     (i) Common-base operations. In this type of operation base terminal is common to both input and output circuits. Transistor circuit and its equivalent vacuum tube circuits are shown in [Fig. 3(i) and (ii)] respectively. In this case, the input impedance is high. 

Fig. 3. Common base operation. 

    (ii) Common-emitter operation. In this type of operation the emitter forms the common electrode. A common non emitter arrangement for a transistor and vacuum tube are shown in [Fig. 4(i) and (ii)]. In this case, the input impedance is low while the output impedance is medium to high. 

Fig. 4. Common emitter operation. 

   (iii) Common-collector operation. The collector forms the common terminal in input and output circuits are shown in [Fig. 5 (i) and (ii)]. In this case, the input impedance is high and the output impedance is low. 

Fig. 5. Common-collector operation. 

     There can be a number of ways in which transistor characteristics can be plotted. Two very commonly used characteristics of a transistor are given below :

Transistor characteristics

Corresponding to the three types of connections for operation of transistor, we have a three types of transistor characteristics. 

     1. Common base connection (CB mode). The circuit diagram of CB mode of N-P-N transistor is shown in Fig. 6(i) while that of P-N-P transistor is shown in Fig. 6(ii). Three milliammeters A, B and C indicate emitter current 'Ie', base current 'Ib' and collector current 'Ic' respectively. Veb is the emitter base voltage while Vcb is the collector base voltage. It may be noted that emitter circuit is forward biased while collector circuit is reverse biased. Circuit between emitter and base is the input circuit while that between collector and base is the output circuit. 

Fig. 6. Circuit diagram. 

     Following characteristics can be drawn from these connections. 

     (a) Input characteristics. Input characteristics of a transistor, is common base operation is a graph between emitter current (Ie) and emitter-base voltage (Veb) at constant collector-base voltage (Vcb). 

     Input characteristics for N-P-N and P-N-P transistors in common base mode are shown in Fig. 7(i) and (ii), respectively. 

     Input characteristics can be yield the value of input resistance of the transistor. 

     Input resistance (ri) of a transistor in common base operation is defined as the ratio between change in emitter-base voltage (∆Veb) to the change in emitter current (∆Ie) at constant collector-base voltage (Vcb). 

            ri = [∆Veb/∆Ie]Vcb = Constant

Unit of ri is 'ohm'. 

Fig. 7. Input characteristics. 

    (b) Output characteristics. Output characteristics of a transistor in common base operation is a graph between collector-base (Vcb) voltage and the collector current (Ic) at constant emitter current (Ie). 

     Output characteristics for N-P-N transistor and P-N-P transistor in common base operation are shown in Fig. 8(i) and (ii), respectively. 

Fig. 8. Output characteristics (CB mode). 

     Output characteristics can be yield the value of output resistance (r0) of the transistor. 

     Output resistance of a transistor in common base operation is defined as the ratio between change in collector-base (∆Vcb)  voltage to the change in collector current (∆Ic) at constant emitter current (Ie). 

                r0 = [∆Vcb/∆Ic]Ie = Constant

Unit of r0 is 'ohm'. 

     (c) Transfer characteristics. It is a graph between collector current (Ic) and emitter current (Ie) keeping collector-base (Vcb) constant. 

Fig. 9. Transfer characteristics. 

     Transfer characteristics is shown in Fig. 9. This characteristics is very useful in determining the effect of change in current of input circuit (due to signal) in the output. 

     2. Common emitter connection. The circuit diagrams for CE connection of N-P-N transistor and P-N-P transistor are shown in Fig. 10 (i) and (ii), respectively. In the case, the emitter is common to both input and output circuits. Circuit between base and emitter is the input circuit while that between collector and emitter is the output circuit. 

Fig. 10. Circuit diagram. 

     Following characteristics can be drawn from these connections. 

(a) Input characteristics

     Input characteristics of a transistor in common emitter operation in the graph between emitter base voltage (Veb) and base current (Ib) at a constant, collector emitter (Vce) voltage. 

     Input characteristics of N-P-N transistor and P-N-P transistor in common emitter operation are shown in Fig. 11 (i) and (ii), respectively. 

Fig. 11. Input characteristics (CE mode). 

     We can calculate the value of input resistance (ri) from the input characteristics. 

     Input resistance of a transistor in common emitter operation is defined as the ratio between change in emitter-base (∆Veb) voltage to change in base current (∆Ib) at constant collector-emitter (Vce) voltage. 

                ri = [∆Veb/∆Ib]Vce = Constant

Unit of ri is 'ohm'. 

(b) Output characteristics

     Output characteristics of a transistor in common emitter operation is a graph between collector-emitter (Vce) voltage and collector current (Ic) keeping base current (Ib) constant. 

     Output characteristics of N-P-N transistor and P-N-P transistor in common emitter operation are shown in Fig. 12 (i) and (ii), respectively. 

     We can calculate the value of output resistance (r0) from output characteristics. 

Fig. 12. Output characteristics (CE mode). 

     Output resistance of transistor in common emitter operation is defined as the ratio between change in collector emitter (∆Vce) voltage to the change in collector current (∆Ic) at constant base current (Ib). 

                r0 = [∆Vce/∆Ic]Ib = Constant

Unit of r0 is 'ohm'. 

(C) Transfer characteristics

     It is a graph between collector current (Ic) and base current (Ib) at constant collector emitter voltage, Vce . 

          It is a straight line as shown in Fig. 13.

Fig. 13. Transfer characteristics. 

3. Common collector connection : (CC mode) 

     The circuit diagrams of CC mode of N-P-N and P-N-P transistors in common collector mode of connections are shown Fig. 14 (i) and (ii), respectively. 

     Collector base circuit forms the input circuit while the emitter-collector circuit forms the output circuit. Generally, its input characteristics are not drawn because of low voltage and power gain in this mode of connection. 

Fig. 14. Common collector mode. 

Transfer characteristics

     Transfer characteristics of a transistor in common collector mode of connections is a graph between base current (Ib) and emitter current Ie at constant emitter collector (Vce) voltage. 

     The transfer characteristics is shown in Fig. 15. 

Fig. 15. Transfer characteristics. 

Transistor constants

Depending upon the mode of operations the performance of a transistor is specified in terms of some constants known as transistor constants. 

Important notes 

1. The base region of a transistor is always narrow. 
2. The base region is always low doped. 
3. Input circuit of a transistor is always forward biased while the output circuit is always reverse biased. 

Key words

1. Transistor. A semi-conductor device having one type of semi-conductor sandwiched between two other types of semi-conductor. 

2. Transistor action. Process of conduction of a transistor. 

3. Transistor region. A small region having a potential gradient due to contact potential. 

Key Formulae

Transistor constants

   

     (a) Current amplification factor or forward current transfer ratio (∝). 

   

     (i) ∝ = [∆Ic/∆Ie]Vcb = constt. = [Ic/Ie]Vcb = constt. 

                [For common base operation]

(ii) β = [∆Ic/∆Ib]Vcb = constt. = [Ic/Ib]Vcb = constt. 

               [For common emitter operation]

     (b) Current transfer ratio (γ) 

γ = [∆Ie/∆Ib]Vce = constt. = [Ie/Ib]Vce =constt.

                [For common collector operation]

(c) Relation between transistor constants

(i) β terms of ∝ : β = ∝/1 - ∝

(ii) ∝ in terms of β : ∝ = β/1 + β

(iii) γ in terms of ∝ : γ = 1/1 - ∝

(iv) γ in terms of β : γ = 1 + β

Semi-conductor, its types and Junction diodes

What is semiconductor ? 

The substance whose conductivity lies between conductor and insulator is known as semi-conductor. 

Examples - Silicon (S), Germanium (G) are known as semi-conductors. 

Semi-conductor is covalent bond. 

Semi-conductors

In case of solids the individual atoms are confined to single spot in the ordered array, called a crystal lattice. Most of the electrons stick tightly to their atoms and do not wander through the lattice. They are called bound electrons. There is a certain number of electrons which are free to move about. These are called free electrons. Free electrons belong to the outmost orbits. It is the number of free electrons which determine the resistivity of the orbits. 

(1) Substances having low resistivity are called good conductors, e.g., copper, silver, gold, etc. 

(2) Substances having a high resistivity are called insulators, e.g., quartz, mica, sulphur, etc. 

(3) The resistivity of a good conductor is as low as 10-7 or 10-8 ohm metres compared to values as high as 106 ohm metres for an insulator like quartz. A large number of solids have resistivity lying in between this range. They are called semi-conductors. 

     Number of free electrons in case of a semi-conductor is small and more only when it is subjected to strong electric field of hundred of thousands of volts per metre. Typical examples of semi-conductors qre silicon and germanium. 

     At temperatures close to absolute zero all the electrons are tightly bound to their atoms making their resistivity very large. Atomic number of 'Ge' is 32. The distribution of electrons in various orbits is 2, 8, 18, 4. Thus, each germanium atom has four electrons in its outmost orbit. Every atom of germanium shares one electron each with four neighbouring atoms and thus they are bound to each other by covalent bond (Fig. 1). No electrons being free to move, resi of 'Ge' crystal is very large at low temperatures. 

Fig. 1. Structure of Ge crystal. 

     Semi-conductors are classified into following two categories.

1. Intrinsic semi-conductors
2. Extrinsic semi-conductors

1. Intrinsic semi-conductors. A semi-conductor (say G) in its pure form, is an insulator since all its electrons are occupied with each other in covalent bonds. Such a semi-conductor is called intrinsic semi-conductor. At absolute zero temperature it has its valence band completely full while its conduction band is vacant. Application of electric field does not increase the energy of electrons to move from one place to other. Therefore, it behaves like an insulator. Above absolute zero, say at room temperature, some of the covalent bonds get broken due to thermal agitation. As a result of this, an electron is set free. This free electron has acquired a small amount of energy. Since the gap between conduction band and valence band in case of semi-conductor is small, this free electron can be classified as a one belonging to conduction band and becomes capable of responding to the applied electric field. The place from where this electron was detached, acquires a deficiency of electron and is equivalent to a carrier carrying '+e' charge. This is named as hole. In an intrinsic semi-conductor, the number of free electrons and holes are equal to each other. If an electric field is applied from left to right direction, free electrons move to the left while the holes move towards right. Net current flowing through the semi-conductor will be the sum total currents due to motion of both the charge carriers, called minority charge carriers.                                                          
2. Extrinsic semi-conductors. If some specific impurity is added to the semi-conductor, it is found that its conductivity increases million times. Additional of impurity is called 'doping' and the doped semi-conductor is called extrinsic semi-conductor. The impurity to be added, may be pentavalent or trivalent so that it releases one free electron or a hole per atom of added impurity. These externally added electrons or holes are responsible for the immense increase of conductivity. These charge carriers are called majority charge carriers. 

Fig. 2. Creation of electron-hole pair. 

P-type or N-type semi-conductors (Extrinsic) 

Under normal circumstances that conductivity of a germanium crystal is very small. This can be substantially increasing if some external element of suitable atomic number is added to it. 

     The process of increasing the conductivity of semiconductor by addition of a suitable impurity in a small amount is called doping. 

     The crystals are doped with impurities either having five valence electrons or having three Valence Electrons. Accordingly there are two types of doped  semiconductors such as charge N-type and P- type respectively. These are called extrinsic semi-conductors. 

 

     (i) N-type semi-conductor. To obtain a N-type semi-conductor, germanium crystal is doped with arsenic (Z = 33). The distribution of electrons in the orbits of 'As' is 2, 8, 18, 5.

     Each atom of arsenic enters into covalent bonds by sharing one electron with four neighbouring germanium atoms [Fig. 3(i)]. In this process it exhausts four of its five valence electrons. One electron is left unattached and becomes a free electron. These free electrons conduct electricity. With arsenic present in quantities one to million, there are about 10¹⁷ arsenic atoms and 10¹⁷ free electrons per cubic centimetre. In a good conductor like copper there are approximately 10²³ free electrons per cubic centimetre. 

 

     This can also explained from bond theory. The position of conduction band, valence band of germanium along with the top most band of arsenic is shown in [Fig. 3(ii)]. The top most band of arsenic lies in the forbidden band gap of germanium and also very close to the conduction bands of a germanium. The gap between them is very small and of the order of 0.01 eV. If an extra energy of 0.01 eV is given to the electron it  jumps to the conduction band and a conducts electricity. 

           (Click on image to see it clearly) 

Fig. 3. N-type crystal. 

     Since Impurity (arsenic) atom donates electrons to the material, it is called donor impurity and the level in which the additional electron occupy is called donor level. Semi-conductors doped with donor type impurity are known as N-type semi-conductors. 

    (ii) P-type semi-conductor. A P-type semi-conductor can be obtained by doping germanium crystal with an impurity which possesses 3 valence electrons e.g., indium (Z = 49). The distribution of electrons in various orbits of 'In' is 2, 8, 18, 18, 3. Each indium atom enters into covalent bond with four neighbouring germanium atoms [Fig. 4(i)]. In this process it not only exhausts all these valence electrons, but borrows one electron from one of the nearest germanium atoms. By giving one electron to 'In', one germanium atom is left behind with the deficiency of one electron which is equivalent to a free positive charge and hence it is called a hole. 

     The band structure of germanium when doped with radium is given in [Fig. 4(ii)]. The topmost level of indium lies in between the forbidden gap of germanium and also very near to the valence band of germanium. The band gap between the band of indium and valence band of germanium is very small i.e., nearly 0.01 eV. Thus, Even room temperature from electrons from valence band of a germanium are excited to the band of indium. This completes the indium level creating a vacancy of electron (hole) in the valence band. This hole (positive charge) contributes to the conductivity of the material. 

               (Click on image to see it clearly) 

Fig. 4. P-type crystal. 

     The impurity (indium) electrons from the material and hence is called the acceptor atom and the corresponding level is called acceptor level. The semi-conductors doped with acceptor impurities are called P-type semi-conductors. 

     Negativity charged electrons, in case of N-type semi-conductors and positively charged holes, in case of P-type semi-conductors are responsible for conductivity of the semi-conductor. They are called majority charge carriers. When a semi-conductor is doped one to million, the number of majority charge carriers to the minority charge carriers is 10,000 to 1.

     It may be clearly kept in mind that both N-type and P-type semi-conductors are electrically neutral. 

Electrical conductivity of semi-conductors

In case of breaking of covalent bond in an intrinsic semi-conductor, a pair of electron-hole is created. A hole is theoretical concept developed to explain the shortage of an electron. It can be treated to be a particle having same mass and charge as that of electron with a difference that the nature of charge on it is positive. When an electron gets elevated from valence band to conduction band, it again results in production of electron-hole pair. 

     When a potential difference V is applied to the two ends of a semi-conductor it produces an electric field inside it. As a result of this, the electrons and holes drift in opposite directions, thus contributing to the total current in the circuit. Holes move only within the semi-conductor while the current outside it is due to motion of electrons only. 

     Let ie and ih be the electric current due to motion of electrons and holes respectively, then the total current i is given by

                     i = ie + ih

    

      Let  and  be electron density and hole density respectively, 

ie = neAeve        and      ih = nhAevh

 

     Here, A is the cross-sectional area of the semi-conductor while ve and vh are the drift velocities of electron and holes, respectively, 

i = neAeve + nhAevh

or i = Ae (neve + nhvh) ... (1)

But                     i = V/R = V/ ρ. l/A = VA/ ρl

where ρ is the resistivity and 'l' is the length of semi-conductor. 

     If 'E' is the strength of electric field inside the semi-conductor, 

                       V = El

∴                      i = ElA/ρl

or                    i = EA/ρ                                ... (2) 

     From equation (1) and (2), 

              EA = Ae (neve + nhvh)

∴           1/ρ = e [ne . ve/E + nh . vh/E]             ... (3) 

     Electrical mobility of a charge carrier is defined as the drift velocity acquired by it in an electric field of unit strength. It is denoted by μ. 

     If 'μe' and 'μh' are the electric mobilities of electrons and holes respectively, 

             μe = ve/E ,  μh = vh/E          

     Making  these substitutions in equation (3), 

                          1/ρ = e [neμe + nhμh]

     Since           1/ρ = σ (conductivity) 

     ∴                      σ = e [neμe + nhμh]

     Thus,  the conductivity 'σ' of a semi-conductor depends on μe and μh in addition to its dependence on ne  and nh. 

     It can be verified experimentally that the mobility of charge carriers do not very much with a change in temperature. So variation of 'σ' with a change in temperature is mainly due to the variation of  ne  and nh. 

PN junction diode/Semi-conductor diode/Crystal diode

It is an integrated in which semi-conductors of 'P-type' and 'N-type' are brought into contact [Fig. 5(i)]. In actual practice it is obtained by 'doping' the two halves of a germanium crystal by an accepter and a doner during the growth of the crystal. As 'N-type' and 'P-type' crystals lie close to each other, a could of free electrons in 'N-type crystal' diffuses across the boundary to the right. As a result of this, 'N crystal' (which was previously neutral) acquires a positive potential. The electrons on reaching 'P-type' crystal neutralise some of the holes. So the 'P-type' crystal now contains a lesser number if holes and hence acquires a positive potential. This potential difference between 'N-type' and 'P-type' crystal is called contact potential and is shown in [Fig. 5(ii)]. Contact potential opposes further transference of electrons and an equilibrium is established.

 

Fig. 5. Junction diode. 

     It may be noted that the rate of change of potential in the region around junction (known as transition region) is very large. This gives rise to a large electric field 'E'. 

     For a typical 'P-N' junction the transition region is about 6 × 10-15  mm thick. The contact potential varies from a small fraction of a volt of 1 V Or 2 V depending upon the materials in contact. These values indicate an electric field 'E' of several million volts per metre. This is called diffusion field 'E'. 

Biasing a PN junction - junction - diode characteristics

There are two ways in which a voltage can be applied to a junction diode. 

      (i) Forword biasing. In this type of biasing positive terminal and negative terminal of the source of e.m.f. are connected to 'P-type' and 'N-type' crystal respectively. In this case applied potential 'Va' is opposite to contact potential 'Vc' (Fig. 6).

Fig. 6. Forward biasing of a junction diode. 

     The electrons which had diffused from left to right and had created an equilibrium get pulled to get towards right due to the positive potential of B. Similarly, holes which are diffused to the left get pulled towards left due to the negative potential of 'A'. This transference of charges constitutes an electric current through the circuit. 

    Due to forward biasing -

1. Width of depletion layer decreases
2. Resistance decreases
3. Current conduction increases. 

    (ii) Reverse biasing. In this type of biasing positive and negative terminals of the source of e.m.f. are connected to 'N-type' and 'P-type' crystals respectively (Fig. 7). In this case the applied potential 'Va' and the contact potential 'Vc' are in same direction. As a result of this the cause due to which equilibrium was established is further strengthened. No current flows through the circuit. However, a small current may flow through the circuit due to an accidental breakage of a covalent bond. 

Fig. 7. Reverse biasing of a junction diode. 

     Due to reverse biasing

1. Width of depletion region increases
2. Resistance increases 
3. Current conduction decreases

     Variation of the current through the circuit with a change in bias voltage is shown in (Fig. 8). The curve is called junction diode characteristics curve. 'F' corresponds to the forward biased junction diode while the curve 'R' is for reverse biased junction diode. It is clear from the diagram that a small variation in applied voltage results in an appreciable change in current provided the junction diode is forward by biased. There is no variation in current due to variation of applied voltage, if it is reverse biased. In other words, a forward biased junction diode is a low resistance instrument while a reverse biased junction diode is high resistance instrument. 

Fig. 8. Junction diode characteristics. 

Some other types of junction diodes

1. Zener diode

The characteristics of a junction diode [Fig. 9(ii)] indicates that reverse biased are given a proper high voltage a breakdown occurs and a current flows in negative direction. The voltage at which this happens is called "Zener breakdown voltage". The mechanism of breakdown can be to one of the following two ways. 

     (i) Zener breakdown. The potential difference across the reverse biased junction diode may be just sufficient to tear off the electron away from the atom, thus creating an electron-hole pair. This results in an increase in the number of minority charge carriers which in turn results in an increase in current due to a variation in potential difference. This process is a reversible process. On decreasing the potential difference, the current falls back to similar value. 

    (ii) Avalanche breakdown. When the potential difference of a reverse biased junction diode is very high, the electric field is high enough to provide sufficient kinetic energy to a charge carrier which enables it to cause ionisation due to collision against an immobile atom. The new pair of electron-hole, thus created, also gets accelerated and becomes capable of producing ionisation. This multiplication takes place and soon an avalanche of charge carriers is produced causing a flow of large current in the opposite direction. 

     When a junction diode operates beyond Zener voltage, the characteristics indicate that the curve is nearly parallel to I-axis. This means whatever may be the current through the diode, the potential difference across it remains constant. This means a Zener diode can be made to act as a source of constant voltage. The symbolic representation of a Zener diode is shown in [Fig. 9(i)] while the circuit diagram indicating that it acts as a source of constant voltage is shown in [Fig. 9(i)].

Fig. 9. Zener diode. 

     Since Zener diode and the load  resistance RL are connected in parallel with each other, potential difference across them is same. Let it be 'V0'. The main current I is divided and load, therefore, 

                           I = IZ  +  IL   ... (5)

     

     Voltage equation of the first mesh can be written as 

        

                        V0 = V - IR                               ... (6)

 Also                V =  IL RL ... (7)

    

      Case (i) V remaining constant and RL changing 

     Since V is a constant quantity,          

                      σV = 0

     Since V0 is also a constant quantity, 

 

                    σV0 = 0

     

     Differentiating equation (6),  

          

                    σV0  = σV - RσI

     Substituting for σV0 and σV in equation (6), we get 0 = 0 - RσI

where σI is the variation in net current due to a variation in RL. 

     ∴                                               σI = 0

     From equation (5), we get  σI = σIZ + σIL

     Substituting                           σI = 0

                                            σIZ + σIL = 0

                                                     σIZ = - σIL

     If load resistance RL is changed without changing V, the current flowing through Zener diode and that through RL adjust themselves in such a way that the net current in the circuit remains unaffected. 

     Cast (ii) Changing V keeping RL fixed 

     Since σV0 = 0 always, using equations (6) and (7), we get

             0 = σV - RσI       or      σV = RσI

             0 = RL σIL                     (RL = constant) 

     From equation (5), we get     σI = σIL + σIZ

     Putting σI = 0, we get              σI = σIZ 

     

     Thus, if the supply voltage is changed keeping load resistance constant, the change in current through Zener diode is same as the change in total current, keeping current through the load resistance constant. 

Zener dynamic resistance (rZ) 

     D.C. resistance of a zener diode is defined as the inverse of the slope of junction diode characteristics. 

                         rZ = σV0 / σIZ         

Here             σV0 = 0,   rZ = 0

     Practically rZ has a finite but very small value. Since V0 is contact while IZ may vary, rZ is not a constant quantity. 

2. Photo Diode

      It consists of a reverse biased junction diode below the breakdown voltage. A beam of light is made to fall on the junction. Energy from photon tears the electron away from the atom thus producing additional electron-hole pair. This produces an electric current thus causing the diode to conduct. [Fig. 10(i) and (ii)] gives the symbolic representation and working of photo diode. 

Fig. 10. Photo diode. 

     It has been found that the current through the circuit increases almost linearly with the increase in the flux of light. This type of diode has found extensive use in light operated switches and reading of computers, punched cards, etc. 

3. Light Emitted Diode (LED) 

   

     We know that some energy is required to pull the electron away from the atom. Thus, reaction of electron-hole pair is an energy absorbing process. Conversely speaking, combination of an electron and a hole should be an energy emitted process. If the emitted radiation lies in visible region, the diode exhibiting this phenomenon is called light emitted diode (LED). It's symbolic representation is given in [Fig. 11(i)]. It consists of a forward biased junction diode connected in series with a variable resistance [Fig. 11(ii)]. As the diode conducts, combination of electron amd hole results in production of light. Such diode find their use in producing signal lamps. 

Fig. 11. Light emitting diode. 

4. Solar Cell

     It is a device which converts light directly into electric energy of the two parts (p and n  type) of a junction diode one is made thin. As a result of this, appreciable absorption of light does not take place before reaching the junction. The thinner region acts as an emitter while the other acts as base. [Fig. 12(i) and (ii)] give the symbolic representation and working of solar cell respectively. 

Fig. 12. Solar cell. 

     As light is incident on the junction diode, additional minority charge carriers are produced in both regions since the two regions are of unequal width, a current due to unequal production of minority carriers is produced. In an unbiased junction diode net current is zero. Now this is possible only if a corresponding current, in opposite direction due to majority charge carriers is set up. This reduces the barrier voltage. In case the external circuit is closed through a resistance [Fig. 12(ii)] a current will be flowing through external resistance. 

     Solar cells are being extensively used in satellites and spacecrafts as the source of energy. 

Rectification

Certain electrical machines like X-ray tube, discharge tune etc. require a very high voltage and uni-directional current while the current available through mains is alternating in nature. To obtain a direct current from an a.c. supply we use some electronic circuit called a rectifier, and the process is called rectification. 

     Rectification is the process by which we can obtain a Uni-directional current from an a.c. supply. 

     Process of rectification can be classified into two categories:

     (a) Half-wave rectifier. It is that type of rectifier in which the output current flows corresponding to have the cycle of input a.c. In this case the current bill be intermittent and will be continuously changing in magnitude. 

    (b) Full-wave rectifier. It is that type of rectifier in which the output current flows for full cycle of input a.c. In this case there will be no gap in between two consecutive impulses of output current while the current will continuously change in magnitude. 

Junction Diode as a Half-wave Rectifier

A Junction diode can also be used to convert alternating current into direct current. 

     Circuit diagram for a junction diode acting as a half-wave rectifier is shown in  [Fig. 13(i)]. Source of a.c. input, a junction diode and load resistance RL are, all connected in series with each other. 

Fig. 13. Junction diode as a rectifier. 

     During positive half of input a.c. junction diode becomes forward biased and hence conducts, while during the negative half, it is reverse biased, cutting the current flowing through the circuit to zero. Variation of input and output current with time are shown in [Fig. 13(ii)]. 

     Mathematical expression for output current and voltage

     Voltage V applied across points A and B is given by 

                          V = Vm  sin ωt

     Here Vm is the peak value of the alternating voltage and ω is the frequency of a.c.

     The peak value of current is given as 

                            Im = Vm/R                          ... (8) 

     Here, R = total resistance in the circuit. 

                            R = RS + RD + RL

where RS is resistance of the secondary of the transformer, RD is the resistance of the diode and RL is load resistance. RD is nearly zero in forward bias and is infinite in case of reverse bias. 

      From the equation (5), we get

∴           Im = Vm/RL          (During forward bias) 

and      Im = 0                 (During reverse bias) 

     Forward bias means positive half of cycle i.e., 0 ≤ ωt ≤ π. Reverse bias means negative half if cycle i.e., π ≤ ωt ≤ 2π. Output voltage V0 is given by, 

            

         V0 = I RL

           I = output current = Im sin ωt

           I = Vm/RL  sin ωt   (During forward bias) 

and    I = 0                      (During reverse bias) 

Therefore, V0 = Vm sin ωt (During forward bias) 

and     V0 = 0                   (During reverse bias) 

     We can see that the output current is unidirectional. 

Full Wave Rectifier (center tap rectifier or two diode rectifier) 

Full wave rectifier make use of two diodes to ensure better rectification than the half-wave  rectifier. The circuit diagram of a full wave rectifier is shown in [Fig. 14(i)]. The two diodes are connected to terminals A and B of centre tapped secondary of the transformer. The load is connected to the central terminal of the secondary as shown in the diagram. 

     Suppose, during the positive half cycle of the input, the terminal A of the secondary becomes positive with respect to B. So, the diode D₁ will conduct and current will flow through the load as shown by the arrow in [Fig. 14(i)]. During negative half cycle of input, the terminal al B will become positive with respect to A. Diode D₂ will conduct and the current flow in the same direction as before. So, the output is d.c. since the current flows for both the cycles of input [Fig. 14(ii)] whereas in case of half-wave rectifier, the current was flowing only during positive half cycle only. So, the efficiency of this rectifier will, obviously, ne more than that of half-wave rectifier. 

     Output voltage and current. Let the voltage across points A and B of the secondary be given by

                        Im = Vm/R                             .... (9) 

where R is total resistance in the circuit. 

                        R = RS + RD + RL   

Fig. 14. Full-wave rectifier. 

     Here RS is resistance of transformer secondary, RD is diode resistance and RL is load resistance. RD is equal to the parallel combination of two diode resistances. When one diode is reverse biased, the other is forward biased. So, RD is always equal to diode is forward bias resistance RF. 

    ∴                 R = RS + RF + RL 

      RS and RF can be neglected comparison to RL . 

From equation (9), we get

                        Im = Vm/RL

               

      So, instantaneous current through the load is given as follows :

                  I = Im sin ωt

or              I = Vm/RL sin ωt. 

Key Formulae

1. Electrical conductivity of a semi-conductor

                 σ = e [neμe + nhμh] 

2. Half wave rectifier

     

     (a) Output current

           I = Vm/RL  sin ωt   (During forward bias) 

           I = 0                      (During reverse bias)  

     (b) Output voltage

            V0 = Vm sin ωt (During forward bias) 

            V0 = 0                   (During reverse bias)

     (c) d.c. value of a.c. = Idc = Im /π

     (d) r.m.s. value of a.c. = Irms  = Im/2 

     (e) Efficiency = η = 4/π² × 1/RF/RL +1 × 100

     (f) Ripple factor = γ = 1.21

3. Full wave rectifier

     (a) Output current = I = Vm/RL sin ωt

     (b) Output voltage = V = Vm sin ωt

     (c) d.c. value of current = Idc = 2Im /π

     (d) r.m.s value of current = Irms  = Im/√2

     (e) Efficiency = η = 8/π² × 1/RF/RL +1 × 100

     (f) Ripple factor = γ = 0.482

Key Words

1. Biasing. Applying d.c. source to semi-conductor device. 

2. Biasing (forward). Mode of biasing which makes a semi-conductor device low resistance device. 

3. Biasing (reverse). Mode of biasing which makes a semi-conductor device high resistance device. 

4. Charge carriers (majority). Charge carriers liberated as a result of doping. 

5. Charge carriers (minority). Charge carriers liberated as an accidental breakage of bond between atoms. 

6. Doping. Addition of a very small amount of impurity from outside to increase the conductivity of semi-conductor. 

7. Hole. A charge carrier equivalent to an electron carrying +e charge. 

8. Junction diode. A combination of P-type and N-type semi-conductor. 

9. Light emitting diode (LED). Junction diode capable of emitted light in visible region. 

10. N-type semi-conductor. A semi-conductor doped with pentavalent atom to have electrons as majority charge carriers. 

11. P-type semi-conductor. A semi-conductor doped with a trivalent substance so as to liberate holes as majority charge carriers. 

12. Photo diode. Junction diode which conducts due to incidence of light. 

13. Solar cell. Diode circuit which converts solar energy into electricity. 

14. Rectifier. Device which converts a.c. into d.c.

15. Rectifier (half wave). Rectifier which conducts for one half cycle of a.c. only. 

16. Rectifier (full wave). Rectifier which conducts for both the halves of a.c. input. 

17. Semi-conductor. Substance having conductivity in between that of a conductor and an insulator. 

Important Notes

1. N-type and P-type semi-conductors should not be confused with being negatively charged or positively charged. Both of them are neutral in character. They are so named because the charge carriers in N-type are negatively charged particles (electrons) and in P-type positively charged particles (holes).                                             
2. A hole is a deficiency of electron and is equivalent to a free +e charge. This is also capable of free motion under the effect of a potential difference.                 
3. Mobility of electrons and holes are different from each other.