Semiconductors.pdf

Semiconductors 2012-13

Department of physics, BVB CET,HUBLI. Page 1

Introduction: In our day today life, we are living with modern electronic equipments such as Laptops, mobiles, LCD/LED Television and what not?. No field is free of electronics Ex: Automobile industry is today more of electronics and less of ……..Communication is the revolution that has happened, which has changed our life. It is all because of development in Electronics i.e semiconductor technology. This is because semiconductor technology has helped in having devices which have less size, require less power and reduction in cost of manufacturing in all areas of electronics and communication. Semiconductors, metals and insulators are required for fabricating electronic devices, but the crucial role is played by semiconductors.

Classification of Solids: Solids are classified as; Conductors, Insulators and Semiconductors. Important difference between them is their resistance to current flow, defined in terms of the resistivity of the material. Conductors, such as copper, aluminium and gold, have a resistivity in the order of 10-8 m, and are useful for low resistance wiring and interconnections in electronic circuits. Insulators, such as glass, plastic etc have the resistivity in the order of 1016 m and are used for isolation purposes in electrical devices. Between these two limits the resistivity of the semiconductor material lies; the pure elemental semiconductors, silicon (Si) and germanium (Ge) and compound the most important of which is gallium arsenide (GaAs). Energy bands in solids: Why band structure in solids? An isolated atom has a series of well defined and discrete allowed energy levels/orbits E1, E2, E3…..etc,. The other values of energy or intermediate levels/orbits are forbidden. The orbits to which electrons are confined are called as electron shells and are named as K, L, M…..so on. A shell is characterized by the principle quantum number ‘n’ accommodates a maximum of 2n2 electrons. The value of n increases as the distance of shell from the nucleus increases. Thus, a K shell with n = 1 accommodates 2 electrons; an L-shell with n=2 takes 8 electrons and so on. These shells are built from subshells (s,p,d……etc.) which accommodate electrons of the same value of orbital quantum number ‘l’. Thus electrons that share a certain value of ‘l’ in a shell are said to occupy the same subshell. The number of subshell in a shell is equal to the value of ‘n’. Thus, a K-shell has only 1subshell, L-shell has 2subshells and so on. When atomic spacing is large between the atoms, energy levels of such atoms are not affected by other distant atoms. But when such atoms brought close to each other then there is a significant changes in their energy levels. For a solid containing N number of atoms having N number of electrons then there will be N allowed energy levels. And distribution of electrons among the energy levels fallowed by Pauli’s exclusion principle (no more than two electrons in a given interacting system may have the same quantum state). Thus when N number of atoms are brought close to each other, electrons which have almost same energy will start accumulating one side and they form bands. For example let us consider an atom of lithium in vaporized state. A lithium atom has 3 electrons, two of which occupy the K-



shell, where as the third one occupies the first subshell 2s of the L-shell as showed in the energy level diagram.

Fig (1)

As explained above, 2s subshell can have maximum 2 electrons, but because of only one electron, 2s subshell is half filled and of course subshell 2p is unoccupied. And in solid lithium, 1s and 2s band have N levels each. The 1s band is completely filled as 2N electrons occupy the band and 2s band is half filled. And all higher energy bands are unoccupied because Li atom has no electrons to fill them. Based on the band theory of solids, solids are classified into three types;

Fig (2)

1. Conductors: In conductors, the conduction band is partially filled and the valence band is completely filled, In conductors always fever number of electrons in the conduction band. Hence conductivity of the metals is very high Ex: silver, gold, copper etc .In the absence of electric field there are electrons travelling in random directions with different velocities. When an electric field is applied to such electrons a slight imbalance develops and electrons flow to the direction of the applied electric field.

2. Semiconductors: In semiconductors, the energy band gap ‘Eg’ between conduction band and the valence band is about 2eV, and resistivity between 108 m to 10-3 m Ex: Silicon



(1.1eV), Germanium (0.7eV). Therefore at OK temperature the conduction band is empty and the valence band is completely filled by the electrons. Hence there is no conduction at T=0K. But at room temperature due to thermal energy, few electrons acquire sufficient energy and get excited to the conduction band from the valence band.

3. Insulators: In insulators, the energy band gap ‘Eg’ between conduction band and the valence band is too large of the order of 6 eV. Ex: Diamond, plastic etc. If we supply very high temperatures (high enough to approach the melting point), only few electrons acquire enough thermal energy to be raised to the conduction band from the valence band. Hence conductivity is very low in case of insulators.

Importance of Semiconductors: Semiconductors have Engineering importance from the fact that they can be conductors as well as insulators. Semiconductors are especially important because varying conditions like temperature and impurity content can easily alter their conductivity. The combination of different semiconductor types together generates devices with special electrical properties, which allow control of electrical signals. Semiconductors are employed in the manufacture of electronic devices and integrated circuits. Imagine life without electronic devices. There would be no radios, no TV's, no computers, no video games, and poor medical diagnostic equipment. Direct and Indirect band gap semiconductors: While making semiconductor devices, material selection is very important. Because in some semiconductors due to the recombination of electrons and holes energy dissipated in the form of heat and in some in the form of light. There are two types of semiconductors, direct and indirect band gap semiconductors. If a plot of energy E v/s momentum k(ћk) is made, typical curves are obtained for different semiconductors as shown in the figure (3) (4). In both figures, lower curves represent variation of E with k for holes in valence band and upper curves represent the same variation for electrons in the conduction band. Direct band gap semiconductors: In figure (3), the minima of the conduction band occur at the same value of k as the maxima of the valence band. A direct optical transition is drawn vertically with no significant change of k, because of the absorbed has a very small wave vector. The threshold frequency v for absorption by the direct transition determines the energy gap Eg=h. Examples GaAs, InGa.etc. Fig(3)



Indirect band gap semiconductors: The indirect transition in figure (4) involves both a photon and a phonon because the minima of the conduction band and the maxima of the valence band are located at different momentum positions, between which there exist a high probability of transition. So here conservation of momentum and energy is very much essential. To excite the electron from the valence band to conduction band by absorbing photon here phonon assistance is must. k=k+q Eg=h+h for phonon absorption k=k-q Eg=h-h for phonon emission. Where; k-initial wave vector of electron Fig(4) k-final wave vector of electron q-phonon wave vector h-photon energy h-phonon energy At higher temperatures phonons are already present; if a phonon is absorbed along with a photon the threshold energy is Eg= h+ h In these semiconductors generally release energy as heat. Ex: Silicon, Germanium, AlAs etc. Intrinsic and Extrinsic Semiconductors Intrinsic Semiconductors: Pure (no impurity or defect) semiconductor crystals are known as intrinsic semiconductors. Ex: Pure Germanium and Silicon (Which have forbidden energy gap of 0.7 eV and 1.1 eV respectively)

Fig (5) When T= 0K



Fig (6) When T> 0K In pure silicon at T = 0K, the bonding of Si atoms are linked together by covalent bonds with surrounding atoms and no free electrons available in the conduction band. Hence at 0K temperatures valence band is completely filled and conduction band is empty (fig5). As temperature rises, T > 0K, valence electrons break there covalent bonds and get excited to conduction band leaving an empty space in the valence band (Hole). Hence as temperature increases the density of hole-electron pair also increases and hence conductivity of the semiconductor increases (fig6). Electrical Conductivity and mobility in semiconductors: Electrical conductivity is of the primary importance and interest in semiconductors. Both electrons and holes constitute to electrical current in semiconductors.

Fig. (7)

At thermal equilibrium, the electrons and holes are uniformly distributed in the semiconductor and in the absence of an external stimulus average velocity of electrons and holes is zero and no current flows. The thermal equilibrium can be varied by an external agent (Electric field, temperature and concentration gradients). Drift current: Under the action of electric field, the charge carriers in the semiconductor drift and produce drift current. In case of semiconductors, current flow is due to the movement of electrons and holes in the opposite direction (Fig.7).When an electrical field is applied, electrons drift opposite to the field,



carry a net current Ie, conductivity e and holes drift in the same direction as that of the applied field, carry current Ih and conductivity h .

Idrift = Ie + Ih = enveA + epvhA-----------(1) where n=electron density/m3

p=hole density (per m3) ve=electron drift velocity (ms-1) vh=hole drift velocity (ms-1) A=semiconductor cross-section area (m2)

Now ve = µeE and vh = µhE Then I = e (nµe + pµh) EA I/A = e (nµe + pµh) E Jdrift = e (nµe + pµh) E

Since in an intrinsic semiconductor, n = p = ni Jdrift = e ni (µe + µh) E

Conductivity, = e ni (µe + µh) -----------(2) Carrier concentration in semiconductor: The conductivity of semiconductor depends on number of charge carriers in the material. To calculate conductivity of semiconductors we have to calculate number of holes (p) in valence band and number of electrons in conduction band. The value of n and p depend on the temperature as well as presence of impurities. Carrier concentration of free electrons (n) and concentration of holes (p) can be calculated using density of states equation and Fermi-Dirac distribution function for C.B and V.B. Concentration of electron in conduction band/unit volume at T> 0K The actual number of electrons in the conduction band is given by

n =∫ 푁(퐸)푑퐸

Because the Fermi-Dirac function describes the probability of occupancy of a state under the conditions of thermal equilibrium, the electron concentration obtained from eqn.(3)is the equilibrium concentration.

As the f(E) rapidly approaches zero for higher energies, the integral in eqn.(3) can be written as n =∫ 푁(퐸)푑퐸

The number of electrons/unit volume having energy range E and E+dE in C.B is given as N(E) dE = f(E) g(E) dE

n =∫ f(E)g(E) dE -----------(3)

The density of state equation for C.B is written as

g(E) =

(∗) (E - Ec)1/2 -----------(4)

where 푚 ∗ is the effective mass of the electron.

Substituting eqn.(4) for g(E) and f(E) = e-(E-EF)/K

BT in the above eqn.(3) we get



n = ∫

(∗) (E− E ) 푑퐸

by solving above equation we get;

n = Nc 푒( )

------------ (5)

where, Nc = 2( ∗ ) Nc is effective density of the states in conduction band. 푚∗ is effective mass of the electron. Concentration of holes in valance band: Here ‘hole’ signifies an empty energy space in the Fermi level for a hole is 1-f(E). Where f(E) is probability of occupancy of a state E. The actual number of holes in the valence band is given by

p =∫ [1− 푓(퐸)] 푔(퐸)푑퐸

p = ∫ [1 − 푓(퐸)] 푔(퐸)푑퐸∞ ----------- (6) The density of state holes in V.B is written as

g(E) =

(∗) (Ev - E)1/2--------------------(7)

푚∗ is effective mass of the hole. Substituting eqn.(7) for g(E) and [1-f(E)] = e-(E

F-E)/K

BT in the above eqn.(6) we get

The number of holes in the equation range E and E+dE in V.B is given by.

p=

(∗) (Ev - E)1/2 . e-(E

F-E)/K

BT dE

Total no. of holes/unit volume in valence band is p = ∫ 푝(퐸)푑퐸∞

By solving this we get

p = Nv 푒 ------------(8)

where, Nv = 2 ( ∗ ) In case of intrinsic semiconductors, n=p from equations (5) and (8)

Nc 푒( )

= Nv 푒 푁푁 = 푒 . 푒

( )

= 푒( )

ln

= ( )

2Ef = Ev + Ec –KBT ln

Fig (8)



If the effective masses of electron and holes are equal, then Nc =Nv

Ef = ------(9)

Hence in case of intrinsic semiconductors, Ef lies in the midway between the forbidden energy gap. Total concentration in an intrinsic semiconductor: For intrinsic semiconductors the product of n and p is n.p=ni

2, where ni is concentration of holes and electrons in intrinsic semiconductor.

ni2 = n p = NC NV 푒

( ) 푒

ni2 = NC NV 푒

( )

by solving we get ni2 = 4( ) (푚∗ 푚∗ ) 푒

( )

Substituting Ec-Ev=Eg and substitute the values of constants in the above equation we get

ni = 퐴 푇 .푒

( ) ---------------(10)

Where 퐴 is constant (A=2.322x1043 (∗ ∗

) , Eg is value of band gap at 0K

i.e ni 푇 and ni 푒 Hence intrinsic carrier concentration increases exponentially with increasing temperature. Fermi distribution function: (Applied to metals) In semiconductors electrons and holes are the charge carriers. To obtain expression for carrier concentration (n and p) we must investigate the distribution of carriers over the available energy states. For this we can use Fermi-Dirac distribution function, as electrons in semiconductors obey Fermi-Dirac statistics. The distribution of electrons over a range of allowed energy levels at thermal equilibrium is given by;

푓(퐸) =1

1 + 푒

where; kB-Boltzmann’s constant (1.38x10-23 J/K) T-is absolute temperature, Ef- Fermi energy.(average energy possessed by the electrons at absolute 0K temperature) f(E) gives the probability of an occupancy of an electron in a given energy state.

At T=0 K and E<Ef f(E) =1 At T=0 K and E>Ef f(E) = 0 and At T0 K f(E) =



Fig (9)

Intrinsic semiconductors: In case of intrinsic semiconductors probability of occupancy in conduction band equals the probability of vacancy in valence band.

i.e f(Ec) = 1- f(Ev) ------(11)

Fig (10)

Because of the symmetry of f(E) v/s E diagram, to satisfy the above condition EF must be at the middle of the band gap., i.e the Fermi level in an intrinsic semiconductor is at the middle of the band gap and is called the intrinsic level.



Extrinsic Semiconductors: The intrinsic semiconductors have low conductivity which is not amenable to control and as such of little interest. But however a judicious introduction of impurity atoms in perfect (pure) semiconductors produces useful modifications of its electrical conductivity. Doping: An intentionally adding controlled quantity of impurity into intrinsic semiconductors called doping. The impurity added is called a dopant. A semiconductor doped with impurity atoms is called extrinsic semiconductor. When impurities are added to an otherwise pure semiconductor, additional energy levels are introduced in the band structure of the semiconductor. Usually these energy levels lie within the band gap. Typical doping levels range from 1020 to 1027 impurity atoms/m3.pentavelent elements or trivalent elements are used as dopants. Two types of extrinsic semiconductors, namely n-type and p-type semiconductors are produced depending upon the type of impurity atom.

n-type semiconductors:

Fig (11) A semiconductor doped with pentavalent impurity (Ex:P,AS,Sb..etc) is called n-type semiconductor. Pentavelent impurity introduces energy level in the band gap, close to the conduction band edge.

Fig ( 12 )

At very low temperature region, electrons in the conduction band are only due to the transition of electrons from the donor levels. Therefore, the Fermi level EFn lies between the donor level ED and the bottom edge of the conduction band EC.



EFn = (Ionization region)

As the temperature increases, the donor levels gradually get depleted and Fermi level shifts downward. At the temperature of depletion Td the Fermi level coincides with the donor level.

EFn =ED (at T=Td) As temperature further increases above Td, the Fermi level shifts downward in an approximately linear fashion, though the concentration in the conduction band remains constant. At a temperature Ti, where intrinsic process contributes to electron concentration significantly, the Fermi level approaches the intrinsic value EFi=Eg/2. With further increase in the temperature, the behavior of extrinsic semiconductor same as that of an intrinsic semiconductor and Fermi level stays at EFi. In n-type semiconductors majority charge carriers are electrons and minority charge carriers are holes. i.e n>>p. The conductivity of n-type semiconductor is given by;

= nµee ------(12) In the depletion region, the electron concentration in the conduction band is nearly identical to the concentration of the dopant atoms. If ND is the impurity concentration then, n=ND

n = NDeµe According to charge neutrality condition;

n+NA = p+ND Thus, the charge neutrality for n-type semiconductor requires that;

NA=0, n>>p, hence nND

In n-type material free-electron concentration is approximately equal to donor. n.p=푛

p= The number of holes in n-type semiconductor is given by

p= ------(13)

Fermi Distribution function in case of n-type semiconductors: In case of n-type semiconductors probability of occupancy in conduction band is much greater than the probability of vacancy in valence band.

i.e f(Ec) >> 1-f(Ev) --------(14)

To satisfy this condition Ef must be above the middle of the band gap. As doping increases Ef moves towards Ec.



Fig (13)

Calculation of exact position of Fermi level in n-type material can be done by using the equations

ND = Nc.푒( )

EF = Ec - kBT ln -----------(15)

p-type semiconductors: A p-type semiconductor is obtained by doping an intrinsic semiconductor with trivalent such as boron and aluminium.

Fig (14) The addition of acceptor impurities contributes hole levels low in the semiconductor the band gap so that electrons can easily excited from the valence band into these levels, leaving mobile holes in



the valence band. This shifts the effective Fermi level to a point about halfway between the acceptor levels and the valence band. At a very low temperature holes are produced in the valence band due to electrons jump from valence band to accepter level(EA) .As temperature goes on increases , EFp raises and co insides with the EFi.

Fig(15 )

In p-type semiconductors majority charge carriers are holes and minority charge carriers are electrons .i.e p>>n. The conductivity of p-type semiconductor is given by;

p = pµhe ------- (16) and if NA is the impurity concentration p=NA p = NA µh e According to charge neutrality condition

n+NA = p+ND Thus, the charge neutrality for p-type semiconductor requires that;

ND = 0, p>>n, hence p NA

In p-type material hole concentration is approximately equal to acceptor. n.p = 푛

n =

The number of holes in n-type semiconductor is given by

n = --------(17)

Fermi Distribution function in case of p-type semiconductors: In case of p-type semiconductors probability of vacancy in valence band is much greater than the probability of occupancy in conduction band at room temperature. Therefore, Fermi level must be closer to Ev compared to Ec.

i.e f(Ec) << 1-f(Ev)



Fig (16) Calculation of exact position of Fermi level in p-type material can be done by using the equation

EF=Ev + KBT ln --------------(18)

Hall Effect When a magnetic field is applied to a current carrying conductor, a voltage is developed across the specimen in a direction perpendicular to both the current and magnetic field. This phenomenon is called the “Hall Effect”. The voltage developed across the specimen is called Hall voltage (VH).

Fig (17)

When current carring conductor is placed in an external magnetic field ‘B’, which exert a transverse magnetic deflecting force called as “Lorentz force” acting on the charge carriers.

FL = e Vh B--------(19) Where FL is Lorentz force, B is applied magnetic field, Vh=hole drift velocity (ms-1)

Consequently the sides which are perpendicular to applied magnetic field ‘B’,and current ‘I’ start collecting charges. These excess of –ve and +ve charges on the sides of the conductors creates a



force which opposes the Lorentz force after some time equilibrium is reached in which force due to the accumulation of charges opposes and becomes equal to lorentz force. Steady-state reached when

FL =FH FH is force due to the accumulation of charges.

FH= e EH

FH = e ( )------(20)

From equations (19) and (20)

e Vh B = e ( ) VH = d B Vh ---------(21)

Since I = p e Vh (d x t) for p-type and I = n e Ve (d x t) for n-ytype

Vh =

------(22)

Sustitute equation (22) in (21)

VH = ----(23)

Where VH- Hall voltage. B-magnetic field I-Current through the conductor n-Density of free electrons t-Thickness of the conductor

VH = ------(24)

RH is Hall co-efficient and is given by for p-type RH =1/pe and for n-type RH =-1/ne

p = -------(25)

which gives concentration of current carriers and mobility of electrons and holes can be determined by the formula µe = /en (for n-type) and µh= /ep (for p-type) It is Hall effect which showed there exist two types of charge carriers in semiconductors. Applications of hall effect:

1. It helps in finding sign of the carrier. 2. To determine carrier concentration 3. To determine mobility of charge carriers if is known. 4. Hall generator: A Hall generator is a device that makes use of the Hall effect for the

purpose of generating a direct current voltage in the presence of a magnetic field. 5. Hall effect sensor: A Hall effect sensor is a transducer that varies its output voltage in

response to a magnetic field. Hall effect sensors are used for proximity switching, positioning, speed detection, and current sensing applications.



pn-Juction diode: When a p-type semiconductor is joined together with n-type semiconductor, a pn-juction is formed. A pn-juction is also known as semiconductor diode. A pn-juction diode is a very important device, it allows current in only one direction and opposes when it is reversed. This property is known as rectification.

Fig (18)

Formation of pn-junction: pn-juction is formed when a p-type and n-type semiconductors are joined metallargically. The interface lying between the n and p type region is called pn-juction. In P-type majority carriers are holes and in n-type majority charge carriers are electrons. Because of a large concentration gradient exists across the pn-juction for the majority charge carriers. Electrons tend to diffuse from n-type region into p-type region and holes tend to diffuse from p-type into n-type region in order to reduce the concentration mismatch in the region. Due to diffussion of charge carriers, holes give rise to hole diffusion current density component (Jhp) and electrons give rise to electron diffusion current density component (Jen). The first letters ‘h’ and ‘e’ in the subscript denote the carrier and the second letters ‘p’ and ‘n’ indicates the region of their origin.Both the current components are in the same direction and the net diffusion current density is given by

J(Diff) = Jen +Jhp On entering the p-type, electrons recombine with the holes and on entering n-type, hole recombine with electrons, in the vicinity of the junction, there are only uncovered donor ions (positive) on n-side and uncovered acceptor ions (negative) on p-side. Due to these immobile charges, a potential difference(Vo) is set up across the juntion and hence, an internal field is created, known as built in field, which is directed from n-type to p-type and increases with increase in the number of uncovered ions. Since electrons feel force opposite to the electric field while holes feel force in the direction of the electric field, the built-in electric field opposes the diffusion of charge carriers across the junction. When the built-in electric field becomes large enough, it prevents further diffusion of electrons and holes. The region on either side of the junction, which has only uncovered ions and is depleted from the free charge carriers is called



depletion region or space region. The width of this region is called as depletion layer width. The potential difference set up across the deplition region is called barrier potential and is represented by ‘V0’. Drift of minority carriers: It is seen that built-in field across the junction prevents the further diffusion of majority carriers. However, the electric field has the right direction to promote minority charge carriers. The two components, namely electron and hole drift current densities are designated as Jep and Jhn respectively. The direction of Jep and Jhn are the same. Therefore, the net drift current through the junction is given by

J(Drift) = Jep +Jhn Important points are to be remembered regarding minority carriers and the drift current:

1. The minority carriers are generated through breaking of covalent bonds and in each region the minority carrier concentration is slowely determined by he temperature. Therefore the drift current is constant at a given temperature.

2. Due to small number of minority carriers the drift current will be very small. 3. Minority carriers can move across the junction only when the barrier potential exists

across the junction. When the barrier potential is smaller they move slower; when it is greater, they move faster.

4. An externally applied voltage cannot change the magnitude of the current. It can change only the kinetic energy of the minority carriers.

Equilibrium condition: When the diode is not connected to any extexnal circuit, electric current cannot flow across it. And also when the junction is in thermal equilibrium, there cannot be any current across it. It implies that the drift of minority cariers is counterbalanced by the diffusion of the same number of majority carriers across the junction.

J(Diffusion) = J(Drift) Jen + Jhp = Jep + Jhn

There cannot be a net build-up of electrons or holes on either side with time, as the electrical neutrality of each side is to be retained. Therefore, the diffusion and drift current components due to each type of carriers should cancel each other. From the above equation ,the condition For equilibrium may be written as

Jhp = Jhn Jen = Jep

Thus in the equilibrium condition, the drift hole current must be equal in magnitude and opposite in direction to the diffusion hole current. Similarly, the drift electron current must be equal and opposite to the diffusion electron current, resulting in net zero electron current.



As shown in the fig. (19). the electric potential on n-type region of the juction is higher (as +ve donor ions are there on the n-type region) than the p-type region of the juction. Because of that energy bands on the p-type region will lie higher in energy than the energy bands on the n-type region of the juction. From the energy level diagram, we can see that electrons cannot diffuse from the n-type region to p-type region, as there is potential barrier of height’V0’, which they cannot cross as they are having smaller energy. So, in the absence of any external voltage across the juction, the net current through the junction is zero. Fig (19) Biasing of the P-N junction The process of applying proper voltage to the deivce is called biasing. A pn-junction can be biased in two ways. Forward Biasing mode

Fig (20 )

A pn-junction is said to be forward biased when p-region is connected to positive and n-region is connected to negative treminal of the power supply.

When an external field applied across the pn-junction, which acts opposite to the internal potential barrier ‘V0’ reduces the effective voltage across the junction to (V0-V). It means a decrease in the electric field acting across the deplition layer. As the field intensity decreases the majority carriers push into the deplition layer and width of the deplition layer becomes narrow which urges majority carriers to flow across the juction hence it offers very less resistance and current increases. As illustrated by solid lines in the above figure (20,a). Hence Jhp and Jen increases and due to very small drift current Jep and Jhn decreases.



Reverse biased mode: A pn- junction is said to be reverse biased if the positive terminal of the battery is connected to N-side and the negative terminal to p-side of the pn-junction. When external field is applied across the junction, the external voltage adds to the barrier voltage V0 and the barrier potential increases to a value (Vo+V). As a result, the electric field in the depletion region increases and the majority carriers are pulled away from the junction and the depletion region becomes thick. The resistance becomes high when reverse biased and so there is no conduction across the junction due to majority carriers. The minority carriers however cross the junction and they constitute a current that flows in the opposite direction. This is the reverse current.

Fig (21)

The reverse current through the pn-junction increases with temperature because it is due to the flow of minority carriers in the semiconductor and the number of minority carriers in the semiconductor increases with increase in temperature.

Forward and reverse bias characteristics:

Fig (22)

Above graph shows the VI characteristics of a pn-junction diode. In forward bias, when the applied voltage V, is increased from zero, initially no current flows through the diode, because diffusion of majority carriers through the junction cannot take place until the potential barrier is overcome. When the forward bias approaches the value of barrier potential, majority carriers



starts diffusing and current starts increasing very rapidly. The forward voltage at which forward current starts increasing is called knee (or cutin, offset, threshold) voltage. The forward current flows through the diode mainly due to the diffusion of the majority carriers, which increases with the voltage exponentially.

IF = I0.(푒 -1) In reverse biasing, diffusion of majority carriers is not possible and current is only due to the drift of minority carriers. But this current is very small as the number of minority carriers is very small. When the reverse voltage is very high, the current through the diode becomes very large which damages the diode due to excessive heating. This is called break down of the diode. The current through the diode is related with the biasing voltage ‘V’, according to the following relation,

IR = - I0.(푒 + 1) In reverse bias, V is opposite to the forward voltage and is represented by a negative sign, so

푒 ≪ 1 in reverse bias, thus the reverse current IRI0. Below the breakdown voltage, the reverse current is therefore very small and almost constant (does not depend on the reverse biasing voltage). So, I0 is also referred as reverse saturation current and it depends only on temperature. Thus pn-junction diodes offer a low current when reverse biased and a very high current when forward biased.



Zener Diode: When we studied about the diode characteristics, it was found that under reverse bias, there is a small amount of current due to the drifting of the minority charge carriers. But as the reverse potential is increased beyond a level, suddenly the current increase, which is called as 'breakdown' and diode, will be damaged. Zener diode is heavily doped diode the depletion region is narrow. When the reverse biase voltage is increased the electric field across the depletion region becomes very strong. When the field is of the order of 3x107 V electrons are pulled out of the covalent bonds. A large number of electron-hole pairs are thereby produced. The reverse current rises rapidly. This effect is zener effect. Fig (23)

I-V characteristics of a zener diode:

Fig(24) : Volt-ampere characteristics of zener diode. There are two ways in which the breakdown can occur. When a reverse bias is given it hinders diffusion but it aids drifting. The velocity of minority carriers is proportional to the applied bias voltage. So the minority carriers namely electrons in 'P' type and holes in n-type get accelerated and they attain very high kinetic energy. These highly energetic charge carriers collide with valence electrons breaking their bond creating hole - electron pair, this is called as 'avalanche breakdown'. The high electric field inside the semiconductor may also break the covalent bonds this is called as 'zener breakdown'. A diode operating in this type of zener breakdown is called as a zener diode.



Bipolar junction transistor (BJT) Introduction A transistor is a device made from semiconductor material, has three terminals and two pn junctions. They have found a number of applications in electronic circuits. Invention of transistor revolutionized the entire field of electronics and has largely replaced vacuum tubes. In analogue circuits their basic function is to amplify a signal (i.e., as amplifier) while in digital circuits they act as a switch or gate. We shall confine our study to the first property. A junction transistor is simply a sandwich of one type of semiconductor material between two layers of the other type, as shown in the figure (25).

Fig(25)

These two junctions give rise to three regions. The central region is base. It may be p-type or n-type semiconductor the two outer regions are called as emitter and collector. Emitter: Emitter region of the transistor is more heavily doped than any of the other regions because its main function is to supply majority charge carriers (electrons in case of npn or holes in case of pnp). Base: The middle section of the transistor is called base. Base region is moderately doped and is very thin (10-6m) as compared to either emitter or collector so that it may pass most of the injected charge carriers to the collector. Collector: In most transistors, collector region is made physically large in size than the emitter region, because it has to dissipate much greater power. Because of this difference, there is no possibility of inverting the transistor. And this is lightly doped There are two types of transistors: npn and pnp transistor.



pnp transistor: If base is n-type, the emitter and collector are p-type such transistor is called as npn transistor.( Fig 25,a) npn transistor: If base is p-type, the emitter and collector are n-type such transistor is called as npn transistor.(Fig 25,b) Formation of depletion regions: Transistor consists of two pn junctions. The junction between the emitter and base region is known as the emitter-base junction (EB junction) and the junction between the collector and base region is known as the collector-base junction (CB junction). During the process of formation of junctions diffusion of majority carriers take place and depletion layers form.

Fig (26)

As the doping levels of three regions are different, the two depletion layers will have different widths. Because the emitter is heavily doped and the base region is lightly doped, the depletion layer at EB junction penetrates only slightly into the emitter region and deeply into the base region. Similarly, at the CB junction the depletion layer extends deep into the base region while it penetrates to a lesser extent into the collector region. The result is narrow emitter depletion layer and a wide collector depletion layer. The base region becomes thinner compared to its actual physical dimension, as the two depletion layers encroach on it. The EB junction acts as input diode and CB junction acts as output diode. As both the diodes they base as common, they influence each other strongly. Transistor Biasing: For proper working of a transistor, it is essential to apply voltages of current polarity across its two junctions. 1. emitter-base junction is always forward biased. 2. collector-base junction is always reverse biased. Transistor circuit configurations: Transistor can be connected in three configurations they are;

1. Common Base (CB) configuration 2. Common Emitter (CE) configuration 3. Common Collector (CC) configuration

The term ‘common’ is used to denote the electrode that is common to the input and output circuits.



Action of a Transistor:

Fig(27)

Make the connections with NPN transistor as shown in the circuit diagram. If the switch S1 is closed the emitter junction is forward biased by the battery VEE. If the switch S2 is closed the collector junction is reversed biased. When the two switches are open both the junctions are unbiased. There will be depletion or space regions at both the junctions. When S1 is closed

Fig. (28)

Suppose the switch S1 is closed with S2 open. Then the EB-junction will be forward biased as shown in the Fig.(28). When it is forward biased the width of the EB-junction will be reduced in size and a large current flows across the junction. This current consists of the electron diffusion current from the emitter into the base and the hole diffusion current from the base into the emitter. The base is very lightly doped whereas the emitter is heavily doped. Hence then total current IE across the junction is due to mostly the electron diffusion. The emitter current IE and the base current are large and equal to each other. The collector current IC is zero.



When S2 is closed

Fig. (29)

Next we close the switch S2 keeping S1 open as show in the fig. (29). The CB-junction is reversed biased. A very small current flows from the collector into the base across the collector base junction. The only current flows across the CB-junction will be the reverse leakage current made up of thermally generated minority carriers which are accelerated by the potential barrier and relatively small and dependent on temperature. There is no emitter current. The small collector current is designated as ICBO. This symbol CBO indicates that the current is between the Collector and Base when the third terminal (emitter) is Open. Suppose now both the switches are closed. Then on the basis of the above discussion we should expect large values of the emitter and base currents and a small collector current. But what we actually observe is a large emitter current as expected. But the base current becomes very small and the collector current is very large. The behavior of a transistor: When both the switches in Fig. (27) are closed the transistor is said to be forward-reversed biased. It is in an active operation as shown in Fig. (30). The EB-junction is forward biased by the battery VEE. The CB-junction is reversed biased by the battery VCC. The directions of the emitter, base and collector currants are as shown in the figure. The direction of each current is opposite to the direction of motion of the electrons.

Fig. (30)



When the emitter-base junction is forward biased reduces the potential barrier and leads to diffusion of majority carriers. The electron current is made much larger than the hole current by doping the base region more lightly than the emitter region. The sum of the electron and hole current constitutes the emitter current IE. The ratio of the electron current to the total emitter current Ien/IE is known as emitter junction ratio, . The value of typically of the order of 0.995. It means that only 0.5% of IE consists of hole current. The electrons that enter the base from emitter form minority carriers in the base. Because of very light doping and very thin base only few electrons and holes recombine in the base region. For example the electron 3 is shown to recombine with the hole 6. The majority of the electrons injected into the base together with the thermally generated electrons in the base cross the CB-junction and enter the collector region. A few of thermally generated electrons in the collector may cross into the base. Their number is very small. For example the electron 5 and the hole 8 cross the CB-junction. The movement of 5 and 8 across the junction constitutes the leakage current ICBO. The movement of electron 3 and hole 7 across the EB-junction forms part of the emitter current IE. These two currents are not equal. Actually the number of electrons and holes crossing the emitter junction is much more than the number of electrons and holes crossing the collector junction. The difference between these two current constitutes the base current IB. A part of the emitter current consists of holes that do not contribute to the collector current. Further not all the electrons that are injected into the base reach the collector. For these two reasons the base current is less than the emitter current. The ratio of the number of electrons that reach the collector to the number are injected into the base is called the base transportation factor. It is denoted by β. Thus

β= 풏풐.풐풇 풆풍풆풄풕풓풐풏풔 풕풉풂풕 풓풆풂풄풉 풕풉풆 풄풐풍풍풆풄풕풐풓풏풐.풊풏풋풆풄풕풆풅 풆풍풆풄풕풓풐풏풔 풊풏풕풐 풕풉풆 풃풂풔풆

The ratio of collector current to the emitter current is called the dc alpha of the transistor. Thus dc = β

The dc alpha is of the order of 0.99 for most transistors. A typical value of β is 0.995 Transistor currents: The three primary currents which flow in a properly-biased transistor are IE, IB and IC.

Fig(31)



Fig (31) shows the directions of flow as well as relative magnitudes of these currents for a pnp- transistor connected in a common-base mode. It is seen that

IE= IB + IC Dividing both sides by IC we get

II = 1 +

II

The ratio of the collector current to the emitter current is alpha dc. The ratio of the collector current to the base current is called beta dc (훃퐝퐜 ). There fore we get the relation between alpha

and beta as

= 1 +

βdc = dc/ (1-dc)

The amplifying action of a transistor:

The transistor can perform a number of functions. But its main function is amplification.

(a) Voltage amplifier: The reversed biased collector junction is equivalent to a high resistance (rc) due to small current and the forward biased emitter junction is equivalent to a low input resistance (ri) because of large emitter current. If for instance, we take emitter E as the input terminal and apply a signal Vs to that in addition to the biasing current IE an additional current IE flows then we shall get at the collector current IC in addition to dc current IC. Hence from eqn.(2) IC = iC = IE

Fig(32) Although IC is less than IE by definition of yet the situation is different if we consider the voltage output at collector, where a load RL is also connected V0 = RL IC = [IE] RL The signal voltage at input is Vi = ri IE

So voltage gain is AV = 푽ퟎ푽풊

= ( )

( ∆ )=

Now, although is less than 1, but generally RL >> ri so V0 >> Vi



i.e. output voltage is quite larger than input voltage. Thus it give rise to voltage amplification.

(b) Current amplification

Fig (33)

CE Configuration: In a CE amplifier the base current IB is the input current. The collector current IC is the output current. The base current amplification factor is defined as the ratio of the change in collector current to the change in base current at constant VCC. Thus

βac = 푰푪푰푩

The current flowing through the base is generally less than 5%. Hence the value of β is generally more than 20. Its value usually ranges from 20 to 500. Here, input signal is applied between the base and emitter and output signal is taken out from collector and emitter circuit. As seen from fig (33), IB is the input current and IC is the output current. The ratio of dc collector to dc base current is called dc beta (βdc) or just β of the transistor.

β = 푰푪푰푩

or IC = β IB

It is also called common-emitter dc forward transfer ratio and written as hFE. It is possible for β to have as high a value as 500. While analyzing ac operation of a transistor, we use ac β which is given by

βac = 푰푪푰푩

The flow of various currents in a CE configuration is given by, IE = IB + IC = IB + β IB = (1+ β) IB

The ratio of collector current to emitter current is called dc alpha (dc) Relation between and β

= 휷ퟏ 휷



Transistor Characteristics: These are the curves which represent relationship between different dc currents and voltage of a transistor. These are helpful in studying the operation of a transistor when connected in a circuit. The three important characteristics of a transistor are; 1. input characteristic 2. output characteristic 3. current transfer characteristic. Common-emitter static characteristics: The circuit to draw the characteristics of the transistor in CE configuration as shown in the Fig (34). Here the emitter junction is forward biased by the battery VBB and the corresponding input voltage and current is read by voltmeter VBE and ammeter IB. The collector junction is reversed biased by the battery VCC and the corresponding output voltage and current is read by voltmeter VCE and ammeter IC.

Fig.(34).

(a) Input Characteristic: The input characteristics are drawn by noting the input voltage VBE and the corresponding base current IB keeping output voltage VCE constant Graph shows how IB varies with change in VEE when VCE is kept constant at a particular value. To begin with, voltage VCE is maintained constant at a convenient value and then VBE is increased in steps. Corresponding values of IB are noted at each step. Fig(35) shows a typical input characteristic. Curve is exactly similar to forward characteristics of a pn-junction; this characteristic is used to find the input resistance of the transistor. Fig(35) Its value is given by the reciprocal of its slope.

풓풊풏 = 푽푩푬푰푩

(VCE is constant)



Due to initial non-linearity of the curve, rin varies considerably from a value of 4K near the origin to a value of 600 over the more linear part of the curve. (b) Output or collector characteristic To obtain output characteristic, first IB is set to a convenient value and maintained constant and then VCE is increased from zero in steps, IC being noted at each step. Next, VCE is reduced to zero and IB increased to another convenient value and the whole procedure repeated. In this way output curve is obtained.

Fig(36)

It indicates the way in which IC varies with change in VCE when IB is held constant. Hence we get different curves for different values of IB. It is seen that as VCE increases from zero, IC rapidly increases to a near saturation level for fixed value of IB. As shown, a small amount of collector current flows even when IB=0. It is called ICEO. Since main collector current is zero, the transistor is said to be cut-off. It may be noted that if VCE is allowed to increase too far, collector-base junction completely breaks down and due to this avalanche breakdown occurs, and IC increases rapidly and may cause damage to the transistor. When VCE has very low value, the transistor is side to be saturated and it operates in the saturation region of the characteristic. Here, change in IB does not produce any corresponding change in IC. This characteristic is used to find β at a specific value of IB and VCE.

β = 푰푪푰푩



We may select any two points A and B on the IB=60µA and 40µA lines respectively and measure corresponding values of IC from the diagram for finding IC. Since IB =(60-40)=20µA, β can be easily found. The value of output resistance ROUT (=VCE/IC) over the near horizontal part of the characteristic varies from 10k to 50k.

(c ). Current transfer characteristic. This characteristic shows how IC varies with change in IB when VCE is held constant at a given value. Such a typical characteristic is shown in below figure (37,a).Its slope gives

β = 푰푪푰푩

Fig (37)

From the above fig (37,b), shows that a small collector current flows even when IB = 0. It is the common-emitter leakage current ICEO = (1+β) ICO, It is also due to minority carriers across the reverse-biased collector-base junction.

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