Unit No. 1 Notes Semiconductor new PDF

Engineering Physics UNIT I -------------------------------------------------------------------------------------------------------- Solid State Physics: Classification of solids on the basis of energy band diagram, Intrinsic and Extrinsic semiconductors...

Engineering Physics UNIT I -------------------------------------------------------------------------------------------------------- Solid State Physics: Classification of solids on the basis of energy band diagram, Intrinsic and Extrinsic semiconductors. Fermi level in intrinsic semiconductor, semiconductor conductivity with derivation, P-N junction diode, Zener diode, Light Emitting Diode, Hall effect. --------------------------------------------------------------------------------------------------------  What is energy band gap?  Explain the formation of various energy bands in a solid.  Explain the formation of energy band in a solid. Formation of energy band in a solid? (Just read) Solid consist of no of atoms. There is regular periodic arrangement of atoms. Then there is interaction between neighboring atoms. This interaction is called as inter atomic interaction. Due to this interaction energy level of the atom will split up into number of energy levels. The spacing between energy is very small i.e. the energy levels are much closed to each other. Hence they will form continuous spectra & this spectrum is called energy band. Solid consist of number of atoms. An atom consists of positively charge nucle- us around which negatively charge electron revolve in a different circular orbit. The electron revolves around the nucleus only in certain permitted orbits. The electrons in each permitted orbit have a certain fixed amount of energy. The larger the orbit great- er is the energy of electron. The effect of interaction is minimum on inner most electrons because they are tightly bound to nucleus & the effect of interaction will be maximum on outermost electron because they are away from the nucleus. Hence energy level will be split up into number of energy levels they will form an energy band. The electron in the outermost orbit is called as valance electron. The range of energies possessed by the valance electron is known as valance band. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 1  Engineering Physics When the electron in the valance band gets sufficient energy then they will jump from valance band to higher energy band. This band is called as conduction band. The range of energies possessed by the conduction band electron is known as conduction band. This valance band & conduction band may be separated by forbidden energy gap or forbidden energy band. The electron may be jump from valance to conduction band or vice versa but they cannot found in forbidden gap. Fig:- Energy band diagram  Explain the solids are classified into conductor, semiconductor & insulator on the basis of band theory of solid.  Explain the classification of solids on the basis of band theory & draw the neces- sary diagram. On the basis of band theory solids are classified into three groups as follows: 1) Conductor 2) Insulator 3) Semiconductor 1) Conductor: The conductor are those substances which easily allow the pass electric current through them. It is because the large numbers of free electrons are available in a con- ductor. In terms of energy band gap valance band and conduction band are overlap to each other. There is no forbidden gap due to this electron can easily moved from val- ance band to conduction band. e.g.:- Metal & Aluminum. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 2  Engineering Physics 2) Insulator: Insulators are those substances which do not allow passing the electric through them. In terms of energy band gap valance band is completely full and conduction band is empty. There is very large forbidden gap between valance band and conduc- tion band it is nearly equal to 15eV. Hence electron cannot easily jump from valance band to conduction band. e.g.:- Glass & Plastic. 3) Semiconductor: Semiconductor are those substances whose electrical conductively lies between conductor & insulator. In terms of energy band gap the valance band is full & conduc- tion band is empty and they are separated by small energy gap (forbidden gap) it is nearly equal to 1eV. Hence at low temperature electron cannot jump from valance band to conduction band & hence at low temperature it acts as an insulator. But when the temperature increases electrons gets sufficient energy to jump from valance band to conduction band & hence it act as a conductor. At low temperature it acts as an in- sulator & at high temperature it act as a conductor hence it called as semiconductor. e.g.:- Silicon & Germanium. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 3  Engineering Physics Types of Semiconductor: There are two types of semiconductor. 1) Intrinsic semiconductor. 2) Extrinsic semiconductor.  Explain what is mean by hole & Define the term intrinsic semiconductor.  Explain the intrinsic semiconductor. Intrinsic semiconductor: The semiconductor which is extremely pure form i.e. it does not contain any impurities is called as intrinsic semiconductor. There are only two element Silicon & Germanium which can be consider as an intrinsic semiconductor. These elements are belonging to fourth group of the periodic table. There are four valance electrons in the outermost orbit & hence they are called as tetravalent. Hence each atom is surrounded by four equidistance atom as shown in fig. Let us consider a two dimensional germanium crystal each valance electron of Ge atom shared with the valance electron of neighboring electron of Ge atom & they will form a bond. This bond is called covalent bond. In Intrinsic semiconductor at low temperature there is no free e- because cannot get sufficient energy hence they cannot move from valance band to conduction band. But when the temperature increases some e- get sufficient energy & they will break the covalent bond due to this e- jump from valance band to Conduction band. Create the vacancy in the valance Band (V.B.). This vacancy is act as hole. It is +ve charge carrier. The deficiency of e- is called as hole. As the temp increases number of covalent bonds will be break thus we get number of e- & hole pairs. But in the intrinsic semi- conductor no. of holes equal to the no. of e-. Hence total current inside the intrinsic semiconductors is sum of the current due to free e- & hole. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 4  Engineering Physics Extrinsic Semiconductor:  What are the departs as pertains to semiconductors? Explain the formation of P- type semiconductors & N- type semiconductors form intrinsic germanium.  Explain N- Type & P- type semiconductors with the help of energy band diagram. The semiconductor which contains small amount of Impurities is called as Extrinsic Semiconductor. The process of addition of very small amount of impurities is called as doping. Hence this semiconductor is also called as doped semiconductors. The doping is very small generally one or two atom of impurities is added to 106 atoms of semiconductor. The semiconductors are belonging to IVth group of the periodic table & hence the impurity may add form IIIrd or IVth group. These are two types of impurities. 1) Impurity from Vth group Arsenic, Antimony etc is pentavalent impurities. 2) Impurity from IIIrd group like Aluminum, Indiam etc are the trivalent impurities N-Type Semiconductor: Let a pentavalent impurity like Arsenic (As) is added to the Germanium (Ge) crystal. The Arsenic atom will replace one of the Germanium atoms. Arsenic atom has five valance e- out of these four valance e- of Arsenic shared with valance e- of four Germanium atoms & form a covalent bonds. But one valance e- act as a free e-.It does not take part in bonding as shown in fig. Thus the impurity atom will donate one free e- to the crystal hence this impurity is called as doner impurity. If the number of impurity atoms doped the each atom donate one free e-. Thus number of free is equal to the number of impurity atom. As the temperature increases covalent bond may be break & due to the break- ing of bonds we get number of e- hole pairs. But in this case number of e- is greater than number of holes. Hence e- is called as majority charge & holes are called minori- Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 5  Engineering Physics ty charge carrier. In this case no of – ve charges i.e. e- are more & hence it is called as N- type semiconductor. P-type Semiconductor: Consider a pure crystal of Germanium (Ge). Let a Ge atom is replaced by a tri- valent impurity like Boron. It has 3 valance e-. They will form the three covalent bond with 3 neighboring Ge atom; but 4th bond is incomplete. Thus there exists a vacancy in 4th bond. This vacancy is act as a +ve charge carrier i.e. hole as shown in fig. When temperature increases, some covalent bond may be break to give e- & hole pair. The e- which is produced due to breaking of bond will be captured by the impurity atom to complete the covalent bond. Thus the impurity atom will accept the free e- from the Ge atom. Such impurity is called as ‘acceptor impurity’. In this, no. of holes is equal to the no. of impurity atom. In this case, no. of holes are more as compared to e- & hence holes are called as ‘majority charge carrier’ & e- are ‘minority change carriers’. As there are large no of +ve charge (hole) carrier, hence it is called as ‘P-type semiconductor’. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 6  Engineering Physics  Explain Fermi energy.  Explain Fermi energy & show that fermi level in intrinsic semiconductor lies in the middle of band gap.  What is fermi level? prove that fermi level in intrinsic semiconductor lies in the 𝐸𝑔 middle of band gap& obtain the relation EF=. 2 Fermi level (Intrinsic semiconductor): Fermi level is the characteristics energy of the material. We know that in an in- trinsic semiconductor there is equal no. of electron and holes. The concentration of electrons decrease above the bottom of conduction band and similarly concentration of holes decrease below the top of the valance band as shown in fig. This shows that center of gravity of electron and hole lies exactly at the middle of forbidden energy gap. The central level is known as Fermi level. This fermi level is the energy that corresponds to center of gravity of conduction electron and holes weighted according to their energies. In an intrinsic semiconductor there is equal no. of electron and holes. ni = pi ………….(1) no. of electron in conduction band is given by ni = Nc e -(EC - EF) / KT ………….(2) no. of hole in valance band is given by pi = Nv e -(EF - EV) / KT ………….(3) put the value of eq(2) and (3) in eq(1) Nc e-(EC - EF) / KT = Nv e-(EF - EV) / KT Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 7  Engineering Physics 𝑵𝒄 𝐞−(𝑬𝑭 − 𝑬𝑽 )/ 𝐊𝐓 ∴ = 𝑵𝑽 𝐞−(𝑬𝑪 − 𝑬𝑭 )/ 𝐊𝐓 Taking log on both sides 𝑵𝑪 𝐞−(𝑬𝑭 − 𝑬𝑽 )/ 𝐊𝐓 ∴ 𝐥𝐨𝐠 ( ) = 𝐥𝐨𝐠 ( −(𝑬 − 𝑬 )/ 𝐊𝐓 ) 𝑵𝑽 𝐞 𝑪 𝑭 𝑵𝑪 ∴ 𝐥𝐨𝐠 ( ) = 𝐥𝐨𝐠 𝒆 −(𝑬𝑭 − 𝑬𝑽 )/ 𝐊𝐓 - 𝐥𝐨𝐠 𝒆 −(𝑬𝑪 − 𝑬𝑭 )/ 𝐊𝐓 𝑵𝑽 𝑵𝑪 ∴ 𝐥𝐨𝐠 ( ) = - (EF - EV) / KT + (EC - EF) / KT 𝑵𝑽 𝑵𝑪 −𝑬𝑭 + 𝑬𝑽 + 𝑬𝑪 − 𝑬𝑭 ∴ 𝐥𝐨𝐠 ( ) = 𝑵𝑽 𝐊𝐓 𝑵𝑪 𝑬𝑪 + 𝑬𝑽 − 𝟐𝑬𝑭 ∴ 𝐥𝐨𝐠 ( ) = 𝑵𝑽 𝐊𝐓 𝑵𝑪 ∴ 𝐊𝐓 𝐥𝐨𝐠 ( ) = 𝑬𝑪 + 𝑬𝑽 − 𝟐𝑬𝑭 𝑵𝑽 𝑵𝑪 𝟐𝑬𝑭 = 𝑬𝑪 + 𝑬𝑽 − 𝐊𝐓 𝐥𝐨𝐠 ( ) ………….(4) 𝑵𝑽 Dividing eq (4) by 2 𝑬𝑪 + 𝑬𝑽 𝐊𝐓 𝑵𝑪 𝑬𝑭 = – 𝐥𝐨𝐠 ( ) 𝟐 𝟐 𝑵𝑽 If the effective mass of electron is equal to the effective mass of hole i.e. mn = mp then Nc = Nv, ∴ log (1) = 0,Therefore equation (4) becomes 𝑬𝑪 + 𝑬𝑽 𝑬𝑭 = 𝟐 This show that fermi level in intrinsic semiconductor lies in the middle of Forbidden band gap. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 8  Engineering Physics Fermi Level in Extrinsic Semiconductors:-  Explain position of Fermi level in N-type & P-type semiconductor. Fermi Level in P-type Semiconductors:- When acceptor impurity is added to an intrinsic semiconductor it becomes P- type. Due to this acceptor impurity after breaking of covalent bond e- & hole pair is created. e- which are produce due to breaking of bond will be capture by this impurity atom. Hence in this case it has more no. of hole as compare to e- as shown in fig. Thus in a valance band there are large no. of hole. Thus Fermi level in shifted towards the valance band. Fermi Level in N-type Semiconductors:- When donar impurity is added to an intrinsic semiconductor it becomes N- type. Due addition of donar impurity it will donate one free e- to the crystal. After breaking of covalent bond e- & hole pair is created. Now it has more conduction e- as compair to hole as shown in fig. This moves center of gravity up i.e. thus fermi level in shifted towards the conduction band. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 9  Engineering Physics  Explain the term P-N Junction diode & Junction potential barrier.  What is depletion region in junction diode & explain the formation of potential barrier. P- N Junction: When a P-type semiconductor is suitably joined with N-type semiconductor the contact surface is known as P-N Junction. It is possible to manufacture a single piece of a semiconductor material. One half parts is doped with P- type impurity & half part is doped with N-type impurity as shown in fig. When P-N Junction is form charge move higher density to lower densi- ty. The plane dividing to two zones is called as P - N Junction. During formation of P-N Junction following phenomenon takes place. 1) Formation of Depletion layer: Suppose that P-N Junction has just been formed at that instant. In P- type semi- conductor holes are majority charge carrier & e- are minority charge carrier & on other hand in N-type semiconductor electrons are majority carrier and holes are minority carrier. This difference in concentration established a density gradient across the junction resulting in majority carrier diffusion. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 10  Engineering Physics As soon as P-N- Junction is formed, 1) The holes from P - region diffuse it the N-region, then they combine with the free e- in n-region. 2) The e- from the N- region diffuses into P-region thus this free e- combine with the holes. 3) The diffusion of holes & e- are takes place because they cross the junction due to thermal energy also because there is a difference in their concentration in the two regions. i.e. P-region has more holes & N- region has more free e-. One would normally accept the holes from p-region & free e- from n- region to flow each other & combine. Thus all the holes & free e- would have been eliminated. But in actual practice, this does not occurred. The diffusion of hole & e - across the junction occurs for a very short time. After few recombinations of holes & e- at the junction restoring forces is setup automatically. Their force is called as barrier. Fur- ther the motion of change carrier from one side to other side is stopped by this barrier. This is called as potential barrier. For silicon barrier potential is 0.7 V & for germa- nium 0.3 V. How Barrier Force is developed? Some of the holes in P-region & some of the free e- in N- region diffuse to- wards each other & recombine. Each recombination eliminates a hole & a free e-. In this process -ve acceptor ions in the P-region & +ve donor ions in N -region in the immediate neighborhood of the junction are left. This situation is shown in fig. The addition of holes trying to diffuse into N-region are repelled by the +ve donor ions. The e- trying to diffuse into the P- region are repelled by -ve charge on acceptor ions. As the result total recombination of hole & e- cannot occur. The region containing the acceptor & doner ions is called depletion region. That is there is a de- pletion of mobile charges in this region. Since region has immobile ions which are electrically charged it is also referred to as the space charge region. The electric field between acceptor & donor ion is called as barriers. The physical dist. from one side of barrier to other side of barrier is referred as the width of barrier. The difference of potential from one side of the barrier to the other side is referred to as the height of the barrier. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 11  Engineering Physics  Explain forward & reverse biasing in P-N Junction diode.  Discuss the working of P-N Junction diode under the forward & reverse bias con- duction. Biasing of P- N Junction: When P-N- Junction is formed then depletion region will be developed across the junction, it will oppose the motion of change carrier hence the carrier will not able to cross the junction for the motion of change carrier, we have to supply the energy to the change carries. The energy can be supplied by the external source such as battery. The supply of external energy to charge carrier to cross the potential barriers is called biasing. There are two types of biasing - 1) Forward Biasing 2) Reverse Biasing 1) Forward Biasing: If +ve terminal of the battery is connected to P-region & -ve terminal of the battery is connected to N-region then the biasing is called as forward biasing. In P-region majority carrier are holes as +ve terminal is connected to P-region & hence it will repel hole towards the Junction. In N-region majority carrier are elec- tron as -ve terminal is connected to N-region & hence it will repel the e- towards the Junction. Thus the width of depletion region decreases. If majority carriers get suffi- cient energy then they will be able to cross the Junction. Hence current will be flow through the diode as applied voltage increase large no. of charge carriers gets suffi- cient energy to cross the junction & hence large current will flow through the (diode) Junction. In this current flow due to majority carrier i.e. electron & hole. Thus the total current flowing through the diode is sum of e- & hole. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 12  Engineering Physics The characteristic of diode is a relation between voltage & current. To study forward characteristic, change applied voltage v & note down corresponding change in current I. Plot the graph between v & I as shown in fig. From the graph we can say that, 1) Initially when applied voltage is less i.e. current will not flow up to certain volt- age. This voltage is called as cut in voltage or threshold voltage. 2) Beyond this cut in voltage current increase sharply. 3) In forward bias diode offer less resistance for the flow of current. Reverse Biased P- N Junction: In this -ve terminal of the battery is connected to P-region & +ve terminal of the battery is connected to N- region then the biasing is called as reverse biasing as shown in fig. In P-type the majority carrier are hole & -ve terminal of the battery is connect- ed to P-region & hence hole will be attract towards -ve terminal i.e. they will away from the junction. In N-type majority carrier are e- & +ve terminal is connected to N-region & hence e- will be attract towards the +ve terminal i.e. they will away from the junction. Hence width of depletion region will increase; thus current should not flow through the diode. But in actual practices current flow due to the minority carrier as no of mi- Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 13  Engineering Physics nority carrier is vary less & hence very small current will be flow through the diode & this current is called as reverse current. To study the reverse characteristic of P-N- Junction diode, change the applied reverse voltage Vr & note down the corresponding change in Ir plot the graph between Vr & Ir as shown in fig. From the graph we can say that, 1. Initially Vr increases, Ir also increase attain maximum value (Io). This current is caused as reverse saturation current or leakage current. 2. If we further increase Vr then Ir remain constant up to certain voltage (Vz). This voltage is called as break down voltage. 3. Beyond Vz, Ir increase very sharply this region is called as break down region. 4. In R. B. diode offer large resistance (because very small current flowing through it).  Explain Avalanche and Zener breakdown.  What is Zener diode? Compare between Avalanche and Zener breakdown. Diode which is designed with adequate power dissipation capabilities to oper- ate in current increases with an increase in applied voltage. This forward current is limited by the parameters of the circuit. When it is biased, a small reverse current, is called saturation current. The current remains relatively constant in reverse bias, until the zener breakdown region; in the vicinity of zener voltage Vz is reached. From the voltage Vz onwards, the current rises rapidly even for a small change in a voltage. This voltage is called as breakdown voltage. The breakdown voltage depends upon the width of the depletion region which in turn depends upon the doping level. Hence zener diode is heavily doped as compared to ordinary diodes. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 14  Engineering Physics Breakdown mechanism:- In reverse biased condition beyond the breakdown voltage large current is flow through the diode. This is due to the breakdown mechanism there are two types of breakdown mechanism. 1) Avalanche breakdown. 2) Zener breakdown. 1) Avalanche breakdown:- In reverse biased condition current flows due to minority charge carriers. When we increase the reverse voltage the charge carrier get energy & they collide with the atoms of crystal. During the collision energy of the charge carrier will be transferred to the atoms. If this energy is sufficient then they will break the covalent bonds. After breaking the covalent bonds give rise to electron & hole pairs. As applied voltage is high the newly created charge carrier also gets sufficient energy & they will collide with the atoms of the crystal & break the bonds. Thus we get large no. of charge carrier due to this collision process. This process is multiplicative hence we get no. of charge carrier.Thus large current will flow through diode.  Some important points : 1) The process in which formation of charge carrier due to collision process is called Avalanche breakdown. 2) The diode in which Avalanche multiplication is takes place is called Avalanche diode. 3) Avalanche diode is lightly doped. 4) Avalanche breakdown voltage is greater than 6 volt. 5) As temperature increases Avalanche breakdown voltage also increases. 2) Zener breakdown:- In reverse biased condition current is flow due to minority charge carrier. The amount of minority charge carrier depends amount of doping.If diode is heavily doped then the width of depletion region is very small. Thus their exist a very strong electric field across the junction. This will exert a force on covalent bond. If this force is sufficient then it will break the covalent bond & give the electron and hole pairs. This process is called zener breakdown. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 15  Engineering Physics  Some important points : 1) The process in which formation of charge carrier takes place due to strong electric field is called Zener breakdown. 2) The diode in which Zener breakdown takes place is called Zener diode. 3) Zener diode is heavily doped. 4) Zener breakdown voltage is less than 6 volt. 5) As temperature increases Zener breakdown voltage also increases. Zener diode or Breakdown diode:- It is a P-N junction diode. It works in breakdown region of reverse biased con- dition. In this reverse voltage remains almost constant for large change in current. Hence it is used as a voltage regulator or voltage stabilizer. Its breakdown voltage depends upon the amount of doping. Thus by changing the amount of doping we can change the breakdown voltage. Thus we get the zener diode from few volts to several hundred of volts. The circuit symbol for zener diode is as shown in fig. It is similar to ordinary diode expect the change is that the bar is turned into letter Z.  Explain the working of forward characteristics of Light Emitting Diode & give its application. Light emitting diode (LED) Light emitting diode is a solid state light source. It is an optoelectronics device, which convert electrical energy into light energy. LED is a P-N junction diode which emits light when forward bias. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 16  Engineering Physics When P-N junction is F.B., the majority carrier moves towards the junction and carrier recombination takes place. During recombination, the electron in the C.B. on N-side falls into the holes in the V.B. of P-side, which is on the lower level i.e. elec- tron jumps from higher level to lower level. Hence difference of energy is radiated in the form of heat and light. In ordinary P-N junction diode, this energy is given out in the form of heat. But in LED greater percentage of energy is given out in the form of light because of material used in making LED. The semiconducting materials used for manufacturing LED are compound semiconductors like 1. Gallium arsenide (GaAs) 2. Gallium phosphide (GaP) 3. Gallium arsenide phosphide (GaAsP) The colour of emitted light depends upon the type of semiconductor used 1. GaAs LED emits light in infrared region. 2. GaP emits green or red light. 3. GaAsP emits red or yellow light depending upon its composition. Applications of LED LED operates at low voltage level from 1.5V to 3.3V. They have long life of about 10,000 hours. Some important applications of LED are 1) Infrared LED is used in burglar alarms. 2) In optical switching applications. 3) For power oh-off condition, power level indicator or stereo amplifier. 4) For solid state video display. 5) In 7-segment, 16 segment and dot matrix display which are used to indicate alphanumerical characters and symbol. 6) In the field of optical communication. 7) In image sensing circuit for picture phone. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 17  Engineering Physics V-l Characteristics of LED: The V-l characteristic of LED is as shown in fig. It is seen that currents zero upto certain voltage (V0) and then it start increasing rapidly. The voltage at which LED glow and current start increasing is called striking potential or conduction volt- age.  Derive the conductivity equation for semiconductor. Electrical conductivity of semiconductors:- The conductivity of semiconductor is different from metal because in semi- conductor the charge carriers are electrons as well as holes. We know that from free electron theory, conductivity of metal is given by, σ = n.e.ue -----------(1) Where η= number of free electron per unit volume that is charge density e = charge on electrons ue =mobility of an electrons. But in semiconductor conduction is due to both charge carriers that is holes and electrons. Let n be the free electron density in C.B. and ue is electron mobility then conductivity due to e- in C.B. is given by σn = n.e.ue ---------------(2) Let p be the holes density in the V.B. un is hole density mobility then con- ductivity due to holes in V.B. is given by σP = p.e uh ----------(3) Then total conductivity is given by σ = σn + σp Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 18  Engineering Physics σ = n.e ue + p.e uh σ = e (n. ue + p.uh) -----------------(4) This equation gives the expression for conductivity of semiconductors in general. 1) Conductivity of an intrinsic semiconductor In intrinsic semiconductor the number of free electrons is equal to Number of holes hence N = p = ni Where ni= intrinsic carrier concentration σ = e (niue+niuh) σ = e ni (ue+uh) --------(5) This is the expression for conductivity of an intrinsic semiconductor. 2) Conductivity of an extrinsic semiconductor a) N-type In N-type semiconductor, the electron concentration is much greater than the hole concentration. The electron concentration is now represented by Nd that is concentration of donar atoms n = Nd As n >> p n ue >> p uh (n ue + p uh) ≅ n ue ≅ Nd. ue σ = e (n. ue + p.uh) σ n = e Nd. ue (From equation 4) This is the expression for conductivity of N-type semiconductor. b) P-type In p-type semiconductor, the hole concentration is much greater than the electron concentration. The hole concentration is now represented by Na that is concentration of acceptor atoms. p = Na That is p >> n P uh>>n ue (n ue + p uh) ≅ p uh ≅ Na. uh σ p = e Na uh This is the expression for conductivity if p-type semicondors. Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 19  Engineering Physics Atomic Structure: (Just Read) The atomic structure of materials, as conceived by Bohr, has a nucleus at the centre around which the electrons move in orbits. This can be conceived to be similar to planets around the sun. The nucleus consists of proton which is positivity charge and neutrons having no electrical charge. The electrons are negatively charge. Charge of an electron is 1.6 x 10-19 Coulomb. The entire electrons do not belonging to same orbit (or shell). Further, within each shell there are subshells. The maximum number of electron which can be present in any shell is given by 2n2. Where, n is the orbit number. For example Orbit Number (Shell) Maximum number of electrons 1 2 2 8 3 18 4 32 The electrons fill up the first shell first, and then second shell and so on. The number of electrons will be the same as the number of proton in the nucleolus. Let us take an example of germanium. It has the atomic symbol Ge and has atomic number 32. This means an atom of germanium has 32 protons in the nuclei and 32 electrons. These 32 electrons occupy different shell as follows: 1st shell (K) = 2 electrons 2nd shell (L) = 8 electrons 3rd shell (M) = 18 electrons 4th shell (N) = 4 electrons Total = 32 electrons Note that the outermost shell has 4 electrons similarly, silicon (Si) has atomic number 14. It has 14 protons in the nucleus and 14 electrons, distributed as follows. 1st shell (K) = 2 electrons 2nd shell (L) = 8 electrons 3rd shell (M) = 4 electrons Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 20  Engineering Physics Total = 14 electrons Here the outermost that s 3rd shell has 4 electrons. Drift Velocity: - When steady electric field is applied to the metal, electrons move towards the positive terminal of applied voltage, these electrons will gain an average velocity called as an average drift velocity. Mobility: - Mobility can be defined as the average drift velocity gain by electron per unit electric field. 𝑽𝒅 ue = 𝑬 E = Volt/m Vd = m/s The unit of mobility is m2/sec.volt Prof. S.D. Thakre. (IBSS College of Engineering, Amravati.) Page 21