BES00002 Study Material PDF

Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Study Material Name of the Course: Basic Elec...

Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Study Material Name of the Course: Basic Electrical and Electronics Engineering Course Code: BES00002 Module Topic Page Number(s) M1 EMF, Current , Potential difference, Power, Energy 2-4 Magnetic Circuits 4-11 Flemings Left and Right hand rule 12-13 Introduction to Metal, Insulator and Semiconductor 13-16 Introduction to semiconductor 16-22 Majority and Minority Carriers: 22-23 Drift current and diffusion currents 23-25 Conductivity of Semiconductor 25-26 Charge Densities in P-type and N-type Semiconductor 27-28 Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 1 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Electromotive Force (EMF) Definition: Electromotive Force (EMF) is a measure of the energy provided by a source of electrical energy, such as a battery or generator, per unit charge that flows through the circuit. It is not a force but a potential difference that drives current through a circuit. Formula: The EMF (E) is given by: E=WQ where: W = Work done by the source, Q = Charge moved Units: The unit of EMF is the volt (V), which is equivalent to 1 joule per coulomb (1 J/C). Sources of EMF: Chemical Cells: Batteries and galvanic cells. Electromagnetic Induction: Generators and alternators. Photoelectric Effect: Solar cells. Thermoelectric Effect: Thermocouples. Internal Resistance: Every real source of EMF has some internal resistance (r). The observed voltage (V) across the terminals is less than the EMF due to this internal resistance: V=E−Ir where: I = Current, r = Internal resistance EMF in Circuits: In a closed circuit with internal resistance, the EMF drives the current through the circuit, and the voltage across the external components is the EMF minus the voltage drop due to internal resistance. Faraday’s Law of Electromagnetic Induction: The EMF induced in a circuit is proportional to the rate of change of the magnetic flux through the circuit: E=−dΦ\dt where: Φ= Magnetic flux, dΦ\dt= Rate of change of magnetic flux Applications: Batteries: Provide EMF to power electronic devices. Generators: Convert mechanical energy into electrical energy. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 2 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Transformers: Use EMF principles to transfer electrical energy between circuits. Electric Current(I): Electric current is the flow of electric charge through a conductor, typically measured in amperes (A). It occurs when there is a potential difference (voltage) across the conductor, causing charge carriers (usually electrons) to move. 1. Types: o Direct Current (DC): Flows in one direction; used in batteries and electronic devices. o Alternating Current (AC): Changes direction periodically; used in household power supplies and transmission lines. 2. Measurement: Measured with an ammeter, it indicates the rate of flow of charge. 3. Ohm's Law: I = V/R: Current (I) equals voltage (V) divided by resistance (R). 4. Applications: Powers electrical devices, systems, and machinery. 5. Safety: Proper handling is crucial to avoid electric shocks and ensure safe operation. Potential Difference: Potential difference, often referred to as voltage, is the measure of the difference in electric potential between two points in a circuit. It drives the flow of electric current from a region of higher electric potential to one of lower potential. 1. Definition: Potential difference is the work done per unit charge to move a charge between two points. It is measured in volts (V). 2. Formula: V = W/Q: Voltage (V) equals work done (W) divided by charge (Q). 3. Role in Circuits: It creates the driving force for current flow. Higher potential difference results in greater current, assuming resistance is constant. 4. Sources: Batteries, generators, and power supplies provide potential difference. 5. Measurement: Measured with a voltmeter across two points in a circuit. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 3 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Electrical Power and Energy: Electrical Power: Electrical power is the rate at which electrical energy is transferred or converted in a circuit. It is measured in watts (W) and represents the amount of energy consumed or produced per unit time. Formula: P=V×I o P = Power (watts) o V = Voltage (volts) o I = Current (amperes) Types: o Active Power: The real power consumed by devices to perform work (measured in watts). o Reactive Power: Power stored and released by reactive components like inductors and capacitors (measured in volt-amperes reactive, VAR). o Apparent Power: The total power supplied to the circuit (measured in volt-amperes, VA). Electrical Energy: Electrical energy is the total work done or energy transferred by an electric current over a period of time. It is measured in joules (J) or kilowatt-hours (kWh). Formula: E=P×t o E = Energy (joules or kilowatt-hours) o P = Power (watts) o t = Time (seconds or hours) Electrical energy is used to power devices and systems, with efficiency and consumption directly related to power and time. Understanding these concepts is essential for managing energy usage and designing electrical systems. Magnetic Circuits: The Magnetic Field and Faraday’s Law: Magnetic fields are generated by electric charge in motion, and their effect is Measured by the force they exert on a moving charge. The vector force f exerted on a charge of q moving at velocity Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 4 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 u in the presence of a magnetic field with flux density B is given by f = qu×B Where the symbol × denotes the (vector) cross product. If the charge is moving at a velocity u in a direction that makes an angle θ with the magnetic field, then the magnitude of the force is given by f = qu×B Where the symbol × denotes the (vector) cross product. If the charge is moving at a velocity u in a direction that makes an angle θ with the magnetic field, then the magnitude of the force is given by f = quBsin θ and the direction of this force is at right angles with the plane formed by the vectors B and u. The magnetic flux φ is then defined as the integral of the flux density over some surface area. φ = A BdA ∫ in webers ⇒ = φ B A. Faraday’s law states that a time-varying flux causes an induced electromotive force, or emf d e dt φ Faraday’s law states that a time-varying flux causes an induced electromotive force, or emf Faraday’s Law Faraday’s law of electromagnetic induction (referred to as Faraday’s law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction. Faraday’s law states that a current will be induced in a conductor which is exposed to a changing magnetic field. Lenz’s law of electromagnetic induction states that the direction of this induced current will be such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it. The direction of this current flow can be determined using Fleming’s right-hand rule. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 5 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Faraday’s law of induction explains the working principle of transformers, motors, generators, and inductors. The law is named after Michael Faraday, who performed an experiment with a magnet and a coil. During Faraday’s experiment, he discovered how EMF is induced in a coil when the flux passing through the coil changes. Faraday’s Experiment In this experiment, Faraday takes a magnet and a coil and connects a galvanometer across the coil. At starting, the magnet is at rest, so there is no deflection in the galvanometer i.e the needle of the galvanometer is at the center or zero position. When the magnet is moved towards the coil, the needle of the galvanometer deflects in one direction. When the magnet is held stationary at that position, the needle of galvanometer returns to zero position. Now when the magnet moves away from the coil, there is some deflection in the needle but opposite direction, and again when the magnet becomes stationary, at that point respect to the coil, the needle of the galvanometer returns to the zero position. Similarly, if the magnet is held stationary and the coil moves away, and towards the magnet, the galvanometer similarly shows deflection. It is also seen that the faster the change in the magnetic field, the greater will be the induced EMF or voltage in the coil. In practical applications, the size of the voltages induced by the changing magnetic field can be significantly increased Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 6 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 if the conducting wire is coiled many times around, so as to multiply the area crossed by the magnetic flux lines many times over. For an N-turn coil with cross-sectional area A, for example, we have the emf When N-turn coil linking a certain amount of magnetic flux, then the flux linkage λ φ = N The relation between flux linkage and current is gven by λ = Li so that the effect of a time-varying current was to induce a transformer voltage across an inductor coil, according to the expression L is the self-inductance which measures the voltage induced in a circuit by magnetic field generated by a current flowing in the same circuit. Magnetic Susceptibility: The dimensionless proportionality constant which generally provides an indication of the magnetization degrees of materials is determined as the magnetic susceptibility. This indication of magnetization degrees is always provided in response to the applied field of magnets. This phenomenon occurs due to the interaction between nuclei and electrons in an atom with their eternal magnetic field. A material’s magnetic susceptibility is usually denoted by X m. Xm is equivalent to the ratio of M denoting the magnetization within the substance to the strength, H of its external magnetic field. The formula of magnetic susceptibility can be written in the form: Xm=M/H Types of magnetic materials: Paramagnetism − The type of magnetism in certain substances that get attracted weakly towards the externally Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 7 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 applied magnetic field is denoted as Paramagnetism. Here, internally induced magnetic fields are produced in the same direction as magnetic fields. Paramagnetism has magnetic permeability which is a little greater than 1 and has positive magnetic susceptibility. Diamagnetism − This is the very weak form of magnetism that gets induced by the orbital change in the motion of electrons because of an external magnetic field. Diamagnetism is not permanent and can persist in presence of an external field only. Some Diamagnetic materials are glass, silver, gold, NACL, copper, water, and marble. Ferromagnetism − This is the strongest form of magnetism that gets easily magnetized in the external magnetic field. Ferromagnetism, occurs mainly in some rare elements found on the earth and also in. Some Ferromagnetic materials are nickel, iron, cobalt, and other alloys that have more than 1 of these elements. It remains even if externally applied magnetic field is removed. Ferromagnetism, Diamagnetism, and Para-magnetism are mainly denoted by the state of the substance and how they are responding to their magnetic fields. There are various differences between these substances. In Paramagnetic and Ferromagnetic substances there are effects of temperature but in the case of Diamagnetic substances there are no temperature effects. Magnetic Susceptibility is positive and higher in Paramagnetic and Ferromagnetic but negative and lower in Diamagnetic substance. The theory mainly highlights the breaking of magnets into tiny magnets, demagnetization, and limiting the magnetic strength. The magnetism of a substance can be destroyed by heating, hammering, and even by utilizing reduced alternating current by wrapping a coil around the magnet. Retentivity Let’s assume that we have an electromagnetic coil with a high field strength due to the current flowing through it, and that the ferromagnetic core material has reached its saturation point, maximum flux density. If we now open a switch and remove the magnetising current flowing through the coil we would expect the magnetic field around the coil to disappear as the magnetic flux reduced to zero. However, the magnetic flux does not completely disappear as the electromagnetic core material still retains some of its magnetism even when the current has stopped flowing in the coil. This ability for a coil to retain some of its magnetism within the core after the magnetisation process has stopped is called Retentivity or remanence, while the amount of flux density still remaining in the core is called Residual Magnetism, BR. The reason for this that some of the tiny molecular magnets do not return to a completely random pattern and still point in the direction of the original magnetising field giving them a sort of “memory”. Some ferromagnetic materials have a high retentivity Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 8 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 (magnetically hard) making them excellent for producing permanent magnets. While other ferromagnetic materials have low retentivity (magnetically soft) making them ideal for use in electromagnets, solenoids or relays. One way to reduce this residual flux density to zero is by reversing the direction of the current flowing through the coil, thereby making the value of H, the magnetic field strength negative. This effect is called a Coercive Force, HC. If this reverse current is increased further the flux density will also increase in the reverse direction until the ferromagnetic core reaches saturation again but in the reverse direction from before. Reducing the magnetising current, i once again to zero will produce a similar amount of residual magnetism but in the reverse direction. Then by constantly changing the direction of the magnetising current through the coil from a positive direction to a negative direction, as would be the case in an AC supply, a Magnetic Hysteresis loop of the ferromagnetic core can be produced. Magnetic Hysteresis Loop: Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 9 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 The Magnetic Hysteresis loop above, shows the behaviour of a ferromagnetic core graphically as the relationship between B and H is non-linear. Starting with an un-magnetised core both B and H will be at zero, point 0 on the magnetisation curve. If the magnetisation current, i is increased in a positive direction to some value the magnetic field strength H increases linearly with i and the flux density B will also increase as shown by the curve from point 0 to point a as it heads towards saturation. Now if the magnetising current in the coil is reduced to zero, the magnetic field circulating around the core also reduces to zero. However, the coils magnetic flux will not reach zero due to the residual magnetism present within the core and this is shown on the curve from point a to point b. To reduce the flux density at point b to zero we need to reverse the current flowing through the coil. The magnetising force which must be applied to null the residual flux density is called a “Coercive Force”. This coercive force reverses the magnetic field re-arranging the molecular magnets until the core becomes un-magnetised at point c. An increase in this reverse current causes the core to be magnetised in the opposite direction and increasing this magnetisation current further will cause the core to reach its saturation point but in the opposite direction, point d on the curve. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 10 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 This point is symmetrical to point b. If the magnetising current is reduced again to zero the residual magnetism present in the core will be equal to the previous value but in reverse at point e. Again, reversing the magnetising current flowing through the coil this time into a positive direction will cause the magnetic flux to reach zero, point f on the curve and as before increasing the magnetisation current further in a positive direction will cause the core to reach saturation at point a. Then the B-H curve follows the path of a-b-c-d-e-f-a as the magnetising current flowing through the coil alternates between a positive and negative value such as the cycle of an AC voltage. This path is called a Magnetic Hysteresis Loop. Analogy between electric and magnetic circuits Electric Circuits Magnetic Circuits Voltage (V) Magnetomotive Force (MMF) The driving force for current flow. The driving force for magnetic flux. Current (I) Magnetic Flux (Φ) The flow of electric charge. The flow of magnetic field lines. Resistance (R) Reluctance (Rₑ) Opposition to magnetic flux in a magnetic Opposition to current flow in a conductor. material. Ohm's Law Flux Law V=I×R MMF=Φ×Re Relationship between voltage, current, and Relationship between MMF, flux, and resistance. reluctance. Power (P) Magnetic Power P=V×I Magnetic Power=MMF×Φ Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 11 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Rate at which electrical energy is used or Rate at which magnetic energy is transferred. transferred or used. Capacitors Magnetic Capacitors (or Air Gaps) Store magnetic energy in a magnetic field Store electrical energy in an electric field. gap. Inductors Magnetic Coils Store magnetic energy in a coil or Store electrical energy in a magnetic field. solenoid. Principle of Self and Mutual Inductance 1. Self-Inductance: Definition: Self-inductance is the property of a coil (or any inductor) by which it induces an electromotive force (EMF) in itself as a result of a change in its own current. This self-induced EMF opposes the change in current due to Lenz's Law. Formula: VL=−LdI\dt o VL= Induced EMF (volts) o L = Self-inductance (henries, H) o dI\dt= Rate of change of current (amperes per second) Explanation: When the current through the coil changes, it creates a changing magnetic field that induces a voltage opposing the change. The coil's self-inductance quantifies its ability to oppose changes in current. 2. Mutual Inductance: Definition: Mutual inductance is the property of two coils by which a change in current in one coil induces an EMF in the other coil. This interaction occurs due to the magnetic field produced by the first coil influencing the second coil. Formula: V=−MdI\dt o V= Induced EMF in the second coil (volts) o M = Mutual inductance (henries, H) o dI\dt= Rate of change of current in the first coil (amperes per second) Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 12 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Explanation: The mutual inductance measures the extent to which a change in current in one coil induces a voltage in another coil placed nearby. The induced voltage is proportional to the rate of change of current in the first coil and the mutual inductance between the two coils. Applications: Self-Inductance: Used in transformers, inductors, and filters. Mutual Inductance: Utilized in transformers, coupling in circuits, and wireless power transfer systems. Fleming’s Left-Hand Rule The first finger points in the direction of the magnetic field (first - field), which goes from the North pole to the South pole. The second finger points in the direction of the current inthe wire (second - current). The thumb then points in the direction the wire is thrust or pushed while in the magnetic field (thumb - torque or thrust). Fleming's Right-Hand Rule Fleming's Right-Hand Rule is a principle used to determine the direction of force experienced by a current-carrying conductor placed in a magnetic field. It is primarily applied in electric generators and motors. How to Apply the Rule: Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 13 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 1. Positioning Your Hand: o Extend your right hand with your thumb, forefinger, and middle finger all perpendicular to each other, forming an "L" shape. 2. Direction of Fingers: o Thumb: Points in the direction of the Force (F) exerted on the conductor. o Forefinger: Points in the direction of the Magnetic Field (B), which is typically represented from North to South. o Middle Finger: Points in the direction of the Current (I) flowing through the conductor. Usage: This rule helps in determining the direction of motion or force in electric motors and generators, where magnetic fields and currents interact. Introduction to Metal, Insulator and Semiconductor In an atom, the electrons in inner shells are tightly bound to the nucleus while the electrons in the outermost shell (i.e the valance electron) are loosely bound to the nucleus. During the formation of a solid, a large number of atoms are brought very close together; the energy levels of these valence electrons are affected most. The energies of inner shell electrons are not affected much. The band formed by a series of energy levels containing the valence electrons is called the Valence Band (VB). Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 14 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 It is highest occupied energy band. It may be completely filled or partially filled with electrons. The next higher permitted energy band is called the Conduction Band (CB). It may also be defined as the lowest unfilled permitted energy band. It may be empty or partially filled with electrons. The electrons can move freely in the conduction band and hence the electrons in conduction band are called conduction electrons. The energy gap between the VB and CB is called the Forbidden Energy Gap or Forbidden Band. This band is formed by a series of non-permitted energy levels above the top of valence band and below the bottom of the conduction band. It is denoted by Eg and is the amount of energy to be supplied to the electron in VB to get excited into the CB. When an electron gains sufficient energy, it is ejected from the valence band. Because of this, a covalent bond is broken and a vacancy for electron, called Hole, is generated. It is supposed to behave as a positive charge. This Hole can travel to the adjacent atom by acquiring an electron from an atom. When an electron is captured by a Hole, the covalent bond is again reestablished. Thus conduction electrons are found in and above freely in the conduction band. The Holes exist in and move in the valence band. Distinction between Metal, Insulator and Semiconductor There are many energy bands in solids as there are energy levels in parent atom. The electrical conduction properties of solids are concerned, only the valance band and conduction band energies of the electron are considered. Completely filled bands and completely empty bands do not contribute to electrical conduction. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 15 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 The electrons in the innermost filled shell do not take part in conduction process. The electrons in conduction band are free and move easily under an electric field. The electrons in valance band are attached to the lattice and are not free to move If they acquire sufficient energy to cross the forbidden gap eg, they occupy the conduction band states are available for conduction. Based on the electrical conductivity all the materials in nature are classified as insulators, semiconductors, and conductors. Insulator: An insulator is a material that offers a very low level (or negligible) conductivity when voltage is applied. E.g. Paper, Mica, glass, quartz. Typical resistivity level of an insulator is of the orderof 1010 to 1012 Ω-cm. The energy band structure of an insulator is shown in the fig.1.1. Band structureof a material defines the band of energy levels that an electron can occupy. Valance band is the range of electron energy where the electron remains bonded to the atom and do not contribute to the electric current. Conduction bend is the range of electron energies higher than valance band where electrons are free to accelerate under the influence of external voltage source resulting in the flow of charge. The energy band between the valance band and conduction band is called as forbidden band gap. It is the energy required by an electron to move from balance band to conduction band i.e. the energy required for a valance electron to become a free electron. 1 eV = 1.6 x 10-19 J Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 16 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 For an insulator, as shown in the fig.1.1 there is a large forbidden band gap of greater than 5 ev. CB CB CB Forbidden band Eg =≈0.2eV -2.5eV gap Eg ≈6eV o VB VB VB Insulator Semiconductor Conductor Fig:1.1 Energy band diagrams insulator, semiconductor and conductor Because of this large gap there a very few electrons in the CB and hence the conductivity of insulator is poor. Even an increase in temperature or applied electric field is insufficient to transfer electrons from VB to CB. Conductors: A conductor is a material which supports a generous flow of charge when a voltage is applied across its terminals. i.e. it has very high conductivity. Eg: Copper, Aluminum, Silver, Gold. The resistivity of a conductor is in the order of 10-4 and 10-6 Ω-cm. The Valance and conduction bands overlap (fig1.1) and there is no energy gap for the electrons to move from valance band to conduction band. This implies that there are free electrons in CB even at absolute zero temperature (0K). Therefore, at room temperature when electric field is applied large current flows through the conductor. Semiconductor: A semiconductor is a material that has its conductivity somewhere between theinsulator and conductor. The resistivity level is in the range of 10 and 104 Ω-cm. Two of the most commonly used are Silicon (Si=14 atomic no.) and germanium (Ge=32 atomic no.). Both have 4 valance electrons. The forbidden band gap is in the order of 1eV. For eg., the band gap energy for Si, Ge and GaAs is 1.21, 0.785 and 1.42 eV, respectively at absolute zero temperature (0K). At 0K and at low temperatures, the valance band electrons do not have sufficient energy to move from V to CB. Thus, semiconductors act an insulator at 0K. as the temperature increases, a large number of valance electrons acquire sufficient energy to leave the VB, cross the forbidden band gap and reach CB. These are now free electrons as they can move freely under the influence of electric field. At room temperature there are sufficient electrons in the CB and hence the semiconductor is Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 17 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 capable ofconducting some current at room temperature. Inversely related to the conductivity of a material is its resistance to the flow of charge or current. Typical resistivity values for various materials are given as follows. Insulator Semiconductor Conductor 10-6 Ω-cm (Cu) 50Ω-cm (Ge) 1012 Ω-cm (mica) 50x103 Ω-cm (Si) Typical resistivity values Introduction to semiconductor Semiconductors: A semiconductor material is one whose electrical properties lie in between those of insulators and good conductors. Examples are: germanium and silicon. In terms of energy bands, semiconductors can be defined as those materials which have almost an empty conduction band and almost filled valence band with a very narrow energy gap (of the order of 1 eV) separating the two. Semiconductor Types A pure form of semiconductors is called as intrinsic semiconductor. Conduction in intrinsic semiconductor is either due to thermal excitation or crystal defects. Si and Ge are the two most important semiconductors used. Other examples include Gallium arsenide GaAs, Indium Antimonide (InSb) etc. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 18 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Intrinsic Semiconductors An intrinsic semiconductor is one which is made of the semiconductor material in its extremely pure form. Examples of such semiconductors are: pure germanium and silicon which have forbidden energy gaps of 0.72 eV and 1.1 eV respectively. The energy gap is so small that even at ordinary room temperature; there are many electrons which possess sufficient energy to jump across the small energy gap between the valence and the conduction bands. Alternatively, an intrinsic semiconductor may be defined as one in which the number of conduction electrons is equal to the number of holes. Schematic energy band diagram of an intrinsic semiconductor at room temperature is shown in Fig. below. Let us consider the structure of Si. A Si atomic no. is 14 and it has 4 valance electrons. These 4 electrons are shared by four neighboring atoms in the crystal structure by means of covalent bond. Fig. 1.2a shows the crystal structure of Si at absolute zero temperature (0K). Hence a pure SC acts has poor conductivity (due to lack of free electrons) at low or absolute zero temperature. Covalent bond Valence electron Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 19 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Fig. 1.2a crystal structure of Si at 0K At room temperature some of the covalent bonds break up to thermal energy as shown in fig 1.2b. The valance electrons that jump into conduction band are called as free electrons that are available for conduction. Free electron Valance electron hole Fig. 1.2b crystal structure of Si at roomtemperature 0K The absence of electrons in covalent bond is represented by a small circle usually referred to as hole which is of positive charge. Even a hole serves as carrier of electricity in a manner similar to thatof free electron. The mechanism by which a hole contributes to conductivity is explained as follows: When a bond is in complete so that a hole exists, it is relatively easy for a valance electron in the neighboring atom to leave its covalent bond to fill this hole. An electron moving from a bond to fill a hole moves in a direction opposite to that of the electron. This hole, in its new position may now be filled by an electron from another covalent bond and the hole will correspondingly move one more step in the direction opposite to the motion of electron. Here we have a mechanism for conduction of electricity which does not involve free electrons. This phenomenon is illustrated in fig1.3 Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 20 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Fig. 1.3b Fig. 1.3c Fig. 1.3a Electron movement Hole movement Fig 1.3a show that there is a hole at ion 6. Imagine that an electron from ion 5 moves into the hole at ion 6 so that the configuration of 1.3b results. If we compare both fig1.3a &fig 1.3b, it appears as if the hole has moved towards the left from ion6 to ion 5. Further if we compare fig 1.3b and fig1.3c, the hole moves from ion5 to ion 4. This discussion indicates the motion of hole is in a direction opposite to that of motion of electron. Hence we consider holes as physical entities whose movement constitutes flow of current. In a pure semiconductor, the number of holes is equal to the number of free electrons. Extrinsic Semiconductor Intrinsic semiconductor has very limited applications as they conduct very small amounts of current at room temperature. The current conduction capability of intrinsic semiconductor can be increased significantly by adding a small amounts impurity to the intrinsic semiconductor. By adding impurities, it becomes impure or extrinsic semiconductor. This process of adding impurities is called as doping. The amount of impurity added is 1 part in 106 atoms. Doping Doping is adding very small amounts of group 3 or group 5 elements to a group 4 semiconductor such as silicon. Adding a group 5 element causes the material to contain electrons that are free to move around (just like in a metal). Because electrons are negatively charged particles these semiconductors known as n-type semiconductors. Adding a group 3 element causes the material to contain holes. These are gaps in the covalent bonds between atoms that will move around and act just like positively charged particles (hence these semiconductors being Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 21 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 known as p-type). The process of adding impurities to the semiconductor materials is termed as doping. The impurities added, are generally pentavalent and trivalent impurities. Pentavalent Impurities: The pentavalent impurities are the ones which has five valence electrons in the outer most orbit. Example: Bismuth, Antimony, Arsenic, Phosphorus The pentavalent atom is called as a donor atom because it donates one electron to the conduction band of pure semiconductor atom. Trivalent Impurities: The trivalent impurities are the ones which has three valence electrons in the outer most orbit. Example: Gallium, Indium, Aluminum, Boron The trivalent atom is called as an acceptor atom because it accepts one electron from the semiconductor atom. N type semiconductor: If the added impurity is a pentavalent atom then the resultant semiconductoris called N-type semiconductor. Examples of pentavalent impurities are Phosphorus, Arsenic, Bismuth, Antimony etc. A pentavalent impurity has five valance electrons. Fig 1.4a shows the crystal structure of N-type semiconductor material where four out of five valance electrons of the impurity atom(antimony) forms covalent bond with the four intrinsic semiconductor atoms. The fifth electron is loosely bound to the impurity atom. This loosely bound electron can be easily. Fifth valance electron of SB CB Ec Ed VB Donor energy level Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 22 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Ev Fig. 1.4a crystal structure of N type Semiconductor Fig. 1.4b Energy band diagram of N type Excited from the valance band to the conduction band by the application of electric field or increasing the thermal energy. The energy required to detach the fifth electron form the impurity atom is very small of the order of 0.01ev for Ge and 0.05 eV for Si. The effect of doping creates a discrete energy level called donor energy level in the forbidden band gap with energy level Ed slightly less than the conduction band (fig 1.4b). The difference between the energy levels of the conducting band and the donor energy level is the energy required to free the fifth valance electron (0.01 eV for Ge and 0.05 eV for Si). At room temperature almost all the fifth electrons from the donor impurity atom are raised to conduction band and hence the number of electrons in theconduction band increases significantly. Thus every antimony atom contributes to one conduction electron without creating a hole. In the N-type semiconductor the no. of electrons increases and the no. of holes decreases compared to those available in an intrinsic sc. The reason for decrease in the no. of holes is that the larger no. of electrons present increases the recombination of electrons with holes. Thus current in N type semiconductor is dominated by electrons which are referred to as majority carriers. Holes are the minority carriers in N type semiconductor P type semiconductor: If the added impurity is a trivalent atom then the resultant semiconductor is called P- type semiconductor. Examples of trivalent impurities are Boron, Gallium, indium etc. The crystal structure of p type semiconductor is shown in the fig1.5a. The three valance electrons of the impurity (boon) forms three covalent bonds with the neighboring atoms and a vacancy exists in the fourth bond giving rise to the holes. The hole is ready to accept an electron from the neighboring atoms. Each trivalent atom contributes to one-hole generation and thus introduces a large no. of holes in the valance band. At the same time the no. electrons are decreased compared to those available in intrinsic sc because of increased recombination due to creation of additional holes. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 23 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 hole Fig. 1.5a crystal structure of P type semiconductor Thus, in P type semiconductor, holes are majority carriers and electrons are minority carriers. Since each trivalent impurity atoms are capable accepting an electron, these are called as acceptor atoms. The following fig 1.5b shows the pictorial representation of P type semiconductor hole (majority carrier) Electron (minority carrier) Acceptor atoms Fig. 1.5b crystal structure of P type semiconductor The conductivity of N type semiconductor is greater than that of P type semiconductor as the mobility of electron isgreater than that of hole. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 24 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 For the same level of doping in N type semiconductor and P type semiconductor, the conductivity of an N-type semiconductor isaround twice that of a P type semiconductor Majority and Minority Carriers: In a piece of pure germanium or silicon, no free charge carriers are available at 0ºK. However, as its temperature is raised to room temperature, some of the covalent bonds are broken by heat energy and as a result, electron-hole pairs are produced. These are called thermally-generated charge carriers. They are also known as intrinsically-available charge carriers. Ordinarily, their number is quite small. An intrinsic of pure germanium can be converted into a P- type semiconductor by the addition of an acceptor impurity which adds a large number of holes to it. Hence, a P-type material contains following charge carriers: (a) Large number of positive holes—most of them being the added impurity holes with only a very small number of thermally generated ones. (b) A very small number of thermally- generated electrons (the companions of the thermally generated holes mentioned above). Obviously, in a P-type material, the number of holes (both added and thermally generated) is much more than that of electrons. Hence, in such a material, holes constitute majority carriers and electrons form minority carriers as shown in Fig. below (a). Similarly, in an N-type material, the number of electrons (both added and thermally-generated) is much larger than the number of thermally-generated holes. Hence, in such a material, electrons are majority carriers whereas holes are minority carriers as shown in Fig. below (b). Drift current and diffusion currents In case of semiconductors we observe two kinds of currents. I. Drift current II. Diffusion current Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 25 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Drift current Definition:- The flow of electric current due to the motion of charge carriers under the influence of external electric field is called drift current. When an electric field E is applied across a semiconductor material, the charge carriers attain a drift velocity 𝑣𝑑. So drift velocity 𝑣𝑑 = 𝜇 𝐸. So, current density, 𝐽𝑑𝑟𝑖𝑓𝑡 = 𝑛. 𝑞. 𝜇 𝐸. Where n is the carrier concentration q is the charge of electron or hole 𝜇 is the mobility of charge carriers The above equation shows the general expression for drift current density. Drift current density due to electrons is 𝐽𝑒,𝑑𝑟𝑖𝑓𝑡 = 𝑛. 𝑞. 𝜇𝑒. 𝐸. Drift current density due to holes is 𝐽ℎ,𝑑𝑟𝑖𝑓𝑡 = 𝑝. 𝑞. 𝜇ℎ. 𝐸. Total drift current density 𝐽𝑑𝑟𝑖𝑓𝑡 (𝑇𝑜𝑡𝑎𝑙) = 𝐽𝑒,𝑑𝑟𝑖𝑓𝑡 + 𝐽ℎ,𝑑𝑟𝑖𝑓𝑡 = 𝑛. 𝑞. 𝜇𝑒. 𝐸 + 𝑝. 𝑞. 𝜇ℎ. 𝐸. =(𝑛. 𝜇𝑒 + 𝑝. 𝜇ℎ ) 𝑞. 𝐸 =𝜎 𝐸 ; 𝜎 is the conductivity. Diffusion current Definition:- The flow of electric current due to the motion of charge carriers under concentration gradient is called diffusion current Or The motion of charge carriers from the region of higher concentration to lower concentration leads to a current called diffusion current. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 26 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 So, the diffusion current density due to holes is 𝜕𝑝 𝐽ℎ,𝑑𝑖𝑓𝑓 = −𝑞. 𝐷ℎ. 𝜕𝑥. the diffusion current density due to electron is 𝜕𝑛 𝐽𝑒,𝑑𝑖𝑓𝑓 = 𝑞. 𝐷𝑒. 𝜕𝑥 The expression for total diffusion current density is 𝐽𝑑𝑖𝑓𝑓 (𝑇𝑜𝑡𝑎𝑙) = 𝐽𝑒,𝑑𝑖𝑓𝑓 + 𝐽ℎ,𝑑𝑖𝑓𝑓 𝜕𝑛 𝜕𝑝 = 𝑞. 𝐷𝑒. 𝜕𝑥 − 𝑞. 𝐷ℎ. 𝜕𝑥 The expression for total current density due to holes is 𝐽ℎ,𝑑𝑟𝑖𝑓𝑡 + 𝐽ℎ,𝑑𝑖𝑓𝑓 𝜕𝑝 = 𝑝. 𝑞. 𝜇ℎ. 𝐸 − 𝑞. 𝐷ℎ. 𝜕𝑥 The expression for total current density due to electrons is 𝐽𝑒,𝑑𝑟𝑖𝑓𝑡 + 𝐽𝑒,𝑑𝑖𝑓𝑓 𝜕𝑛 = 𝑛. 𝑞. 𝜇𝑒. 𝐸 + 𝑞. 𝐷𝑒.. 𝜕𝑥 Einstein relation The relation between mobility and diffusion coefficient of charge carriers in a semiconductor is known as Einstein relation. At equilibrium conducting condition, the drift and diffusion currents must be equal and opposite in direction. Any disturbance in equilibrium leads to diffusion of charge carriers resulting in diffusion current which creates an internal electric field. This field causes the drifting of charge carriers resulting in a drift current. Then at equilibrium the drift and diffusion currents balance each other. 𝐷 𝐾𝑇 = 𝜇 𝑒 Conductivity of Semiconductor Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 27 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 In a pure semiconductor, the no. of holes is equal to the no. of electrons. Thermal agitation continues to produce new electron- hole pairs and the electron hole pairs disappear because of recombination. with each electron hole pair created, two charge carrying particles are formed. One is negative which is a free electron with mobility µn. The other is a positive i.e., hole with mobility µp. The electrons and hole move in opposite direction in an electric field E, but since they are of opposite sign, the current due to each is in the same direction. Hence the total current density J within the intrinsic semiconductor is given by 𝐽 = 𝐽𝑛 + 𝐽𝑝 = 𝑞𝑛𝜇𝑛 𝐸 + 𝑞𝑝𝜇𝑝 𝐸 = (𝑛𝜇𝑛 + 𝑝𝜇𝑝 )𝑞𝐸 =𝜎𝐸 Where n = no. of electrons / unit volume i.e., concentration of free electrons p= no. of holes / unit volume i.e., concentration of holes. E= applied electric field strength, V/m q= charge of electron or hole in Coulombs Hence, σ is the conductivity of semiconductor which is equal to (𝑛𝜇𝑛 + 𝑝𝜇𝑝 ) 𝑞. The resistivity of semiconductor is reciprocal of conductivity. 𝜌 = 1⁄𝜎 It is evident from the above equation that current density within a semiconductor is directly proportional to applied electric field E. For pure semiconductor, 𝑛 = 𝑝 = 𝑛𝑖 where 𝑛𝑖 = intrinsic concentration. The value of 𝑛𝑖 is given by −𝐸𝑔𝑜 𝑛𝑖2 = 𝐴𝑇 3 exp( ⁄𝐾𝑇) therefore, 𝐽 = 𝑛𝑖 (𝜇𝑛 + 𝜇𝑝 )𝑞𝐸 Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 28 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 Hence conductivity in intrinsic semiconductor is 𝜎𝑖 = 𝑛𝑖 (𝜇𝑛 + 𝜇𝑝 )𝑞 Intrinsic conductivity increases at the rate of 5% per o C for Ge and 7% per o C for Si. Conductivity in extrinsic semiconductor (N Type and P Type): The conductivity of intrinsic semiconductor is given by 𝜎𝑖 = 𝑛𝑖 (𝜇𝑛 + 𝜇𝑝 )𝑞 = (𝑛 𝜇𝑛 + 𝑝 𝜇𝑝 )𝑞 For N type, n>>p Therefore σ = 𝑞 𝑛 𝜇𝑛 For P type, p>>n Therefore σ = 𝑞 𝑝 𝜇𝑝 Charge Densities in P-type and N-type Semiconductor: Mass Action Law: Under thermal equilibrium for any semiconductor, the product of the no. of holes and the concentration of electrons is constant and is independent of amount of donor and acceptor impurity doping. n.p = 𝑛𝑖2 where n= electron concentration, p = hole concentration and 𝑛𝑖2 = intrinsic carrier concentration. Hence in N type semiconductor, as the no. of electrons increase the no. of holes decreases. Similarly, in P type as the no. of holes increases the no. of electrons decreases. Thus, the product is constant and is equal to 𝑛𝑖2 in case ofi intrinsic as well as extrinsic semiconductor. The law of mass action has given the relationship between free electrons concentration and hole concentration. These concentrations are further related by the law of electrical neutrality as explained below. Law of electrical neutrality: Semiconductor materials are electrically neutral. According to the law of electrical neutrality, in an electrically neutral material, the magnitude of positive charge concentration is equal to that of negative charge concentration. Let us consider a semiconductor that has ND donor atoms per cubic centimeter and NA acceptor atoms per cubic centimeter i.e., the concentration of donor and acceptor atoms are ND and NA respectively. Therefore, ND positively charged ions per cubic centimeter are contributed by donor atoms and NA negatively Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 29 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 charged ions per cubic centimeter are contributed by the acceptor atoms. Let n, p is concentration of free electrons and holes respectively. Then according to the law of neutrality ND + p = NA + n................................................................................................................... eq 1.1 For N type semiconductor, NA = 0 and n>>p. Therefore ND ≈ n..................................................... eq 1.2 Hence for N type semiconductor the free electron concentration is approximately equal to the concentration of donor atoms. In later applications since some confusion may arise as to which type of semiconductor is under consideration at the given moment, the subscript n or p is added for N-type or P type respectively. Hence eq1.2 becomes ND ≈ nn Therefore, current density in N type semiconductor is J = ND µn q E And conductivity σ = ND µn q For P type semiconductor, ND = 0 and p >> n. Therefore NA ≈ p Or NA ≈ pp Hence for P type semiconductor the hole concentration is approximately equal to the concentration of acceptor atoms. Therefore, current density in N type semiconductor is J = NA µp q E And conductivity σ = NA µp q 2 Mass action law for N type, 𝑛𝑛 𝑝𝑛 = 𝑛𝑖 𝑝𝑛 = 𝑛𝑖2 /𝑁𝐷 since (𝑛𝑛 ≈ 𝑁𝐷 ) 2 Mass action law for P type, 𝑛𝑝 𝑝𝑝 = 𝑛𝑖 𝑛𝑝 = 𝑛𝑖2 /𝑁𝐴 since (𝑝𝑝 ≈ 𝑁𝐴 ) Effective Mass When an external field is applied to a semiconductor, the charge carriers, i.e. the electrons and the holes, experience forces due to the applied field and also due to the internal periodic field produced by the crystal. If the applied field is much weaker than the internal field, the effect of the latter is to modify the mass of the carriers in such a way that the carriers respond to the applied field with this modified mass obeying classical mechanics. This modified mass is termed the effective mass of the carrier and is usually different from the electronic mass in vacuum. The effective Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 30 Program Name: B. Tech CSE (AIML/DS), Bio Technology Semester: I Course Name: Basic Electrical and Electronics Engineering (Course Code: BES00002) Academic Session: 2023 - 2024 mass approximation avoids the quantum nature of the problem and permits us to use Newtonian mechanics to study the effect of the external forces on the electrons or the holes inside the crystal. While the effective mass of the electrons in most semiconductors differs significantly from the rest mass m0, in most metals this difference is not large. Name of the Faculty: Mr. Suptasish Sarkar + Anu Samanta Designation: Assistant Professor Department: EE + ECE Brainware University, Kolkata 31