What is a Hall Effect in Metals and SemiconductorHall Effect was introduced by an American Physicist Edwin H.Hall in the year 1879. It is based on the measurement of the electromagnetic field. It is also named as ordinary Hall Effect. When a current-carrying conductor is perpendicular to a magnetic field, a voltage generated is measured at right angles to the current path. Where current flow is similar to that of liquid flowing in a pipe. Firstly it was applied in the classification of chemical samples. Secondly, it was applicable in Hall Effect Sensor where it was used to measure DC fields of the magnet, where the sensor is kept stationary.Principle of Hall EffectHall Effect is defined as the difference in voltage generated across a current-carrying conductor, is transverse to an electrical current in the conductor and an applied magnetic field perpendicular to the current. Hall Effect = induced electric field / current density * the applied magnetic field –(1)hall-effectTheory of Hall EffectElectric Current is defined as the flow of charged particles in a conducting medium. The charges that are flowing can either be Negative charged – Electrons ‘e- ‘/ Positive charged – Holes ‘+’.ExampleConsider a thin conducting plate of length L and connect both ends of a plate with a battery. Where one end is connected from the positive end of a battery to one end of the plate and another end is connected from the negative end of a battery to another end of the plate. Now we observe that currently starts flowing from negative charge to the positive end of the plate. Due to this movement, a magnetic field is generated.theory-of-hall-effectLorentz ForceFor instance, if we place a magnetic bare nearby the conductor the magnetic field will disturb the magnetic field of charge carriers. This force which distorts the direction of charge carriers is known as Lorentz force.Due to this, the electrons will move to one end of the plate and holes will move to another end of the plate. Here Hall voltage is measured between two sides of plates with a multimeter. This effect is also known as the Hall Effect. Where the current is directly proportional to deflected electrons in turn proportional to the potential difference between both plates. Larger the current larger is the deflected electrons and hence we can observe the high potential difference between the plates.Hall Voltage is directly proportional to the electric current and applied magnetic field.VH = I B / q n d —– ( 2 )I – Current flowing in Sensor B – Magnetic Field Strength q – Charge n – charge carriers per unit volume d – Thickness of the sensorDerivation of Hall CoefficientLet current IX is current density, JX times the correctional area of the conductor wt.IX = JX wt = n q vx w t ———-( 3 )According to Ohms law, if current increases the field also increases. Which is given asJX = σ EX , ————( 4 )Where σ = conductivity of the material in the conductor.On considering the above example of placing a magnetic bar right angle to the conductor we know that it experience Lorentz force. When a steady state is reached there will be no flow of charge in any direction which can be represented as,EY = Vx Bz, ————–( 5 )EY – electric field / Hall field in the y-directionBz – magnetic field in the z-directionVH = – ∫0w EY day = – Ey w ———-( 6 )VH = – ( (1/n q ) IX Bz ) / t , ———– ( 7 )Where RH = 1/nq ———— ( 8 )Units of Hall Effect: m3 /CHall Mobilityµ p or µ n = σ n R H ———— ( 9 )Hall mobility is defined as µ p or µ n is conductivity due to electrons and holes.Magnetic Flux DensityIt is defined as the amount of magnetic flux in an area taken right angles to the magnetic flux’s direction.B = VH d / RH I ——– ( 1 0 )Hall Effect in Metals and SemiconductorAccording to the electric field and magnetic field the charge carriers which are moving in the medium experience some resistance because of scattering between carriers and impurities, along with carriers and atoms of material which are undergoing vibration. Hence each carrier scatters and loses its energy. Which can be represented by the following equationhall-effect-in-metals-and-semiconductorsF retarded = – mv/t , ————– ( 1 1 )t = average time between scattering eventsAccording to Newtons seconds law ,M (dv/dt )= ( q ( E + v * B ) – m v) / t ——( 1 2 )m= mass of the carrierWhen a steady state occurs the parameter’ v ‘ will be neglectedIf ’B’ is along z-coordinate we can obtain a set of ’ v ‘ equationsvx = ( qT Ex) / m + (qt BZ vy ) / m ———– ( 1 3 )vy = (qT Ey ) / m – (qt BZ vx) / m ———— ( 1 4 )vz = qT Ez / m ———- ( 1 5 )We know that Jx = n q vx ————— ( 1 6 )Substituting in the above equations we can modify it asJx = ( σ/ ( 1 + (wc t)2)) ( Ex + wc t Ey ) ———– ( 1 7 )J y = ( σ * ( Ey – wc t Ex ) / ( 1 + (wc t)2) ———- ( 1 8 )Jz = σ Ez ———— ( 1 9 )We know thatσ n q2 t / m ———– ( 2 0 )σ = conductivityt = relaxation timeandwc q Bz / m ————– ( 2 1 )wc = cyclotron frequencyCyclotron Frequency is defined as in a magnetic field frequency of rotation of a charge. Which is the strength of the field.Which can be explained in the following cases to know if it is not strong and/or “t” is shortCase (i) : If wc t << 1It indicates a weak field limitCase (ii) : If wc t >> 1It indicates a strong field limit.AdvantagesThe advantages of the hall-effect include the following.Speed of operation is high i.e, 100 kHzLoop of operationsCapacity to measure large currentIt can measure Zero speed.DisadvantagesThe disadvantages of the hall-effect include the following.It cannot measure the flow of current greater than 10cmThere is a large effect of temperature on carriers, which is directly proportionalEven in the absence of a magnetic field small voltage is observed when electrodes are at centered.Applications of Hall EffectThe applications of the hall-effect include the following.Magnetic Field senorUsed for multiplicationFor direct current measuring, it uses Hall Effect Tong TesterWe can measure phase anglesWe can also measure Linear displacements transducerSpacecraft propulsionPower supply sensing Thus, the Hall Effect is based on the Electro-magnetic principle. Here we have seen the derivation of Hall Coefficient, also Hall Effect in Metals and Semiconductors. Here is a question, How is Hall Effect applicable in Zero speed operation? Share This Post: Facebook Twitter Google+ LinkedIn Pinterest Post navigation ‹ Previous What is Weight Sensor Working and Its SpecificationsNext › What is a IMX586 Sensor : Working and Its Features Related Content What is a Sampling Oscilloscope & Its Working What is a BCD Counter : Circuit & Its Working What is a Shunt Capacitor & Its Working What is Static VAR Compensator : Design & Its WorkingAdd Comment Cancel replyComment:Name * Email * Website