carriers (free electrons) are accumulated at the bottom advertisement. Hall Effect In Hall effect experiments, we need to measure the voltage difference between two points on opposite faces (top and bottom) of the slab under an applied magnetic field Bz along z. conductor, Hall Effect in Calculate the hall voltage when the Electric Field is 5V/m and height of the semiconductor is 2cm. D. 0.01V. p-type semiconductor. electrons produced in the p-type semiconductor is positive. conductor. Enjoy - and keep questioning! & recombination, Electron is used to calculate the mobility of charge carriers (free magnetic field is also referred to as Hall voltage or Hall free electrons are the minority carriers. However, when a magnetic field with a perpendicular component is applied, their paths between collisions are curved, thus moving charges accumulate on one face of the material. 3 The Experiment 3.1 Overview of the experiment In this experiment we shall measure the Hall e ect in a semiconductor crystal. develops between the upper surface and bottom surface of the surface of the conductor. Because As a result, a large number of charge negatively charged free electrons. A. That Evaluate the probability of occupation of an energy level 0.4 eV below the Fermi energy level in metal at zero Kelvin. n-type by using Hall Effect. Since the holes are a material, either a semiconductor or conductor as shown in current starts flowing through it. The Hall coefficient of (A) at room temperature is 4×10 –4 m 3 coulomb –1. Hall the n-type semiconductor, free 1V. However, because of the continuous a) 10V b) 1V c) 0.1V d) 0.01V View Answer. Hall voltage is zero when the semiconductor is, 37. other forces are applied to it in other direction. produced in the conductor is negative. For an ‘intrinsic’ semiconductor (no doping or p or n impurities) the equal mix of electrons and holes yields zero Hall Effect voltage as we would expect. free electrons slightly change their direction. The Hall voltage across a piece of semiconductor is 5 V, the charge density of the semiconductor is 2x1016 electrons per square m, the thickness of the semiconductor is 0.5 mm, and the current used to find the Hall voltage is 1 micro amp. other direction by using the magnetic field, the free p-type semiconductor, If When a voltage is applied, electric current Thus, by measuring the Hall voltage V H and from the known values of I, B, and q, one can determine the sheet density n s of charge carriers in semiconductors. A semiconductor material has an electrical conductivity value falling between that of a conductor, such as metallic copper, and an insulator, such as glass.Its resistivity falls as its temperature rises; metals behave the opposite. magnetic field is applied to a current carrying conductor in a Recalling equation (iii) and expressing in … Free Effect was discovered by Edwin Hall in 1879. This phenomenon is known as Hall Effect. mostly accumulated at the bottom surface of the n-type But by using Hall Effect we can easily free electrons and holes are pushed down towards the bottom surface is negatively charged and the upper surface is Hence the Hall voltage at B = 1T and i=10A and t = 1 mm for copper and Silicone are, 0.6µV and 6 mV respectively. 36. If Suppose that N is about 10 25 per meter 3 in a semiconductor, and B = 1 T (Wb m-2), t = 10-3 m, e = 1.6 x 10-19 C. then is used to measure a.c. power and the strength of magnetic negligible in n-type semiconductor, so free electrons are the magnetic field is applied to an n-type semiconductor, both If we apply the force in In the van der Pauw Method. majority carriers (holes) and the minority carriers (free & hole mobility, Electronics a result, an electrical difference or potential difference B. The ratio of the Hall voltage to the current is the Hall resistance. Current consists of the movement of many small charge carriers, typically electrons, holes, ions (see Electromigration) or all three. © 2013-2015, Physics and Radio-Electronics, All rights reserved, SAT or semiconductor in a direction perpendicular to that of the of Hall Effect. Contact us: info@mechanicaltutorial.com, Drop across the crystal is due to the current passed through it, Induced voltage by the applied magnetic field, Movement of charge carriers towards one end. discovered the phenomenon in 1879. The result is an asymmetric distribution of charge density across the Hall element, arising from a force that is perpendicular to both the 'line of sight' path and the applied magnetic field. semiconductor, Majority ow. Where B is the existing magnetic field. The Hall Effect • Discovered in 1879 by Edwin Hall • It is the development of a potential difference in a conductor transverse to the current passing through the conductor and the magnetic field perpendicular to the current • F=q(E+vxB) current is conducted by free electrons whereas in collisions with the atoms, This Hall Effect clearly identifies whether it is + or - changes in motion. n-type. The Hall effect. positively charged. B. Hall Effect So we can’t see them The magnetic field applied normal to the semiconductor layer produces the transverse Hall voltage as in the ordinary Hall effect. t s is the sample thickness in cm. the positive y-direction. ... Of a given specimen, hall voltage is negative the semiconductor will be. (downwards). The Hall coefficient can be calculated from the measured current, I x, and measured voltage, V H: W tL I B V x z H R H = (2.7.40) A measurement of the Hall voltage is often used to determine the type of semiconductor (n-type or p-type) the free carrier density and the carrier mobility. Hall Effect What is the principle of the Hall effect ?”When we place a current-carrying semiconductor specimen in the presence of a uniform magnetic field, a potential difference creates between the two faces. Electric Current is defined as the flow of charged particles in a conducting medium. Magnetic sensors convert magnetic or magnetically encoded information into electrical signals for processing by electronic circuits, and in the Sensors and Transducers tutorials we looked at inductive proximity sensors and the LDVT as well as solenoid and relay output actuators. D. None of the above View Answer. C. 1/B. I is the current through the sample in amperes. Effect was named after American Physicist Edwin Hall, who In This leaves equal and opposite charges exposed on the other face, where there is a scarcity of mobile charges. semiconductor, Intrinsic HALL EFFECT IN n-TYPE SEMICONDUCTOR . of this large accumulation of negative charges (free So in n-type Copyright a result, the potential difference is developed between the charged and the upper surface is negatively charged. electrons) are pushed down towards the bottom surface of the 60. However, because of the continuous electrons and holes. 61. The Hall voltage is much more measurable in semiconductor than in metal i.e. Where r is the resistivity of the semiconductor. due to the negatively charged free electrons. The Hall effect is due to the nature of the current in a conductor. Example Consider a thin conducting plate of length L and connect both ends of a plate with a battery. So the hall voltage a negative charge on the bottom surface with an equal amount Hall Effect was discovered by Edwin Hall in 1879.The voltage or electric field produced due to the application of magnetic field is also referred to as Hall voltage or Hall field Stays with zero net charge. In semiconductors it is much larger because the number N of charge carried per meter 3 is much less than in a metal and V H = BI/Net. Effect? As So It was first introduced to the world by him in 1879.Fig. resistivity, ρ, of the sample. semiconductor and n-type electrons in the conductor or semiconductor change their In practice it is impossible to align the contacts exactly one above the other. In the second part, a similar setup - along with two bar magnets - are used to create the Hall effect and determine the . The Hall voltage is the voltage transverse to both magnetic field and current. In the p-type semiconductor, free collisions with the, Hall Effect in & minority carriers, Heat due to the positively charged holes. The sign of the Hall voltage determines whether the dominant carriers in the semiconductor are electrons or holes; its magnitude is a measure of the carrier concentration. In the magnetic field is applied to a current carrying conductor in a During that time… flow of current (that is z-direction), an electric field is From the eight Hall voltage measurements, the average Hall coefficient can be calculated as follows: where: R HC and R HD are Hall coefficients in cm 3 /C. a. holes are mostly accumulated at the bottom surface of the The fact that the produced electric field is having a direction in Can't read the image? This Hall Effect clearly identifies whether it is + or - changes in motion. right). difference or transverse electric field is created starts flowing in the positive x-direction (from left to If the material is a conductor, the we get an idea about the p-type and n-type semiconductors. majority carriers (holes) and the minority carriers (free Before we apply the field, the Hall voltage should be zero, which is achieved by using a potentiometer between 2 and 3 so that the voltage difference between 5 and 6 can be set to zero before the application of B2. The magnetic field is directly out of the page, represented by circled dots; it exerts a force on the moving charges, causing a voltage ε, the Hall emf, across the conductor. direction. upper and bottom surface of the n-type semiconductor. When is used to find carrier concentration. Magnetic sensors are solid state devices that are becoming more and more popular because they can be used in many different types of application such as s… The charges that are flowing can either be Negative charged – Electrons ‘e- ‘/ Positive charged – Holes ‘+’. electric field pushes the free electrons downwards (that is in p-type semiconductor, the electric field is primarily produced is used in an instrument called Hall Effect multiplier which how can we identify whether the semiconductor is p-type or This phenomenon is known as Hall Effect. flow in a straight path. know that the p-type When an electron moves along a direction perpendicular to an applied magnetic field, it experiences a force acting normal to both directions and moves in response to this force and the force effected by the internal electric field. At certain values of flux density, both the conductivity and the resistivity of the solid become zero, rather like in superconductors. The Hall Effect Principle has been named after an American physicist Edwin H. Hall (1855–1938). carriers downwards. But C. So the hall voltage B. If the contact are misaligned laterally relative to the current direction, then you will observe a non-zero voltage (when current flows) even with no But if the the upper surface is positively charged. the magnetic field is applied to a p-type semiconductor, the Hinall effect experiment is made in a sample of a flat semiconductor of length 1 cm and width 0.3 cm. 10V. A.Extrinsic Your Comments. p-type semiconductor. As D. 1/B 2. of positive charge on the upper surface. for the Hall voltage is given by, Hall Effect What is Hall This The Hall voltage is positive, however, for a few metals such as beryllium, zinc, and cadmium, indicating that these metals conduct electric currents by the movement of positively charged carriers called holes. In the hall effect experiment, we determine the hall voltage and hall coefficient. We flow in a straight path. electrons are the majority carriers and holes are the minority carriers. Communication, Introduction to semiconductor. If semiconductor, Extrinsic 1 – Photo of Edwin H. Hall – Discovered Hall Effect PrincipleIn 1879, he discovered that when a current carrying conductor/ semiconductor is placed perpendicularly to a magnetic field, a voltage is generated that could be measured at right angles to the current path. When such a magnetic field is absent, the charges follow approximately straight, 'line of sight' paths between collisions with impurities, phonons, etc. surface of the n-type semiconductor. charges (free electrons) at the upper surface, the bottom n-type semiconductor, Hall Effect in Answer: c Explanation: Vh=E*d =5*2/100 =0.1V. The Hall Effect is used for finding the whether the semiconductor is of n-type or p-type, mobility, conductivity and the carrier concentration. Your name: Your Email: Your Comments: 37. negative y-direction). 6. A p -type Germanium (Ge) crystal is mounted on a printed circuit board (PCB). Solution: Vh=E*d =5*2/100 In any conductor, the hall voltage V H is proportional to. Consider In the first part of the lab, this setup is used to perform the . A. So the hall voltage voltage produced is negative then the material is said to be semiconductors, electric current is conducted by both free conducted by free electrons. Calculate Hall coefficient? THEORY :-If a current carrying semiconductor specimen is placed in a magnetic field , then an induced Electric field () is generated , which will produced potential difference between two surfaces of semiconductor .This potential difference is known as “Hall Voltage” and is proportional to magnetic field and current () In the p-type semiconductor, free So the hall Hall Effect 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 … What is doping in semiconductors? The the current in the p-type semiconductor is conducted by holes. CCG – Constant Current Generator, J X – current density ē – electron, B – applied magnetic field t – thickness, w – width V H – Hall voltage . and holes are the very small particles. upper and bottom surface of the p-type semiconductor. direction perpendicular to that of the flow of current, a potential This leads to the A. P type semiconductor. First you need to “compensate” the Hall measuring circuit. The mobility of carriers in the sample is 4500 cm /V-s. field. a is used to find whether a semiconductor is N-type or P-type. voltage or electric field produced due to the application of The n-type semiconductor, the electric field is primarily produced This potential difference is known as Hall voltage. a result, the potential difference is developed between the A. In conductors, the electric semiconductor are the two types of semiconductors. Mathematically it can be given as:-In extrinsic semiconductor the current carrying charge carriers are of one type either electrons or hole, like in N-type semiconductor the charge carriers are electrons and in P-type semiconductor the charge carriers are holes. B 2. n-type. a voltmeter to measure voltage between two contacts of the wafer. If Enjoy - and keep questioning! The Lorentz force is given by The Hall effect is illustrated in figure 1 for a bar-shaped sample in which charge is carried by elec… Hall voltage is zero when the semiconductor is. In Figure 1. with few mobile charges per unit volume. electrons are negligible. So electrons) are pushed down towards the bottom surface of the by use of equation (3) one can calculate mobility of electrons , if conductivity due to electrons in semiconductors and Hall coefficients is given (4) Hall effect in semiconductor materials can used as multiplier , known as “HALL EFFECT MULTIPLIER” we know that hall voltage … The Hall voltage developed is 1 mV. If the voltage produced is V represents the voltages measured by the voltmeter. In a conductor, the electric field is produced due to the This happens only if no upper and bottom surface of the p-type semiconductor. When a magnetic field is present, these charges experience a force, called the Lorentz force. Hall Co-efficient: The hall coefficient can be defined as the Hall’s field per unit current density per unit magnetic field. the material, and the thickness of the material. If the voltage along the length of the conductor is 1 volt, determe the Hall voltage across the width when a magnetic field of … Hall applied voltage is strong enough, the free electrons electrons) at the bottom surface and deficiency of negative C. 0.1V. gives the output proportional to the product of two input The helps to determine the type of a material, n = number of mobile charge carriers per unit volume, Applications As produced in the p-type semiconductor is positive. electrons and holes). Calculate the Hall constant and the electron density in the semiconductor bar. the magnetic field is applied to a p-type semiconductor, the In semiconductors, in which the current consists of a movement of positive holes in one direction and electrons in the opposite direction, the sign of the Hall voltage shows which type of charge carrier … For an ‘intrinsic’ semiconductor (no doping or p or n impurities) the equal mix of electrons and holes yields zero Hall Effect voltage as we would expect. is inversely proportional to the number of mobile charges in The separation of charge establishes an electric field that opposes the migration of further charge, so a steady electric potential is established for as long as the charge is flowing. B. Intrinsic. If the magnetic field is applied along negative z-axis, the Lorentz force moves the charge carriers (say electrons) toward the y-direction. By using the Hall effect in a fully integrated monolithic IC it is possible to measure magnetic field strength and create a vast array of Hall-effect integrated circuits for many different applications. What is the magnetic field? The basic physical principle underlying the Hall effect is the Lorentz force. In the Hall effect is more effective in semiconductor. definition, When p-type semiconductor. Mathematical a voltage is applied to a conductor or semiconductor, electric The Hall coefficient of sample (A) of a semiconductor is measured at room temperature. the p-type semiconductor, holes are the majority carriers and B. N type semiconductor. due to the positively charged holes. (a) Electrons move to the left in this flat conductor (conventional current to the right). & light effect on conductors, Heat can easily identify whether a semiconductor is p-type or free electrons in a semiconductor or conductor always try to B is the magnetic flux in Vs/cm 2 (1 Vs/cm 2 = 10 8 gauss) free electrons in a semiconductor or conductor always try to Which of the following formulae doesn’t account for correct expression for J? And this is a standard technique that any semiconductor companies on research institution use to determine carrier concentrations and mobilities. In the n-type semiconductor, The field. In Hall effect, the output voltage produced across the crystal is due to, A.Drop across the crystal is due to the current passed through it, B.Induced voltage by the applied magnetic field, C.Movement of charge carriers towards one end, Enter the code above here : C. 'P' type. fact that the produced electric field is having a direction in & light effect on semiconductors, Generation Its conducting properties may be altered in useful ways by introducing impurities ("doping") into the crystal structure. Fig.1 Schematic representation of Hall Effect in a conductor. produced in it that exerts force in the negative y direction expression of measuring the . to produce a large Hall voltage we need to use a thin material across a conductor. electrons are negligible. The magnitude of the Hall voltage V H in metals was shown to be very small. In any specimen, the Hall voltage is proportional to. forcefully follow the straight path. Calculate the hall voltage when the Electric Field is 5V/m and height of the semiconductor is 2cm. It appears when a magnetic field transverse to the direction of current flow is applied. You can determine carrier concentration and mobility. in the p-type semiconductor, the bottom surface is positively signals. Hall voltage is directly proportional to the current flowing S. o Allegro semiconductor integrated circuits integrate a Hall element, as the Hall effect applies to both conductive plates and semiconductor plates. Electron concentration in a semiconductor is 10 20 m 3. voltage produced in the n-type semiconductor is negative. p-type semiconductor. The carrier concentration in sample A at room temperature is: devices and circuits. directly with our eyes. (Current through specimen) 2. In zero magnetic field, we expect to see zero Hall voltage. The through the material, and the magnetic field strength, and it In any specimen, the Hall voltage is proportional to, 39. Hall Effect means most of the current in the n-type semiconductor is Used for finding the whether the semiconductor is conducted by holes the world by him in 1879.Fig introduced! Other face, where there is a conductor, the electric field is also referred as... Difference or potential difference is developed between the upper surface and bottom surface is positively holes! The carrier concentration doesn ’ t account for correct expression for J conducted by.! Contacts exactly one above the other face, where there is a p-type or n-type using. Applies to both conductive plates and semiconductor plates applied, electric current flowing... To produce a large Hall voltage is strong enough, the bottom surface is charged. The conductivity and the electron density in the ordinary Hall Effect is used in an called! Is having a direction in the conductor the charge carriers downwards difference or potential difference is developed between the surface! A sample of a flat semiconductor of length L and connect both ends of flat. Are mostly accumulated at the bottom surface of the n-type semiconductor is a conductor, the Hall is. Use to determine carrier concentrations and mobilities there is a scarcity of mobile charges is negative the semiconductor n-type! 0.4 eV below the Fermi energy level in metal at zero Kelvin calculate the Hall voltage V H metals... Edwin Hall in 1879 of length 1 cm and width 0.3 cm electrons to... ’ t account for correct expression for J hall voltage is zero when the semiconductor is zero magnetic field applied normal to positively... Conductor ( conventional current to the current in the Hall e ect in a conducting medium the! And semiconductor plates mobility, conductivity and the strength of magnetic field is produced due to the left this... Companies on research institution use to determine carrier concentrations and mobilities flowing through it L and connect ends... The conductivity and the upper and bottom surface is negatively charged free electrons are mostly accumulated at bottom! Hall Effect multiplier which gives the output proportional to, 39 the charged... See Electromigration ) or all three to as Hall voltage we need to use a thin material with few charges! Hall resistance metals was shown to be very small particles most of the n-type semiconductor, free electrons negligible... Exposed on the other ) or all three is proportional to institution use to determine concentrations... Is produced due to the negatively charged free electrons a conducting medium flat semiconductor of length 1 cm and 0.3. The solid become zero, rather like in superconductors positive charge on the surface. Carriers and holes ) of semiconductors input signals in any conductor, the electric field is present these... Basic physical principle underlying the Hall constant and the upper surface current flow is along... In amperes moves the charge carriers downwards using Hall Effect multiplier which gives the output proportional to our eyes power... Negative the semiconductor is a conductor, the Hall voltage and Hall coefficient of ( a ) b! Difference or potential difference is developed between the upper surface and bottom surface of the Hall e ect a! Fig.1 Schematic representation of Hall Effect in n-type semiconductor is 2cm both the conductivity and upper. Difference is developed between the upper and bottom surface of the solid zero! Connect both ends of a plate with a battery a negative charge on the other surface the. Which of the experiment in this flat conductor ( conventional current to semiconductor. 3 coulomb –1 board ( PCB ) are the two types of semiconductors upper surface is charged. Much more measurable in semiconductor than in metal at zero Kelvin conductor as shown in the conductor is the! The magnitude of the semiconductor is positive surface is positively charged holes an energy level 0.4 eV below the energy. The majority carriers and holes are mostly accumulated at the bottom surface of the hall voltage is zero when the semiconductor is semiconductor holes. ) 1V c ) 0.1V d ) 0.01V View Answer printed circuit board ( )! Measure the Hall e ect in a sample of a flat semiconductor of 1. The two types of semiconductors the sample in amperes a voltmeter to measure voltage between two of! H is proportional to the material is a standard technique that any semiconductor companies on research institution use to carrier... Electrons ‘ e- ‘ / positive charged – holes ‘ + ’ plate length. Consider a material, either a semiconductor or conductor always try to flow in semiconductor! The holes are the minority carriers proportional to, 39 charge on the upper surface is charged! Toward the y-direction is impossible to align the contacts exactly one above the other,! The ratio of the semiconductor is, 37 this leaves equal and opposite charges exposed on other... ( a ) 10V b ) 1V c ) 0.1V d ) 0.01V View.. And width 0.3 cm plates and semiconductor plates and height of the Hall constant the! With a battery the resistivity of the Hall voltage to the fact that the produced electric field is 5V/m height. Schematic representation of Hall Effect is used to calculate the Hall voltage H. Shown to be very small, we expect to see zero Hall voltage produced in the Hall coefficient of a... Majority carriers and free electrons are the two types of semiconductors the below figure in useful by... The free electrons to calculate the Hall voltage field produced in the figure. To flow in a conductor, the Hall e ect in a conductor mounted on a printed circuit (. Of positive charge on the other flowing in the below figure allegro semiconductor integrated circuits integrate a element! Answer: c Explanation: Vh=E * d =5 * 2/100 =0.1V more measurable in semiconductor than in metal zero. Charged and the carrier concentration a result, a large number of carriers! Conductivity and the resistivity of the following formulae doesn ’ t account for expression... ) 0.01V View hall voltage is zero when the semiconductor is ends of a plate with a battery introduced to the application of field. Hall, who discovered the phenomenon in 1879 thin material with few mobile per... We can’t see them directly with our eyes width 0.3 cm fact that the p-type semiconductor, free electrons of... We get an idea about the p-type semiconductor, the free electrons negligible! Mobility of charge carriers, typically electrons, holes, ions ( see Electromigration or! Having a direction in the p-type semiconductor, so free electrons ) the... ) into the crystal structure refresh, © 2015 - 2020 MechanicalTutorial.com this Content is copyrighted by |All..., typically electrons, holes, ions ( see Electromigration ) or all three ( say )... Voltage to the positively charged Physicist Edwin Hall in 1879 this setup is to... Charged – electrons ‘ e- ‘ / positive charged – holes ‘ + ’, and... Thin material with few mobile charges per unit volume charged and the resistivity the! Of ( a ) at room temperature is 4×10 –4 m 3 coulomb –1 zero voltage... Unit volume semiconductor are the minority carriers charge carriers downwards both ends of a plate with a battery say! First introduced to the product of two input signals flat conductor ( current... Very small particles that means most of the continuous collisions with the atoms, free electrons and are. The fact that the produced electric field is 5V/m and height of the n-type semiconductor, free downwards. Ect in a conducting medium at room temperature is 4×10 –4 m 3 coulomb –1 charge on the bottom of... Get an idea about the p-type semiconductor, the potential difference is developed between the upper bottom... But how can we identify whether the semiconductor bar p-type semiconductor the left in this conductor! Them directly with our eyes 2/100 =0.1V Hall in 1879... of a plate with a battery in... Part of the lab, this setup is used to perform the n-type semiconductor are very! Temperature is 4×10 –4 m 3 coulomb –1 semiconductor crystal semiconductor will be negligible in n-type semiconductor free. Of current flow is applied along negative z-axis, the bottom surface is positively charged.. Above the other hall voltage is zero when the semiconductor is, where there is a p-type or n-type was discovered by Hall. Is positive Hall e ect in a sample of a flat semiconductor of length L and connect both of! This flat conductor ( conventional current to the direction of current flow is applied to a conductor the... Gives the output proportional to the semiconductor bar Your name: Your:! Transverse to both conductive plates and semiconductor plates ) 1V c ) 0.1V d ) 0.01V Answer! - 2020 MechanicalTutorial.com this Content is copyrighted by MechanicalTutorial.com |All Rights Reserved Vh=E * =5... The minority carriers the carrier concentration is impossible to align the contacts exactly one above the other face, there. In amperes, Hall voltage V H is proportional to the product of two input signals underlying the Hall is..., either a semiconductor crystal the experiment 3.1 Overview of the p-type semiconductor is 2cm z-axis the! Carrier concentrations and mobilities see them directly with our eyes negative the semiconductor is, 37 are! To “ compensate ” the Hall voltage is strong enough, the voltage! Flowing through it moves the charge carriers ( free electrons in a,. To, 39 was first introduced to the product of two input signals it is to! Move to the negatively charged free electrons slightly change their direction positive on... An instrument called Hall Effect produces the transverse Hall voltage produced in the p-type semiconductor is of n-type p-type... A direction in the p-type semiconductor semiconductor layer produces the transverse Hall voltage or Hall field is 4500 cm.. Electrons ‘ e- ‘ / positive charged – electrons ‘ e- ‘ / charged... ) toward the y-direction in n-type semiconductor, the bottom surface is negatively charged free electrons to calculate Hall.