Hall effect Experiment

Hall effect presentation

1. Determination of HALL COEFFICIENT of hall field of Germanium crystal. Determination of the carrier mobility and carrier density By – Group G4 Guided by – Prof. Binay Kumar Prof. Sorav Sur HALL EFFECT By – Group G4 Keshav,Twinkle,Pradyumn , Komal,Bhoomika Guided by – Prof. Binay Kumar Prof. Sourav Sur

2. The modern theory of  electromagnetism  was systematized by  Maxwell in the paper " On Physical Lines of Force ", which was published in four parts between 1861–1862. While Maxwell's paper established a solid mathematical basis for electromagnetic theory, the detailed mechanisms of the theory were still being explored. One such question was about the details of the interaction between magnets and electric current, including whether magnetic fields interacted with the conductors or the electric current itself. In 1879  Edwin Hall  was exploring this interaction, and discovered the Hall effect while he was working on his doctoral degree at  Johns Hopkins University in  Baltimore ,  Maryland . Eighteen years before the  electron  was discovered, his measurements of the tiny effect produced in the apparatus he used were an experimental  tour de force , published under the name "On a New Action of the Magnet on Electric Currents“. Edwin Hall  

3. AIM To determine the Hall voltage developed across the sample material. To calculate the Hall coefficient and the carrier concentration of the sample material.

4. Hall effect setup

5. Constant current power supply

6. Hall effect Probes Measure magnetic field Magnetic field is directly proportional to current Commonly called hall sensor Can measure both sign and amplitude

7. Electromagnets ELECTROMAGNETS An  electromagnet  is a type of  magnet  in which the  magnetic field is produced by an  electric current . Electromagnets usually consist of wire wound into a  coil . A current through the wire creates a magnetic field which is concentrated in the hole, denoting the centre of the coil. The magnetic field disappears when the current is turned off. The wire turns are often wound around a  magnetic core  made from a  ferromagnetic  or  ferrimagnetic  material such as  iron ; the magnetic core concentrates the  magnetic flux  and makes a more powerful magnet. The main advantage of an electromagnet over a  permanent magnet is that the magnetic field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a continuous supply of current to maintain the magnetic field

8. Examples of Electromagnets

9. Digital Gauss Meter The Gaussmeter operates on the principle of Hall Effect in semiconductors. A semiconductor material carrying current develops an electro-motive force, when placed in a magnetic field, in a direction perpendicular to the direction of both electric current and magnetic field. The magnitude of this e.m.f. is proportional to the field intensity if the current is kept constant, this e.m.f. is called the Hall Voltage. This small Hall Voltage is amplified through a high stability amplifier so that a millivoltmeter connected at the output of the amplifier can be calibrated directly in magnetic field unit (gauss).

10. Digital Gauss Meter

11. THEORY

12. Hall effect It is the production of a potential difference (maximum) across the ends of an electrical conductor when a magnetic field is applied in a direction perpendicular to that of flow of current.

13. I e 0V B v B F m v F m Vh w t

14. e e e e e e e e E h e F e F m Saturated state -> Final value of hall voltage

15. At saturated state, F e F m = q E h = q v B E h = v B I = n q A v v = I / n q A V h E h = w V h = v B w V h = (I B w)/(n q A) V h = (I B w)/(n q w t) V h = (I B)/(n q t) V h = (I B)/(t) R h × V h = R h × t I × B = R h 1 n q

16. FORMULA USED

17. n = 1 / R H q Where, Rh is hall coefficient of the material, Vh is the hall voltage developed across the ends of the conductor, t is the thickness of the conductor, I is the current flowing through the conductor, B is the magnetic field being provided to the hall probe. Where, n is the number density of carriers or the carrier concentration, Rh is hall coefficient of the material, q is the charge of an electron

18. Procedure And simulation : I am going to explain the procedure in two parts : Simulation on virtual lab: Procedure we did in real lab : So lets see how to perform the experiment after going through so much of theory 🙈👉👉

19. Simulation on virtual lab: Controls: select procedure : this is used to select the part of the experiment to perform Magnetic field Vs current Hall effect setup Select material : This slider activate only if hall effect setup is selected and this is used to select the material for finding hall cofficient and carrier concentration Buttons: Insert probe/remove probe: This button is used to insert/remove the probe in between the solenoid Show voltage/current : T his will activate only if Hall effect selected and it is used to display the hall voltage /current in the digital meter Reset : This button is used to repeat the experiment

20. Procedure for doing the simulation : To measure the magnetic field generated in the solenoid and to plot a graph between current flowing through the solenoid and the magnetic field: Select magnetic field Vs current from the procedure combo box. 2. Click the insert probe button then place the probe in between the electromagnet by clicking the wooden stand in the simulator. Using current slider, we vary current slightly and noted magnetic field corresponding to different current from gauss meter And Graph is plotted b/w I (x axis) and M(Y axis) Which is a straight line .

21. Hall effect procedure: Select hall effect setup from the combo box then insert the probe in between the electromagnet by clicking on the wooden stand. Now for plotting the graph between hall voltage and magnetic field , keep the hall current at a constant value and vary the current passing through solenoid slowly and corresponding to it note down the value of hall voltage and magnetic filed . Now keeping the solenoidial current Constant , Set the hall current slider value to minimum and then vary the hall current using the slider and note down the corresponding hall voltage by clicking on “show voltage” button Then plot the curve between hall voltage and hall current and find the slope of the curve. Then by using the equation ( Rh *B/t )=slope ; (B = magnetic field ,t =thickness of the material ) calculate the hall cofficient and the carrier concentration

22. Procedure for doing in real lab: Connect constant current source to the solenoid/electromagnet Gauss probe is connected to the gauss meter and placed at the middle of the two solenoid. Then switch on the gauss meter and constant current source. Vary the current through the solenoid from 1 A to 5 A and note the corresponding gauss meter readings Switch off the gauss meter and constant current source and turn the knob of constant current source towards the minimum current Fix the hall probe on a wooden stand and. Connect the green wires to constant current generator and the red wires to mili voltmeter in the hall effect aapratus Replace the hall probe With four probe and place the sample material at the middle of the two electromagnets and adjust their gap to a minimum so that the poles do not touch the probe Switch on the constant current source and carefully increase the current I and measure the corresponding Hall voltage Vh . Repeat this for different magnetic field .And plot the graph between the hall current and hall voltage. Thickness t of the material is used using screw gauge and then hall cofficient is calculated using the equation ( Rh *B)/t= slope

23. Critical Analysis The hall probe must be perpendicular to the magnetic field. Magneto-resistance The length of the hall probe should be nearly three times its width. The current should not be too large to cause heating effect.

24. TABULATIONS

25. 7 4 0.5929 Table - 1 S. No. Current flowing through the solenoid (in mA) Magnetic field generated (in T) 1 1 0.1482 2 1.5 0.2223 3 2 0.2964 4 2.5 0.3706 5 3 0.4447 6 3.5 0.5188 7 4 0.5929 8 9 4.5 5 0.6670 0.7411 9 5 0.7411

26. Table – 2 S. No. Magnetic field generated by the solenoid (in T) Thickness of the probe (in mm) Hall current (in mA) Hall voltage (in mV) 1 0.1482 0.2 1 14.378 2 0.1482 0.2 1.5 21.567 3 0.1482 0.2 2 28.756 4 0.1482 0.2 2.5 35.945 5 0.1482 0.2 3 43.133 6 0.1482 0.2 3.5 50.322 7 0.1482 0.2 4 57.511

27. GRAPHS

28. Magnetic field vs Current Graph Graph - 1

29. Hall Voltage vs Hall current graph Graph - 2

30. CALCULATION

31. ERROR ANALYSIS

32. 0.02862

33. RESULT – Hall Coefficient

34. RESULT – Carrier concentration

35. Conclusion By performing this experiment, we were able to find the hall coefficient and the carrier concentration of the given Germanium probe whose values came out to be, a nd, respectively.

36. QUANTUM HALL EFFECT The  quantum Hall effect  (or  integer quantum Hall effect ) is a  quantized  version of the   Hall effect , observed in  two-dimensional electron systems   subjected to low  temperatures  and strong  magnetic fields , in which the Hall  resistance R xy  exhibits steps that take on the quantized values at certain level . where  V Hall   is the  Hall voltage ,  I channel  is the channel  current ,  e  is the  elementary charge  and  h  is  Planck's constant . The divisor  ν  can take on either integer ( ν  = 1, 2, 3,... ) or fractional ( ν  = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,... ) values.The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether  ν  is an integer or fraction, respectively.

37. The Nobel Prize in Physics 1985 was awarded to Klaus von Klitzing "for the discovery of the Quantized Hall effect ”

38. Applications Of Hall Effect in Daily life Speed detection Current sensing application Used as Magnetometers to measure magnetic field Magnetic position sensing in brushless DC motors Automotive fuel level indicator

39. Speed detection These sensors are composed of a hall Element and a permanent magnet near a toothed disc attached on the rotating shaft.

40. Current Sensor When Current flow through a conductor,a magnetic field is created.

41. Manetometers Smartphones are equipped with magnetic compass. These magnetometer are sensors based on hall effect.

42. Electric Motor Control Some types of brushless DC electric motors use hall effect sensors to detect the position of the rotor and feed that information to the motor controller.This allows for more precise motor control.

43. Automotive Fuel Level Indicator The fuel level is indicated and displayed by proper signal condition of Hall voltage .

44. OBSERVATIONS, GRAPHS AND CALCULATIONS BY: TWINKLE DAHIYA

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58. TWINKLE DAHIYA SOME OTHER INFORMATION: Recently, researchers have replicated the Hall Effect, using radio waves (photons) instead of electric current (electrons). This technique could be used to create advanced communication systems that boost signal transmission in one direction while simultaneously absorbing signals going in the opposite direction. We can also use the concept of Hall Coefficient Inversion to find out the ratio of carrier concentration in case of a lightly doped semiconductor.

59. 1. Observation Table 2. Graphs 3. Calculations 4. Error Analysis 5. Result presented By – KOMAL (group-4)

60. Observation table :

61. GRAPHS : 1 .

62. GRAPH : 2

63. GRAPH : 3

64. C A L C U L A T I O N

65. Error Analysis :

66. RESULT

67. GRAPHS AND CALCULATION -:PRADYUMN

68. Table - 1 S. No. Current flowing through the electromagnets (in A) Magnetic field generated (in T) 1 1 0.1482 2 1.5 0.2223 3 2 0.2964 4 2.5 0.3706 5 3 0.4447 6 3.5 0.5188 7 4 0.5929 8 4.5 0.6670

69. Table – 2 S. No. Magnetic field generated by electromagnets (in T) Thickness of the probe (in m) Hall current (in mA) Hall voltage (in mV) 1 0.4447 0.0001 1 86.26 2 0.4447 0.0001 1.5 129.40 3 0.4447 0.0001 2 172.53 4 0.4447 0.0001 2.5 215.66 5 0.4447 0.0001 3 258.80 6 0.4447 0.0001 3.5 301.93 7 0.4447 0.0001 4 345.06

70. CALCULATION

71. Observations: ( BY BHOOMIKA) Table 1: magnetic field vs current :

72. TABLE 2: We fix the current as 5 ampere, So, magnetic field will be 0.7411 G as constant magnetic field. And, thickness of the material is taken as 0.0003 metre .

73. CALCULATIONS:

74. ERROR ANALYSIS :

75. Results: The Hall coefficient for the Germanium sample was found to be (1.94+0.07)*10 -2 m 3 /C, and the number of carriers was found to be 3.22*10 20 +0.12*10 20 /m 3 .