Semiconductor testing: practical steps involved in semiconductor testing:

AIM:  To determine the value of e/m of electron using the bar magnet method.

To determine the value of e/m of electron using the bar magnet method.

 J.J. Thomson, the discoverer of the electron, first determined in 1897 the ratio of the charge e of the electron to its mass m by applying electric and magnetic fields to a narrow beam of cathode rays. A Cathode Ray Tube (CRT) is a convenient device for determining e/m ratio of the electron. A narrow electron beam is produced in it and the beam can be manipulated by impressed electrical and magnetic fields over a small length of the electron path. The electric field produced by a short length of deflection plates and the magnetic field is applied from outside over the same length.

APPARATUS:  A cathode ray tube (CRT), a power supply, two bar magnets, deflection magnetometer, and wooden frame with scales fixed on its arms.

FORMULA                                    VD

e/m =   ----------------     x 10¹¹ C/Kg

                                                        (LldB²)

                                                                                                                    

where,  D is the total deflection of the spot of the electron beam,

             V is the voltage applied to the plates,

              l is the length of the deflecting plates =  16 x 10^-3m,

              L is the distance of screen from edge of the

                y-deflection plates = 130x 10^-3m,

             B is the intensity of the magnetic field,

             d  is the separation of the deflecting plates = 6 x 10^-3m.

THEORY      

            J.J. Thomson, the discoverer of electron, first determined in 1897 the ratio of the charge e of the electron to its mass m by applying electric and magnetic fields to a narrow beam of cathode rays. A Cathode Ray Tube (CRT) is a convenient device for determining e/m ratio of electron. A narrow electron beam is produced in it and the beam can be manipulated by impressed electrical and magnetic fields over a small length of the electron path. The electric field produced by a short length of deflection plates and the magnetic field is applied from outside over the same length.

Let us consider the case when a magnetic field, B alone is applied on the electron beam. In such a case, the electron beam undergoes a deflection along the arc of a circle whose radius is given by   R = mv / eB
Where, m is mass of electron and v is the velocity of   the electron.

Rearranging the terms, we get

                                                e/m = v/BR                                                     (1)

Let an electric field E be applied to deflection plates. This field will exert a force on electrons given by F_e = eE                                                         (2)

l : length of the plates. V : potential applied to plates d : distance between plates L : distance of screen from centre of plates D : deflection observed on the screen r : radius of the circular path B : magnetic field strength.

Now, let both the electric and magnetic fields be applied simultaneously. The electric force and magnetic force act in opposite directions. The intensities of the fields are so adjusted that electrons are not deflected. Under this condition,

                            F_E = F_B

    So   eE=evB   Or,v=E/B              (3)

       From (1) & (3), we get                 

            e/m = E/B²R

from geometry of adjacent fig; R can be written in terms of constant quantities as,

                     R = lL/D

 Therefore,       e/m = ED/LlB²

Using                     E = V/d,

                        e/m = VD/LldB²

Thus the value of e/m can be computed from this equation.

Tangent Law to measure the magnetic field:

If a small bar magnet is suspended in two mutually perpendicular uniform magnetic fields B₁ and B₂ such that it comes to rest making an angle Φ with the direction of field B₁, then

                                               B₂ = B₁ tanΦ

PROCEDURE

1. The C.R Tube mounted in armed wooden stand such that the C.R. tube faces towards north and south while arms of the stand towards EAST and WEST.

2. The CRT is connected to the power supply and is switched on. Adjusting the intensity, focus and x position controls, a spot of sufficient brightness is obtained on the screen.

3. The initial reading of the spot on the scale attached to the screen is

      noted, say it be –0.3cm.

4. Apply forward deflecting volt such that spot gets deflected in upward direction through 1 cm. Note down this voltage. 

5. Two bar magnets of equal pole strength and equal magnetic length are kept on either sides of the CRT on wooden stand arms with their unlike poles facing each other such that their common axis perpendicular to the axis of C.R Tube.

6. The bar magnets are then moved simultaneously towards CRT. If the spot moves again in upward direction; then change the polarities of both magnets. Now; move the bar magnets again till the spot is at its original position which was noted in step 3. Ensure that the bar magnets are at equal distance from CRT.  This produces uniform magnetic field.

7. The distance of the poles of the magnets nearer of C.R Tube on both the scales is noted. These are denoted as r₁ and r₂.

9. The magnets from the arms of the wooden stands are removed and the polarity of the voltage, applied to the deflecting plates, is reversed. Again a deflection is given in opposite direction so that D = 1cm and voltage V is noted down.

10. The steps 5 and 6 are repeated. The distances of the poles of the magnets on both the scale are denoted as r₃ and r_4.

11. The CRT power supply is switched off and the CRT is taken away from the wooden frame. The magnetometer compass box is introduced on a wooden bench such that its center lies on the common axis of magnets. The pointer of the compass box is adjusted to read 0-0.

12. The bar magnets are placed exactly at distance r₁ and r₂ respectively. It causes deflection of magnetometer needle. Deflection f₁ and f₂ are recorded for both ends of the pointer.

13. After this magnets are placed exactly at r₃ and r₄. The deflections f₃ and f₄ of both the ends of the pointer are noted.

14. The procedure given in above steps is repeated for various sets, varying the deflecting voltage. The measurements recorded in TABLE-1.                       

RESULT

         The e/m of electron is found to be    ---------              

PRECAUTIONS

    1. The spot on screen is adjusted as minimum visible brightness level.

    2. The potentiometer controls are always brought to minimum before switching on or off the power supply.

    3. The oscillations of magnetic needle should be of small amplitude.

    4. Ensure that no magnetic material is in vicinity of the set up.   

Answer the following

Q1. What is tangent law?
Q2. What precautions will you take while placing the bar magnets?
Q3. What is the value of e/m ratio for proton?
Q4. What is the significance of e/m ratio?
Q5. How will you find the intensity of the applied electric field?
Q6. What precaution will you take while changing the direction of electric field?

Q7. What do you mean by fluorescence and phosphorescence?
Q8. Why the earth’s magnetic component varies from place to place?
Q9. What will happen if the magnetic field does not act perpendicular to the direction

       of motion of electron?
Q10. Why the magnets are placed at equal distance from CRT?
Q11. Can you find e/m ratio for positively charged particle using Thomson’s method?

Q12. Explain. How an electron beam is produced?

Semiconductor testing: practical steps involved in semiconductor testing: