Hall Effect New

7/28/2019 Hall Effect New

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Aim of the experiment: To study Hall effect and hence determine the Hall co

efficient, types of charge carrier, carrier concentration and carrier mobility.

Apparatus used: Hall Effect setup, constant current supply, electromagnet and

hall probe.

Theory: As we know that a static magnetic field has no effect on charge unlessthey are in motion. When the charges flow, a magnetic field directed perpendicular

to the direction of flow produces a mutually perpendicular force on the charge

particle. When this happens, electrons and holes will be separated by opposite

forces. They will in turn produce an electric field ( ) which depends on the cross

product of the magnetic intensity, and the current density as shown in the fig 1.

1

Where R is called Hall coefficient

Now let us consider a bar of semiconductor having dimensions x, y and z.

let is directed along x and along z then will be along y as shown in the fig2

Then we could write

.2

Where is the Hall voltage appearing between the two surfaces perpendicular to yand I.

In general Hall voltage is not a linear function of magnetic field applied, i.e

the Hall coefficient is not generally a constant, but a function of the applied

magnetic field. Consequently, interpretation of the Hall voltage is not usually a

simple matter. However it is easy to calculate this voltage if we assume that all

carriers have the same drift velocity. We will do this in two steps

(a)By assuming that carriers of only one type are present and(b)By assuming that carriers of both type are present.

One type of carrier:Metals and doped semiconductors are the example of this

type where one carrier dominates.


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The magnetic force on the carriers is and is compensated

by the Hall field , where is the drift velocity of the carriers. Assumingthe directions of the various vectors as before.

But the current density = qn

Hence from equation 2 we have.

From this equation it becomes clear that the sign of H depends upon the sign of q.

this means, in a p type semiconductor the R would be positive, while in n type it

would be negative. Also for a fixed magnetic field and input current, the Hall

voltage is proportional to 1/n or its resistivity. When one carrier dominants, the

conductivity of the material is

, where is the mobility of the charge carriers.

Thus .4

(c)Two types of carriers:Intrinsic and the lightly doped semiconductors are the examples of this type.

In such cases , the quantitative interpretation of Hall coefficient is more difficult

since both type of carriers contribute to the Hall field. It is also clear that for the

same electric field, the Hall voltage of p-carriers will be opposite in sign to that

from n-carriers. As a result both mobilites enter into any calculations of Hall

coefficient and a weighted average is the result i.e.

..5

here and are the mobility of the electrons and holes respectively. p and n arecarrier densities of electron and holes respectively.

Since they are not constants but functions of temperature (T) the Hall

coefficient given by equation 5 is also a function of T and it may become zero


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change sign. In general so that inversion may happen if p thus Hallefficient inversion is characteristics only of p type semiconductors.

At the point of zero Hall possible to determine ratio of mobilites and their

relative concentration coefficient it is.

Procedure:

1. Adjust the spacing between the pole pieces to a suitable value. Connect theelectromagnet to the magnet terminals of the hall kit. Place the hall probe at

the center of the gap with its face parallel to the faces of the pole pieces of

the electromagnet. Keep magnet control and probe control in maximum

anticlockwise position and switch ON the instrument. The experiment is

performed by two methods.

Method A: (magnet current Im

is fixed)

2. With the selector switch at the current position in the magnet set the magnetcurrent Im at 100mA.

3.Now note down the voltage recorded by the digital voltmeter in the Halleffect setup when the Hall probe is outside the magnet and nullify the

voltage with the help of the zero control facility.

4. Keeping current Im fixed at 100mA, set the hall current or the samplecurrent Is to a suitable fixed value between 40mA to 100mA (in steps of

10mA) and note down the corresponding values of the Hall voltages VHdeveloped.

5. Plot VH versus IS and find the slop. Hence calculate RH.Method B: (specimen current IS fixed)

6. Set the current Is to a suitable fixed value between 40mA to 100mA. Afternullifying the offset voltage of the probe increase Im and note down the

values of VH for various values of Im viz. 100mA, 200mA, 300mA,400mA

and 500mA.7. Ettingshausen effect can be eliminated by repeating steps 2, 3 and 4for Im

and Is in the forward and reverse direction i.e, other three situations

Im ( - ) Is ( + )

Im ( + ) Is ( - )


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Im ( - ) Is ( - ) and find the corresponding Hall voltages VH1, VH2, VH3,

VH4 for each value of IS. calculate average Hall voltage VH for each

values of Is

8. Find B corresponding to Im9. Plot VH versus B. Find the slop and calculate RH.

Observation:Thickness of the sample =

Conductivity =

Method A: Magnet current (Im) fixed.

Im = 100mA

Sl no Is (mA) VH1 VH2 VH2 VH3 VH

1

2

3

.

.

.

40

50

60

..

..

..

Method B : Hall current (Is ) fixed:

Is = 50mA

Sl no Im (mA) B VH1 VH2 VH3 VH4 VH

1

2

3

.

.

.

100

200

300

..

..

..

Graphs :


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Calculations:

1. From graph (a) , slope =

=

B =

t =

RH =

2. From graph ( b ): slope =

=

B =

t =

RH =

Mean RH= ..

3. Carrier density, n =

4. Mobility of charge carriers, Results:

The Hall coefficient =

Carrier density =

Mobility of charge carriers =

Sources of errors and precautions:

.

Hall Effect New

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