study of magneto resistance sid

8/2/2019 Study of Magneto Resistance Sid

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Study of Magnetoresistance

Semiconductor Devices and Technology Lab

Electronics Department

IIT Roorkee

GROUP MEMBERS:

1) Siddharth Jindal

2) Tangirala Bhargav

3) Yogesh kapila


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Study of Magnetoresistance

By: Siddharth Jindal, Tangirala Bhargav and Yogesh Kapila

Aim-

Calibrate a magnetic field sensor using magnetoresistance effect in Ge

Apparatus Required-

Sample(Ge: n type),Magnetoresistance set-up ,Four probe arrangement ,Electromagnet, EMU- 50,

Constant Current Power Supply, DPS- 50,Digital Gauss Meter, DGM-102

Theory-

MAGNETORESISTANCE SETUP:

Magneto resistance is the property of a material to change the value of its electric resistance when anexternal magnetic field is applied to it. This effect was first discovered by William Thomson in 1956. Due

to magneto resistance the drift velocity of all the carrier is not same. The Hall voltage is

V = Et = |vxH|

Where,

v = drift velocity

E = applied electric field

t = thickness of the crystal

H = Magnetic field

Four Probe Arrangement

When the magnetic field on, Hall effect compensates the Lorentz force for carrier with the average

velocity; slower carriers will be over compensated and faster one under compensated resulting in

trajectories that are not along the applied field. This results in an effective decrease of the mean free

path and hence an increase in resistivity.

Calculation of mobility

(m-)/ = (*xB)2

where.

m = Resistivity with magnetic field

= Resistivity without magnetic field

* = Hall mobility

B = Magnetic field


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* = xr

where,

r = scattering factor

= electron mobility

Procedure:

1. Set the suitable air gap, i.e., 19 mm between the electromagnets.2. Turn on the constant current supply, digital gauss meter and magnetoresistance set up.3. Place the probe between electromagnet and measure the magnetic field on changing the

value of current.

4. Now set up the probe current (I) = 4 mA (constant for whole set of readings)5.

Measure the voltage V for different value of currents and magnetic field, keeping probecurrent constant.

6. Calculate the magnetic field resistance by using the formula:R = V / I

7. R= 174.7/4= 43.675 where R is sample resistance without magnetic field.8. Draw a graph between R/R vs Magnetic field.9. Draw a graph between log ( R/Rx 10^-3) vs log (magnetic field x 10^-2)

Here,

R= Rm

RWhere

R = sample resistance without magnetic field

Rm = sample resistance with magnetic field


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OBSERVATION TABLE

CURRENT(A) MAGNETIC FIELD(Gauss) VOLTAGE(mV) Rm (Rm-R)/R

Log((Rm-

R)/R) Log(B)

0.0 12 144 36.3636364 0.00702399 -2.15341597 1.079181246

0.2 178 144 36.3636364 0.00702399 -2.15341597 2.250420002

0.4 361 144 36.3636364 0.00702399 -2.15341597 2.557507202

0.6 558 144.1 36.3888889 0.00772331

-

2.112196276 2.746634199

0.8 758 144.1 36.3888889 0.00772331

-

2.112196276 2.879669206

1.0 944 144.2 36.4141414 0.00842264

-

2.074551928 2.974971994

1.2 1132 144.2 36.4141414 0.00842264

-

2.074551928 3.053846427

1.4 1321 144.4 36.4646465 0.00982128

-

2.007831854 3.120902818

1.6 1536 144.6 36.5151515 0.01121993

-

1.950010021 3.186391216

1.8 1734 144.8 36.5656566 0.01261857

-

1.898989856 3.239049093

2.0 1921 145 36.6161616 0.01401721 -1.85333828 3.283527365

2.2 2130 145.3 36.6919192 0.01611518

-

1.792764808 3.328379603

2.4 2310 145.6 36.7676768 0.01821315

-

1.739614988 3.36361198

2.6 2500 145.9 36.8434343 0.02031111

-

1.692266246 3.397940009

2.8 2700 146.3 36.9444444 0.0231084

-

1.636230061 3.431363764

3.0 2880 146.6 37.020202 0.02520637

-

1.598489693 3.459392488

3.2 3070 146.9 37.0959596 0.02730434 -1.56376837 3.487138375

3.4 3260 147.3 37.1969697 0.03010163

-

1.521410052 3.5132176


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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 1000 2000 3000 4000

(Rm-R)/R

(Rm-R)/R

-2.5

-2

-1.5

-1

-0.5

0

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Log/Log Plot

Log/Log Plot

(Rm-R)/R vs Magnetic Field

Magnetic Field

(Rm-R)/R

log((Rm-R)/R)

lo B


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Calculation of mobility

(m-)/ = (*xB)2

Where,

m = Resistivity with magnetic field

= Resistivity without magnetic field

* = Hall mobility

H = magnetic field

And,

* = xr

Where,

r= scattering factor

= electron mobility

General model-

f(x)= a*x^2

As calculated from graph, coefficient, (with 95% confidence bounds)

a=355 x 10^5 (approx.)

a= ^2

= 5960

= x r (r=1.5)

= 5960 x 2/3= 3973.33 cm^2 per V per s

Result-

Calculated mobility of Germanium is 3973.33 cm^2 per V per S


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Conclusion-

Some materials undergo a change in their electrical resistance when subjected to anexternal magnetic field. This effect is known as magnetoresistance.

This is due to the fact that the drift velocity of all charge carriers are not the same. In thepresence of magnetic field, the Hall voltage compensates the Lorentz force on the charge

carriers moving with average velocity.

Slower carriers will be over compensated, while faster carriers will be undercompensated.As a result of this, the carriers do not move in the direction of the applied electric field.

Consequently the mean free path of the electrons decreases, resulting in greater electrical

resistance.

Thus, in short, we may state that-

As observed from the graph, the resistance of sample increases with significantincrease in magnetic field

Hence, we may conclude that magnetoresistance does exist in increases withincrease in magnetic field.

study of magneto resistance sid

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