Measurement of Magneto resistance

It is noticed that the resistance of the sample changes when the magnetic field is turned on. The phenomenon, called magnetoresistance, is due to the fact that the drift velocity of all carriers is not same. With the magnetic field on; the Hall voltage V is given as:

which compensates exactly the Lorentz force for carriers with the average velocity; slower carriers will be over compensated and faster one undercompensated, 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.

Here the above referred symbols are defines as: v = drift velocity; E = applied electric field; t = thickness of the crystal; H = Magnetic field

Description of the experimental setup
The set-up consists of the following:

• Four probe arrangement
• Sample
• Magnetoresistance set-up,
  
  
• Electromagnet, 
• Constant Current Power Supply,
  
  
• Digital Gaussmeter

Four Probe arrangement
It consists of 4 collinear, equally spaced (2mm) and individually spring loaded probes mounted on a PCB strip. Two outer probes for supplying the constant current to the sample and two inner probes for measuring the voltage developed across these probes. This eliminate the error due to contact resistance which is particularly serious in semiconductors. A platform is also provided for placing the sample and mounting the Four Probes on it.

Sample
Ge Crystal (n-type) dimensions : 10 x 10 x 0.5 mm.

Magnetoresistance Set-up
This unit consists of a digital millivoltmeter and constant current power supply. The voltage and probe current can be read on the same digital panel meter through a selector switch.