Hall Effect

Semiconductor Devices

AIM

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

APPARATUS

  • Two solenoids
  • Constant current supply
  • Four probe
  • Digital gauss meter
  • Hall effect apparatus (consisting of Constant Current Generator (CCG), digital milli voltmeter, and Hall probe)

THEORY

If a current-carrying conductor is placed in a perpendicular magnetic field, a potential difference will generate in the conductor which is perpendicular to both magnetic field and current. This phenomenon is called Hall Effect. In solid-state physics, Hall effect is an important tool to characterize the materials, especially semiconductors.

FORMULA

$$ V_H = Ew = vBw = \frac{IB}{net} $$

Where:

  • $V_H$ = Hall voltage
  • $I$ = Current through the sample
  • $B$ = Magnetic field
  • $n$ = Carrier concentration
  • $e$ = Charge of electron
  • $t$ = Thickness of the sample
  • $R_H$ = Hall coefficient

CIRCUIT DIAGRAM

OBSERVATION TABLE

S.No. Magnetic Field (B) Thickness (t) Hall Current (I) Hall Voltage (VH) RH
1
2
3
4
5

PROCEDURE

  1. Connect the constant current source to the solenoids.
  2. Connect the four probe to the Gauss meter and place it at the middle of the two solenoids.
  3. Switch ON the Gauss meter and constant current source.
  4. Vary the current through the solenoid from 1A to 5A with the interval of 0.5A, and note the corresponding Gauss meter readings.
  5. Switch OFF the Gauss meter and constant current source and turn the knob of the constant current source towards minimum current.
  6. Fix the Hall probe on a wooden stand. Connect green wires to Constant Current Generator (CCG) and connect red wires to the milli voltmeter in the Hall Effect apparatus.
  7. Replace the four probe with Hall probe and place the sample material at the middle of the two solenoids.
  8. Switch ON the constant current source and CCG.
  9. Carefully increase the current $I$ from CCG and measure the corresponding Hall voltage $V_H$. Repeat this step for different magnetic field $B$.
  10. Measure the thickness $t$ of the sample using a screw gauge.
  11. Calculate the Hall coefficient $R_H$.
  12. Calculate the carrier concentration $n$.

PRECAUTIONS

  • Hall voltage should be measured very carefully and accurately.
  • The current through the probe should not exceed a certain minimum value.
  • The digital voltmeter should be handled carefully.
  • The distance between pole pieces of the electromagnet should not be changed during the whole experiment.

RESULT

  • Hall coefficient of the material =
  • Carrier concentration of the material =