Hall Effect

Three circuits, one gap. The two magnetic coils are wired in series and fed from the bottom loop — battery, key, rheostat and ammeter — so one knob sets the field. The sample sits in the gap with its own loop, where the milliammeter sets the current I through it. The Hall voltage is tapped from the two sides of the sample, across the current, and read on the voltmeter above. The same gap does double duty: a Hall probe sits in it for Part I, the semiconductor sample for Part II, and the pole-piece separation d is set once and left alone for both.

Part I — Calibration of the Gauss Meter

1. 1.

   Set a suitable distance between the pole pieces of the electromagnet — this separation, d, stays fixed for the rest of the experiment.

2. 2.

   Place the Hall probe (the Gauss meter probe) between the pole pieces.

3. 3.

   Switch on the electromagnet power supply, then switch on the Gauss meter and zero it.

4. 4.

   Set a suitable current through the electromagnet and note the Gauss meter reading while increasing the current, in equal steps, up to a suitable maximum.

5. 5.

   Decrease the current back down in the same steps, noting the Gauss meter reading at each step.

6. 6.

   Tabulate the increasing and decreasing readings for every current value.

For each current, average the reading taken on the way up and the reading taken on the way down — the iron core lags behind the current, so a single sweep reads slightly high or low depending on direction. Averaging the two cancels that out:

That mean reading is the calibrated magnetic field, in gauss, for each current — and the pole-piece separation d set above carries over unchanged into Part II.

Part II — Determination of Hall Voltage / Hall Coefficient

1. 1.

   Keep the pole-piece separation the same as in Part I.

2. 2.

   Place the semiconductor sample between the pole pieces so the field is perpendicular to its flat face.

3. 3.

   Connect the sample to the constant current source and the millivoltmeter as per the circuit diagram.

4. 4.

   Switch on the electromagnet and set its current to the same values used in Part I, so as to reproduce the same fields.

5. 5.

   Pass a suitable constant current I through the sample.

6. 6.

   Note the Hall voltage Vₕ across the sample while increasing the electromagnet current in the same steps, then again while decreasing it.

7. 7.

   Tabulate the electromagnet current, the corresponding field B read off the Part I calibration, and the average Hall voltage Vₕ.

Analytical Calculation

For each reading, work out the Hall coefficient:

Average Rₕ over all the readings — that mean is the analytical value reported as the result — then use it to get the Hall mobility:

Graphical Calculation

Plot Hall voltage Vₕ against magnetic field B and determine the slope of the straight line, then use it for the graphical value of the Hall coefficient:

and, from that, the Hall mobility again: