I determined the band gap of an undoped sample of germanium. I Measuring the Hall voltage of both n-type and p-type germanium. Calculated the hall coefficient RH, the carrier

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The Hall Effect in Germanium

Abstract

  1. I determined the band gap of an undoped sample of germanium.
  2. I Measuring the Hall voltage of both n-type and p-type germanium. Calculated the hall coefficient RH,  the carrier mobility μH and the carrier concentration, n.

Theory

The Hall Effect

A beam of electrons can be deflected by a magnetic field. Metals are full of free electrons that freely roam around the stationary protons. Edwin H. Hall found that these drifting conduction electrons can also be deflected when a magnetic field is applied.  The diagram below taken from “The Fundamentals of Physics” by Halliway, Resnick and Walker, shows the Hall Effect on a strip of metal. A piece of metal, in our case Germanium as a current applied to it, (indicated as i below.) which run from the top to the bottom. Electrons (the charge carriers) drift in the opposite direction to the current at a drift speed of Vd. A magnetic field,  is applied and to the strip and the drifting electrons are deflected by the magnetic deflecting force, FB. This is shown below in the diagram labelled (a) where the black line represents the path of the drifting electrons which move to the right of the Ge strip.

“As time goes on, electron move to the right, mostly piling up on to the right edge of the strip, leaving uncompensated positive charges in fixed positions at the left edge”(1). An electric field is produce by the separation of the negative and positive charge within the strip, shown above in the diagram labelled (b). The electrons deflected to the right by the magnetic force, FB are now being deflected to the left by an electric force FE. “An equilibrium quickly develops in the which the electric force on each electron builds up until it just cancels out the magnetic force”(1). The diagram labelled (b) above shows that FB and FE are balanced and the drifting electrons drift in a straight line from bottom to top a drift speed of Vd. no more electrons build up on the right so the  does not increase anymore.

“The Hall potential difference V is associated with the electric field across the strip width d”(1)

The potential difference is given by

If a voltmeter is connected across the width of the strip, the potential difference can be measured. The voltmeter can also indicate which side of the strip has a higher potential and with this information we can find out whether the charge carriers are positive or negative. We can find this out because if the charge carrier was positive (shown above in the diagram labelled (c)) moving from top to bottom, they would also be pushed to the right by the FB and the right edge of the strip (instead of the left edge with negatively charged carriers) would have a higher potential.

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“The conductivity, σo, carrier mobility, μH, and the carrier concentration, n are all connected by a factor called the Hall coefficient, RH”(3).

Crystal Doping

“Crystal doping is an efficient method of increasing current flow in semiconductors is by adding very small amounts of selected additives to them, generally no more than a few parts per million” (2). Doping therefore increase the amount of free charges that can flow.

“The N-type impurity loses its extra valence electron easily when added to a semiconductor material, and in so doing, increases the ...

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