PHY 4822: Hall effect documentation
WHAT YOU HAVE TO DO:
- understand equipment: base unit, plugin board, Gaussmeter (read manuals)
- record direction of magnetic field, direction of cross current, sign
of Hall voltage (direction of electric field corresponding to Hall voltage)
[see note 1] (make a drawing). You'll need this in order to interpret signs of Hall
coefficient in terms of charge carrier charge.
- set cross current to 30 mA and measure Hall voltage for zero magnetic field;
twiddle compensator if necessary to make Hall voltage zero for zero field.
In your report, discuss why you think it is necessary to make this adjustment.
(What could cause a non-zero voltage between the terminals used for measuring
the Hall voltage?)
- For three different values of the cross current (e.g. 10, 20, 30 mA),
measure the Hall voltage and voltage drop across the crystal as a function
of the magnetic field (at least 10 different field values)
- For three different values of the magnetic field strength (e.g. 20, 50,
100 mT), measure the Hall voltage and voltage drop across the crystal as a
function
of the cross current (at least 10 different current values in range 0 to 30 mA).
- From every set of B, I, VH, Vdrop, determine the Hall coefficient and the density
and mobility of the charge carriers (with uncertainties -- make appropriate
assessment of your measurement precision).
- Show graphs of Hall voltage vs B for three different cross currents, as
well as graphs of Hall voltage vs cross current for different values of B.
- perform straight line fits for each of the graphs and assess the
quality of the straight line fits.
Determine slopes of straight lines and calculate Hall coefficient from slope
in the graphs of Hall voltage vs B for three different cross currents, as
well as graphs of Hall voltage vs cross current for different values of B.
Determine uncertainty of slopes and thus uncertainty of Hall coefficients and
charge carrier density derived from these slopes.
- What would you expect the intercepts of the straight lines to be?
Discuss any deviations from your expectation.
- Quote your best estimates of the Hall coefficient and the density
and mobility of the charge carriers.
- Give an estimate of the doping concentration (i.e.
the fraction of Ge atoms that has been replaced by an impurity atom)[see note 2].
State and explain the assumptions / approximations made in this estimate.
- Notes, questions, remarks:
- about sign of charge carriers:
In your report,
- show your experimental setup, including coordinate system
(if used), directions of current, magnetic field;
- Using Lorentz-force, directions of current and magnetic field
(and with help of right-hand rule), explain what happens and what
is the direction of the electric field created due to the displacement
of the charge carriers
(do this for both positive and negative charge carriers)
- explain how you define the sign of the Hall voltage
(voltage is potential difference -- specify what minus what),
- under what condition would you call the Hall voltage positive?
- Show your reasoning that leads you to your conclusion about the sign
of the charge carriers in your sample.
- about doping concentration:
- assume that charge carrier density is dominated by contribution
from dopant atoms (justify this assumption)
- from this assumption it follows that (nb. density of dopant atoms) = (nb. density of charge carriers)
- get ratio of (nb. density of dopant atoms)/(nb. density of Ge atoms)
- note that you measured nb density of charge carriers
- how to get number density of Ge atoms:
- remember that the number of atoms per mole of Germanium = Avogadro number
- find density of Germanium (look it up somewhere)
- find volume of a mole of Germanium (= (mass of one mole of Ge)/(density of Ge))
- (nb. density of Ge atoms) = (nb. of atoms per mole)/(volume of one mole)
- If you moved along a straight line through your sample, how many Ge atoms
would you expect to encounter (on the average) before hitting on a dopant
atom?
equipment information:
