I have done Hall effect measurements at an arbitrary value of thickness (500nm) in order to scale them after having the real thicknesses. Once I measure the actual thickness, what are the equations relating Hall quantities to the film thickness.?
Best regards,
Dear Ahmed, If the sample is uniformly conductive and current spreading effect can be neglected, Hall volage is simply inversely proportional to the film thickness.
Bulk carrier concentration will be
n=IB/(ehU) [m^-3], where I-current, B-magnetic field induction, e- electron charge, U-Hall voltage, h- conductive layer thickness.
Nevertheless If you consider nonuniformly conducting sample, this scaling isn't correct (e.g. for the samples with two-dimensional electron or hole gas) and only sheet carrier concentration is calculated as
n2D=IB/(eU) [m^-2], that are not scalable
Good luck!
Thank you Dr. Vasil'evskii
What about the resistivity and mobility?
Regards
Mobility is kinetic value that not scalable, as it is the velosity that carrier achieved at the 1 V/m electric field strength.
Though when the mobility is calculated from specific resistance also the dimensionality of the resistance will be the different in 3D or 2D case.
For 3D ro=Rwh/l in dimensionality [Ohm*m], where R- resistivity of rectangular layer with height h, length l and width w.
For 2D ro is sheet resistivity and h doesn't included,
ro2D=Rw/l, i.e. it is the resistance of square sample.
in the both 2D or 3D case ro=1/enu, where u - carrier mobility
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