I have seen evidence of a lower limit of this equation, but want to determine the resistivity of a composite semiconductor that has a cross section on the order of 100's mm^2 and about 100 mm in length. Is this definition of electrical resistance still viable in this situation.
Dear David,
Definition of resistance is always derivided from the
basic equation for the relationship between
current density j and the electric field E which has the
form j=sigma*E (sigma - conductivity)
Note that the integral relation I=G*U where G=1/R
can be be easily evaluated only under certain conditions for
semiconductor and electrodes geometry e.g. for
parallelepiped but electrodes have to cover completely its
two opposite walls. If you use point electrodes measurements result
of U/I will be different than for proper electrodes.
Generally one has to solve Laplace equation to find the electric potential
distribution and the proper relationship between measured resistance
and resistivity for the second case.
How are you contacting the sample? Assuming a a small contact on the ends you'll need to consider that the current has to flow not only along what you are calling the length, but also outward towards the sides. As a result the resistance path along the edge of your sample may be much longer than the path through the center. Relatively little current will flow along the farthest paths because they have higher resistance.
You can accurately calculate this with the basic equation if you consider the sample to be a mesh of many small resistors. You'll also want to consider that if the region being measured is diffused, your dopant concentrations will not be uniform.
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