MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

Electronic and Magnetic Measurements 25
portion of the sample is sensed with two other contacts. The voltmeter has a
high input impedance so that very little current is drawn from the voltage
contacts. If there is almost no current flowing through the voltmeter circuit,
then there is almost no voltage drop across the contacts or contact wires. In
this way, the voltage measured is the voltage across the sample. Since the
voltage contacts are separated from the current contacts, one must be cautious
of the tacit assumption that the current flows uniformly through the entire
sample. If the current avoids the voltage contacts, the results will be
spurious. For high resistance samples, two probe measurements, where the
voltage contacts are the same as the current contacts, can be used. The
resistance due to the contacts and grain boundaries can be determined with
AC impedance spectroscopy. Extremely high resistance measurements can be
done with an electrometer where a constant voltage is applied and the
electrometer measures the tiny trickle of current that passes through.
The simplest geometry is the bar sample. The resistivity of a bar is the
resistance times the cross-sectional area divided by the length between the
voltage contacts. Samples can either be shaped into bars or rods, or films can
be patterned. Patterned films can be ideal for transport measurements since
the geometric ratio is well known, and the effects of the contacts can be
minimized by patterning small contact wires in the film. Unfortunately the
patterning process can damage the films.
For isotropic two-dimensional samples, the physical dimensions (other
than the thickness) need not be measured. In some cases the geometric ratio
can be calculated analytically using conformal mappings. The geometric ratio
has been calculated for a sheet where four collinear and equally spaced
contacts are in the center of a sheet [51]. The Van der Pauw [52, 53]
configuration uses four contacts placed anywhere on the edge. By switching
one of the current and voltage leads, the geometric ratio can be calculated.
The Van der Pauw configuration can also be used for the Hall effect.