Lake Shore Cryotronics Measure Ready M91 FastHall, Руководство пользователя

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1.5.1 Field Hall
Nomenclature This section provides an explanation of the naming conventions and nomenclature
used in this manual and in the MeasureLINK™-MCS software. The units used for the
quantities defined here, and conversion between common systems of units can be
found in section 1.5.2.
Hall mobility (µ
H
) is the ratio of the Hall coefficient (R
H
) to the resistivity (

):
Hall coefficient (R
H
) is the Hall voltage (V
H
) times the thickness (t) divided by the
current (I) and magnetic field (B).
Hall voltage is the most critical measurement needed in order to determine the
Hall
coefficient. Later sections will describe the exact methods used in the M91
FastHall™ measurement controller to get the best possible measurement of the Hall
voltage. The Hall voltage contains other information about the electrical
transportation properties of the material. For instance, the sign of the Hall voltage is
positive if the carriers in the material are holes, and it is negative if the carriers in the
material are electrons.
Hall voltage (V
H
) is the ratio of the current (I) and field (B) to the thickness (t), density
of free carriers (n) and electronic charge (e) in many materials.
The previous two equations relating the Hall voltage to the carrier density and Hall
coefficient to Hall voltage can be used to derive the relationship between the Hall
coefficient and carrier density. This result assumes a model using free electron gas or
spherical energy bands for the semiconductor:
The Hall factor (h
f
) is the correction term used when this assumption is not realized.
With the correction term, the relationship between the Hall coefficient and carrier
density should be modified to include the correction term, the Hall factor (h
f
):
This same Hall factor is also the ratio of the Hall mobility to the drift mobility. Drift
mobility is defined as the carrier velocity per applied electric field. Although the Hall
factor can be calculated, the calculation can be difficult and often only represents an
approximation. Absent of any better information, it is reasonable to use a Hall factor
of 1. This manual will assume the Hall factor is 1, but the MeasureLINK™-MCS
software will allow the user to enter a Hall factor and use the Hall factor to calculate
results.