a relative simple way of measuring the carrier density, electrical resistivity and the
mobility of carriers in semiconductors.
The principle underlining the Hall effect is Lorenz force which is defined as a force
exerted on a charged particle in an electromagnetic field. Figure 3-2 shows an n-type,
bar-shaped semiconductor. It is assumed that a constant current I flows along the x-axis
from left to right in the presence of a z-directed magnetic field. Under Lorenz force
electrons drift toward the negative y-axis and accumulate on the side of the sample to
produce an electrical surface charge. As a result, a potential drop across the sample called
Hall voltage is formed. The induced electric field increases until it counteracts to the
opposite Lorenz force. In this case,
eEy = evuB = -eBjx /ne (3-2)
where eEy is the induced electric field force, evB is the Lorenz force,jx=-nev, is the total
current density. The Hall coefficient RH is defined as
RH =- (3-3)
ne
The mobility is defined as the coefficient of proportionality between v and E and
measured as follows:
S= = =- RHor (3-4)
E neE
where a is the conductivity. For p-type semiconductors, a hole has a positive charge e.
Therefore, the Hall coefficient is positive in sign.
The Van der Pauw technique which requires no dimension measured for the
calculation of sheet resistance or sheet carrier density solves the potential problem in a
thin layer of arbitrary shape. Thus, this method has increased in popularity relative to the
Hall-bar configuration. The validity of the van der Pauw method requires that the sample