Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-12 GTBL042-Callister-v2 August 13, 2007 18:22

488 • Chapter 12 / Electrical Properties

12.14 THE HALL EFFECT

For some material, it is on occasion desired to determine its majority charge car-

rier type, concentration, and mobility. Such determinations are not possible from

Hall effect a simple electrical conductivity measurement; aHall effectexperiment must also

be conducted. This Hall effect is a result of the phenomenon whereby a magnetic

field applied perpendicular to the direction of motion of a charged particle exerts a

force on the particle perpendicular to both the magnetic field and the particle motion

directions.

In demonstrating the Hall effect, consider the specimen geometry shown in

Figure 12.20, a parallelepiped specimen having one corner situated at the origin

of a Cartesian coordinate system. In response to an externally applied electric field,

the electrons and/or holes move in thexdirection and give rise to a currentIx.

When a magnetic field is imposed in the positivezdirection (denoted asBz), the

resulting force brought to bear on the charge carriers will cause them to be deflected

in theydirection—holes (positively charged carriers) to the right specimen face and

electrons (negatively charged carriers) to the left face, as indicated in the figure.

Thus, a voltage, termed theHall voltage VH, will be established in theydirection.

The magnitude ofVHwill depend onIx,Bz, and the specimen thicknessdas follows:

VH=

RHIxBz

d

(12.18)

Dependence of Hall

voltage on the Hall

coefficient, specimen

thickness, and

current and magnetic

field parameters

shown in Figure 12.20

In this expressionRHis termed theHall coefficient, which is a constant for a given

material. For metals, wherein conduction is by electrons,RHis negative and equal to

RH=

1

n|e|

Hall coefficient for (12.19)

metals

Thus,nmay be determined, inasmuch asRHmay be measured using Equation 12.18

and the magnitude ofe, the charge on an electron, is known.

d

z

y

c

VH

x

Ix

Bz

−+

Figure 12.20 Schematic demonstration

of the Hall effect. Positive and/or

negative charge carriers that are part of

theIxcurrent are deflected by the

magnetic fieldBzand give rise to the Hall

voltage,VH.