Page 219 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Transport Theory
ate the terms from the thermodynamic expressions that we have obtained
before. Many solid-state silicon devices have been invented that exploit
these effects. We discuss some of these in Section 7.3.6.
6.2.3 The Hall Effect

Taking a magnetic field into account in the carrier drift force term
(
F = – q E + v × B) , one part of is given by the electric field and the
F
other by the Lorenz force. This Lorenz force causes the electrons to move
to the one side of the conductor, while the electrons move to the opposite
side (see Figure 6.6). This results in a potential difference perpendicular
to the current direction. Therefore, the equipotential lines are shifted by
an angle Θ . Placing two contacts on the boundary of the conductor as
shown in Figure 6.6, the potential difference can be measured. The so–

θ
V S
w V H

B

Figure 6.6. Schematic diagram of a Hall plate showing the electric potential distribution
due to an out–of–plane magnetic field.

called Hall voltage is directly proportional to the component of the
applied magnetic field perpendicular to the Hall plate.

F
To describe this effect we first insert the expression for containing the
Lorenz force directly into (6.30) and see that the effect of the magnetic

216 Semiconductors for Micro and Nanosystem Technology