**Branch :**Computer Science and Engineering

**Subject :**Fundamental of Electronic Devices

## The Hall Effect

**Introduction:
**

This section derives the equation of the hall effect & also explains it.

**The Hall Effect:**

If a magnetic field is applied perpendicular to the direction in which holes drift in a p-type bar, the path of the holes tends to be deflected (Fig. given below).

Using vector notation, the total force on a single hole due to the electric and magnetic fields is

equ (1)

In the y-direction the force is equ (2)

The important result of Eq. (2) is that unless an electric field ξ_{y} is established along the width of the bar, each hole will experience a net force (and therefore an acceleration) in the -y-direction due to the qv_{x}B_{z} product. Therefore, to maintain a steady state flow of holes down the length of the bar, the electric field ξ_{y} must just balance the product v_{x}B_{z}: equ (3)

so that the net force F_{y} is zero. Physically, this electric field is set up when the magnetic field shifts the hole distribution slightly in the -_y-direction. Once the electric field ξ_{y} becomes as large as v_{x}B_{z}, no net lateral force is experienced by the holes as they drift along the bar. The establishment of the electric field ξ_{y} is known as the Hall effect, and the resulting voltage V_{AB} = ξ_{y}w is called the Hall voltage.

The drift velocity (using q and p_{0}for holes), the field ξ_{y}becomes

equ (4)

Thus the Hall field is proportional to the product of the current density and the magnetic flux density. The proportionality constant R_{H} = (qp_{o})^{-1} is called the Hall coefficient. A measurement of the Hall voltage for a known current and magnetic field yields a value for the hole concentration p_{0
}

equ (5)

Since all of the quantities in the right-hand side of Eq. (5) can be measured, the Hall effect can be used to give quite accurate values for carrier concentration.

If a measurement of resistance R is made, the sample resistivity p can be calculated:

equ (6)

Since the conductivity σ = 1/p is given by qμ_{p}P_{o}, the mobility is simply the ratio of the Hall coefficient and the resistivity:

equ (7)

Measurements of the Hall coefficient and the resistivity over a range of temperatures yield plots of majority carrier concentration and mobility vs.temperature. Such measurements are extremely useful in the analysis of semiconductor materials.