Hall Effect

1 Streetman and Banerjee, Solid State Electronic Devices 5 ed., Prentice Hall, 2000 p. 101

Figure 3—25The Hall effect.1

VH • VH = Hall voltage

• cross-sectional area A = t.w

The Hall Voltage

n-type sample

wVH

Ix

t

For current in the positive x direction, electrons flow in the negative x direction. With B directed out of the plane, electrons are deflected to the bottom of the sample, so the Hall voltage is negative. The sample width is w and the thickness is t.

B

Hall Effect Calculations

0 EBvqF

zzxx aBBandavv

yzx

xx

EBnq

J

nqvJ

In steady state, the total force on the charge carrier is 0:

The current density is defined as:

The orientation of the velocity and magnetic field are as follows.

Calculations Continued

zx

yH BJ

ER

8101

zx

HH BI

tV

nqR

We define the Hall Coefficient as follows.

For the sample geometry given above, Ey = VH/w, and Jx = Ix/w.t, so…

The factor of 108 allows us to use Gauss (instead of Wb/cm2) for B.

Hall Mobility

The Hall coefficient gives the carrier density; the sign gives the carrier type (negative for electrons and positive for holes).

8101

zx

HH BI

tV

nqR

HR

We can also find the Hall Mobility if we know the resistivity (or equivalently the conductivity ).

Recall that R = L/A and A = w.t so that if we make a measurement of the sample resistance we have everything we need.

Hall Effect Sensor

B(B is emerging from the paper.)

The sample is a FH-500 Series Hall Generator manufactured by F. W. Bell. The material is bulk InAs.

IxVH

+ -

w = 0.10 cm t =

0.025 cmL = 0.20 cm

Data Analysis

8101

zx

HH BI

tV

nqRIn principle, we can calculate RH

with a single pair of values Ix, VH.

However, if we make a plot of VH vs. Ix and then calculate RH from the slope, we can account for experimental error and get a more accurate value.

You will need to look at the equations describing RH to see how it relates to the slope of this curve.

This graph assumes that VH increases with

increasing Ix. Your data may be different.

VH

Ix

xx x

xx

xx

Least-squares fit

x

NI ELVIS

We will use a measurement station from National Instruments (NI) known as ELVIS (Electronic Laboratory Virtual Instrumentation Suite). ELVIS has:

• a breadboard electrically connected to a box containing… • a DMM (digital multimeter)• power supplies• function generator• oscilloscope connections

• computer control of supply settings and DMM reading

So What Should I Include in My Report?

You should include the following:

• A brief discussion of the Hall effect, including why it is useful.

A review of Lenz’s law would also be nice.• Definitions of any terms that might not be familiar to someone

who has not done the experiment.• Mathematical expressions for anything you calculate. A brief

review of how those formulae are obtained should be given.

Include unitsInclude units for all quantities you use.

What to Include, Con’t:

• A drawing of the sample geometry and something to indicate

the measurement apparatus (nothing fancy is required).

•An explanation of your data analysis procedure (but a review

of linear regression analysis is not necessary).

One Last Thing…

• You must reference the handout(s), as well as every other source you use, even if you do not quote the source directly.• Your abstract should include quantitative conclusions; it is not simply an introduction.

We can’t emphasize enough: