Hall Effect

1
Hall Effect
Figure 325 The Hall effect.1
VH

• VH Hall voltage
• cross-sectional area A t.w

1 Streetman and Banerjee, Solid State Electronic
Devices 5 ed., Prentice Hall, 2000 p. 101
2
The Hall Voltage
Ix
w
VH
t
n-type sample
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.
3
Hall Effect Calculations
In steady state, the total force on the charge
carrier is 0
The orientation of the velocity and magnetic
field are as follows.
The current density is defined as
4
Calculations Continued
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.
5
Hall Mobility
The Hall coefficient gives the carrier density
the sign gives the carrier type (negative for
electrons and positive for holes).
We can also find the Hall Mobility if we know the
resistivity (or equivalently the conductivity s).
Recall that R rL/A and A w.t so that if we
make a measurement of the sample resistance we
have everything we need.
6
Hall Effect Sensor
B
(B is emerging from the paper.)
w 0.10 cm
t 0.025 cm
L 0.20 cm
The sample is a FH-500 Series Hall Generator
manufactured by F. W. Bell. The material is bulk
InAs.
7
Data Analysis
In 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.
8
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

9
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 Lenzs 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 units for
  all quantities you use.

10
What to Include, Cont

• 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).

11
One Last Thing
We cant emphasize enough

• 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.