Semiconductors in the Classroom
An Introduction to Semiconducting Materials using Hall
Measurements
Scott Maloney
UW Nanotech 2012
Introduction
The purpose of this activity is to introduce high school students to basic
concepts of semiconductor materials. Students will learn:
-
what makes semiconductors different from conductors and insulators
the difference between n-type and p-type semiconductors
how magnetic fields affect mobile charges
Many semiconductor concepts can be demonstrated by performing Hall effect
measurements. The Hall effect is the establishment of an electric field across a bar
perpendicular to the current flow through the bar and an applied magnetic field:
If the bar is p-type (meaning ‘holes’ are the majority charge carrier), a
magnetic field in the +z direction will deflect positive, holes traveling in the +x
direction, to the +y direction. This lateral charge imbalance will create a voltage
across the width of the bar. This is called the Hall voltage. Knowing the current Ix,
magnetic field strength, Bz, charge of a single carrier (q ≈ 1.60×10-19C), sample
thickness, d, and the Hall voltage, VH, the carrier concentration, po can be easily
calculated using:
po (or no) = IxBz/(qdVH)
(1)
Carrier concentration is usually expressed in units of cm-3, and magnetic field
in units of Teslas (T), kilogauss (kG) or Webers per square centimeter, (Wb/cm2),
where 1kG = 10-5 Wb/cm2. The carrier type (p or n) can be determined by weather
the Hall voltage is positive or negative. The resistivity, ρ, of the sample can also be
determined from the dimensions of the sample:
ρ = WVxd/(LIx)
(2)
The mobility of the charge carriers is defined as the ratio of the applied
electric field (i.e. the voltage from the battery) and the drift velocity of the charge
carriers. For this experiment we use:
μ = 1/ρqpo
(3)
Mobility is a very important value and is used in virtually all semiconductor
analysis. Higher quality semiconductors such as silicon have a higher crystallinity
and thereby a higher mobility value. The units of mobility are cm2/(Vs).
Materials
Wires with alligator clips
Square silicon wafer
½” diameter magnet of known strength
Multimeter
Conductive copper tape
Batteries
Electrical tape
Procedures
(i)
(ii)
(iii)
(iv)
(v)
Measure the dimensions of the sample.
Check that the conductive copper tape is making a good connection with
the edges of the silicon by measuring the resistance across the length. (A
typical value for heavily doped n-type Si might be 50 – 200kΩ)
Connect both wires to the terminals of the battery. Note which side is
positive and which side is negative.
Set the multimeter to read current and connect the Si piece and
multimeter in series with the battery. Measure the current through the Si.
Remove the multimeter from the series circuit. Carefully put the magnet
underneath the Si piece between the two alligator clips. The clips are
magnetic so be sure the magnet is insulated from them (use electrical
tape as shown or paper).
(vi)
Switch the multimeter to read voltage and take a voltage reading across
the width of the Si.
Applications
Many switches in your car use Hall switches! As a magnet is brought near a
semiconductor device a Hall voltage is created and sensed.