2. Warming semi-conductors
• Many semiconductors suffer from thermal
runaway. As the temperature rises, so
more and more charge carriers are freed
to conduct, allowing a larger current to
flow. In many cases this larger current, if
unchecked, produces a significant heating
effect, so releasing more charge carriers.
Positive feedback drives the thermal
runaway.

3. • The mechanism for increasing conduction is
this: an occasional atom acquires, by borrowing
from its neighbours, enough energy to ionise an
electron. So the Boltzmann factor can be used to
find the ratio of those atoms in the higher state,
with sufficient energy to liberate charge carriers,
to those in the lower state, without such energy.
If the current is proportional to the number of
free carriers, then a check that the description
given is correct, at least in outline

4. You will need:
• a thermistor
• crocodile clip holder
• power supply, 5 V D.C.
• 4 mm leads
• thermometer
• beaker, 250 ml
• kettle to provide hot water
• digital multimeter, used as a milliammeter

5. Measuring change of current with
temperature
water
A
thermister
5 V

6. What to do
• Use supplies of warm and cold water to measure
the current at different steady temperatures. You
will need to make sure that the thermistor is at
the temperature of the water, and that the water
is all at one temperature, so go carefully: don’t
rush!
• You will need to establish a reasonable range of
temperatures and a suitable increment in
temperature before starting the main
experimental run. Make sure you will not end up
changing scales on the multimeter!

7. T
1
I ∝ e
ε
kT
so
lnI = + const
ε
kT
–
–

8. Now comes the tricky bit
• Try out this graph to see if current I at a given p.d. (or
conductance G) is proportional to the Boltzmann factor
exp(–e/kT). Do this by plotting the logarithm ln I of
current I against the reciprocal 1/T of the temperature in
kelvin. A straight line of negative slope is expected since
ln I = –e/kT + constant. As a further check you can get
an estimate of the energy to release one charge carrier
from the gradient of the graph.
• In fact, the extra charge carriers are not the only thing
which affects the conductivity. At higher temperatures
the charge carriers may also be more mobile, increasing
the conductivity in this way too. This extra complication
has been ignored above.

9. You have shown
1.That conduction in a semiconductor
depends in some ways on a process like
ionisation.
2.That this is an activation process,
dominated by the Boltzmann factor.
3.The key exponential behaviour of
processes where lucky particles gain
above average energy by chance.

10. You have shown
1.That conduction in a semiconductor
depends in some ways on a process like
ionisation.
2.That this is an activation process,
dominated by the Boltzmann factor.
3.The key exponential behaviour of
processes where lucky particles gain
above average energy by chance.