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.

• 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

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

Measuring change of current with temperature

water

A

thermister

5 V

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!

T1

I e

kT

so

lnI = + const

kT

–

–

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.

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.