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Charge carrier number density in metals, semiconductors and insulators

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on the number density of charge carriers in metals, semiconductors and insulators, how heating changes the conductance of a semiconductor and a metal, light-dependent resistors, calculating n = I/(Avq) for copper, tiny drift speeds, why thermistors are made from semiconductors, and insulators at very high temperatures.

What you need to know

Answer each one before you reveal it.

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Key term

Explain the high conductivity of a metal in terms of number density.

Key term

Explain why an insulator conducts so poorly.

Key term

Explain why the conductance of a semiconductor rises steeply as it is heated.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is meant by the number density of charge carriers?

    Model answer

    It is the number of mobile charge carriers per cubic metre of the material.

  2. 2

    Explain the high conductivity of a metal in terms of number density.

    Model answer

    Roughly one electron per atom is delocalised, giving about 10²⁹ mobile charge carriers per cubic metre.

  3. 3

    Explain why an insulator conducts so poorly.

    Model answer

    Almost all of its electrons are bound to particular atoms, so the number density of mobile carriers is extremely small.

  4. 4

    Where does a semiconductor sit between a metal and an insulator in terms of carrier number density?

    Model answer

    Between the two, typically 10¹⁶ to 10²³ mobile carriers per cubic metre at room temperature.

  5. 5

    Explain why the conductance of a semiconductor rises steeply as it is heated.

    Model answer

    Thermal energy frees many additional charge carriers, and the rise in number density greatly outweighs the extra scattering.

  6. 6

    Explain why the conductance of a metal falls slightly as it is heated.

    Model answer

    The number density of carriers is unchanged, but the ions vibrate more strongly and scatter the drifting electrons more often.

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