Video Transcript
In a pure semiconductor at a
temperature of 320 kelvin, the number of free electrons in the semiconductor is
𝑛. The temperature of the
semiconductor is increased to 420 kelvin. Which of the following correctly
describes how 𝑛 changes? The semiconductor is in thermal
equilibrium at both temperatures. (A) 𝑛 increases. (B) 𝑛 decreases. (C) 𝑛 remains constant.
In this example, we’re working with
a pure semiconductor. An example of this is silicon. A neutral atom of silicon has four
electrons in its valence shell. This means that when silicon atoms
form a lattice, some electron sharing occurs so that interior atoms in that lattice
have a full complement of eight valence electrons. From an energy perspective, it
doesn’t take the addition of much energy to one of these valence electrons to
liberate it and turn it into a free electron.
Our question tells us that when a
lattice of silicon atoms has a temperature of 320 kelvin, there are 𝑛 free electrons
roaming about through that lattice. The reason there are free electrons
at all in such a sample is due to the transfer of thermal energy to valence
electrons in the lattice. As we’ve said, if sufficient energy
is transferred to such an electron, it becomes free. The thermal energy available for
doing this depends on the temperature of the lattice. The higher the temperature, the
more thermal energy is available to make valence electrons become free
electrons. The higher the temperature then,
the more free electrons exist in a lattice.
This shows us then how to answer
our question. If the number of free electrons in
our semiconductor at a temperature of 320 kelvin is 𝑛, then that number must
increase when we increase the semiconductor’s temperature. We therefore choose answer option
(A) 𝑛 increases.
