Electrons and Holes
Most recent answer: 10/22/2007
Q:
Why do we always speak about "holes" when studying semiconductors, while NOT for conductors? do conductors have no "holes"? What`s the problem if we think of elecrons only when studying semiconductors?
Thanx.
- Pin Yin (age 30)
Singapore
Thanx.
- Pin Yin (age 30)
Singapore
A:
That’s a great question. Here’s some background first for other readers. In solids, there are ’bands’ of possible states for the electrons, which exist as spread-out waves. The states in a band have a range of different energies, but there are usually gaps between bands- ranges of energies where there aren’t any states. The electrons sit in the lowest energy states, except for a few which pick up enough thermal energy to go up some in energy.
If there are just enough electrons to fill up a band, and if there’s not enough thermal energy around (the temperature is low) for any to jump up to the next band, there’s no current. That’s because there are exactly as many states with electrons flowing East as West, so the currents all cancel. In a semiconductor, adding a few impurity atoms can add a few extra electrons, which run around freely in the next higher "conduction" band. Or they can soak up a few electrons, leaving a few empty "holes" in the last filled "valence" band, and these holes can run around like positive charges.
This simple description would not let us make a distinction between holes and electrons in an ordinary metal, with a half-filled band. The current is carried by variations in the occupancy of the states moving different directions, but these don’t amount to just a few filled electron states or just a few holes in a filled band. There are more general definitions of ’electrons’ and ’holes’ that apply to metals, based on the shape of the surface of half-occupied states, as a function of the vector momentum. These categories are used in more technical literature, but are not needed to make a simple picture of metallic conduction.
It would be possible to describe even semiconductors purely in terms of electrons. It’s just that it’s much easier, when almost all the electron currents in the valence band cancel each other out, to focus on the few failures to cancel- the ’holes’.
Mike W.
If there are just enough electrons to fill up a band, and if there’s not enough thermal energy around (the temperature is low) for any to jump up to the next band, there’s no current. That’s because there are exactly as many states with electrons flowing East as West, so the currents all cancel. In a semiconductor, adding a few impurity atoms can add a few extra electrons, which run around freely in the next higher "conduction" band. Or they can soak up a few electrons, leaving a few empty "holes" in the last filled "valence" band, and these holes can run around like positive charges.
This simple description would not let us make a distinction between holes and electrons in an ordinary metal, with a half-filled band. The current is carried by variations in the occupancy of the states moving different directions, but these don’t amount to just a few filled electron states or just a few holes in a filled band. There are more general definitions of ’electrons’ and ’holes’ that apply to metals, based on the shape of the surface of half-occupied states, as a function of the vector momentum. These categories are used in more technical literature, but are not needed to make a simple picture of metallic conduction.
It would be possible to describe even semiconductors purely in terms of electrons. It’s just that it’s much easier, when almost all the electron currents in the valence band cancel each other out, to focus on the few failures to cancel- the ’holes’.
Mike W.
(published on 10/22/2007)