Excitation of Charge Carriers II

Continuing from Excitation of Charge Carriers I:

An example of p-doping will be the inclusion of Boron, a III-element, to silicon.  A Boron atom forms 3 bonds with silicon atoms, but the 4th bond has a hole because it is filled with only one silicon electron.  Upon excitation to mobile state, electrons will come to fill this hole, thereby moving the hole to other bonds.  The original fixed Boron atoms will thus become negatively charged, and the holes will become the majority charge carriers due to its higher density than electrons.  In an electronic band diagram, Boron atoms are represented by acceptor states, whose energy levels also lie in the forbidden band gap, close to the valence band.  At room temperatures, many silicon electrons from the valence band will be excited to the acceptor states, leaving many holes behind.  The Fermi level will also be closer to the valence band.

The law of mass action states that the product of electron density (electron carrier concentration) n and hole density p is constant at a given temperature, regardless of doping concentration changes.  Hence:

n*p = n_i²

where n_i is the intrinsic density of charge carriers in silicon, and for an intrinsic material:

n = p = n_i = 1.1*10¹⁰ cm^-3

Semiconductor materials can also absorb light energy, where photons from light will excite electrons from the valence band to the conduction band.  The energy from each photon must possess energy that's more than the energy required for each electron to jump the band gap.  If the energy from the photon is less than the band gap energy, the light wave will just pass by without being absorbed by the semiconductor material.  If the photon's energy is much larger than the energy to overcome the band gap, an electron deeper inside the valence band can be excited to the conduction band, or the electron can be excited to a much higher level in the conduction band, after which the electron will quickly relax back to the bottom of the conduction band.  Similar effects are seen for holes - holes will relax to the top of the valence band.  This relaxation releases heat energy and makes the semiconductor material hotter.

For a semiconductor material that has been doped, the majority charge carriers will have a density that is much higher than the concentration of charge carriers excited by light absorption.  However, the density of charge carriers created by light absorption is much higher than the density of minority carriers.  This leads to the important conclusion that solar light absorption will increase minority charge carriers effects.



Referencing:
2.3.2 Excitation of Charge Carriers II, Delft University of Technology, https://www.youtube.com/watch?v=MtzaExAnIrg