To me energy band diagram is a one dimensional plot which shows the differences between the energy bands of a material. In case of an insulator an energy band diagram shows a huge gap between the valence band and the conduction band , for a semiconductor a small gap between the conduction and valence bands and for a conductor the minimum permissible energy for existence of an electron in conduction band is less than the maximum amount of energy that a valence band electron can attain. However, as I was going through a CMOS technology text , it mentioned a case of bending of energy bands when the silicon dioxide layer , the aluminium of gate and the substrate of a CMOS comes in contact. Ii wonder what exactly this means in regard to the difference between the minima of conduction band and the maxima of valence band . Can anyone explain this query of mine ? That book also mentions the Fermi level of the bulk of substrate being larger than the fermi level at the interface of substrate and the silicon dioxide layer. I will be glad someone provides a reason for this fermi level difference.
[Physics] Bending of energy bands
semiconductor-physics
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The reason for this apparent contradiction is that you have two "separate" quantum effects.
Fermi-Dirac distribution describes the energies of single particles in a system comprising many identical particles that obey the Pauli exclusion principle. Distribution is calculated for potential-free space and is temperature dependant.
You put electrons into the material, and in the material they feel potential of atomic cores. This potential restrict possible energetic states that are available for electrons, that is it makes bands, where electrons can behave almost freely (according to Fermi-Dirac distribution), but makes energetic states between the bands forbidden.
Semiconductors can be split into two groups. Intrinsic semiconductors have a band gap that is around thermal energies, so a few electrons can be promoted from the valence to conduction band at room temperature. This corresponds to the third picture from the left in your post.
Extrinsic semiconductors have had a dopand added, and this creates new states in the band gap. These extra states can either accept electrons from the valence band or donate electrons to the conduction band. In the former case you get conduction due to holes in the valence band (p type) and in the latter you get conduction due to electrons in the conduction band (n type). This corresponds to the rightmost picture in your post, though whether the dopant states form a band is debatable, though maybe this is just terminology. Note that conduction is movement on holes or electrons in the semiconductor valence or condustion bands, and not due to transport in the dopant states.
Now to your questions:
I suppose all semiconductors have some intrinsic semiconduction, but for an extrinsic semiconductor this is usually negligable. The conductivity is dominated by the doping.
I think this is covered by the into above. An extrinsic semiconductor has either holes in the valance band and an empty conduction band, or electrons in the conduction band and a full valence band, but not both.
In a p type semiconductor I suppose you could excite electrons from lower bands into the holes in the valence band, but the energies required are far greater than thermal energy so this doesn't happen at room temperature. In n type or intrinsic semiconductors you can excite electrons from inner bands into the valence band because the valence band is full.
Extrinsic semiconductivity isn't based on electrons jumping between the valence and conduction bands.
Best Answer
Bending of the band diagram is caused by the volume charge of the depletion layer at the interface. In this region, the difference between conduction and valence band edges remains the same. However, if the electric filed of this charge and, consequently, band bending are strong enough to provide quantum confinement of electrons or holes (forming 2D electron gas), the gap between electron and holes energies can be changed due to quantization of the energy band which leads to its splitting into sub-bands.
The Fermi level should be constant for the structure in thermodynamical equilibrium. However, it can be positional-dependent if the electrical current does not equal zero but the system is still in quasi-equilibrium state. In this case positional-dependence of the Fermi level follows the spatial distribution of non-equilibrium charge carriers.
Useful trick is considering the conduction band edge as potential energy of a single electron (in sense of quasi-particle), as well as the valence band edge as potential energy of a single hole.