The energy bands bend when there is an electric field as exists for example across a p-n junction or across the space-charge layer in an MOSFET or in a Schottky barrier (metal-semicoductor contact). The one-dimensional energy band diagram is a plot of the electron energy versus the x-axis, which is generally the direction of the applied electric field or the current flow. If there is an electric field across a region of the semiconductor, then the electric potential V, hence the potential energy of the electron (-qV) changes with x, resulting in the band-bending. Generally, the energy band diagram shows how the valence band maximum (only potential energy, no kinetic energy) and the bottom of the conduction band (only potential energy, no kinetic energy) change or bend with x.
Described in detail in Chapter 29 of the book Solid State Physics, by Ashcroft and Mermin.
I take the opportunity and recommend you to survey this book in its entirety. It is by no means a complete or an up-to-date book on Solid State physics, however is one of the most important books of its kind which cannot be ignored. Other similarly important books on the subject matter are by Kittel, and by Ziman.
Band bending in fact is the change in potential profile at interface due to charge transfer. Charge transfer starts by diffusion when semiconductors of different charge (electrons or holes) concentration come in contact. You can have look on any basic book on Solid State Physics.
When two different materials having different Fermi levels are contacted with each others, charge carriers will move making Fermi level same at the contact which in turns give band bending.
The energy bands bend when there is an electric field as exists for example across a p-n junction or across the space-charge layer in an MOSFET or in a Schottky barrier (metal-semicoductor contact). The one-dimensional energy band diagram is a plot of the electron energy versus the x-axis, which is generally the direction of the applied electric field or the current flow. If there is an electric field across a region of the semiconductor, then the electric potential V, hence the potential energy of the electron (-qV) changes with x, resulting in the band-bending. Generally, the energy band diagram shows how the valence band maximum (only potential energy, no kinetic energy) and the bottom of the conduction band (only potential energy, no kinetic energy) change or bend with x.
In Nature, all the systems wants to minimize "their" energy. When one do a physical junction between two materials, the charges (electrons or holes) can flow from one material to another. If we are talking about two materials with distinct fermi levels, the electrons on the higher Fermi level material will "see" empty states, with lower energy, in the other material (with lower fermi level). This electrons will flow until the same Fermi level is reached in both sides. That's why the band bending occurs and that's how a pn junction or heterojunctions, in general, are made. The second interesting aspect, is the electrical field that is formed in such a junction. The described electron diffusion flow will left positive ions, on "the higher Fermi level material's side", and negative ions on the other. And voila, we have a charged region producing an electric field. The so called depletion region is that region near to the junction where the strength of the electric field is present. Going out of the junction region the electric field drops to zero.
In heterojunction semiconductors, the Fermi energy levels are different for different materials. But whenever we combine these materials using various experimental techniques, the transfer of electrons from conduction band to Fermi energy levels takes place and they set to form a common Fermi energy level for the heterojunction semiconductor. Hence, the band bending takes place in semiconductors.
Rearrangement of the energy states on either side (VB/CB) near the fermi level due to the applied potential or when one semiconductor is in contact with other with different fermi level position w.r.t the vacuum level.
when two different height persons (tall ,short one )contacted each other,,when ever there is need of communication between them ,,one should bend towards other to have better line of sight (LS) eye contacts........for betterment of LS we use gate potential(voltage) (high heals) to overcome different heights(surface potentials)
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