Energy bands diagram in semiconductors

In summary, the conversation discusses the use of plotting energy versus k, the wave vector, in the energy band diagram for semiconductors. K is the wave vector and is a reciprocal of the space wavelength of the wave. However, this definition does not fully explain the purpose of plotting energy versus k. It is mentioned that in free space, momentum is a good quantum number, but in a lattice, momentum is periodic instead. This is where \hbar k, the momentum modulo crystal momentum, becomes significant.
  • #1
mendes
40
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We usually plot the energy versus k, the wave vector, in the so-called "energy band diagram" for semiconductors. I am trying to understand the significance of "k" in this case. k is the wave vector, which means come kind of reciprocal of the space wavelength of the wave. But this definition does not make me understand the utility of plotting the energy versus k ! Does k mean something else also ?
 
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  • #2
\hbar k is the momentum, modulo crystal momentum.

In free space, symmetry under translations mean that momentum is a good quantum number (i.e. it makes sense to label energy eigenstates with it). In a lattice, you can only translate by lattice vectors; mathematically, you have something like momentum, but is periodic instead.
 

FAQ: Energy bands diagram in semiconductors

What is an energy band diagram in semiconductors?

An energy band diagram in semiconductors is a graphical representation of the energy levels of electrons in a semiconductor material. It shows the energy bands, or allowed energy levels, for both the valence band (occupied by electrons) and the conduction band (unoccupied by electrons). The energy band diagram helps to explain the electrical properties of semiconductors.

How does the energy band diagram differ between conductors, insulators, and semiconductors?

The energy band diagram for conductors has overlapping valence and conduction bands, allowing electrons to easily move between the two. Insulators have a large band gap, with a completely filled valence band and an empty conduction band. Semiconductors have a smaller band gap compared to insulators, allowing some electrons to jump from the valence band to the conduction band when energy is supplied, making them partially conductive.

What is the band gap in a semiconductor energy band diagram?

The band gap in a semiconductor energy band diagram is the energy difference between the valence band and the conduction band. This gap represents the minimum amount of energy required to excite an electron from the valence band to the conduction band, making the material conductive. The size of the band gap determines the electrical properties of a semiconductor.

How does doping affect the energy band diagram in semiconductors?

Doping, the intentional addition of impurities, can change the energy band diagram in semiconductors. N-type doping adds extra electrons to the conduction band, while P-type doping creates extra holes (empty spaces) in the valence band. This results in a shift in the energy levels and can decrease the band gap, making the material more conductive.

What is the difference between an intrinsic and extrinsic semiconductor in an energy band diagram?

An intrinsic semiconductor is a pure material with no intentional doping, while an extrinsic semiconductor has been intentionally doped. In an energy band diagram, an intrinsic semiconductor will have a small band gap and a symmetric distribution of electrons and holes. An extrinsic semiconductor will have a lower or higher band gap depending on the type of doping and a non-symmetric distribution of electrons and holes.

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