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I do not understand why the band gap shrinks due to the giant Stark effect.

In semiconductors such as black phosphorus, it has been confirmed that the band gap shrinks due to a dc electric field. This phenomenon is called as the Giant Stark effect.

But how does it occur? I understand that the wave functions of electrons are modified by the electric field, but I do not understand how this is related to the band gap.

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  1. Stark Effect vs. Giant Stark Effect: Stark Effect: This is the shifting and splitting of electronic energy levels (and consequently, spectral lines) due to an external electric field. It's analogous to the Zeeman effect where energy levels and spectral lines shift due to an external magnetic field.

Giant Stark Effect: This is an exaggerated version of the Stark effect observed in certain materials where the band gap can be significantly altered by the application of an external electric field. The term "giant" indicates the large magnitude of the effect compared to typical Stark effects in other materials.

  1. Mechanism: Perturbation: As mentioned earlier, the external electric field acts as a perturbation to the electronic system of the material. This perturbation can cause significant shifts in the energy levels of the electrons.

Wavefunction Overlap: The electric field can cause the wavefunctions of the electrons in the valence band and conduction band to overlap more or less, depending on the direction of the field and the nature of the material. This change in overlap can lead to a change in the band gap.

  1. Factors Influencing the Giant Stark Effect: Material Structure: The crystal structure and electronic properties of the material play a crucial role. For instance, layered materials or materials with a specific anisotropy in their band structure might show a pronounced Giant Stark effect.

Field Direction: The direction of the applied electric field with respect to the crystallographic axes of the material can influence the magnitude and direction (increase or decrease) of the band gap change.

Initial Band Gap: Materials with smaller initial band gaps might show a more pronounced Giant Stark effect compared to those with larger band gaps.

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