Hello Researchers
I know this is very basic what i am asking but can anyone explain why the band gap of monolayers and bilayers vary by applying compressive and tensile strain and also why their is energy shift even at small band gap?
Will be highly appreciated.
thank you
Hello Haris,
You can kind of think about this in terms of perturbations. Imagine for instance MoS2, which has a honeycomb-like arrangement and is a 2D semiconductor. When you apply uni-axial strain, you are changing the periodic arrangement along the strain axis, which will affect the reciprocal space and the electronic structure of the material by extension. For a bi-axial strain, where you apply a uniform strain along both axes, one other factor that you could take into account is the change in the length of the atomic bonds, which could make changes in the electronic structure as well. If you think about it in terms of temperature, generally speaking, the bandgap should decrease with temperature (there are exceptions! black phosphorous is one of them, check Article From Anomalous to Normal: Temperature Dependence of the Band...
), however, the bond length is not the only culprit, and other effects such as the electron-phonon interaction become very important, particularly for MoS2 and the other transition metal dichalcogenides. I sincerely hope I have not confused you more.
Dear Rafael,
In both 2D and bulk material, the strain cause changes in interatomic distances, and therefore a change in the band structure. More details can be found in my downloadable Chapter (here in ResearchGate):
Chapter Energy Band Theory - Update
Bi-axial strain is an anisotropic strain acting in a plane e.g. (x,y) along two orthogonal directions of space e.g. xOx and yOy.
Bi-axial strain is composed by two components :
1. Hydrostatic component i.e. purely isotropic component of bi-axial strain, and
2. Shear strain or purely anisotropic component of bi-axial strain
Both these strain components induce a shift of the energies of conduction and valence band states
1. the hydrostatic component induces a global shift of conduction band statees with respect to valence band states. This ends up with an increase or a decrease of the energy bandgap Eg depending on the sign of the strain : the increase for a compressive strain (decrease of interatomic spacing) and a decrease for a tensile strain ( increase of interatomic spacing).
2. The shear strain is anisotropic in nature and acts on anisotropic states of the valence band depending on their symmetries i.e. differently on light hole states with respect to heavy hole states:
- A compressive shear strain induces a slight downwards shift of heavy holes and a strong downwards shift of light holes : ending up with a slight increase of the bandgap. d
- A tensile shear strain induces a slight upwards shift of heavy holes and a strong upwards shift of light holes : ending up with a decrease of the bandgap.
In summary :
-Compressive bi-axial strain induces an increase of the energy bandgap due to the hydrostatic component and due to the shear strain component limited by heavy hole downwards shift,
- Compressive bi-axial strain induces a decrease of the energy bandgap due to the hydrostatic component and due to the shear strain component limited by light hole upwards shift,,
The effects of bi-axial strain are stronger in the case of small bandgap material because of two factors:
1. Small bandgap means small effective masses and consequently stronger strain effects. The effect of strain is approximately inversly proportional to the effective mass.
- The smaller the bandgap, the smaller is the effective mass and the stronger is the strain induced shift.
- The wider the bandgap, the larger is the effective mass and the smaller is the strain induced shift.
2. On the other hand, small bandgap means stronger relative variation e.g. 100meV variation due to strain is negligibly small in the case of a wide bandgap e.g BeO with Eg=10eV, but the same 100meV value is very strong for a small bandgap material as InSb where Eg=180 meV.
This does not depend on VASP.
It is basic/advanced solid state physics
Best regards,
Professor A. Kadri
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