# Quantum confinement of transition metal dichalcogenides (TMDs)

TMDs (transition metal dichalcogenides) are materials that can have a layered structure. When moving from bulk to monolayers, the bandgap changes from indirect to direct according to the image (DFT to MoSe$$_2$$). From what I understand, this may be due to the effect of quantum confinement, but I didn't understand what this phenomenon consists of for the specific case of TMDs. What is quantum confinement for TMDs?

(Kumar, A. e Ahluwalia, P., Electronic structure of transition metal dichalcogenides monolayers 1H-­MX$$_2$$ (M = Mo, W; X = S, Se, Te) from ab-­initio theory: New direct band gap semiconductors. European Physical Journal B, 85:1–7, 2012.)

• Quantum confinement is a kind of physical effect, which describes the change of electronic and optical properties when the material sampled is of sufficiently small size----typically 10 nanometers or less.

• For layered TMDC materials, when the materials are downsized to the 2D limit, the dielectric screening environment will be reduced significantly, and hence the interaction between electron and hole will be greatly increased (forming exciton with large binding energy), as illustrated by the following figure.

• In addition, the bandgap of semiconducting materials will be promoted due to quantum confinement and also increase the exciton binding energy, as shown below.

In summary, quantum confinement in 2D TMDC materials will lead to a strong excitonic effect.

• Thanks for the answer. I also read this article, but I missed some things related to dielectric confinement. When the material becomes 2D, outside the monolayer there is vacuum or air, with a different dielectric constant. But what impact does this have on material properties afterwards? And why in this case does the exciton energy increase? In the graphs, an optical absorption appears in bulk that increases after the exciton energy (and the function is continuous), while in the monolayer, after the exciton energy, there is a jump in the function and then a plateau. Why is this happening? Jul 6 at 10:48
• @CarmenGonzález 1. Basically, you can think there is no charge in a vacuum for 2D materials but there is a charge in the 3D bulk materials, that's why the properties are affected. 2. Have you remember the enery level formula of infinite square potential well? Change the width of the potential well, then you will get some physical intuition about quantum confinement.
– Jack
Jul 9 at 9:03
• When the length of the square potential well decreases, the energy increases and is quantized because it depends on $n$: $E_n=\frac{n^2\pi^2\hbar^2}{2mL^2}$. Is that what you meant by quantum confinement in TMDs? Thanks for the answer. Jul 10 at 1:10
• @CarmenGonzález Yes, you can get some insights.
– Jack
Jul 10 at 14:01