Hi, Dr. Mohsen, as for some TMDs, I know when the layer decreases the bandgap of those 2D TMDs increases. This is caused by the quantum mechanical confinement effect, which is a very obvious phenomenon in the pretty thin materials, such as in the order of few interatomic distances.
Not only the bangap value will be influenced by the thickness, but also the types will be changed, such as indirect to direct. This is due to the orbital coupling effect.Take MoS2 as an example, its bandgap highly depend on the localized d orbital of transition metal, which is hardly affected by the interlayer coupling due to its inter position in the until cell of MoS2. The indirect bandgap is dependent on the localized d orbital of Mo and pz orbital of S and is influenced by their inter layer coupling. Therefore, as layer decreases, the direct bandgap property of the MoS2 will become more pronounced. As for other 2D materials, such as graphene and phosphorus hosphorous, I am not very sure, but the mechanism may be referred to.
Xixia Liu
thank you. i need a complete presentation for change of band gap. for example why the behavior of graphene and phosphorene is very different?
In single-layer graphene the single-particle energy dispersions near the touching points of the valence and conduction bands are linear, giving rise to Dirac cones [1]. In bilayers, this linear behaviour turns into quadratic (thus, in the former case one has massless Dirac fermions, and in the latter case massive fermions). Therefore, beginning with a bilayer and theoretically (or in some thought experiment) indefinitely increasing the interlayer distance, the electronic energy dispersions near the touching points will transform from quadratic into linear. For details, consult [2] (see in particular the contribution by Koshino and Ando in Chapter 6 herein). One can also have twisted bilayers and Moiré [3] bands, for which I refer you to [4].
[1] https://en.wikipedia.org/wiki/Dirac_cone
[2] H Aoki, and MS Dresselhaus, editors, Physics of Graphene (Springer, Heidelberg, 2014).
[3] https://en.wikipedia.org/wiki/Moir%C3%A9_pattern
[4] R Bistritzer, and AH MacDonald, PNAS 108, 12233 (2011).
Article Moire bands in twisted double-layer graphene
Mohsen Mehrabi : You are welcome. As for phosphorene, please make a literature search (there are plenty of publications on the subject). Briefly, unlike graphene it is a semiconductor in the form of a single layer, and remains one in the bulk, although the bandgap is smaller in the bulk. Contrast this with single- and double-layer graphene (discussed above), and graphite -- which is a semi-metal.
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