392
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.12 a STEM-ADF image of a MoS 2 monolayer; a unit cell with Mo (S) atom shown in blue (orange) is overlaid
(cf. Fig. 13.1a). Reprinted (with adaptation) with permission from [1275]. ©2013 American Chemical Society. b STEM
image (Fourier filtered) of a Mo 0.47 W 0.53 S 2 monolayer. The bright (dark) spots relate to W (Mo) atoms. Reprinted (with
adaptation) with permission from [1279], ©2013 ACS
Fig. 13.13 Various point defects (vacancies and antisites) in MoS 2 monolayer as revealed by TEM (a)–(e) together with
atomic models (f)–(h). a S vacancy (V S ), b S divacancy (V S2 ), c Mo on S site (Mo S ), d 2Mo on 2S sites (Mo2 S2 ), e S
on Mo site (S Mo ). Adapted from [1280], reprinted under Creative Commons Attribute (CC BY 4.0) license
values [1286, 1287]. The dispersion of 2D MoS 2 [1288] (Fig. 13.15) is quite similar to that of bulk
material [1287, 1289]. Of course, due to the mass difference between Mo and S, a clear gap exists
between acoustic and optical phonons (which is absent for graphene, cmp. Fig. 13.3a).
13.2.2 Band Structures
The band structure of a h-BN monolayer has been calculated to be indirect [1290]. In Fig. 13.16, the
band structure for a typical TMDC is depicted for a monolayer, a bilayer and bulk material. The latter
features an indirect band structure with the valence band maximum at the -point and the conduction
band minimum about half the way to the K-point. Similar band structures are found for multi-layers
down to 2. However, for a single layer the band gap is direct at the K-points. The possible optical
transitions are indicated in Fig. 13.16 as arrows. For the single layer, the direct transition has a lower
energy than the indirect one; in a bilayer it is vice versa. Generally, the band gap increases with
decreasing number of layers; this can be understood by thinking about the slab being a quantum well
surrounded by a vacuum ’barrier’.
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.12 a STEM-ADF image of a MoS 2 monolayer; a unit cell with Mo (S) atom shown in blue (orange) is overlaid
(cf. Fig. 13.1a). Reprinted (with adaptation) with permission from [1275]. ©2013 American Chemical Society. b STEM
image (Fourier filtered) of a Mo 0.47 W 0.53 S 2 monolayer. The bright (dark) spots relate to W (Mo) atoms. Reprinted (with
adaptation) with permission from [1279], ©2013 ACS
Fig. 13.13 Various point defects (vacancies and antisites) in MoS 2 monolayer as revealed by TEM (a)–(e) together with
atomic models (f)–(h). a S vacancy (V S ), b S divacancy (V S2 ), c Mo on S site (Mo S ), d 2Mo on 2S sites (Mo2 S2 ), e S
on Mo site (S Mo ). Adapted from [1280], reprinted under Creative Commons Attribute (CC BY 4.0) license
values [1286, 1287]. The dispersion of 2D MoS 2 [1288] (Fig. 13.15) is quite similar to that of bulk
material [1287, 1289]. Of course, due to the mass difference between Mo and S, a clear gap exists
between acoustic and optical phonons (which is absent for graphene, cmp. Fig. 13.3a).
13.2.2 Band Structures
The band structure of a h-BN monolayer has been calculated to be indirect [1290]. In Fig. 13.16, the
band structure for a typical TMDC is depicted for a monolayer, a bilayer and bulk material. The latter
features an indirect band structure with the valence band maximum at the -point and the conduction
band minimum about half the way to the K-point. Similar band structures are found for multi-layers
down to 2. However, for a single layer the band gap is direct at the K-points. The possible optical
transitions are indicated in Fig. 13.16 as arrows. For the single layer, the direct transition has a lower
energy than the indirect one; in a bilayer it is vice versa. Generally, the band gap increases with
decreasing number of layers; this can be understood by thinking about the slab being a quantum well
surrounded by a vacuum ’barrier’.