390
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.10 a Scheme for interband absorption in the graphene band structure around one of the Dirac points. b Transmission spectrum of graphene, measured using standard spectroscopy for a uniform membrane that completely covered a
30 µm aperture (blue circles) and measured using an optical microscope (red squares). The inset shows a 50 µm aperture
partly covered with monolayer (ML) and bilayer (BL) graphene as labeled (white dashed lines highlight the borders).
Adapted from [1266]
13.1.4 Optical Properties
The transmission of graphene has been investigated in [1266] over apertures and in [1267] on SiO 2
substrate. The band-band absorption process is schematically shown in Fig. 13.10a. A theoretical
analysis of this process yields an absorbance of π α ≈ 0.023, α = e
2
/( c) being the fine structure
constant [1266, 1268]. Effects due to next-to-nearest neighbors are not present theoretically [1269].
This universal number is found in the experimental spectrum in the visible spectral range as shown in
Fig. 13.10b. In order to exhibit this value, half the photon energy may not be too large because the band
structure will deviate from the linear dependence due to the triangular warping and nonlinearities (cf.
Appendix G.3.2 and remember t ≈ 2.8 eV). In the infrared regime, deviations are due to state blocking
due to finite temperature and non-zero Fermi level relative to the Dirac point and due to intraband
transitions [1267]. For FLG, the transmission decreases stepwise; the step sequence deviates from πα
due to inter-layer effects [1270].
13.2 Two-Dimensional Compound Semiconductors
Two-dimensional crystals have been reported also for compound semiconductor materials such as BN,
MoS 2 , NbSe 2 , Bi 2 Sr 2 CaCu 2 O x [1238] or ZnO [1271] and in particular transition metal dichalcogenides
(TMDC) of the type MX 2 , where M represents a transition metal atom and X a chalcogen atom forming
the (W,Mo)(S,Se,Te) 2 system [1272, 1273]. But many other materials also form atomically thin sheets
[1225, 1255, 1274]. The main difference to graphene is that they form a band gap. A few physical
properties are listed in Table 13.1.
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.10 a Scheme for interband absorption in the graphene band structure around one of the Dirac points. b Transmission spectrum of graphene, measured using standard spectroscopy for a uniform membrane that completely covered a
30 µm aperture (blue circles) and measured using an optical microscope (red squares). The inset shows a 50 µm aperture
partly covered with monolayer (ML) and bilayer (BL) graphene as labeled (white dashed lines highlight the borders).
Adapted from [1266]
13.1.4 Optical Properties
The transmission of graphene has been investigated in [1266] over apertures and in [1267] on SiO 2
substrate. The band-band absorption process is schematically shown in Fig. 13.10a. A theoretical
analysis of this process yields an absorbance of π α ≈ 0.023, α = e
2
/( c) being the fine structure
constant [1266, 1268]. Effects due to next-to-nearest neighbors are not present theoretically [1269].
This universal number is found in the experimental spectrum in the visible spectral range as shown in
Fig. 13.10b. In order to exhibit this value, half the photon energy may not be too large because the band
structure will deviate from the linear dependence due to the triangular warping and nonlinearities (cf.
Appendix G.3.2 and remember t ≈ 2.8 eV). In the infrared regime, deviations are due to state blocking
due to finite temperature and non-zero Fermi level relative to the Dirac point and due to intraband
transitions [1267]. For FLG, the transmission decreases stepwise; the step sequence deviates from πα
due to inter-layer effects [1270].
13.2 Two-Dimensional Compound Semiconductors
Two-dimensional crystals have been reported also for compound semiconductor materials such as BN,
MoS 2 , NbSe 2 , Bi 2 Sr 2 CaCu 2 O x [1238] or ZnO [1271] and in particular transition metal dichalcogenides
(TMDC) of the type MX 2 , where M represents a transition metal atom and X a chalcogen atom forming
the (W,Mo)(S,Se,Te) 2 system [1272, 1273]. But many other materials also form atomically thin sheets
[1225, 1255, 1274]. The main difference to graphene is that they form a band gap. A few physical
properties are listed in Table 13.1.