396
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.21 a Photoluminescence spectra (at room temperature) of MoS 2 , WS 2 , MoSe 2 , WSe 2 , and MoTe 2 monolayers
as labeled. From [1300], with permission. b Transition energies of A and B excitons in W x Mo 1−x S 2 alloy monolayers as
a function of composition (spectra were excited at 514.5 nm for x =0-0.61 and at 457.9 nm for x =0.66-1). The dashed
lines are fits with bowing parameters b A = 0.25(4) eV and b B = 0.19(6) eV. Based on data from [1279]
(a)
(b)
Fig. 13.22 a Schematic band structure of MoS 2 monolayer around the K- and K’-point with spin-splitting (band order
according to [1294]). Circularly polarized absorption and recombination processes are shown. b Circularly polarized
detected photoluminescence (T = 83 K) from MoS 2 monolayer (red: σ + , blue: σ − ) after excitation with σ + -polarized
light at 1.96 eV (at the right end of the energy scale). The degree of circular polarization, (σ + − σ − )/(σ + + σ − ) is
depicted as black curve with the left-hand scale. Adapted from data in [1302]
transitions are expected with a high degree of circular polarization [1301], leading to large dichroism
effects (without magnetic ions). However, a maximum degree of circular polarization of about 50%
was found in [1302] for MoS 2 excited with circularly polarized light (Fig. 13.22b). The inter-valley
dynamics reducing the polarization effects depends on the time scales of scattering and recombination
which both can be in the range of several ps [1303]. The two oppositely polarized peaks in Fig. 13.22b
have the same peak energy as expected from time-reversal symmetry; a magnetic field perpendicular
to the layer will lift this degeneracy and introduce a K-K’ splitting (valley Zeeman effect) [1304, 1305]
(Fig. 13.21).
13.2.4 Excitons
The properties of excitons are particular in 2D materials. The purely two-dimensional hydrogen problem [1306, 1307] leads to a series of bound states E = −R/(n − 1/2)
2 , where R denotes the Rydberg
energy and n = 1, 2, . . . as usual. However, for the excitons in 2D material, the case of a stepwise
changing dielectric constant , leading to image charge effects, as known from quantum well het-
13 Two-Dimensional Semiconductors
(a)
(b)
Fig. 13.21 a Photoluminescence spectra (at room temperature) of MoS 2 , WS 2 , MoSe 2 , WSe 2 , and MoTe 2 monolayers
as labeled. From [1300], with permission. b Transition energies of A and B excitons in W x Mo 1−x S 2 alloy monolayers as
a function of composition (spectra were excited at 514.5 nm for x =0-0.61 and at 457.9 nm for x =0.66-1). The dashed
lines are fits with bowing parameters b A = 0.25(4) eV and b B = 0.19(6) eV. Based on data from [1279]
(a)
(b)
Fig. 13.22 a Schematic band structure of MoS 2 monolayer around the K- and K’-point with spin-splitting (band order
according to [1294]). Circularly polarized absorption and recombination processes are shown. b Circularly polarized
detected photoluminescence (T = 83 K) from MoS 2 monolayer (red: σ + , blue: σ − ) after excitation with σ + -polarized
light at 1.96 eV (at the right end of the energy scale). The degree of circular polarization, (σ + − σ − )/(σ + + σ − ) is
depicted as black curve with the left-hand scale. Adapted from data in [1302]
transitions are expected with a high degree of circular polarization [1301], leading to large dichroism
effects (without magnetic ions). However, a maximum degree of circular polarization of about 50%
was found in [1302] for MoS 2 excited with circularly polarized light (Fig. 13.22b). The inter-valley
dynamics reducing the polarization effects depends on the time scales of scattering and recombination
which both can be in the range of several ps [1303]. The two oppositely polarized peaks in Fig. 13.22b
have the same peak energy as expected from time-reversal symmetry; a magnetic field perpendicular
to the layer will lift this degeneracy and introduce a K-K’ splitting (valley Zeeman effect) [1304, 1305]
(Fig. 13.21).
13.2.4 Excitons
The properties of excitons are particular in 2D materials. The purely two-dimensional hydrogen problem [1306, 1307] leads to a series of bound states E = −R/(n − 1/2)
2 , where R denotes the Rydberg
energy and n = 1, 2, . . . as usual. However, for the excitons in 2D material, the case of a stepwise
changing dielectric constant , leading to image charge effects, as known from quantum well het-