Sample preparation and device fabrication
Mono- and few-layer MoS2 samples were prepared by mechanical exfoliation of bulk MoS2 crystals [S1]. The samples were deposited on different substrates for the different modes of spectroscopic characterization. For the optical absorption measurements, fused-silica substrates were chosen, since they are transparent over the relevant spectral range. For the photoluminescence (PL) measurements, suspended samples were used to reduce the influence of external perturbations, such as scattering associated with phonons or impurities in the substrate and (inhomogeneous) doping. To prepare the suspended samples, the MoS2 layers were exfoliated on special substrates in which arrays of circular holes of 1.0 and 1.5 m diameter had been fabricated. This was accomplished using oxide-covered silicon in which the oxide layer was removed by CF4/O2 plasma etching. The arrays of holes were patterned on the substrate prior to etching by nanoimprint lithography [S2]. The samples for photoconductivity measurements were deposited also on oxide-covered silicon substrates to allow, as described below, for the fabrication of an appropriate electrical device.
For all sample geometries, we first found regions with suitable few-layer MoS2 films by means of inspection with an optical microscope. The thickness of the MoS2 samples was determined by optical contrast in the reflection measurements [Fig. S1(a)] which, as we describe below, provides a determination of the sample thickness with monolayer accuracy. We also cross-checked the thickness determinations using atomic-force microscopy (AFM) in contact mode operation, as illustrated in Fig. S1(b). The interlayer spacing of MoS2 is known to be 6.14 Å [S3-S5] and AFM measurements of thickness for each individual layer (0.6 – 0.8 nm) closely matched this value.
The samples for the photoconductivity measurements were prepared on a silicon substrate covered with a 300-nm oxide overlayer as simple field-effect transistors (FETs) with gold source and drain contacts. The silicon substrate was used as a back gate to vary the doping level in the sample films. The transistor characteristics of mono- and bilayer MoS2 devices are shown in Fig. S2. In both cases, the FET devices exhibited a variation of the source-drain current with gate voltage characteristic of an n-doped channel. The origin of this spontaneous doping is not presently known. For bilayer devices under equivalent bias conditions, the source- drain current was several times higher than for devices with MoS2 monolayers. This difference presumably reflects changes both in band structure and in spontaneous doping levels between mono- and bilayer devices.
Optical Spectroscopy Methods
The absorption measurements were performed with a Nikon inverted microscope at room temperature and under ambient conditions. Visible radiation from a quartz-tungsten-halogen (QTH) source was focused by a 100× objective onto the sample to a spot diameter of 1 – 2 m. The reflected light was collected by the same objective and spectrally analyzed with a grating spectrometer equipped with a liquid nitrogen cooled charge-coupled device (CCD) detector.
To obtain the optical absorption, we measured the reflectance spectra of a region of the fused-silica substrate where the sample of interest was located and that of the bare substrate. We then calculated the normalized differential reflectance, δR(ħω), as the difference of these two quantities divided by the reflectance from the bare substrate as a function of photon energy ħω.
Fig. S1(a) displays the measured normalized differential reflectance spectra δR(ħω) for MoS2 samples of layer thickness N = 1 – 6. We see that for all values of N, δR(ħω) is dominated by 3 main absorption features over the photon energy window of 1.3 – 3.0 eV. The two lower-energy features, labeled as A and B, are identified as A1 and B1 excitons, based on studies of the bulk materials. They arise from excitonic transitions between the split valence band maxima and the conduction band minimum at the K-point of the Brillouin zone [S6-S12]. No features from indirect band gap transitions are seen because of the low oscillator strength for such a phonon-assisted process in a sample of atomic-level thickness. With increasing layer thickness, both A and B show slight red-shifts. These shifts arise from the combined effects of interlayer interactions and spin-orbit coupling [S12]. A more significant red-shift of the high-energy feature around 2.7 eV is also seen. Besides these shifts, δR(ħω) is generally similar for N = 1 – 6 and exhibits a linear increase in magnitude with thickness N. The linearity of δR(ħω) with N is illustrated in the inset of Fig. S1(a) for a photon energy of ħω = 2.33 eV. As can be seen, once properly calibrated, measurement of δR(ħω) yields sample thickness with monolayer accuracy.
In the main text, we present data for absorption spectra A(ħω) of MoS2 films. For thin samples with weak light extinction supported by a transparent substrate, this information follows directly from the normalized reflectance change δR(ħω). We make use of the relation [S13], where nsub is the (weakly dispersive) refractive index of the substrate (fused silica). This thin-film approximation is particularly accurate for the mono- and bilayer samples. Light propagation effects are expected to begin to play a role for samples with layer thickness N > 4. We do not, however, expect any change in the qualitative features of the inferred optical response through the use of this simplified analysis.
The photoluminescence (PL) measurements were performed with excitation from a solid-state laser at a wavelength of 532 nm. The laser radiation was focused onto the sample with a spot diameter of ~ 1 m. To avoid sample heating, we used a low excitation power of 50 W (at the sample). To confirm the absence of laser-induced heating or other changes, we compared the PL at a power of 250 W. The spectra were identical. Typical data collection times were 1 s for monolayer samples.
In order to characterize the absolute PL quantum yield (QY) of the samples, we made use of a calibrated reference consisting of a thin film of rhodamine-6G dye molecules. The films were prepared by spin coating a fused silica substrate with a concentrated methanolic solution of rhodamine-6G. Because of the complicated dependence of QY of the film on the concentration of rhodamine-6G molecules [S14], the absolute QY of our reference film was calibrated independently. To this end, we prepared dilute (300 μM) methanolic solutions of rhodamine-6G molecules, which are known to have a QY close to 100% [S15]. Comparative measurements of the absorption and PL of the thin film and the dilute solution were performed under the same conditions. The absolute fluorescence QY for the thin rhodamine-6G film was found to be 4.1 × 10-3. With this reference, we determined the QY of our suspended MoS2 films to be 4.2 × 10-3 for the monolayer and 3.6 × 10-5 for the bilayer.
For the photoconductivity measurements, laser radiation of well-defined wavelength was selected from a supercontinuum white-light source (Fianium) by a monochromator over a spectral range of 450 nm to 1.8 μm. The resulting narrowband radiation was focused onto the sample in the same fashion as for the absorption and PL measurements. In order to detect the relatively weak photocurrents, we modulated the laser intensity at a frequency of 1 kHz with a mechanical chopper and detected the induced change in current with a lock-in amplifier. The photocurrent signal was normalized by the incident power to obtain the photocurrent spectrum. The measurements were carried out at a zero gate bias.
The photocurrent response as a function of the drain-source voltage, VDS, for photoexcitation at 2.04 eV for both mono- and bilayer devices is shown in Fig. S3. Two differences are apparent: 1) the onset of photo-response occurs at a much lower voltage in the bilayer device than in the monolayer device; 2) the photocurrent in the bilayer device saturates at relatively low voltages, while for the monolayer device does not saturate for voltages up to 10 V. The different behavior as a function of layer thickness may reflect the significant difference in the band-gap energies in the two cases and the corresponding influence on the properties of the metallic contacts. The arrows indicate the drain-source voltages used in obtaining the photoconductivity spectra for each sample (Fig. 4b in the main text).
Origin of the excited-state PL features in few-layer MoS2 samples
In the main text, we described the three principal PL features, labeled as A, B, and I, in few-layer MoS2 samples. Feature I was attributed to luminescence from the indirect band gap. Here we provide further justification for the assignment of the higher-lying features A and B to hot luminescence processes.
The close match between the positions of features A and B in the luminescence and absorption spectra provides strong grounds for their assignment as direct transitions. The interesting question is why we see significant luminescence from these states in samples where the (indirect) band gap lies significantly lower in energy. We can exclude the influence of carriers that are thermally excited from the fundamental band gap. The energy difference is at least ten times the thermal energy, so thermally excited carrier populations would be negligible [S15]. We therefore attribute the observed higher-lying PL features to the presence of hot carriers that transiently occupy states near the K-point of the Brillouin zone before fully relaxing. From time-resolved spectroscopy of bulk MoS2, researchers have determined the relaxation time for hot carriers near the K point of the Brillouin zone to be ~ 100 fs [S16]. The measured QY ~ 10-5 for these features in bilayer samples, then implies a radiative lifetime of ~10 ns. This time scale is appropriate for a direct transition in a semiconductor. Note that feature I, although arising from an indirect transition, has a much longer excited state lifetime, so that the reduced radiative rate is balanced by the much longer lifetime. In bilayer samples of good quality, the indirect transition can have a higher PL QY. In thicker samples feature I is often strongly quenched because of increased trap-state density, as demonstrated in Fig. 3.
Figure S1. (a) Spectra of relative change in reflectance, δR(ħω), for MoS2 samples of layer number N =1 – 6 deposited on fused silica substrates probed in the photon energy range of 1.3 to 3.0 eV. The linear dependence of the optical contrast with layer number N, as shown in the inset for a photon energy of 2.33 eV, provides a method of determining the layer thickness N with monolayer accuracy. (b) Confirmation of layer number assignment using AFM (left), which directly measures the sample thickness. The blue line is situated over a region with a sample of monolayer thickness, while the green line corresponds to a sample of 4-layer thickness. The corresponding AFM height traces are shown to the right.
Figure S2. Dependence of the drain-source current on gate voltage for field-effect devices made with mono- and bilayer MoS2 samples. The channel width of both devices is about 5 μm. The drain-source voltage for both measurements is VDS = 40 meV. The characteristics correspond to devices with spontaneous n doping.
Figure S3. Dependence of the photoconductive response on drain-source voltage of mono- and bilayer MoS2 samples under photoexcitation at 2.04 eV. The black arrows indicate the drain-source voltages used in obtaining the photoconductivity spectra (Fig. 4b) for each sample.
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