Terahertz Optoelectronic Properties of Monolayer MoS₂ in the Presence of CW Laser Pumping

Abstract

Monolayer (ML) molybdenum disulfide (MoS₂) is a typical valleytronic material which has important applications in, for example, polarization optics and information technology. In this study, we examine the effect of continuous wave (CW) laser pumping on the basic optoelectronic properties of ML MoS₂ placed on a sapphire substrate, where the pump photon energy is larger than the bandgap of ML MoS₂. The pump laser source is provided by a compact semiconductor laser with a 445 nm wavelength. Through the measurement of THz time-domain spectroscopy, we obtain the complex optical conductivity for ML MoS₂, which are found to be fitted exceptionally well with the Drude–Smith formula. Therefore, we expect that the reduction in conductivity in ML MoS₂ is mainly due to the effect of electronic backscattering or localization in the presence of the substrate. Meanwhile, one can optically determine the key electronic parameters of ML MoS₂, such as the electron density n_e, the intra-band electronic relaxation time τ, and the photon-induced electronic localization factor c. The dependence of these parameters upon CW laser pump intensity is examined here at room temperature. We find that 445 nm CW laser pumping results in the larger n_e, shorter τ, and stronger c in ML MoS₂ indicating that laser excitation has a significant impact on the optoelectronic properties of ML MoS₂. The origin of the effects obtained is analyzed on the basis of solid-state optics. This study provides a unique and tractable technique for investigating photo-excited carriers in ML MoS₂.

1. Introduction

Over about two last decades, the study of monolayer (ML) transition metal dichalcogenides (TMDs), such as ML molybdenum disulfide (MoS₂), has been drawing high attention [1] in the fields of electronics, optics, and optoelectronics due to intriguing and unique valleytronic properties of ML TMDs for potential applications in, for example, polarization optics and information technology [2]. One of the most intriguing aspects of ML TMD is that the electron energies degenerate around K and K’ valleys [3] but with opposite pseudospin orientations [4]. Such phenomenal valleytronic properties suggest that ML TMD can be taken as the basis for studying novel quantum effects such as valley magnetic moment [5], valley Hall effect [6], valley optical polarization [6], and others, and for potential applications in electronics and optoelectronics [7], including field effect transistors [8], photovoltaic elements [9], integrated circuits [10], and so on. In terms of solid-state optics, one of the most prominent aspects of the ML MoS₂ is the exceptional excitonic effect [11,12,13,14]. In ML MoS₂, due to strong quantum confinement and reduced dielectric screening, the Coulomb interaction is largely enhanced among the carriers, which leads to the creation of tightly bound excitons upon photo-excitation even at room temperature [15,16]. These excitons, or electron–hole pairs, can effectively influence the optical and charge-transport properties [17]. Therefore, it is of significance and importance to study the effect of photo-excited carriers on the optoelectronic properties of ML MoS₂ for designing and applying this advanced material to high-performance devices. This is the prime motivation of this study.

It is known that ML MoS₂ can offer an evident optical response over a wide spectral range [18], from ultraviolet to THz [19]. Nowadays, THz time-domain spectroscopy (TDS) has been commonly established as a powerful technique for investigating carrier dynamics in various electronic materials, including oxides, superconductors, and semiconductors [20,21,22]. Very recently, this technique has been applied to explore the optoelectronic properties of ML MoS₂ on different substrates [23]. THz TDS is a contactless experimental technique from which one can straightforwardly determine the complex optical conductivity of an electronic material without involving the Kramers–Kronig transformation. As THz photon energy (f = 1 THz = 4.13 meV) is considerably smaller than the bandgap of ML MoS₂ (of about 1.8 eV), THz irradiation does not induce inter-band electronic transition effects such as excitons and photo-induced carriers. Thus, THz TDS can be employed to examine the free carrier properties of ML MoS₂. In recent years, THz spectroscopy, in combination with time-resolved photo-luminescence, has been used to measure the ultrafast photoconduction in ML MoS₂ [24]. Optical-pump and THz-probe (OPTP) spectroscopy has also been employed to study the photo-excited optoelectronic properties of ML and few-layer TMD systems [7,16,24] where the optical pump source is achieved by ultrafast laser pulses. It should be noted that such an OPTP technique needs a big size and quite an expensive high-power fs laser source which cannot be realized in most laboratories with a THz TDS facility. However, a economic and compact semiconductor continuous wave (CW) laser can also be used as an optical pump in conjunction with THz TDS to study the photo-induced optoelectronic properties of ML MoS₂. The major advantage of using a CW laser as a pumping source is that it can produce a steady stream of photons with a fixed radiation frequency and variable radiation intensity, which may be tuned to induce and excite the electronic transitions and carriers in ML MoS₂. Moreover, the CW laser has a lower noise level compared to the fs laser pulses, which can improve the signal-to-noise ratio for THz measurements and, as a result, can make to increase the sensitivity and precision of the measurements. Recently, the combination of THz TDS and CW laser pumping was applied to study the electronic dynamic properties of ML MoS₂ on a sapphire substrate [25], where the optical conductivity and the related electronic parameters were obtained as the function of the intensity and the polarization of the CW pumping laser at room temperature. It was proposed [25] that the reduction in conductivity in ML MoS₂ with CW laser pumping is due to the generation of trions. Using the conventional Drude formula for optical conductivities induced by both electrons and trions to fit the optical conductivity obtained experimentally, in Ref. [25], the densities and the scattering rates for electrons and trions in ML MoS₂ were obtained as the function of CW laser excitation intensity. However, it was found that the scattering rate for trions in ML MoS₂ was in the order of 10 THz, corresponding to a relaxation time of 0.1 ps which is much shorter than 15~30 ps measured by OPTP at room temperature [7,24]. So, it is of particular importance and significance to re-examine the optoelectronic properties of ML MoS₂ on a sapphire substrate by using the combination of THz TDS and a CW laser. Based on the findings made here, weprovide a variational explanation of the effect of the reduction in conductivity in ML MoS₂ with CW laser excitation.

2. Sample and Experimental Measurements

In this study, ML MoS₂ films were grown on the sapphire substrate through the standard chemical vapor deposition (CVD) method [26]. The procedure for the growth and preparation of the sample was the same as reported earlier [27,28]. ML MoS₂ on a sapphire substrate fabricated by this method is typically the n-type [26,27,29]. The areal size of the sample and the thickness of the substrate are 1 cm × 1 cm and 0.35 cm, respectively. The realization of the ML MoS₂ on the substrate is verified by using the Raman spectrum [28,30] and optical microscope images [26,28].

Figure 1a represents the schematic diagram of the measurement setup used in this study. Here, THz TDS is realized by a standard technique in which (i) a Ti–sapphire-based 800 nm wavelength femtosecond (fs) laser is taken as the THz generation and detection source; (ii) a LiNbO₃ crystal is used as the THz generator via the Cherenkov effect and wavefront tilting [31]; (iii) a ZnTe crystal is applied as the THz detector via electro-optical sampling [32]; and (iv) the time-domain THz detection is achieved via a delay stage to the probe fs laser. The THz transmission measurements are undertaken in this study. Additionally, a semiconductor CW laser (Changchun New Optoelectronics Tech Co., Ltd., Jilin, China) with a wavelength of 445 nm and a maximum laser output of 200 nW was used as an optical pumping source to excite the carriers in the ML MoS₂/substrate sample. This laser was irradiated and focused on the same spot of the incident THz beam but with a titled angle of about 10° to the THz beam. In this way, the transmitted CW laser beam can be blocked so that it cannot enter the THz detector to cause damage. The diameter of the focusing spot for the pump laser on the sample was 7.0 mm with an area of 0.385 cm². The radiation intensity of the CW laser can be varied from 0 to 0.39 $\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The measurement principle is illustrated in Figure 1b. The photon energy of the 445 nm laser is about 2.79 eV, which is larger than the bandgap of ML MoS₂ (E_g ≈ 1.8 eV). Thus, a 445 nm CW laser can pump the electrons in the valence band (VB) into the conduction band (CB) and can achieve the momentum and energy excitation of the electrons and the electron–hole pairs in the material. Meanwhile, the THz TDS measures the consequence of the electronic transition around the Fermi level in the CB of ML MoS₂. As a result, the response of the electrons in the CB in ML MoS₂ to THz radiation can be modulated by CW laser pumping. By using this experimental setup, we examine the influence of the CW laser excitation on the optoelectronic properties of ML MoS₂. The measurements in this study were carried out at room temperature.

We first measure the time-dependent electric field strength of the THz beam transmitted through the sample (ML MoS₂ on sapphire substrate) $E_{\mathrm{s}\mathrm{a}\mathrm{m}+\mathrm{s}\mathrm{u}\mathrm{b}}\left(t\right)$ and through the bare substrate $E_{\mathrm{s}\mathrm{u}\mathrm{b}}\left(t\right),$ respectively. The results are shown in Figure 2, where $E_{\mathrm{s}\mathrm{a}\mathrm{m}+\mathrm{s}\mathrm{u}\mathrm{b}}\left(t\right)$ is plotted as a function of delay time t at different CW laser radiation intensities. One can see that the THz transmission through ML MoS₂ on the substrate increases with CW laser pumping intensity. This implies that the optical absorption decreases with increasing CW laser pumping intensity, in line with the effect found in Ref. [25]. It should be noted that the high-quality and high-resistance sapphire substrate exhibits high THz transparency and minimal absorption, due to its low dielectric loss (relative permittivity ${\epsilon }_r\approx 9.3-11.5$ and loss tangent $\tan \delta \approx {10}^{-4}-{10}^{-3}$) [33,34,35]. As shown in Figure 2a, there is no significant change in THz pulse transmitted through the bare sapphire substrate under different CW laser intensities, further confirming its low-loss behavior in the THz range. Thus, the decrease in THz optical absorption with increasing CW laser intensity is attributed mainly to electronic transitions in ML MoS₂. By Fourier transformation of the measured data, we obtain the corresponding electric field strengths for the sample $E_{\mathrm{s}\mathrm{a}\mathrm{m}+\mathrm{s}\mathrm{u}\mathrm{b}}\left(\omega \right)$ and the substrate $E_{\mathrm{s}\mathrm{u}\mathrm{b}}\left(\omega \right)$, respectively, in the $\omega$-frequency domain. Figure 3 shows the amplitude and the phase angle of $E_{\mathrm{s}\mathrm{a}\mathrm{m}}\left(\omega \right)$ for ML MoS₂ on the sapphire as a function of radiation frequency for different CW laser excitation intensities. It can be seen that ${|E}_{\mathrm{s}\mathrm{a}\mathrm{m}+\mathrm{s}\mathrm{u}\mathrm{b}}\left(\omega \right)|$ depends on the intensity of CW laser pumping, while the phase angles are about the same when the CW laser excitation intensity varies from 0 to 0.39 $\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. It is known that the phase angle of the transmission light beam is proportional to $-\omega n_{1s}\left(\omega \right)$, with $n_{1s}\left(\omega \right)$ the real part of the refractive index of the measured material [36]. $n_{1s}\left(\omega \right)$ is mainly determined by the static dielectric constant of the material, the phase angle increases almost linearly with -ω and depends weakly on the CW laser excitation intensity.

Moreover, as shown in Figure 3, the peak frequency of the transmitted THz amplitude exhibits quite a small, non-monotonic shift with increasing CW laser excitation. Although the imaginary part ${\sigma }_2\left(\omega \right)$ of the optical conductivity $\sigma \left(\omega \right)$ decreases monotonically with pump power (Figure 4, lower), the transmission spectrum is influenced by both the real ${\sigma }_1\left(\omega \right)$ and imaginary ${\sigma }_2\left(\omega \right)$ parts. ${\sigma }_1\left(\omega \right)$, associated with absorption, generally decreases with frequency but exhibits subtle excitation-dependent changes, particularly in the 0.4–0.8 THz range (Figure 4, upper). These variations modulate the transmitted amplitude, while ${\sigma }_2\left(\omega \right)$ primarily affects the phase. Thus, the observed peak shift arises from the interplay between absorptive and dispersive effects, rather than from ${\sigma }_2\left(\omega \right)$ alone.

The complex optical conductivity $\sigma \left(\omega \right)={\sigma }_1\left(\omega \right)+{i\sigma }_2\left(\omega \right)$ in ML MoS₂ can be found by using the Tinkham relation for an air/thin film/substrate system [37]:

$${\displaystyle \frac{E_{\mathrm{sam}+\mathrm{sub}}(\omega )}{E_{\mathrm{sub}}(\omega )}}={\displaystyle \frac{1+n}{1+n+Z_0\sigma (\omega )}},$$

(1)

where $n$ is the refractive index of the substrate, which is about 3.07 for sapphire [23], and $Z_0\approx 377$ is the impedance of the free space. Equation (1), based on the Tinkham formula, describes the transmission of a thin conducting film on a dielectric substrate under normal incidence. Equation (1) is applied when the film thickness is significantly smaller than both the wavelength of the incident radiation and the electromagnetic skin depth, allowing the film to be treated as a two-dimensional conducting sheet. Figure 4 shows the spectra of the real ${\sigma }_1\left(\omega \right)$ and imaginary ${\sigma }_2\left(\omega \right)$ parts of $\sigma \left(\omega \right)$ for ML MoS₂ at different CW laser radiation intensities. One finds that for ML MoS₂ on a sapphire substrate, ${\sigma }_1\left(\omega \right)$ decreases/increases with increasing CW laser pumping intensity in low/high THz radiation frequency regimes. The cross-over point is at about f = 0.95 THz. In contrast, ${\sigma }_2\left(\omega \right)$ always increases with the radiation frequency and decreases with increasing CW laser radiation intensities. Thus, the CW laser pumping has stronger and more interesting effects on ${\sigma }_1\left(\omega \right)$ in ML MoS₂.

It should be noted that when ML MoS₂ is subjected to a THz radiation field, the response of electrons in the sample is attained mainly from intra-band electronic transitions accompanied by the absorption of THz photons. As a result, the electron gas model for optical conductivity can be applied to understand the experimental results obtained from the THz TDS measurement [38,39,40,41]. The Drude model provides most straightforward formula for optical conductivity in an electron gas system [38]:

$$\sigma \left(\omega \right)={\displaystyle \frac{{\sigma }_0}{1-i\omega \tau }}={\displaystyle \frac{{\sigma }_0\left(1+i\omega \tau \right)}{1+{\left(\omega \tau \right)}^2}},$$

(2)

where ${\sigma }_0=e^2{n}_e\tau /m^{\ast }$ is the dc (direct current) conductivity, $n_e$ is the electron density in the sample, $\tau$ is the electronic relaxation time, and $m^{\ast }$ is the effective mass of electron. The Drude model suggests that, with increasing $\omega$, ${\sigma }_1\left(\omega \right)$ must always decrease while ${\sigma }_2\left(\omega \right)$ must first increase and then decrease. Our experimental results on $\sigma \left(\omega \right)$ shown in Figure 4 for ML MoS₂ do not obey Equation (2). It has been demonstrated that when placing ML MoS₂ on a dielectric substrate, photon-induced electronic backscattering or localization can occur [23]. That is, the conventional Drude formula (2) cannot be used here to reproduce the experimental data. In this case, the optical conductivity to obey the Drude–Smith formula [39]

$$\sigma \left(\omega \right)={\displaystyle \frac{{\sigma }_0}{1-i\omega \tau }}\left(1+{\displaystyle \frac{c}{1-i\omega \tau }}\right),$$

(3)

where the coefficient $c=[-1, 0]$ is the photon-induced electronic backscattering or localization factor, describing the fraction of the original velocity for an electron after the collision happens. Namely, when c is of a nonzero value, the electrons in the system are localized, while for $c=0,$ the Drude–Smith model (3) turns into the conventional Drude model (2). Equation (3) takes into account only the first collision for electronic backscattering.

Figure 4 shows ${\sigma }_1\left(\omega \right)$ and ${\sigma }_2\left(\omega \right)$ given by Equation (3) (curves) and one finds that satisfactory fitting is achieved between experiment and theory (fit). One however may notice that at higher frequencies in the presence of CW laser pumping, the theoretical results show some discrepancies with the experiment. This is mainly owing to the usage of quartz windows for the sample chamber which absorb the high-frequency THz wave rather strongly in the presence of CW laser excitation [42]. As a result, the signal-to-noise ratio for THz transmission at high frequency gets weaken.

Moreover, it should be noted that in the presence of CW laser pumping, the photo-generated holes can also contribute to optical conductivity detected by THz TDS. However, for n-type ML MoS₂ in the darkness, electrons are the major conducting carriers in the sample. This is also the case even in the presence of CW laser pumping, where the electron density is considerably larger than the hole density. Together with the observation that the effective hole mass (of about 0.55$m_0$ [43], with $m_0$ the rest electron mass) is heavier than that of the electron mass (of about 0.39$m_0$ [5]) in ML MoS₂, the contribution from holes to $\sigma \left(\omega \right)$ can be neglected. Moreover, in the presence of a pump laser whose photon energy is larger than the bandgap of ML MoS₂, excitons such as trions can be generated [7,25]. However, the photon-induced carrier density is in general smaller than the dark density in an n-type electron gas [44]. As a result, the trion density to be significantly smaller than the electron density in an n-type ML MoS₂ on a substrate. Along with the feature that the effective mass for trions in ML MoS₂ is about 1.54$m_0$ [25], the contribution from trions to $\sigma \left(\omega \right)$ measured by THz TDS is also quite small. Hence, the major carriers attributing to THz optical conductivity in n-type ML MoS₂ on a sapphire substrate are electrons. From the real part ${\sigma }_1\left(\omega \right)$ of low-frequency optical conductivity shown in Figure 4, one finds that the dc conductivity in ML MoS₂ decreases with increasing CW pumping intensity, similar to the effect observed in Ref. [25].

3. Results and Discussions

In this study, data analysis and fitting are performed using standard LabVIEW software. By fitting the experimental data shown in Figure 4 by Equation (3), the key sample and electronic parameters $n_e$, $\tau$, and c to be obtained. In fitting, we set the effective mass for an electron in ML MoS₂ to 0.39$m_0$ [5]. Figure 5 shows the parameters $n_e$, $\tau$, and factor c for ML MoS₂ on the sapphire substrate as a function of CW pumping intensity. The following features are noticeable.

(i)

The electron density $n_e$ increases almost linearly with CW laser pumping intensity. This is due to the feature that stronger CW laser pumping is expected to excite more electrons and electron–hole pairs from VB to CB in ML MoS₂. Therefore, the intense CW laser excitation leads to an increase in electron density in ML MoS₂. It is found that the electron density in the dark or in the absence of laser pumping is about $n_0=3.95\times {10}^{16}$ m⁻². In the presence of CW laser pumping, we have $n_e=n_0+∆n_e$, with $∆n_e$ the photo-induced electron density. The result shown in Figure 5 indicates that the 445 nm wavelength CW laser pumping effectively tunes electron density in an ML MoS₂/substrate sample. When the CW laser radiation intensity is at 0.39 $\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, about a 30% increase in electron density to be achieved.

(ii)

The electronic relaxation time $\tau$ decreases with increasing pumping intensity, suggesting a nonlinear response of electrons in ML MoS₂ to CW pump radiation. In ML MoS₂, the electronic relaxation time measured by THz TDS is determined mainly by electron interactions with scattering centers such as other electrons, impurities, phonons, etc., which are basically the intra-band electronic scattering mechanisms to achieve the momentum and energy relaxation during the scattering events. A shorter $\tau$ implies a stronger intra-band electronic scattering rate.

It should be noted that the inter-band electronic relaxation time induced by excitonic relaxation and direct non-radiative electronic transition in ML MoS₂ is typically in the sub-nanosecond (ns) temporal scale [7,24], which is significantly longer than intra-band electronic relaxation time. Moreover, $\tau$ measured by THz TDS is mainly the momentum relaxation time due to the finding that it is obtained from optical conductivity caused by free-carrier absorption. In contrast, the inter-band electronic relaxation is mainly an energy relaxation process as soon as the direct electron–photon interaction is not expected to change the electron momentum. In the presence of CW laser excitation, the electrons in CB gain energy from the radiation field via optical absorption and lose energy via inter-band transitions to VB and via intra-band interactions with scattering centers to achieve momentum and energy relaxation. When the CW laser excitation is weak, this gain-and-lose process is balanced, and the electrons are in the linear response regime where τ does not depend on the excitation intensity. With increasing excitation intensity, the electrons gain more energy from the radiation field than they lost via inter- and intra-band electronic transitions and relaxations. As a result, the electrons in the CB may be heated or are in the hot-electron regime where the effective intra-band electronic scattering rate increases with the laser excitation intensity. This coincides with the feature that more electrons are pumped into the CB in ML MoS₂ and the electrons in the CB are more strongly excited. Thus, stronger intra-band scattering is required to achieve momentum and energy conservation during the momentum and energy gain-and-loss processes. This is a typical feature of a semiconductor subjected to intense CW laser radiation [45]. As the CW laser pump intensity further increases so that the transition and relaxation of hot electrons no longer releases the energy gained from the radiation field, the sample is then heated, and the system is in the hot-phonon regime. Let us note that, in this study, the maximum laser power applied to the sample was approximately 0.150 W, corresponding to an electric field strength of about 1.71 KV/m. This level of laser excitation may result in the hot-electron effect in ML MoS₂ but is not sufficient to result in the hot-phonon effect heating the sample. We find that $\tau$ measured here by THz TDS differs from that measured by OPTP [7,24] for ML MoS₂. The latter case relates to inter-band electronic transition and excitonic relaxation. The relaxation or decay time measured from the excitation–decay curve in OPTP is typically in the sub-ns time scale [7,24].

(iii)

The photon-induced electronic backscattering or localization effect increases with the CW laser excitation intensity, noting that the c-factor is always negative. This is a straight consequence of the increase in electronic scattering rate with the CW laser radiation intensity.

(iv)

In the presence of photon-induced electronic backscattering or localization, the effective dc conductivity is ${\sigma }^{\ast }\left(0\right)={\sigma }_0\left(1+c\right)$. As soon as both c and $\tau$ decrease with increasing CW laser pumping intensity, which effectively offsets the increase in the electron density, ${\sigma }^{\ast }\left(0\right)$ decreases with increasing CW laser pumping intensity. Hence, the reduction in the conductivity of ML MoS₂ is mainly induced by photon-induced electronic localization.

(v)

Earlier, it has been demonstrated that in the absence of CW laser excitation, the photon-induced electronic backscattering or localization in ML MoS₂ can be induced by the presence of the substrate [23]. Here, we find that such an effect can be enhanced by the presence of CW laser pumping. These findings indicate that the usage of CW laser pumping has a crucial impact on the optoelectronic properties of ML MoS₂ on a dielectric substrate such as sapphire.

In this study, we considered two types of independent experimental data—the real and imaginary parts of $\sigma \left(\omega \right)$—to obtain three fitting material parameters $n,\tau$, and c by using Equation (3). Based on the principle of multi-parameter fitting, the fitting results are considered credible if the optimal combination of the fitting parameters is successfully achieved [46]. From Figure 4 and Figure 5, one finds that the fitting of the experimental data is accurate enough, and the dependence of the fitting parameters on the CW laser excitation intensity appears to be physically reasonable. Therefore, the results presented in Figure 5 are not a result of over-fitting. Parameters $n,\tau$, or c, each has been chosen for its physical relevance to describing disordered systems and the impact of those parameters on the material’s electronic and optical properties.

4. Conclusions

For this study, we fabricated ML MoS₂ on a sapphire substrate using standard chemical vapor deposition (CVD). We have applied a combination of THz TDS and CW laser excitation to observe the THz optoelectronic properties of ML MoS₂. It is discovered that the experimentally obtained real and imaginary parts of the optical conductivity for ML MoS₂ fit the Drude–Smith model exceptionally well. By fitting our experimental results by the Drude–Smith formula, the key electronic parameters for ML MoS₂, such as the electron density, the electronic localization factor, and the electronic relaxation time have been optically determined. The dependence of these parameters upon the CW laser excitation intensity are examined. It is found that the basic electronic properties of ML MoS₂ on a sapphire substrate depend sensitively on the radiation intensity of a 445 nm CW laser. Meantime, one actually cannot straightforwardly measure the electron localization effect using conventional transport experiments. However, nowadays, the THz TDS technique with an optical pump is established as an advanced optical technique to investigate the photon-induced electronic localization effect in electronic gas systems. In addition, in our studies, we used an economic and compact semiconductor laser as the CW laser excitation source which allow to reduce the cost of the measurement. We believe that the outcomes of this study benefits in gaining an in-depth understanding of the electronic and optoelectronic properties of atomically thin electronic materials such as ML TMD-based two-dimensional electronic systems.