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Abstract
Tin diselenide (SnSe2), a layered transition metal dichalcogenide (TMDC), stands out among other TMDCs for its extraordinary photoactive ability and low thermal conductivity. Consequently, it has stimulated many influential researches on photodetectors, ultrafast pulse shaping, thermoelectric devices, etc. However, the carrier mobility in SnSe2, as determined experimentally, remains limited to tens of cm2V-1s-1. This limitation poses a challenge for achieving high-performance SnSe2-based devices. Theoretical calculations, on the other hand, predict that the carrier mobility in SnSe2 can reach hundreds of cm2V-1s-1, approximately one order of magnitude higher than experimental value. Interestingly, the carrier mobility could be underestimated significantly in long-range transportation measurements due to the presence of defects and boundary scattering effects. To address this discrepancy, we employ optic pump terahertz probe spectroscopy to access the photoinduced dynamical THz photoconductivity of SnSe2. Our findings reveal that the intrinsic carrier mobility in conventional SnSe2 single crystal is remarkably high, reaching 353.2 ± 37.7 cm2V-1s-1, consistent with the theoretical prediction. Additionally, dynamical THz photoconductivity measurements reveal that the SnSe2 crystal containing rich defects efficiently capture photoinduced conduction-band electrons and valence-band holes with time constants of ∼20 and ∼200 ps, respectively. Meanwhile, we observe an impulsively stimulated Raman scattering at 0.60 THz. Our study not only demonstrates ultrafast THz spectroscopy as a reliable method for determining intrinsic carrier mobility and detection of low frequency coherent Raman mode in materials but also provides valuable reference for the future application of high-performance SnSe2-based devices.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Layered transition metal dichalcogenides (TMDCs) show unique properties such as excellent carrier transport properties [1,2], tunable band gap [3–5], ultralow out-of-plane thermal conductivity [6–10], which have fueled significant interest in their applications across various fields, including optoelectronics, photonics, and thermoelectric devices. Among the TMDCs, tin diselenide (SnSe2) stands out as an earth-abundant and environmentally friendly material, it exhibits extraordinary photoactive properties and possesses low thermal conductivity. It has become a promising candidate for ambient stable and high performance in visible, infrared, and even Terahertz (THz) range photodetectors with both huge photocurrent and fast response time [11], low bias [12], ability for THz real-time imaging [13], and stability to work at low temperature [14] (10 K). Additionally, SnSe2’s low lattice thermal conductivity allows for thermoelectric application [15–20].
High charge carrier mobility plays a pivotal role in achieving high-performance optoelectronic application and thermoelectric device. At room temperature, the intrinsic charge carrier mobility of SnSe2 has been theoretically predicted to exceed 400 cm2V−1s−1 using Density Functional Theory (DFT) [21,22]. However, experimental Hall measurements [18–20,23–26] consistently yield values in the range of approximately 30∼50 cm2V-1s-1 only. Interestingly, some other well studied tin-based chalcogenides, such as SnSe and SnS2, exhibit much higher experimental charge carrier transport ability [27–30]. It is important to note that traditional Hall characterization relies on long-range carrier transportation measurements, necessitating electrical contacts and being susceptible to the effects of defect scattering, grain boundary scattering, and other inhomogeneities [31]. Furthermore, bulk SnSe2 crystals usually exhibit a high concentration of intrinsic interstitial Sn and Se vacancies [16,32]. Considering first the possibility of grain boundaries in imperfect single crystals and additionally the gas-sensing [33–35] and humidity-sensing [36] ability of SnSe2, it is plausible that carrier mobility measured using long-range transport techniques may underestimate the intrinsic carrier mobility of SnSe2.
The technique of optic pump terahertz probe (OPTP) spectroscopy allows us to monitor the dynamical THz photoconductivity (PC) in semiconductors. Fruitful OPTP studies have delved into the non-equilibrium dynamics of layered materials [37,38], formation of quasi-particles [39] as well as the detection of charge carriers’ mobility [40,41]. Current THz studies in SnSe2 mainly focus on the ultrafast THz photoswitch [42] leveraging its giant photoconductivity as well as the development of an electrically controlled THz emitter based on its ultrafast photo-currents [43]. However, investigations into the carriers’ dynamics and characterization of carrier mobility in SnSe2 using THz transient have been relatively scarce.
Hereby, we employ a homemade OPTP system to investigate the time-resolved dynamical THz PC and its dispersion of a bulk monocrystalline SnSe2. Upon 1.59 eV excitation, we observe a dramatic drop in the transmission of THz pulse before the relaxation of hundreds of picoseconds, which represents the giant positive PC and efficient defect capturing in SnSe2. The capturing of photocarriers shows exponential decaying rule. Our analysis of SnSe2’s static and dynamical THz PC reveals a photoactive Raman mode and a far-infrared phonon mode. After fitting the dynamical THz PC dispersion with Drude-Lorentz model, we confirm the intrinsic DC mobility in SnSe2 crystal is as high as 353.2 ± 37.7 cm2V-1s-1, consistent with the theoretical prediction.
2. Experimental setup and characterizations
The detailed setup information of the homemade OPTP system has been reported in Ref. [44]. All the experiments are carried out in a dry nitrogen atmosphere on a newly cleaved crystallized SnSe2 to eliminate the possible atmospheric influences.
Crystallized SnSe2 is manufactured by using Se as the flux and corresponding details have been reported in previous work [45]. The size of the sample used in this work is 3 mm × 3 mm × 0.1 mm. Figure 1(a) shows the absorption coefficient of our sample and the Tauc plot in the inset, indicating the Γ-L indirect band gap of about 0.96 eV, which is consistent with previous reports [46,47]. The Raman shifts centered around 108.4 cm-1 and 182.8 cm-1 shown in Fig. 1(b), are assigned as the in-plane $E_g^1$ mode and out-of-plane $A_{1g}^1$ mode [48,49], respectively. Figure 1(c) shows the X-ray diffraction (XRD) pattern of a freshly cleaved SnSe2 sample. The XRD pattern demonstrates the good crystalline of the SnSe2 sample with c-cut [50,51]. Figure 1(d) illustrates the out-of-plane (top view) and in-plane (side view) molecular structure of a hexagonal SnSe2. 2H-SnSe2 crystalizes as CdI2-type layered material with a hexagonal $P\bar{3}m1$ symmetry by in-plane Se-Sn-Se layers and out-of-plane van der Waals attachment.
Fig. 1. (a) Absorption coefficient of SnSe2. Inset shows the Tauc plot of SnSe2 with respect to photon energy. (b) Raman scattering. (c) X-ray diffraction pattern. (d) Molecular structure of a bulk orthorhombic SnSe2, from the top view and side view, respectively.
3. Results and discussion
To gain insights into the THz PC evolution in SnSe2, we focus on the photocarriers’ dynamics following optical excitation at 780 nm (1.59 eV). Figure 2(a) displays the pump fluence dependent THz transmission traces, ΔT/T0, of SnSe2 under 1.59 eV excitation at room temperature. Here, ΔT = T-T0 denotes for the transmission change of probe THz beam with pump beam (T) and without pump beam (T0). As is shown in Fig. 2(b), the pump fluence we use here is linear to the signal peak, demonstrating well below saturable absorption. Remarkably, the modulation depth exceeds 30% under the linear excitation limit (176.9 µJ/cm2) and surpasses 60% under higher pump fluence, which is attributed to its high absorption ability and excellent charge carrier mobility. Such a giant modulation aligns with previous report highlighting SnSe2’s superior THz PC compared to other TMDCs [52].
Fig. 2. (a) Transient THz transmission traces (scatters) and fitting curves (lines) with different pump fluence under 1.59 eV excitation. (b) Linear and nonlinear regions identified from the relationship between the signal peak and pump fluence used. (c) Fitting relaxation lifetime with respect to pump fluence.
In this study, the pump fluence used here refers to an injected carrier density of ∼1019 cm-3(see Table S1 in Supplement 1), one order of magnitude higher than the n-type SnSe2’s intrinsic carrier density (1018 cm-3 from literature [18,26,53,54], and the excitation energy 1.59 eV used here is close to the resonance at SnSe2’s direct band gap (1.62 eV from literatures [46,47,55]). Given these considerations, we attribute the observed enhanced absorption primarily to the photoinduced electrons and holes (Δn and Δp) rather than hot carriers cooling, and the subsequent carriers’ relaxation can be explained by the trapping or recombination processes of Δn and Δp.
The relaxation of the average positive PC can be fitted by a bi-exponential decay formula, written as
After discussing the carriers’ dynamics, we delve into the static and dynamical THz PC dispersion of SnSe2. Static time domain THz transmission of Nitrogen gas (cyan line) and SnSe2 (orange line) are shown in Fig. 3(a). The inset in Fig. 3(a) shows the transmission of THz pulse which exceeds 10% within the 0.25-1.40 THz regime, which defines our effective spectral range. From the time-domain-spectroscopy, we directly obtain [58,59] the static refractive index n and absorption coefficient α of bulk SnSe2, shown in Fig. 3(b). We can further obtain the static real part of THz conductivity σ1, which has been presented as inset in Fig. 3(b). Notably, σ1 exhibits a rise at high frequency, suggesting possible phonon absorption.
Fig. 3. (a) Time-domain THz transmission of Nitrogen (cyan), SnSe2 (orange) and SnSe2 at pump fluence (brown) of 176.9 µJ/cm2 and delay time of 1 ps. Inset is the transmission of THz PC. (b) Refractive index (cyan) and absorption coefficient (orange) determined by the Fast Fourier Transform of time-domain THz transmission of Nitrogen and SnSe2. Inset is the calculated real part of conductivity within THz regime (brown). (c) and (d) Real part (cyan) and Imaginary part (orange) of transient THz PC under different pump fluence and at different delay time. Colorful scatters and lines are experimental results and fitting curves of Drude-Lorentz model. (e) Typical real part of THz PC and Drude-Lorentz fitting (cyan scatters and lines). The contribution of Drude term (black) and two Lorentz terms (brown) is listed respectively. (f) Typical pure Drude PC (black) and calculated mobility (purple). Dot lines show the linear extrapolation and the grey dash line points to the calculated DC mobility.
The brown line in Fig. 3(a) represents one of the typical dynamical transmissions at the delay time of 1 ps. It is evident that the pump pulse results in a sudden reduction of the THz transmission. In Fig. 3(c) and (d), we present the derived frequency-dependent THz PC (Δσ) under different pump fluence and at different delay time as scattered data points. Similar to σ1, Δσ also shows a slight rise at high frequency, but Δσ additionally shows an obvious resonance at 0.60 THz. In semiconductor materials, Δσ is primarily govern by the contribution of free carriers that can be described with Drude model. The rising PC with frequency may arouse from the free carriers’ backscattering or phonon resonances. However, we here highlight that Drude-Smith model [60] fails in fitting both the 0.60 THz resonance and the slight rise of PC at high frequency, and we present corresponding fitting results in section 5 in Supplement 1. Above discussion on dynamical response of THz PC reveals the domination of direct defect capturing and defect-assist e-h recombination during the relaxation process rather than scattered by phonon. Consequently, the Smith backscattering term is absent. Interestingly, all evidence points to the slight rise in σ1 and ΔσRe at high frequency being attributed to far-infrared phonon absorption, rather than the contribution of free carriers or carrier backscattering. To explore this further, we recleave the sample and measure the static time-domain THz transmission of SnSe2 using a commercial antenna-based THz-TDS system (as shown in Fig. S1 in Supplement 1). Our analysis indicates that this slight rise corresponds to a far-IR-active phonon mode around 1.45 THz. Future studies could explore this mode further by a broadband far-IR or THz-TDS spectroscopy.
From now on, we conclude that THz PC in SnSe2 composes a coupling of photoinduced free carriers and localized phonon resonances. For convenience, we name the 0.60 THz resonance in the dynamical spectrum as ω0, and the high frequency far-infrared phonon mode as ω1. ω1 enhances the absorption of probe THz pulse, causes the slight rise at high frequency both in the static and dynamical THz PC in the meantime. We fit the Δσ by Drude model combined with two Lorentz terms, written as
We subtract the two Lorentz term to obtain the pure Drude PC, which can be used to evaluate the carrier mobility. In Fig. 3(e), we plot the total conductivity alongside the individual Drude conductivity and two Lorentz conductivity terms under pump fluence of 106.1 µJ/cm2 and delay time of 1 ps (the middle panel of Fig. 3(c)). By considering the injection carrier density, the carrier mobility in THz frequency investigated is shown in Fig. 3(f). Additionally, same operation under various pump fluence is shown in Fig. S2 in Supplement 1, and the average DC mobility of SnSe2 is estimated to be 353.2 ± 37.7 cm2V-1s-1, closing to the theoretical prediction and one order of magnitude higher than the reported Hall mobility. The present result demonstrates that contact-free OPTP technique allows access to the intrinsic carrier conductivity and mobility of a material, circumventing the inevitable carrier scatterings in a long-range transportation measurement.
Then we focus on the free carriers’ behavior in SnSe2. From the plasma ωp we can obtain the photocarrier density n by n = ωp2m*ε0/e2, in which m* = 1.24 m0 is the average effective mass read from literature [15] and e is the elementary charge. From Fig. 4(a), we find that n intuitively represents the dynamic evolution of photocarriers and consists with injected photocarriers’ density calculated in section 2 in Supplement 1, and decrease with the delay time, which again indicates that the density of photocarriers play a dominated role in the average THz PC. Moreover, it is seen from Fig. 4(b) that the momentum scattering time τ does not show obvious dependence with varying pump fluence and it slightly increases from approximately 105 fs to 130 fs after the early 1 ps. This slight increase possibly arouses from the initial carrier-carrier scattering process closely after the photoexcitation, since the width of probe THz pulse is ∼0.4 ps and the zero-delay time determined may contain slight deviation. It is interesting to note that the magnitude of τ obtained here is consistent with the theoretical prediction [22,61].
Fig. 4. Photocarrier density n (a) and momentum scattering time τ (b) with respect to delay time. Center frequency of the oscillation ω0 (c), oscillator strength S (d), and life time broadening parameter Γ (e) extracted from the Lorentz term with respect to delay time.
By the determination of momentum scattering time, we can obtain the THz charge carrier mobility. By taking average effective mass m* = 1.24 ${m_0}$ from literature [15], and $\tau \sim 130\textrm{fs}$ in this work, we finally estimate the effective THz mobility of ${\mu _{\textrm{eff}}} = \frac{{\textrm{e}\tau }}{{{m^\ast }}}$ = 184 cm2V-1s-1, which is the average intrinsic mobility of SnSe2 within the area of pump irradiation in THz frequency and it consists with the calculated mobility in Fig. 3(f), again shows the potential of OPTP spectroscopy to determine the intrinsic charge carrier mobility in the inhomogeneous material systems.
We then focus on the formation of the intriguing resonance mode at 0.60 THz. This mode exhibits a distinctly photoactive character that persists until the depletion of photocarriers. Figure 4(c) presents the fitted ω0 for various pump fluence and delay time, and clearly the photoinduced resonance ω0 at 0.60 THz does not change with pump fluence and delay time. Figures 4(d) and 4(e) present the fitting strength S0 and damping constant Γ0 with respect to pump fluence and delay times, respectively. It is clearly seen from Fig. 4(d) that the magnitude of S0 decreases with the decrease of pump fluence and the increase of delay-time. The strong photocarrier density dependent S0 indicates again that the resonant mode of ω0 is photoactive, which vanishes after the depletion of photocarriers.
The photocarrier independence of ω0 and Γ0 reflects the intrinsic nature of the resonant mode. As seen from Fig. 4(e), the magnitude of damping constant Γ0 remains almost unchanged with varying photocarrier density, which shows similar trend as that of resonance frequency ω0, which excludes the possibility of polaron [41], plasma resonance [62] or excitonic polarization [63,64]. Considering that ω0 has a close frequency and reasonable relaxation lifetime compared with the Raman shift and the full width at half maximum (FWHM) of the already observed $E_g^2$ mode in previous Raman study [49], we claim that ω0 arouses from the photoinduced response of low-frequency shear mode $E_g^2$. Similar observation via an OPTP system has been reported [65] in Cd3As2. Generally, impulsively stimulated Raman scattering (ISRS) contributes to the photoinduced lattice oscillation of the non-totally symmetric mode like $E_g^2$. During the ISRS process, the difference frequency comes from the spectral bandwidth of femtosecond pump pulse couples to $E_g^2$ mode with a same frequency, exerts a transient driving force for coherent vibrations of lattice [66], and then modulate the THz PC at the vibration frequency independently of the pump fluence. The delay-time robustness of resonance frequency indicates, unlike other tin-based chalcogenide SnS [67] and SnSe [68], no phase transition tendency has been observed during the photoexcitation and carrier recombination processes in SnSe2. Our observation suggests the potential of the OPTP system as a valuable alternative or supplement for studying low frequency phonons.
4. Conclusion
In conclusion, we have investigated the ultrafast dynamics and THz PC dispersion of intrinsic n-type single crystalline SnSe2. After 1.59 eV excitation, we observe a giant positive THz PC lasting for hundreds of picoseconds and a bi-exponential decay formula is used to perfectly reproduce the transient THz transmission. Two exponential lifetimes are attributed to defect capturing of electrons and holes processes. By the means of transient THz spectroscopy, the THz photoconductivity dispersion of SnSe2 can be well reproduced with Drude-Lorentz model, from which we obtain the momentum scattering time τ of approximately 130 fs in SnSe2. We estimate the intrinsic carrier mobility of SnSe2 to be 353.2 ± 37.7 cm2V-1s-1, which is approximately ten times the reported Hall value. The present study demonstrates that SnSe2 shows great potential in the charge carrier transport ability. The observed ISRS mode at 0.60 THz in SnSe2 indicates the potential of OPTP system in the detection of low frequency Raman mode till THz regime.
Funding
National Natural Science Foundation of China (92150101); National Key Research and Development Program of China (2023YFF0719200); Science and Technology Commission of Shanghai Municipality (21JC1402600).
Acknowledgments
We sincerely thank the editors and anonymous reviewers for their contributions to this paper.
Disclosures
The authors declare no conflicts of interest related to this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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