Introduction

Germanium sulfide, GeS, belongs to a family of twodimensional (2D) group-IV monochalcogenides with phosphorene-like distorted orthorhombic structure (figure 1(a)). It is a semiconductor with an indirect bulk band gap experimentally determined to lie in the near-infrared range, between 1.55 eV and 1.65 eV [1][2][3][4]. The resulting high optical absorbance across the visible spectrum, combined with a high carrier mobility predicted to exceed 2000 cm 2 V -1 s -1 in monolayer form [5,6], suggests applications in photovoltaics, photodetectors, and other devices [2][3][4][7][8][9][10]. Strong in-plane structural anisotropy and broken inversion symmetry in monolayers and in the surface layers of bulk GeS and other group-IV monochalcogenides, have been theoretically predicted to result in the ferroelectric polarization, pronounced in-plane optical anisotropy, and nonlinear effects such as second harmonic generation and shift current, a second-order nonlinear effect that arises from the spatial separation between valence and conduction band states [11][12][13][14][15][16][17][18][19][20][21]. In prior studies, we demonstrated THz emission from ultrafast surface shift photocurrents in bulk GeS under above-gap photoexcitation with 400 nm pulses [22,23]. For excitation near the band gap (800 nm, 1.55 eV), we found that, despite the low absorption, a photoconductive response occurs as charge carriers are excited throughout the thickness of the multilayer GeS nanoribbons [24]. This photoconductivity exhibits a slow rise due to intervalley scattering between low-and high-mobility valleys in the conduction band, followed by a decay over ∼100 ps timescale as the optical carriers become trapped at bulk defects and nanoribbon edge states. Finally, we discovered that the behavior of carriers excited by near-gap 800 nm excitation can be tuned through the intercalation of zero-valent Cu atoms into the van der Waals gaps. Copper intercalation reduces the carrier lifetime and enhances mobility from 1100 to 1300 cm 2 V -1 s -1 , which we attribute to acoustic phonon damping observed in Brillouin scattering, leading to a reduction in phonon scattering [24].

Here, we report on the distinct behavior of carriers injected near the GeS surface compared to those in the bulk of multilayer nanoribbons. Utilizing the significant difference in optical absorption at near-gap (1.55 eV, 800 nm) and above-gap (3.1 eV, 400 nm) excitations, we use time-resolved THz spectroscopy (TRTS) to probe those variations. We demonstrate that the charge carriers excited at 400 nm have significantly shorter lifetimes, decaying within 30 ps or less, compared to over 100 ps for carriers excited at 800 nm. This difference arises because carriers injected near the surface are more susceptible to trapping in surface states associated with defects and possibly adsorbed species [25,26]. The ability to tune the photoconductivity decay time within a 30 ps-100 ps range by adjusting the excitation wavelength paves the way for applications in wavelength-sensitive ultrafast photodetectors.

Experimental methods

Synthesis and characterization of GeS nanoribbons

Experiments were conducted on GeS nanoribbons synthesized on quartz substrates (figure 1(b)). GeS nanoribbons were synthesized through the vaporliquid-solid method using established procedures [27]. Scanning electron microscopy (SEM) and energy-dispersive x-ray spectra (EDX) were acquired on an FEI Scios Dual Beam FIB/SEM with an Oxford X-MaxN EDX detector operating at an acceleration voltage of 20 kV. Optical images were collected on a Leica microscope DM705M. TEM SAED was collected on a Jeol 2100fac. Raman spectra were collected using a home-built system with a 532 nm Hubner Photonics narrow-linewidth, singlefrequency Cobolt Samba laser operating with 5 mW on the sample, Leica DMi8, Princeton Instruments SCT320 with an 1800 groove/mm grating, and Princeton Instrument Pixis back-illuminated, back thinned CCD. X-ray photoelectron spectroscopy (XPS) was collected using a Kratos Axis Supra with an Al anode. X-ray diffraction (XRD) was collected on a Bruker D8 Eco Advance with a copper source (Cu Kɑ1 = 1.5406 Å and Kɑ2 = 1.5444 Å). SEM images (figure 1(b)) and optical images, such as the one shown in the inset to figure 1(e), show that ribbons are 20-100 µm long, 1-3 µm wide, and ∼0.5 µm thick. Diffraction the XRD (figure 1(g)) and TEM SAED show an orthorhombic crystal structure (space group: Pbnm), and Raman scattering confirms this assignment, as the observed modes are in agreement with known GeS modes [28]. TEM-EDX (figure 1(d)) shows only Ge and S in the nanoribbons, and XPS (figure 1(e)) identifies stoichiometry as 1:1 Ge:S.

TRTS

TRTS is an optical pump-THz probe technique that offers a non-contact probe of microscopic photoconductivity. THz probe pulses with a bandwidth in the 0.5-2.5 THz (1-10 meV) range were generated via optical rectification of 800 nm, 100 fs pulses from an amplified Ti:sapphire laser (Coherent Libra) that operates at a 1 kHz repetition in a 1 mm-thick ZnTe crystal. Off-axis parabolic mirrors focused the THz pulses to a ∼1.5 mm spot on the sample at normal incidence, and the transmitted THz pulses were detected via electro-optic sampling in a second ZnTe crystal. For the optical excitation, we used either 800 nm pulses or 400 nm pulses, the latter generated by second harmonic generation in a BBO crystal. The experimental setup has been described in detail previously [11,29]. Information on transient photoconductivity dynamics is obtained by analyzing changes in the transmitted THz probe pulses in response to photoexcitation, where the negative change in the peak transmission of the THz probe pulse is proportional to the transient photoconductivity (-∆T(t)/T ∝ ∆σ(t)). Additionally, complex, frequency-resolved photoconductivity spectra at different times post-excitation were obtained by analyzing the amplitude and phase of THz pulses transmitted through the excited and unexcited sample within the framework of thin film approximation using the Tinkham equation [30].

Results and discussion

Time-resolved photoconductivity

Although the bulk bandgap of GeS is ∼1.55-1.65 eV, 400 nm and 800 nm excitation are absorbed differently in the nanoribbons with <500 nm thickness. Based on reported absorption coefficients [31], 400 nm light is absorbed near the ribbon surface, within ∼17 nm, whereas 800 nm light has a penetration depth of ∼2µm in GeS. Thus, the small fraction of 800 nm light that is absorbed injects free carriers nearly uniformly across the nanoribbon thickness (figure 2(a)). At 800 nm, the photon energy is resonant or nearly resonant with transitions to the lowest conduction band valley at the Γ point, as illustrated schematically in figure 2(b). This is followed by scattering of photoexcited electrons into nearby satellite valleys, such as the valley in Y direction [32][33][34][35], accompanied by the emission or absorption of LO phonons. In contrast, 400 nm photons are absorbed in the uppermost layers. The inversion symmetry breaking in the surface layer generates an ultrafast shift current, causing the photoexcited nanoribbon to emit THz radiation [23]. Consequently, the signal reaching THz detector includes both the probe THz pulses and those emitted by the photoexcited GeS. To isolate the transient photoconductivity trace, the THz emission from the sample, detected with the THz probe pulse blocked, must be subtracted from the total recorded signal when both beams are present (figure 2(c)). In the following sections, transient THz photoconductivity decays and spectra for 400 nm excitation are shown after subtracting the THz emission from the GeS nanoribbons. Figures 2(d) and (e) show the normalized transient photoconductivity for 400 nm excitation, alongside the transient photoconductivity response to 800 nm, which does not produce experimentally detectable THz emission.

For 800 nm excitation, carriers injected at the bottom of the conduction band undergo scattering to nearby valleys with higher mobility, leading to a slow (∼1-1.5 ps) photoconductivity rise, consistent with prior reports [24]. This rise time decreases with increasing excitation fluence (figure 3(a)). In contrast, 400 nm excitation produces a much faster, fluence-independent photoconductivity rise over ∼0.5 ps (figure 3(d)) as 400 nm photons inject carriers high into the conduction band. For both 800 nm and 400 nm photoexcitation, the photoconductivity decay is bi-exponential, suggesting multiple recombination and trapping mechanisms, such as defects and edge states, contribute to the relaxation process. Both decays times are approximately three times shorter for the carriers injected near surface, as carrier trapping and recombination is dominated by defect-assisted processes that have much higher rates at the surface layers than in the inner layers, as has been observed in other 2D materials [36,37]. In GeS, some surface trap states may be also be associated with adsorbed species, as surface ferroelectric polarization facilitates binding polar molecules [38,39]. Figures 3(c)-(f) show the two decay times as functions of excitation fluence for both 800 nm and 400 nm excitations. The longest decay times for both excitation wavelengths, along with the fast decay time for 400 nm excitation, increase with increasing excitation fluence, indicating trap state.

Complex photoconductivity spectra

We can gain further insights into the behavior of photoexcited carriers in both the surface layer and bulk by analyzing the frequency-resolved photoconductivity spectra at different times after excitation. The photoconductivity spectrum can be extracted by comparing the THz probe pulses transmitted through the excited sample ( Ẽpump (ω)) with those transmitted through the unexcited sample ( Ẽref (ω) ) using the relation

, where n is the refractive index of the quartz substrate in the THz frequency range (2.156, assumed to be constant as reported variations are <1% within the 0.25-2.5 THz range) [40], Z 0 is the impedance of free space (377 Ω), and d is the photoexcited layer thickness. In calculating the complex conductivity spectra for 400 nm excitation, we approximate the photoexcited layer thickness to be 17 nm, based on the reported absorption coefficient at 400 nm [31]. For 800 nm, the absorption coefficient is significantly lower, ∼5 × 10 3 cm -1 and we assume uniform excitation throughout the entire ribbon thickness (approximately 500 nm). Here, only 34% of the incident excitation is absorbed by the nanoribbon, as estimated from measurements of the incident and transmitted fluences. Representative complex photoconductivity spectra at different times are shown in figures 4 and 5.

Since the nanoribbons are multi-layer structures with lateral dimensions on the order of micrometers or larger (figure 1), the photoexcited carriers do not experience significant confinement, allowing their behavior to be effectively described by the Drude model, a phenomenological model that provides a good description of free carrier conduction in bulk metals and semiconductors [30,[41][42][43]. The Drude model assumes that the free carriers elastically scatter with the average time between collisions (scattering time). The complex conductivity is then given by

where m * is the charge carrier effective mass, and N is the instantaneous photoexcited carrier density. Given that our sample consists of many randomly oriented ribbons within the THz probe pulse focus spot, we assume that transport along the armchair directioncharacterized by a lower carrier effective mass (0.20 m e for electrons, compared to 0.41 m e in the zigzag direction) [6]-contributes most significantly to the observed signal. Therefore, we use m = 0.2 m e in our estimates. By extracting τ from spectra at different times, we can further determine the mobility of the carriers, where µ = eτ m * . The resulting fitting parameters-momentum scattering time and carrier density-as a function of time for different excitation fluences for both 400 nm and 800 nm photoexcitation are presented in figure 6. Consistent with the prior report [24], carrier density for 800 nm excitation appears to increase over the first approximately 3 ps. This observation is an artefact stemming from the use of a smaller effective mass (0.2 m e ), which corresponds to the higher mobility valley, in contrast, the carriers are initially injected into the lower mobility valley at the Γ point (see figure 2(b)). Another notable observation is the disparity in photoexcited carrier density for comparable fluence values. We estimate the upper bound of the photoinjected carrier density for both excitation wavelengths based on incident fluence, penetration depth (17 nm for 400 nm and greater than the ribbon thickness for 800 nm), and a coverage density of approximately 25%, representing the fraction of the beam spot covered by the ribbons. Additionally, we assume a unity quantum efficiency, meaning one electron-hole pair is generated per absorbed photon. We find that 340 µJ cm -2 , 800 nm pulses inject at most ∼7.4 × 10 1 cm -3 photons across the thickness of the ribbons, while 330 µJ cm -2 , 400 nm pulses inject up to ∼9.0 × 10 1 cm -3 carriers within the top 17 nm layer. We compare these upper limits of the photoinjected carrier density with the carrier density values obtained by fitting the complex photoconductivity spectra to the Drude model (equation ( 1 to time = 0 ps, we find values of ∼2 × 10 1 cm -3 and ∼3 × 10 1 cm -3 for 800 nm and 400 nm excitation, respectively. These correspond to only ∼3% of the maximum possible values under the assumption of unity quantum efficiency, suggesting that most carriers are either trapped or undergo recombination on timescales shorter than the temporal resolution of our measurement (∼0.4 ps).

We also observe that the momentum scattering time is influenced by both the time after excitation and the excitation fluence (figures 6(c) and (d)). However, the trends differ significantly between 800 nm and 400 nm excitations: for 800 nm excitation, the momentum scattering time increases over time, while for 400 nm excitation, it decreases. Figure 7 presents the scattering time as a function of the photoexcited carrier density. For both excitation wavelengths, the scattering time extracted from the complex photoconductivity spectra at various times after excitation, under different excitation fluence values, follows consistent trends. This indicates that the instantaneous carrier density influences the scattering time; however, the trends observed for the two wavelengths are notably distinct. In the case of 800 nm excitation, which reflects the behavior of carriers distributed throughout the bulk of the GeS ribbons, the observed momentum relaxation rate (1/τ ) is accurately described by the sum of two components: the scattering rate in the low-density limit (1/τ 0 ), which arises from scattering by defects and equilibrium phonons (not generated by hot carrier relaxation), and of the carrier-carrier scattering rate (1/τ c ). As the carrier-carrier scattering rate increases with the carrier density, to first approximation we represent the carrier scattering time dependence on carrier density (N) as

where a is a proportionality constant [44]. From the fit (figure 7(a)), we determine that τ 0 ∼ 105 fs for the bulk carriers in GeS nanoribbons. This leads to a calculated photoexcited carrier mobility in the limit of low carrier density of µ 0 (GeS) = eτ0(GeS) m * ≈ 920 cm 2 V -1 s -1 . The value is slightly lower than the previously reported mobility of approximately 1100 cm 2 V -1 s -1 , which can be attributed to sampleto-sample variations in defect density.

For 400 nm excitation, the carriers are primarily excited within the top few surface layers. The diffusion of photoexcited carriers into the bulk layers is restricted, as carrier motion perpendicular to the layers in GeS, and in other 2D materials, occurs primarily through hopping rather than through valenceband transport [45,46]. The shorter lifetimes of the photoexcited carriers, as discussed previously, further indicate that their behavior is significantly influenced by defects. Given this observation and considering the higher injected carrier density, we propose that the apparent increase in carrier scattering time (or, equivalently, a decrease in the carrier scattering rate) at higher carrier densities can be attributed to the screening of charged defect potentials by free electrons. This screening effect outweighs the contributions from carrier-carrier scattering, as suggested by Cui et al for MoS 2 [47] building on an earlier model by Stern that describes the screening of interfacial Coulomb potentials by free carriers [48]. A dashed line in figure 7(b) serves as a guide to the eye, illustrating this trend. Notably, at the higher end of the scale, where this effect reaches saturation as most surface-adjacent defects are screened, the momentum scattering time approaches the lower limit observed for high carrier densities in the bulk layers.

In summary, we found significant differences in the behavior of carriers injected near the GeS surface compared to those in the bulk of the multilayer nanoribbons. Carriers in the bulk exhibit a longer lifetime and higher mobility because they are shielded from trap states. In contrast, carriers injected close to the surface are affected by surface states, leading to shorter lifetimes and lower mobilities. This work suggests that, in addition to previously proposed applications in photovoltaics and polarizationsensitive optoelectronic devices, GeS may also have potential uses in wavelength-sensitive ultrafast photodetectors.