Sub‐µm Hot Carrier Diffusion in 2D MoS₂ on High‐κ Metal‐Oxide Substrate

Abstract

Harnessing the potential of hot carriers is a promising approach for advancing the efficiency of photovoltaic and optoelectronic devices. However, their rapid energy dissipation through carrier‐phonon scattering and recombination significantly limits practical applications. Dielectric engineering has emerged as a promising strategy to modulate carrier transport properties in low‐dimensional materials, including transition metal dichalcogenides. In this study, the impact of dielectric screening is investigated on hot carrier dynamics in monolayer MoS₂ using transient absorption microscopy. The results demonstrate that a high dielectric constant (high‐κ) metal‐oxide substrate effectively suppresses the Coulomb potential, reducing carrier scattering and recombination while significantly enhancing hot carrier diffusion length and coefficient compared to a conventional quartz substrate. These findings establish dielectric engineering as a powerful tool for improving hot carrier transport without requiring complex material modifications or external stimuli, offering a scalable and efficient strategy for next‐generation electronic and optoelectronic devices.

This study investigates the enhancement of hot carrier diffusion in monolayer MoS₂ through dielectric engineering. By comparing MoS₂ on quartz and high‐κ LaAlO₃ (LAO) substrates, it demonstrates how substrate‐induced dielectric screening suppresses carrier scattering and recombination, prolonging hot carrier lifetimes. These findings offer insights into optimizing hot carrier dynamics without altering material composition, advancing optoelectronic applications.

1. Introduction

Harnessing the potential of hot carriers stands as a pivotal pathway toward revolutionizing the efficiency of photovoltaic and optoelectronics.^{[ 1} , ^{2 ]} The controllable high‐energy carriers offer unparalleled advantages in overcoming energy barriers, driving intense research efforts toward their efficient extraction.^{[ 3} , ^{4 ]} However, a critical hurdle arises as hot carriers rapidly dissipate their energy through carrier‐phonon interaction and charge carrier trapping, curtailing their practical utility.^{[ 5} , ⁶ , ^{7 ]} This challenge underscores the pressing need for strategies capable of inducing swift and expansive diffusion of hot carriers before relaxation. Intensive research has explored hot carrier transport across various materials,^{[ 8} , ⁹ , ¹⁰ , ¹¹ , ^{12 ]} with recent attention focused on transition metal dichalcogenides (TMDs).^{[ 13 ]} Recently, the extraordinarily fast hot carrier diffusion has been reported in WSe₂ through theoretical modeling as well as experimental validation.^{[ 6} , ^{14 ]} Despite exhibiting promising long‐range hot carrier diffusion, the mobility and propagation length of hot carriers in TMDs remain constrained, typically on the scale of a few hundred nanometers. Maximizing and controlling hot carrier behavior are therefore imperative for hot carrier device integration and performance.

Dielectric engineering stands out as a promising method for enhancing carrier transport properties in various materials, including perovskites, graphene, and TMDs.^{[ 15} , ¹⁶ , ^{17 ]} By creating high‐dielectric environments, dielectric engineering effectively screens the Coulomb potential and defect trapping rate, promoting higher carrier mobility. While numerous studies have investigated these effects, most have primarily focused on time ranges from nanoseconds to microseconds, corresponding to cold carrier dynamics (bandedge states).^{[ 18 ]} However, the specific impact of dielectric screening on hot carrier transport remains largely unexplored. Previous studies on hot carrier transport have largely been confined to intrinsic approaches that focus on material‐internal properties.^{[ 14} , ¹⁹ , ^{20 ]} While understanding the intrinsic hot carrier properties of materials is essential, achieving tunability through external environments is equally critical for practical device applications. Given that hot carriers typically cool within a few picoseconds, there is a critical need to investigate hot carrier transport in dielectric environments. This exploration would shed light on how dielectric engineering affects the behavior of hot carriers, offering insights into their dynamics within these high‐dielectric environments. Such research could provide valuable guidance for optimizing carrier transport properties in various semiconductor materials, advancing the development of next‐generation electronic and optoelectronic devices.

In this study, we performed space‐resolved transient absorption microscopy (TAM) to spatially visualize carrier diffusion in atomically thin monolayer MoS₂, engineering a dielectric environment to achieve long‐range hot‐carrier diffusion. By employing a substrate with a high dielectric constant, the dielectric environment effectively suppresses the Coulombic interaction of hot carriers, such as carrier‐carrier scattering and defect‐assisted recombination, resulting in enhanced hot carrier diffusion. The hot carrier diffusion coefficient in monolayer MoS₂ was observed to increase significantly, approximately doubling on a high‐κ metal‐oxide LaAlO₃ (LAO) substrate compared to on a typical quartz substrate. This work provides insight into improving hot carrier transport without the need for complex material composition changes, high fluence, or an external electric field, offering a promising avenue for enhancing the performance of photovoltaic and optoelectronic devices.

2. Results and Discussion

We performed ultrafast TAM to investigate the exciton response in monolayer MoS₂ transferred on quartz and LAO substrates with different dielectric constants. Figure  1a presents a typical contour plot of the TAM map image for MoS₂ on a quartz substrate (ɛ = 3.9) under 2.76 eV excitation. The color map depicts two negative signals (photobleaching, PB) corresponding to the A exciton (1.89 eV) and B exciton (2.04 eV), along with positive signals: photoinduced absorption (PIA) spectra. The bleaching signal originates from the band filling effect at exciton states, specifically the resonant energy of the A and B excitons at the K point of the Brillouin zone.^{[ 21} , ^{22 ]} The PIA results from the shift in absorption spectra and the broadening of exciton linewidth, attributed to photoinduced changes in the refractive index.^{[ 23 ]}

Figure 1.

Transient absorption (TA) spectra for monolayered MoS₂ to analyze hot carrier dynamics. a) A pseudo‐color TA map image of MoS₂ monolayer transferred on a quartz substrate excited with a 2.76 eV pump. b) TA spectra extracted from the TA map image at various time delays, highlighting the resonant exciton energy and photo‐induced absorption of MoS₂ (indicated by the dashed lines). c) The normalized carrier dynamics (open dots) at the resonant probe energy are depicted with the fitting curve (solid line). d) The carrier dynamics of the photo‐induced absorption (PIA) state on quartz and LAO substrates. A slower build‐up dynamic is revealed for the case on the LAO substrate.

The detailed transient absorption spectra at various time delays are depicted in Figure 1b. The A and B excitons exhibit PB at the initial time delay (1 ps), followed by carrier relaxation. Figure 1c presents normalized carrier dynamics corresponding to resonant exciton energies, including the A (red) and B excitons (green), as well as the PIA between A and B (blue). Open dots, extracted from Figure 1a, are overlaid with multi‐exponential fitting curves depicted as solid lines. The cold exciton states of A and B excitons show initial decay with 0.50 ps, resulting from exciton‐exciton annihilation.^{[ 24 ]} The A exciton state changed flip over to a positive signal due to PIA signals located on both sides, while B exciton relaxed over 31.22 ps with slow defect capture. The PIA (1.94 eV) between A and B excitons initially shows negative behavior, attributed to the linewidth broadening of PB at the B exciton. This PIA state plays a crucial role in hot carrier dynamics owing to the high‐energy tail (Maxwell‐Boltzmann distribution) of the minimum exciton state (A exciton), which includes aspects of both hot carrier and cold exciton relaxation.^{[ 14} , ^{25 ]} Further exploration of the decay dynamics of PIA is detailed below.

To explore the impact of dielectric constant on carrier dynamics, we replicated the same procedure using TAM for a MoS₂ monolayer transferred on a high‐κ substrate, LAO (ɛ = 25). The comparative investigation of carrier dynamics at PIA is provided in Figure 1d. On quartz (grey), the carrier dynamic reveals two distinct decay components: i) 0.23 ps, linked to B exciton broadening, and ii) 49 ± 9.27 ps, associated with non‐radiative defect capture. The MoS₂ on LAO (red) exhibits a mono‐exponential decay with a time constant of 32.08 ± 10.01 ps, falling within a similar order. An intriguing observation is the delayed build‐up process on the LAO substrate compared to quartz. On quartz, the rising time is approximately 0.45 ps, whereas the LAO shows 0.65 ps. This elongated rising time is attributed to the reduction of Coulombic interaction induced by the higher dielectric constant of the LAO substrate. The enhanced Coulomb screening not only reduces carrier‐carrier Coulombic interaction between adjacent carriers but also suppresses defect‐related recombination losses, leading to the retardation of intraband relaxation.^{[ 26 ]} It suggests that the hot carrier relaxation process can be managed by controlling Coulombic interaction via the dielectric screening effect.

Such a slow relaxation process significantly contributes to the enhancement of the mobility within the lattice. In order to visualize the in‐plane diffusion of these hot carriers in MoS₂ on quartz and LAO substrates, we employed spatially resolved TAM using 2.76 eV excitation and 1.94 eV probe energies. Figure  2a presents contour maps illustrating carrier diffusion on a quartz substrate. The carrier density, represented by intensity, is initially generated by pump excitation and rapidly diffuses along the in‐plane direction before undergoing recombination. The temporal evolution of carrier distribution, as depicted in Figure 2b, was modeled using Gaussian functions:

$$\mathrm{\Delta }\mathrm{A}\left(x,t\right)\approx N\left(x,t\right)=N\left(0,t\right)\ast \exp \left[-\frac{{\left(x-x_0\right)}^2}{2\ast {\sigma }^2\left(t\right)}\right]$$ (1)

where N is the carrier population represented by ΔA intensity, x is the distance between the pump and probe, and σ is the Gaussian full width at half maximum. To quantitatively analyze the diffusion profile (Figure 2b), we extracted the squared width distribution (SWD, Δσ²(t)  =  σ²(t)  −  σ²(0)). Figure 2c displays SWD as a function of time delay on the quartz substrate, revealing ultrafast carrier diffusion within the initial 2 ps. The diffusion coefficient D and diffusion length L can be expressed by.

$$D=\frac{\mathrm{\Delta }{\sigma }^2\left(t\right)}{2\mathrm{\Delta }t}=\frac{{\sigma }^2\left(t\right)-{\sigma }^2\left(0\right)}{2\mathrm{\Delta }t}$$ (2)

$$L=\sqrt{\mathrm{\Delta }{\sigma }^2\left(t\right)-{\sigma }^2\left(0\right)}$$ (3)

where the initial diffusion coefficient is 1000 cm² s⁻¹ and the diffusion length is 470 nm on the quartz substrate. Subsequently, the negative diffusion is observed over time owing to the hot carrier cooling process, which we will discuss later.^{[ 8} , ^{14 ]}

Figure 2.

Hot carrier expansion in monolayered MoS₂ transferred onto quartz and LaAlO₃ substrates. a,d) Spatial and temporal‐resolved ΔA color maps are presented up to 20 ps, b,e) Gaussian distribution of carrier concentrations at spatial dimension, and c,f) the squared width distribution plot, showing the hot carrier diffusion dynamics for the monolayered MoS₂ on quartz and LAO substrates.

The same experimental procedure was conducted for the MoS₂ monolayer on a LAO substrate (Figure 2d). Owing to the slower intraband relaxation as depicted in Figure 1d, Figure 2f exhibits the rapid increase of SWD until 3 ps compared to the observation on a quartz substrate (Figure 2c). The initial diffusion coefficient on a LAO was higher at 1200 cm² s⁻¹, with a longer diffusion length of 500 nm (Figure 2g). After initial diffusion, reduction of SWD was observed similarly to the MoS₂ layer on a quartz substrate, followed by a subsequent recovery of diffusion. The recovered diffusion coefficient reaches up to 30.05 cm² s⁻¹.

This ultrafast initial diffusion corresponds to hot carrier diffusion. As evidenced by the obtained diffusion coefficient and length, the hot carrier diffusion in the MoS₂ monolayer is more efficient on the LAO substrate compared to the quartz. This efficiency stems from the slower relaxation process within the LAO substrate, facilitated by the enhanced dielectric screening effect. In a scenario where the same number of photoexcited carriers are present in both MoS₂/quartz and MoS₂/LAO, the density of hot carriers primarily depends on the cooling rate (Figure 1d). The stronger dielectric screening in LAO effectively preserves the high kinetic energy of carriers by circumventing Coulombic interactions such as charge impurity scattering and carrier‐carrier scattering.

The implementation of dielectric engineering aims to enhance hot carrier properties; however, altering the substrate can modulate material properties owing to undesired doping and strain effects.^{[ 27} , ^{28 ]} To isolate and clarify the influence of these effects, Raman spectroscopy measurements were conducted for the MoS₂ layers on quartz and LAO substrates. The Raman spectra in Figure  3a illustrate distinctive peaks corresponding to the in‐plane phonon E_2g mode (386 cm⁻¹) and the out‐of‐plane A_1g mode (405 cm⁻¹) on quartz (blue) and LAO (red). The difference between E_2g and A_1g, close to 20 cm⁻¹, is consistent with the characteristic feature of monolayer MoS₂. Substrate‐induced electron doping typically results in shifts of the E_2g and A_1g peaks toward the red and blue regions, respectively, while strain effects are sensitive to the in‐plane mode. However, the dielectric environment does not affect peak shifts, except for the negligible peak shifts between MoS₂ layers on quartz and LAO substrates. This exclusion of strain and doping effects indicates that only dielectric screening influences our system. To further validate the similarity in the interfacial properties of monolayer MoS₂ on quartz and LAO substrates, steady‐state photoluminescence (PL) measurements and spectral analysis are performed, as presented in Figure S2 (Supporting Information).

Figure 3.

Raman spectra and simulation of dielectric screening effect. a) Raman spectra of MoS₂ on the quartz (blue) and LAO (red) substrates. There are two representative Raman peaks, E_2g (385 cm⁻¹) and A_1g (405 cm⁻¹). b) Coulomb potentials of MoS₂ with different dielectric fields are simulated. Coulomb potentials are suppressed by a high dielectric environment induced by the LAO substrate.

To elucidate the impact of the dielectric environment on hot carrier dynamics, we conducted a Coulomb potential simulation influenced by different dielectric constants (see Supporting Information). Figure 3b shows the simulation results of the Coulomb potential distribution when a monolayer of MoS₂ is situated on substrates with different dielectric constants. The MoS₂ layer with a thickness of 0.6 nm is positioned on quartz (ɛ = 3.9, top panel of Figure 3b) and LAO (ɛ = 25, bottom panel of Figure 3b), with both substrates assumed to have infinite thickness. The image charges, separated by 1.2 nm within the MoS₂ layer, generate a Coulomb potential that extends throughout the material and to the substrate. For the case of quartz substrate, the Coulomb potential from internal charges is less effectively suppressed owing to a low dielectric environment, resulting in a broad electric potential distribution across the MoS₂ layer. Conversely, for the case of LAO substrate, the higher dielectric environment induces strong dielectric screening, leading to significant suppression and confinement of the internal Coulomb potential. The suppression of the Coulomb potential mitigates the trapping behavior of carriers by the charged defect. Furthermore, the highly suppressed internal Coulomb field prevents the potential from propagating throughout the MoS₂ layer, thus minimizing scattering events with charge defects.

As briefly mentioned above, the suppression of the Coulomb potential significantly improves energy conservation during intraband relaxation and also facilitates the prolonged lifetime of hot carriers. This phenomenon, governed by the dielectric environment, becomes more pronounced with increasing carrier density, enabling a greater number of hot carriers to diffuse over longer distances and at faster rates. To further investigate these dynamics, we conducted an excitation density‐dependent analysis, comparing the behavior of hot carriers across various pump fluences. Figure  4a,b present the SWD profiles of the Gaussian fit on quartz and LAO substrates, respectively, reflecting intricate dynamics of hot carrier evolution within a 20 ps time window. The rapid expansion of hot carriers on both substrates persists across all pump fluences until 2 ps, with an augmentation in both expansion rate and distance observed at higher fluences. This enhancement is attributed to the elevated carrier temperature within the MoS₂.^{[ 29 ]}

Figure 4.

Fluence dependence of hot carrier diffusion. a, b) Squared width distribution plotted with different pump fluences. c) The SWD was zoomed in up to 3 ps for MoS₂/quartz (blue) and MoS₂/LAO substrates (red). It shows that the initial diffusion induced by hot carriers increases with increasing pump influence on both substrates. d) Diffusion coefficient and diffusion length mappings as functions of fluence. The parameters for the MoS₂ layer on the LAO substrate are larger than those on the quartz.

Subsequent to the initial expansion, negative diffusion occurs as a result of hot carriers cooling and their transition into bound excitons.^{[ 14} , ^{30 ]} While this contraction may suggest a reduction in the diffusivity of bound excitons in real space, it is important to note that the diffusion of bound excitons is not undergoing actual contraction. This phenomenon is ascribed to the coexistence of non‐equilibrium transport and exciton‐limited diffusion. In Figure 4a, an increase in SWD during contraction is observed at higher fluence, indicating the filling of defect sites by an elevated carrier population, which in turn reduces the restrictions imposed by defects.^{[ 31 ]}

The dielectric environment plays a critical role in this stage. On the LAO substrate, the contraction is consistently slower than on quartz, as demonstrated by the extracted contraction coefficients at various pump fluences (Figure S4 and Table S1 in Supporting Information). This slower contraction suggests that stronger dielectric screening in LAO reduces Coulomb interactions, thereby suppressing exciton binding and delaying the formation of bound excitons. This observation is consistent with a delayed transition from hot carriers to excitons under enhanced screening conditions (Figure 1d).

While the slower contraction on LAO may suggest the presence of a hot‐phonon bottleneck effect,^{[ 20 ]} we find no clear fluence‐dependent trend in the contraction coefficients that would support this mechanism. We attribute the absence of a bottleneck signature to the significantly lower excitation fluences used in our experiment (50 pJ, 318 µJ cm⁻²) compared to the high fluence regime (up to 50 mJ cm⁻²) required to induce phonon bottleneck effects. Under our experimental conditions, carrier‐phonon scattering remains efficient, and the phonon population does not reach the nonequilibrium state needed to sustain a bottleneck.

In contrast to the behavior on the quartz substrate, Figure 4b exhibits slow linear diffusion at 50 and 75 pJ on the LAO substrate. This observation indicates that the transport of bound excitons within the lattice is facilitated by the dielectric environment; as discussed in Figure 3b, the stronger dielectric screening effect leads to the suppression of the Coulomb potential, confining it into the MoS₂ layer. The reduction of interaction with the lattice enables the carriers to propagate more freely, thereby decreasing the trap‐capture rate. However, it is noteworthy that the rate of slow linear diffusion decreases as a function of fluence, and eventually non‐linear diffusion is observed at a fluence of 100 pJ (see Figure 4b). It is attributed to the excessive concentration of excitons, shortening the exciton lifetime through processes such as Auger recombination or exciton annihilation (see Figure S5 and Table S2 in Supporting Information). We also evaluated alternative factors that could contribute to non‐linear behavior, such as local heating and fluence‐dependent trap filling effect, and determined these effects to be negligible under our experimental conditions (see Note S4 in the Supporting Information).

The hot carrier expansion rate in the MoS₂ layer increases on the LAO substrate, contrary to the case on the quartz substrate. Figure 4c provides a detailed depiction of the diffusion dynamics within the timeframe from 0 to 3 ps. This indicates the process of diffusion governed by hot carriers under various excitation fluences. On the LAO substrate, the SWD exhibits a more rapid increase, indicating faster hot carrier expansion. The determination of the hot carrier diffusion coefficient and diffusion length as functions of fluence is illustrated in Figure 4d through the utilization of Equations 2 and 3, respectively. The enhancement of the length and coefficient as functions of fluence is attributed to an increase in hot carrier temperature, as corroborated by prior reports.^{[ 14} , ^{32 ]} Noteworthy is the marked superiority of these values on the LAO substrate compared to those on the quartz, with the diffusion coefficient exhibiting a twofold increase as 2842 cm²s⁻¹ at 100 pJ fluence. This phenomenon is attributed to the increased surrounding permittivity for the MoS₂ layer on the LAO substrate. As elucidated in Figure 1d, it reduces carrier‐carrier scattering and charged impurity‐induced scattering, promoting the population of hot carriers and elaborate hot carrier temperature, which accelerated hot carrier diffusion. This mechanism is also schematically illustrated in Figure  5 . Moreover, the external dielectric screening induces notable blueshifts in the valence band, while the electronic band remains largely unaffected, as reported previously.^{[ 33 ]} The screening effect by the substrate theoretically reduces the electronic bandgap of the monolayer MoS₂ by up to ≈250 meV.^{[ 34 ]} This reduction in the electronic bandgap of MoS₂ leads to an increase in excess energy, elevating the kinetic energy of the system.

Figure 5.

Schematic illustration of hot carrier dynamics in monolayer MoS₂ on quartz and LAO substrates. On quartz, weak dielectric screening permits strong Coulomb interactions, resulting in frequent carrier‐carrier scattering and efficient energy redistribution (thermalization), as well as enhanced trapping by positively charged defects. On LAO, the stronger dielectric screening reduces both the carrier‐carrier scattering rate and the interaction with charged defect sites. Consequently, hot carriers remain in a non‐thermal state longer and are less likely to be captured, enabling enhanced hot‐carrier diffusion.

Although the observation of initial hot carrier diffusion may resemble a Coulomb explosion, our findings indicate that it is significantly influenced by the dielectric environment. It is supported by a two‐fold enhancement in the diffusion coefficient on the LAO substrate compared to quartz (Figure 4d), despite the identical excitation condition on both substrates. Given that the Coulomb explosion mechanism is primarily dictated by carrier density,^{[ 35 ]} this enhancement under the same carrier density cannot be solely attributed to such a mechanism.

One of the additional possibilities provided by the LAO substrate is that the suppression of the Coulomb potential facilitates the initial generation of hot carriers. The reduction of exciton‐exciton annihilation prevents energy loss and provides an opportunity to generate more hot carriers.^{[ 18 ]} The other thing is the mitigation of electron‐phonon coupling, as reported in high‐κ dielectric environments.^{[ 16} , ^{26 ]} According to these reports, dielectric screening weakens the exciton binding energy, increasing the likelihood of electrons and holes existing as free carriers. Consequently, dielectric screening reduces the electron‐phonon interaction, suggesting the potential applications of hot carriers.

To contextualize the enhancement in hot‐carrier diffusion, we include a comparison of reported values for TMDs in Table S3 of the Supporting Information. While diffusion coefficients can vary depending on experimental conditions such as excitation energy, pulse width, and substrate, this comparison shows the clear improvement achieved in our work. On the high‐dielectric LAO substrate, the maximum diffusion coefficient reaches 2842 cm² s⁻¹, which is notably higher than MoS₂ on quartz (1730 cm² s⁻¹, this work) and any previously reported value. This result highlights the potential of dielectric engineering using high‐κ substrates to enhance hot‐carrier transport in 2D materials.

3. Conclusion

In summary, we have demonstrated the diffusion of hot carriers in the MoS₂ layer within environments characterized by different dielectric constants. The dielectric screening effect imposed by the LaAlO₃ substrate leads to a reduction in the Coulombic carrier‐carrier scattering and carrier trapping events by suppressing the Coulomb potential. These offer favorable conditions for hot carrier, leading to a retardation of cooling and a prolonged hot carrier lifetime. Furthermore, the decreased electronic bandgap enhances hot carrier kinetic energy in accordance with the conservation of energy. Consequently, the dielectric screening effect results in a substantial improvement in both the diffusion coefficient and diffusion length compared to the MoS₂ layer on the quartz substrate (2842 cm² s⁻¹, 597 nm). Our findings provide valuable insights into the substantial enhancement of hot carrier expansion through the integration of high‐κ metal oxides, without the need for complex composition exchanges, high fluence, or external electric fields. The demonstration of the fastest and longest hot carrier diffusion characteristics in monolayered MoS₂ through dielectric engineering underscores its potential in future optoelectronic device technologies.

4. Experimental Section

Sample Preparation

The MoS₂ monolayer flakes were synthesized by the chemical vapor deposition (CVD) method (elucidated in detail in the Supporting Information). The monolayer MoS₂ flakes synthesized on a SiO₂/Si substrate were spin‐coated with poly (methyl methacrylate) (PMMA) C4 at 3000 rpm for 60 s. Subsequently, monolayer MoS₂ flakes on the silicon wafer were detached from the substrate through etching with a sodium hydroxide 0.1 mol L⁻¹ solution. Following this step, the sample underwent six rinses with deionized water before being transferred onto the quartz and LaAlO₃ substrates.

Space‐resolved Transient Absorption Microscopy

Space‐resolved transient absorption microscopy (SR‐TAM) was conducted utilizing transient absorption spectroscopy in conjunction with a microscopy extension (Helios, Ultrafast Systems, USA). The laser source was a Ti: Sapphire amplifier (Legend Elite, Coherent, USA) with 1 kHz repetition rate and a sub‐25 fs pulse duration. The pulse was split into a 75:25 ratio by a beam splitter, serving as pump and probe pulses, respectively. The pump laser was converted to 450 nm, using an optical parametric amplifier (OPA, Light Conversion, Lithuania). To control the relative time delay between the pump and probe pulses, a delay stage was employed for the probe, enabling time delays of up to 7 ns with respect to the pump pulse. The probe laser was focused onto a nonlinear crystal, generating a white‐light continuum in the range of 450 to 780 nm. The pump and probe pulses entering the Microscope extension were reduced in beam size below 1.6 µm using an objective lens (Nikon, TU Plan ELWD, ×50, 0.60 NA). The transmitted probe signal from the sample was collimated using an additional objective lens (Nikon, TU Plan ELWD, ×50, 0.60 NA) and directed through an optical fiber, which was coupled into a spectrometer. By fixing the position of the probe pulse and laterally scanning the pump in 0.2 µm increments, this approach facilitated the spatial and temporal resolution of carrier dynamics.

Associated Content

Supporting Information Available: monolayer MoS₂ grown by chemical vapor deposition; photoluminescence (PL) spectra of monolayer MoS₂ on quartz and LAO substrates; MATLAB simulation of Coulomb potential; other possible contributions to non‐linear diffusion on LAO substrate.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

D‐Y.Y., J.K., and S.O. contributed equally to this work. J‐H.K. conceived the idea and designed the experiments. D‐Y.Y. carried out all the experiments, analyzed the data, and conducted a simulation of the Coulomb potential. V.K.D. synthesized the MoS₂ sample. J.H.S. provided the LAO sample and funding. D‐Y.Y., and J‐H.K. interpreted the results and wrote the original draft. J.K., S.O., and J‐H.K. reviewed and edited the manuscript. A.S.A. and J.K. conducted additional PL measurements during revision. M.C.N. and W.J.Y. conducted additional AFM measurements during revision. All authors reviewed and commented on the manuscript. J‐H.K. supervised the project.

Supporting information

Supporting Information

Yee D.‐Y., Kim J., Oh S., et al. “Sub‐µm Hot Carrier Diffusion in 2D MoS₂ on High‐κ Metal‐Oxide Substrate.” Small Methods 10, no. 2 (2026): 2500435. 10.1002/smtd.202500435

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.