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# Bandgap control in two-dimensional semiconductors via coherent doping of plasmonic hot electrons

## Abstract

Bandgap control is of central importance for semiconductor technologies. The traditional means of control is to dope the lattice chemically, electrically or optically with charge carriers. Here, we demonstrate a widely tunable bandgap (renormalisation up to 550 meV at room-temperature) in two-dimensional (2D) semiconductors by coherently doping the lattice with plasmonic hot electrons. In particular, we integrate tungsten-disulfide (WS2) monolayers into a self-assembled plasmonic crystal, which enables coherent coupling between semiconductor excitons and plasmon resonances. Accompanying this process, the plasmon-induced hot electrons can repeatedly fill the WS2 conduction band, leading to population inversion and a significant reconstruction in band structures and exciton relaxations. Our findings provide an effective measure to engineer optical responses of 2D semiconductors, allowing flexibilities in design and optimisation of photonic and optoelectronic devices.

## Introduction

Two-dimensional (2D) semiconductors, such as transition metal dichalcogenides (TMDCs)1,2, have direct bandgap at their monolayer limit, exhibiting tremendous potential in development of next-generation nanoscale devices. Like in their bulk counterparts, bandgap control plays a vital role in 2D semiconductor technoglogies, since it enables the creation of desirable optoelectronic properties that are required in numerous applications, ranging from lasers3 to modulators4, photodetectors5, and photocatalysis6. The traditional means of control is to dope the lattice chemically7, electrically8, or optically9 with charge carriers, the practicality of which is, however, limited by many factors, e.g., the irreversible bandgap modification, contact-type control and requirement of ultrastrong pump.

Here, we report that one can effectively modify the electronic band structures of 2D semiconductors by establishing coherent coupling between the semiconductor excitons and a plasmonic resonator10,11. In particular, plasmonic resonators are metallic nanostructures that support collective oscillation of electrons, known as plasmons. The excitation of plasmons can produce hot electrons, i.e., highly energetic electrons with non-equilibrium thermal distributions12,13, which, when plasmons are coupled to 2D semiconductors, can repeatedly dope the lattice along with the coherent plasmon-exciton energy exchange. As a result, the bandgap of 2D semiconductors is significantly renormalised and the renormalisation can be easily altered via detuning plasmons from excitons.

## Results

### Sample introduction and steady-state optical properties

The schematic of our sample in Fig. 1a demonstrates a WS2 monolayer (ML) deposited onto a plasmonic crystal (PC)14,15, which comprises of a periodic array of silver capped silica nanospheres that are coated with an ultrathin Al2O3 spacer with a thickness of t = 2.5 ± 2 nm. This metal-insulator-semiconductor configuration constitutes PC-WS2 hybrid systems, supporting plasmon lattice modes propagating on the PC-WS2 interface. Here the top WS2 MLs belong to the family of atomically thin TMDCs, having been extensively studied16,17,18,19,20 for their unusual exciton-dominated optical responses, such as high absorption and emission efficiency. These properties make the PC-WS2 systems a suitable platform to study plasmon–exciton interactions15.

The PC geometries were chosen to excite two sets of plasmon lattice modes10,11,14,15 (PC-01 and PC-02) that can match the frequency (E = 2.05 eV) of exciton A (XA) and the frequency (E = 2.42 eV) of exciton B (XB) in WS2 MLs at different incident angles θ. Specifically, both PC-01 and PC-02 modes show red-shift dispersion at higher θ (Fig. 1b), with PC-01 being tuned in resonance with exciton A at θ = 22° and PC-02 being tuned in resonace with exciton B at θ = 26°. [Please see Supplementary Figs. 1 and 2 and relevant discussions in the Supplementary Information (SI) for more details of the optical properties of bare PCs.]

As a result, within the angle range (0 − 40°), PC-01, PC-02, XA, and XB mutually interact. To analyse the couplings between them, we have used a coupled Lorentz model that builds on four sets of Lorentz oscillators (Supplementary Eq. S1) to fit the transmission spectra of the PC-WS2 sample. Figure 1c shows examples of these fittings at different incident angles. The spectral positions of the fitted resonances were then extracted and plotted as a function of angles (blue dots in Fig. 1d). The complicated dispersive behaviours of these resonances were then fitted using a (4 × 4) matrix of coupled oscillators (Supplementary Eq. S2) to give the critical coupling parameters.

Specifically, the PC-01 mode couples with exciton A, presenting as splitting transmission maxima flanking XA (Fig. 1b, d). The spectral splitting at the tuned state (θ = 22°) has a value of ~140 meV, corresponding to the plasmon-exciton coupling strength g1A ≈ 87 meV, exceeding the widely used intermediate coupling criterion 2g1A > (κ1 + γA)/221,22, where κ1 is the dissipation of the PC-01 mode and γA is the exciton A decay rate. Such a coupling leads to the formation of plasmon–exciton polaritons, i.e., half-light half-matter quasiparticles that inherit properties from both the plasmonic and excitonic components. The frequencies of these maxima change with θ, displaying dispersions that follow the upper polariton (UP) and lower polariton (LP). In contrast, the coupling between PC-02 and XB only lies in the weak coupling regime, incapable of establishing coherent energy exchange. More detailed analysis of plasmon–exciton couplings involved with other oscillators, e.g., PC-02 and XB, can be found in Section 1 of SI.

### Ultrafast optical properties

Upon photoexcitation by an optical pulse (3.1 eV and 100 fs), the transient optical responses of PC-WS2 samples can be characterised using femtosecond transient absorption (TA) spectroscopy (Fig. 2a and see “Methods” section), which enables incident angle-resolved probes of the system’s relaxation dynamics23. Figure 2b shows the tuned state (θ = 22°) transient transmission spectra (ΔT/T) under a pump fluence of 12 μJ cm−2, in which the polaritonic system displays two split relaxation traces that flank the spectral position of exciton A, apparently corresponding to UP and LP. (See Supplementary Fig. 4 for discussions of transient spectral lineshapes.) This ultrashort timescale result confirms again the coherent coupling nature of the PC-WS2 systems.

When the lattice plasmons are detuned from exciton A, e.g., at θ = 30°, the resonances red-shift to ~1.93 eV [Supplementary Fig. 1a]. In this case, the transient spectra of PC-WS2 (Fig. 2c) only show a single relaxation trace at ~2.08 eV, which, by comparing with ΔT/T spectra of bare WS2 MLs (Supplementary Fig. 4), can be attributed to the relaxation of exciton A. However, no relaxation features from the detuned plasmons are observed. We also note that the plasmon features at the tuned frequency (2.05 eV) are absent in ΔT/T of bare PCs too (Supplementary Fig. 5). As a previous study24 pointed out, this is the result of very ineffective excitation of plasmons under the off-resonance pump (3.1 eV). In other words, the lattice plasmons can only be effectively excited by coupling to excitons under current pump conditions.

What is interesting is that when the PC-WS2 system is in tune (Fig. 2b), there appears a ΔT/T maximum lasting for ~1 ps at the frequency range from E = 1.6–1.8 eV, which, according to the integrated ΔT/T spectrum near zero probe delay (Fig. 2d), has positive magnitudes, indicating negative optical absorption or positive gain. In contrast, this feature is remarkably weaker in the detuned state (Fig. 2c, g) and is completely absent in bare WS2 MLs (Supplementary Fig. 6) and the bare PC samples (Supplementary Fig. 5).

To confirm our observations, we have performed meaurements under ~10 times higher pump fluence (100 μJ cm−2) for the tuned polaritons (Fig. 3a), where the broad maxima become much more pronounced. In addition, we can see large spectral shift (Supplementary Fig. 15) as well as remarkably delayed occurance of UP and LP maxima (Fig. 3b and Supplementary Fig. 16), which indicate significant enhancement of the system’s nonlinear optical responses (Details in Section 8 of SI). Similar to the low-power case, the transient variation of the broad maximum (Fig. 3c) takes ~1.5 ps from initial excitation to fading. Figure 3d shows the development of the broad maximum upon pump fluence, where the magnitude and width of the maximum are highly dependent on pump intensity. Under 100 μJ cm−2 pump fluence, the full-width at half-maximum reaches at ~200 meV with highly enhanced magnitudes as compared to the maximum under 5 μJ cm−2 pump, also contrasting the flat spectral features in bare WS2 MLs.

### Possible mechanisms of bandgap renormalisation

According to the previous works9,25,26, the broad maxima are a clear evidence of bandgap renormalisation accompanied by population inversion, which is broadly understood as a population of high-density carriers in semiconductor lattice. In particular, when semiconductors are pumped, the generated non-equilibrium photo-carriers will occupy electron and/or hole states, leading to the formation of new quasiparticle bandgaps, which is described by27:

$${{\Delta }}{E}_{\text{g}}\,=\,-\mathop{\sum}\limits_{q\ne 0}{V}_{\text{s}}(q)\ [{f}_{\text{e}}(q)+{f}_{\text{h}}(q)]-\mathop{\sum}\limits_{q\ne 0}[{V}_{\text{s}}(q)-V(q)],$$
(1)

where Vs(q) and V(q) represent fourier transforms of screened and unscreened Coulomb potentials, while fe(q) and fh(q) are occupation probabilities of electron and hole with momentum q. The onset of the new bandgap can be extracted from the low-energy end of the broad maximum9 (red dashed vertical line in Fig. 3c). It means that in our experiments, the renormalised bandgap starts at Eg ≈ 1.60 eV, lying ~400 meV below LP and ~550 meV below the bandgap of WS2 MLs (given that the binding energy of exciton A is decreased to ~100 meV when deposited on metal substrates28, i.e., about a half of its initial value19).

These results demonstrate a giant bandgap renormalisation in 2D semiconductors under such low pump fluence (down to ~10 μJ cm−2). Specifically, this is three orders of magnitude lower than the photoexcitation (3400 μJ cm−2 at room temperature) used in similar studies9. In their case, the ultrastrong pump enormously enhances exciton–exciton interactions in WS2 single/bi-layers, reducing exciton binding energy, finally breaking excitons into unbound electron-hole plasma. This effect is known as Mott-transition, resulting in a high-density carrier population that leads to a large bandgap renormalisation9,25.

In our system, the carrier density may be increased by plasmonic absorption enhancement (PAE), which, however, can not provide enough carrier population according to our calculation. Specifically, the excitation of plasmons can enhance the absorption of the pump by the system, which naturally results in an elevation of carrier numbers in the lattice. In the PC-WS2 system, the pump intensity can be amplified at the position of the WS2 ML (Supplementary Fig. 13), which, according to our calculation, gives a ~5 times average increase of absorption in the semiconductor. As a result, the carrier density can achieve up to ~1.2 × 1013 cm−2 if the absorbed pump energy is fully converted. However, even this overestimated value is still one order of magnitude lower than the density level (~1014 cm−2)9 required to cause a Mott-transition at 70 K, let alone the level at room-temperature. Furthermore, PAE should also enhance carrier generation in the detuned systems. However, in our experiments, only the tuned system shows a large bandgap renormalisation (Fig. 2b, d). Hence, there must be other mechanisms that can enhance carrier population in addition to PAE.

It is also noted that the photoinduced absorption maxima (presenting as minima in negative ΔT/T magnitudes) in the tuned polaritons are clearly delayed as compared to its counterpart in the detuned polaritons (blue curves in Fig. 2e, f and blue dashed line indicated areas in Fig. 2b, c). In bare TMDC MLs17,18,19,29, such postponed absorption maxima are usually observed under high-intensity pumps (e.g., Supplementary Fig. 6c and Supplementary Fig. 7), which, similar to Mott-transition, owes to enhanced exciton–exciton and/or exciton–electron interactions induced by high-power pump (see Section 3 and 7 in SI for detailed discussions). In contrast, the delayed maxima in our hybrid systems appear under much weaker pump and are only associated with the tuned polaritons. Together with the bandgap renormalisation, all these evidences suggest that the presence of additional carriers highly relate to the plasmon–exciton coupling.

### Coherent doping of plasmonic hot electrons

In this case, another source is more likely to contribute sufficient carriers, i.e., hot electrons from the plasmonic crystal. Specifically, the excited plasmon modes may dephase from wave-like states through non-radiative decay, which generates electrons with non-equilibrium thermal distributions13. As a result, if plasmonic resonators are integrated with semiconductors, the non-equilibrium electrons that have energies higher than the charge barrier formed at the metal–semiconductor interface can enter the lattice through direct electron transfer (DET)30,31, known as “hot electrons”. As the barrier can prevent charges from returning back to the metals30,32, hot electrons can dope adjacent semiconductors33, modifying their photovoltaic and photocatalytic performance12. (See Section 4 in SI for details.)

The sign of hot electron doping has already been shown in the transient spectral features of our system. Specifically, the polaritons at the tuned state (Fig. 2e) show slower relaxations than those of the detuned state (Fig. 2f and Supplementary Table II) and uncoupled excitons (Supplementary Table I). This, according to a previous study24, is the result of coupling between plasmons and semiconductor excitons. In particular, the generated plasmonic hot electrons can populate the semiconductor lattice accompanying the coherent energy exchange between plasmons and excitons. Since the exchange rate is very high (2g1A ≈ 174 meV), the hot electron population runs at an ultrashort period of ~25 fs (TR = 2π/2g1A)34, which is greatly shorter than the exciton formation (<1 ps)29, the non-radiative decay (at scales of 10 ps) and the radiative decay process (up to few-hundred ps) in WS2 MLs17,18. It means that during polariton relaxation, hot electrons can repeatedly fill the unoccupied states in the WS2 conduction band, which slows down the exciton relaxation via Pauli blocking, leading to extended lifetimes24.

### Calculation of hot electron density

To prove that hot electron doping can induce the observed bandgap renormalisation, we need to understand how the hot electrons are generated in our system as well as quantify the net carrier density in the lattice. As explained before, due to the off-resonance frequency of the pump, plasmons in the PC-WS2 system can only be effectively excited by coupling to excitons. Specifically the pump energy is absorbed by the semiconductor and down-converted to excite the plasmon–exciton polaritons, which, as half-plasmon half-exciton hybrid states, naturally excite their plasmonic component and result in the generation of plasmonic hot electrons. These charges then overcome the tunnelling barrier (ΔϕTB) formed at the Ag–Al2O3–WS2 interface to dope the WS2 lattice. During this process, the hot electron doping is subject to several major losses, including (i) the limited pump absorption by the WS2 MLs, (ii) the losses in energy down-conversion and (iii) the losses due to the hybrid nature of polaritons.

Following this process, we have developed a model to numerically estimate the density (Ne) of hot electrons doped in the WS2 lattice, which starts with the Hamiltonians of an electron Fermi gas and is then involved with plasmonic excitations35 and losses in the conversion process:

$${N}_{\text{e}}=\frac{{F}_{\text{pump}}\cdot {\eta }_{\text{A}}\cdot {\eta }_{\text{D}}\cdot {\eta }_{\text{pl}}}{2c{\epsilon }_{0}}\cdot {\mathcal{F}}\cdot \frac{1}{{\pi }^{2}}\frac{{e}^{2}{E}_{\,\text{F}\,}^{2}}{\hslash }\frac{\hslash \omega -{{\Delta }}{\phi }_{\text{TB}}}{{(\hslash \omega )}^{4}},$$
(2)

where e is the electron charge, ω is the frequency, EF is the Ag Fermi-level, c is the light of speed, ϵ0 is the vacuum permittivity and Fpump = 12 μJ cm−2 is the pump fluence. Here we take ηA ≈ 55% as the absorption coefficient, ηD ≈ 66% as the energy down-conversion ratio and ηpl ≈ 50% as the excitation ratio of the plasmon component in polaritons. As a result, FpumpηAηDηpl corresponds to the process that the pump energy is absorbed, down-converted and coupled to the plasmonic components in polaritons with major losses included. As optical modes, the excited polaritons gain a spatial distribution (Fig. 4b) at the tuned frequency, spreading over the Ag cap surface with hot spots at the interstices between caps. This can be mathmatically expressed as $${\mathcal{F}}=| {\bf{E}}/{{\bf{E}}}_{\text{0}}{| }^{2}$$, where E0 refers to the incident field and E stands for the enhanced field. In addition, the tunnelling barrier ΔϕTB is set to be 1 eV, which is a typical value for the ultrathin Al2O3 layers used in our system31,36, and this setting can help address other dissipations that are not considered in the whole excitation process. (See Section 6 in SI for detailed discussions about the model development and parameters taken.)

Using Eq. (2), we are able to plot the spatially distributed hot electron density in the WS2 monolayer (Fig. 4c). The density naturally acquires identical distributions as do the plasmonic excitations, exhibiting inhomogeneous distribution over the area. It has values typically higher than 1 × 1013 cm−2 in most of the areas, peaking at the interstices between caps with maxima larger than 2 × 1014 cm−2. We want to point out that these heavily doped areas are the parts that can be optically detected in transient experiments. As discussed in our previous works14,37, the far-field optical signals directly relate to the near-field distributions. As the result, the detected spectral features mainly result from the photons that are radiated from the hot spots, but not other locations in the PC-WS2 system. Therefore relevant spectral features should be analysed on the basis of spatially distributed carrier density but not the averaged one.

## Discussion

We note that with major losses taken into account, our model provides a relatively accurate estimation of carrier density in the WS2 lattice. Specifically, the development of a complete Mott-transition in a WS2 monolayer requires a carrier density up to ~1014 cm−2 9. However, the injected carriers in our system are hot electrons, which are different from the dessociated electron-hole pairs induced by pure optical pumping9,26, but are more similar to free charge carriers by electrical injection8,38, where a ~550 meV bandgap renormalisation in WS2 MLs can occur at the electron density of 3 × 1013 to 1.1 × 1014 cm−2 8. These results share high similarity with our observation, suggesting that the hot electron doping in our system is able to achieve the threshold to induce a bandgap redshift up to ~500 meV with carriers draining from conduction band K to Σ valley39 that renders the semiconductor indirect.

Given that there is little evidence for other possible carrier sources, e.g., polariton condensates40, we conclude that coherent doping of plasmonic hot electrons is dominantly responsible for the spectral and transient features that require high-density population. In particular, the hot electron population starts with polariton formation and repeatedly takes place throughout the whole relaxation process. Owing to the existence of the tunnelling barrier, hot electrons can be accumulated in the lattice before they decay (within 1 ps13), which simultaneously competes with rapid exciton relaxations, transiently converting the intrinsic WS2 monolayers to “n-doped” ones. This leads to the giant bandgap renormalisation with population inversion that peaks at few-hundred femtoseconds (Figs. 2b and 3c), and also induces the delayed maxima in Fig. 2b, e. When we enhance pump power, the hot electron density is accordingly increased, even capable of delaying the occurance of excition relaxation (Fig. 3b and Supplementary Fig. 16).

As discussed above, the intermediate plasmon–exction coupling dramatically modifies the electronic band structures of WS2 monolayers, which is induced, to a large degree, by plasmonic hot electron doping via coherent plasmon–exciton coupling. This effect can hardly be observed in traditional exciton-polaritons40, being a non-trivial factor that has to be considered when studying light-matter interactions using plasmonic resonators, which, on the other hand, provides effective measures to engineer bandgap of 2D semiconductors and benefit relevant applications41,42.

## Methods

### Sample preparation

Plasmonic crystals were prepared by self-assembly techniques together with thermal evaporation. In particular, silica spheres with diameter of 425 nm were self-assembled to a hexagonally packed monolayer on quartz substrates using a reported method14, which is followed consecutively by evaporation of 40 ± 5 nm thick silver film and 2.5 ± 2 nm thick Al2O3 film. The metal and dielectric evaporation acquires the shape of semi-spheres, resulting in an array of silver caps with a hexagonal lattice. The thickness of the metal and dielectric layers are characterised using an ellipsometer measuring identical evaporations on flat silicon substrates.

WS2 monolayers were prepared using chemical vapour evaporation with sulfur powder and tungsten dioxide powder being precursors, respectively. Using the poly(methyl methacrylate)-assisted transfer method43, we can transfer the prepared WS2 monolayer onto the PC surface. It is noted that the presence of WS2 monolayers is hardly seen from SEM images of our sample due to the ultrathin thickness of the monolayer (<1 nm). For more details about the fabrication and the monolayer morphology of the PC-WS2 samples please see our previous publication15.

### Optical characterisation

The large sample areas (2–4 cm2) allow us to conveniently perform femtosecond pump-probe absorption measurements44 with different incident angles. Specifically, as shown in Fig. 2a, the PC-WS2 samples were excited by a pump pulse, followed by a delayed broadband illumination to probe the photoexcitation induced changes, which can be characterised by measuring the differential transmission, defined as the normalised change of the probe transmission induced by the pump ΔT/T = (T − T0)/T, at different delayed times. The spectrometer in the pump-probe set-up is composed of a camera and a spectrograph, while the spectrograph is a home-built device using a prism to disperse the incident probe beam. The pump pulse has a frequency of 3.1 eV (400 nm), much higher than exciton A (~2.05 eV), while the probe pulse has a broadband frequency from 0.5 to 2.5 eV. The whole ultrafast system acquires a pulse resolution of 100 fs, and were converted to p-polarisation (electric field parallel to the plane of incidence) before entering samples. The transmission spectra of PC-WS2 samples in equilibrium states (without photoexcitation) were preformed using the reported method15. All optical characterisations were carried out at room temperature.

## Data availability

All data present in the main text and/or the Supplementary Information are avaiable from the authors upon request.

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## Acknowledgements

The authors acknowledge the New Idea Research Funding 2018 (Dodd-Walls Centre for photonic and quantum technologies), the Marsden Fast-start Fund by Royal Society of New Zealand through contract MFP-UOO1827 and MFP-VUW1715 and the Smart Ideas Fund by Ministry of Business, Innovation and Employment, New Zealand through contract UOOX1802. In addition, this work was supported in part by the National Key Research and Development Program of China (No. 2017YFA0205700) and the National Natural Science Foundation of China (Nos. 6192782 and 51861135201), Beijing Municipal Natural Science Foundation (1214027), the Science and Technology Innovation Project of Beijing Institute of Technology and the NSFC funding (12004313). The authors also acknowledge the visiting Fellowship awarded by New Zealand Centre at Peking University. We thank Dr. M. Yan and Dr. F. Hong for their help with thin-film deposition, AFM, and SEM measurements. The authors appreciate valueable discussions with Dr. Michael Price.

## Author information

Authors

### Contributions

B.D. and Y.-H.C. conceived the project; Z.Z. and B.D. prepared the samples; R.T., K.C., Y.-H.C., F.L. and B.D. carried out the optical and other characterization; Y.-H.C. and B.D. performed the simulation; Y.Z., M.Q., R.J.B., J.M.H. and B.D. supervised the projects; B.D. prepared the manuscript; all authors discussed and analyzed the results.

### Corresponding authors

Correspondence to Boyang Ding or Min Qiu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks Christoph Lienau and the other anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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Chen, YH., Tamming, R.R., Chen, K. et al. Bandgap control in two-dimensional semiconductors via coherent doping of plasmonic hot electrons. Nat Commun 12, 4332 (2021). https://doi.org/10.1038/s41467-021-24667-8

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