Multicolor x-rays from free electron–driven van der Waals heterostructures

Abstract

The emergence of van der Waals (vdW) heterostructures has led to precise and versatile methods of fabricating devices with atomic-scale accuracies. Hence, vdW heterostructures have shown much promise for technologies including photodetectors, photocatalysis, photovoltaic devices, ultrafast photonic devices, and field-effect transistors. These applications, however, remain confined to optical and suboptical regimes. Here, we theoretically show and experimentally demonstrate the use of vdW heterostructures as platforms for multicolor x-ray generation. By driving the vdW heterostructures with free electrons in a table-top setup, we generate x-ray photons whose output spectral profile can be user-customized via the heterostructure design and even controlled in real time. We show that the multicolor photon energies and their corresponding intensities can be tailored by varying the electron energy, the electron beam position, as well as the geometry and composition of the vdW heterostructure. Our results reveal the promise of vdW heterostructures in realizing highly versatile x-ray sources for emerging applications in advanced x-ray imaging and spectroscopy.

Multi-layer nanomaterials provide a means of generating versatile, customizable, multi-peak X-ray spectra on a compact scale.

INTRODUCTION

Versatile, multicolor x-ray sources are widely used for x-ray pump-probe experiments, which provide an indispensable tool to study the dynamic properties of materials (1). For example, two-color x-rays are obtained from synchrotron and free-electron laser facilities where gigaelectron volt (GeV) electrons interact with two undulators and emit two-color x-rays (2–4). On one hand, synchrotron and free-electron laser facilities are usually enormous in size and expensive in construction. On the other hand, table-top x-ray tubes lack the versatility of these large x-ray facilities. This dichotomy has motivated interest in developing complementary sources that can straddle the middle ground by providing a solution for versatile x-ray generation on a table-top scale for applications where the ultrahigh brightness of large facilities is not needed. The unique properties of van der Waals (vdW) materials—including their high in-plane thermal conductivity (5) and strong plasmonic confinement (6)—have fueled much interest in them as prospective platforms for compact, versatile free electron–driven x-ray sources (7–18). Recently, Shi et al. showed that strained atomically thin vdW heterostructure and crystals with chirped interlayer spacings can be designed to form x-ray caustics (16, 17, 19), which provides a way to generate focused x-rays at the source. In these sources, incident free electrons scatter off a periodic dipole array and periodic atomic potential, furnished by the vdW material, into high energy photons (e.g., x-rays). However, no experiments have been conducted to demonstrate or even explore the potential of these platforms—wherein multiple vdW materials are combined into a single vdW heterostructure—to serve as versatile, multicolor x-ray sources.

The discovery of vdW heterostructures is a watershed in the history of materials development made possible by leveraging a unique aspect of vdW materials: their dangling bond–free interfaces, which allows any two or more of them (either in single-layer or bulk form) to be stacked into heterostructures without the limitation of lattice matching (20). This directly surmounts the famous challenge of realizing heterostructures with dissimilar single crystals before the advent of vdW materials and advanced vdW fabrication techniques (20). Despite this discovery, an experimental demonstration of x-ray generation from free electron–driven heterostructures has remained elusive.

Here, we experimentally demonstrate the use of vdW heterostructures for multicolor x-ray emission. Specifically, we send moderately relativistic electrons from table-top sources to impinge on a vdW heterostructure, resulting in the emission of multicolor x-rays. Unlike all previous demonstrations of x-ray generation from vdW materials, we do not use single crystals but instead the hitherto unexplored vdW heterostructures, which involve the integration of multiple single crystals into a single target. We show that the selection of the constituent vdW materials in the vdW heterostructure determines the unique correlation between the various photon energy peaks—one associated with each material, per emission order—as we tune them across the x-ray spectrum. This tunability can in turn be achieved by controlling the electron kinetic energy and/or the tilt angle of the vdW heterostructure with respect to the electron beam. Furthermore, the choice of constituent materials and electron beam position can be used to control the relative intensities of the x-ray peaks. We design and fabricate vdW heterostructures to experimentally demonstrate not only tunable two-color x-ray sources but also tunable three-color x-ray sources. Our experimental results are in good agreement with our theoretical predictions, showing that our theory is a powerful tool for designing of vdW heterostructures even beyond our experimental findings. Our findings prove that the ability to build atomically precise vdW heterostructures directly translates into the ability to generate x-ray spectra with precisely tailored relative intensities and peak photon energies. Such sources have potential applications in multicolor x-ray pump-probe experiments and quantum optics.

RESULTS

Theory

Multicolor x-rays are generated in our scheme by the passage of a free electron beam through a chip-scale vdW heterostructure (Fig. 1A) via two mechanisms, namely, parametric x-ray radiation and coherent bremsstrahlung (21–26). Parametric x-ray radiation is emitted by the polarization currents in the crystalline material induced by the incident electron beam, and can be regarded as an atomic version of Smith-Purcell radiation (27, 28). At the same time, the undulation of the electron beam by the periodic crystal potential generates coherent bremsstrahlung x-ray radiation. These two types of x-ray radiation (parametric x-ray radiation and coherent bremsstrahlung) share the same output x-ray photon energies in our regime of interest and are collectively referred to as parametric coherent bremsstrahlung (PCB) (10, 29). Among the crystalline materials, vdW materials have attracted much interest (10, 11, 13) because they encompass a wide range of atomic compositions, allowing the lattice spacing to be fine-tuned and the emitted x-ray photon energies to thus be precisely controlled. Combining more than one type of vdW material results in a vdW heterostructure (20, 30, 31) where each type of vdW material acts as a grating. When the vdW heterostructure is excited by an electron beam, it emits multicolor x-rays via the PCB mechanism. It should be noted that when free electrons penetrate the sample, other types of free electron radiation such as transition radiation are also produced (32–34). However, the contribution of transition radiation is substantial only at much lower photon energies and is negligible at x-ray photon energies because the refractive indices of target materials are close to unity in the x-ray regime.

Fig. 1. Multicolor x-ray emission from free electron–driven vdW heterostructures.

(A) A free electron beam impinges on a vdW heterostructure, generating multicolor x-rays via parametric x-ray radiation and coherent Bremsstrahlung. (B) A Light microscope image of MoS₂/graphite heterostructure on a silicon substrate coated with 285 nm SiO₂ film. (C) A SEM image of the heterostructure. (D) A transmission electron microscopy image of the portion where we generate the multicolor x-rays. (E) The multicolor x-ray spectra generated by a free electron beam impinging on the MoS₂/graphite heterostructure. Two x-ray peaks are observed at around 850 and 1500 eV contributed by the MoS₂ and graphite layers, respectively. The two peaks can be tailored in photon energy by varying the electron kinetic energy, as we show by considering kinetic energies of 80, 100, and 120 keV. The experimental spectra are represented by filled circles and the Monte Carlo simulated spectra are represented by solid curves where electron scattering has been taken into consideration. The vertical dotted lines indicate the analytic predicted peak photon energies (Eq. 2 with m = 2 and θ_obs ≈ 113.0°), where electron scattering has been ignored. The value of ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ for the overall tilt angle of MoS₂/graphite heterostructure is set to be 25° with the help of Kikuchi lines. The insert in e shows the Kikuchi lines generated in pure graphite region. The estimated SE of the photon count number is around 1%, which is estimated using three measurements.

The peak energy of the output PCB x-rays generated from a vdW material is given as (13)

$$E_{\mathrm{pk}}=\hslash c\frac{\mathrm{\beta }\hat{z}\cdot (\hat{U}{\mathit{g}}_0)}{1-\mathbf{\text{β}}\cdot \hat{k}}$$ (1)

where ℏ is the reduced Plank constant, c is the speed of light in free space, β ≡ ∣β∣ = ∣v/c∣ (v being the electron velocity), $\hat{k}=(\sin {\mathrm{\theta }}_{\mathrm{obs}}\cos {\mathrm{\varphi }}_{\mathrm{obs}},\sin {\mathrm{\theta }}_{\mathrm{obs}}\sin {\mathrm{\varphi }}_{\mathrm{obs}},\cos {\mathrm{\theta }}_{\mathrm{obs}})$ is the unit vector of the emitted photon wave vector, θ_obs is the polar angle of the observation direction, i.e., the angle between the incident electron beam and the observation direction, ϕ_obs is the azimuth angle of the observation direction, g₀ is the reciprocal lattice vector of the crystal in the unrotated frame, $\hat{z}\cdot (\hat{U}{\mathit{g}}_0)=-(\sin {\mathrm{\varphi }}_{\mathrm{til}}\cos {\mathrm{\theta }}_{\mathrm{til}})g_{0x}+(\sin {\mathrm{\varphi }}_{\mathrm{til}}\sin {\mathrm{\theta }}_{\mathrm{til}})g_{0y}+(\cos {\mathrm{\theta }}_{\mathrm{til}})g_{0z}$. Here, $\hat{U}$ is the rotation matrix, θ_til is the angle between the incident electron beam and the [001] zone axis of the vdW material (Fig. 1A), and ϕ_til is the rotation angle of the crystal about the z axis. The rotation of ϕ_til is performed after the rotation of θ_til. In our experiments, the value of ϕ_til is 0 and the PCB spectrum is mainly contributed by (001) planes of the vdW materials, which reduces Eq. 1 into

$$E_{\mathrm{pk}}=\hslash c\frac{2\mathrm{\pi }m\mathrm{\beta }\cos {\mathrm{\theta }}_{\mathrm{til}}}{d_{(001)}(1-\mathbf{\text{β}}\cdot \hat{k})}$$ (2)

where we have used g₀ = 2πm/d₍₀₀₁₎, m being an integer, d₍₀₀₁₎ being the interlayer distance of (001) planes.

In vdW heterostructures comprising multiple types of vdW materials, different types of vdW material have different d₍₀₀₁₎, resulting in multicolor PCB radiation even when considering only the lowest-order emission. The lowest-order emission typically has the highest intensity among all the orders of emission and is henceforth what we refer to in this paper.

The free electrons also experience electron scattering events besides PCB emission when penetrating the vdW heterostructure. The electron scattering events change the velocity of the electrons, which affects the PCB spectrum. This has implications for the thickness of each material layer, because a top layer that is too thick will result in too few electrons penetrating subsequent layers. Hence, these multilayer structures must be carefully engineered to optimize the trade-off between the amount of x-ray generated by each layer, versus the amount of electron scattering induced by the same layer. To account for the effect of electron scattering in our simulations, the velocity of an electron after each scattering event is determined via Monte Carlo simulation and used to determine the PCB emission resulting from the electron’s travel through the material. The multicolor PCB radiation spectrum resulting from a single electron traveling through a vdW heterostructure with N_layer layers of vdW materials is determined by [see details in Supplementary Materials (SM) section S1]

$$\frac{d^2{N}_{\mathrm{photon}}}{d\mathrm{\omega }d\text{Ω}}\approx {\displaystyle \sum _{l=1}^{N_{\mathrm{layer}}}}[\frac{\mathrm{\alpha }}{4{\mathrm{\pi }}^2{c}^2}{\displaystyle \sum _{j=1}^{N_{\mathrm{coll},l}}}{\sum }_s{\mathrm{u}}_{j,s,l}(\mathrm{\omega })]$$ (3)

where N_photon is the number of emitted photons, ω is the photon angular frequency, Ω is the solid angle, l denotes the vdW material layer type in the heterostructure, α is the fine-structure constant, j enumerates the scattering events, N_coll,l is the number of electron trajectory segments in layer l, s enumerates the two possible polarizations (s-polarized and p-polarized), and

$$u_{j,s,l}(\mathrm{\omega })=\frac{1}{b\sqrt{2\mathrm{\pi }}}{\displaystyle {\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}}{h}_{j,s,l}(\mathrm{\omega }-\mathrm{\tau })\exp (-\frac{{\mathrm{\tau }}^2}{2b^2})\mathrm{d}\mathrm{\tau }$$ (4)

Here, h_j,s(ω) defines the intrinsic PCB peaks, given as

$$h_{j,s,l}(\mathrm{\omega })=\mathrm{\omega }{|{\displaystyle {\int }_0^{t_j}}{\mathit{v}}_j(t)\cdot {\mathit{E}}_{l,s}({\mathit{r}}_j,\mathrm{\omega })e^{-i\mathrm{\omega }t}\mathrm{d}t|}^2$$ (5)

where t_j is the interaction time between two adjacent collisions of the electron, v_j(t) is the velocity of the electron between each collision, E_l,s(r_j, ω) is an eigenmode of the crystal, r_j denotes the trajectory of the electron between two collisions, and t denotes the time variable. Because of the resolution of energy-dispersive x-ray spectroscopy (EDS) detector and the finite observation angle range, the measured bandwidth of PCB peaks is broadened in a way that can be captured by a convolution of the intrinsic peak function h_j,s,l(ω) with a Gaussian function (probability density function), shown in Eq. 4. The parameter b in Eq. 4 describes the bandwidth broadening, given as

$$b=\frac{1}{2\sqrt{2\ln (2)}\hslash }\sqrt{R^2+{\left(\frac{\mathrm{\partial }{E}_{\mathrm{pk}}}{\mathrm{\partial }{\mathrm{\theta }}_{\mathrm{obs}}}\text{Δ}{\mathrm{\theta }}_{\mathrm{obs}}\right)}^2}$$ (6)

The first term under the square root of Eq. 6 is the energy resolution of the EDS detector. The second term describes the broadening due to the finite range of the observation angles. The bandwidth broadening due to the beam divergence and other electron scattering events has been taken into consideration via Monte Carlo simulations. The total emitted x-ray spectrum is obtained by summing over all spectra generated by all electrons calculated by Eq. 3.

Experimental demonstration and analysis

Theoretically, the x-ray generation method proposed in the present work can be used to generate multicolor x-rays. As a proof of concept, we have experimentally demonstrated multicolor x-ray generation in a MoS₂/graphite heterostructure comprising a layer of MoS₂ stacked on a layer of graphite. Our experimental results are in good agreement with our theoretical predictions obtained using Eqs. 1 to 6. To fabricate the MoS₂/graphite heterostructure, graphite is mechanically exfoliated onto a silicon substrate coated with 285-nm SiO₂ film. On the other hand, few-layer MoS₂ is mechanically exfoliated onto a polydimethylsiloxane substrate from bulk MoS₂. The few-layer MoS₂ is then transferred on the top of the graphite via dry transfer method, resulting in the MoS₂/graphite heterostructure (Fig. 1B). Last, the heterostructure is transferred onto an Au grid for transmission electron microscope (TEM) measurements with the aid of the wet transfer method. More details are available in Materials and Methods. A scanning electron microscopy (SEM) image of the vdW heterostructure is shown in Fig. 1C. A TEM image of the sample area we use to generate the multicolor x-rays is shown in Fig. 1D. The thickness of the graphite and MoS₂ layers is about 138 ± 1 nm and 29 ± 1 nm, respectively, as measured by convergent beam electron diffraction (see SM section S2 for details). Here, an MoS₂/graphite heterostructure is used since the interlayer distance of (001) planes of MoS₂ (12.89 Å) is approximately twice of graphite (6.70 Å), which guarantees that the x-ray peaks from MoS₂ and graphite are detectable and resolvable by an EDS detector.

The x-ray measurements are carried out in a TEM that provided a source of free electrons. The output x-ray spectra are measured by an EDS detector. Figure 1E shows the two-color x-ray spectra when the free electron beam impinges on the MoS₂/graphite heterostructure. For an electron kinetic energy of 100 keV, two x-ray peaks are observed at photon energies of about 850 and 1500 eV, respectively. The x-ray peak around 850 eV (1500 eV) is contributed by the MoS₂ (graphite) layer. Equation 2 reveals the output photon energies can be tuned via changing the electron energy. The experimental results indicate the output photon energies are tuned from 788 to 896 eV for MoS₂ and from 1394 to 1585 eV for graphite when the electron kinetic energy is varied from 80 to 120 keV. The experimental spectra (filled circles) are in good agreement with theoretical predictions (solid curves) where electron scattering has been fully taken into consideration via Monte Carlo simulations. The value of ${\mathrm{\theta }}_{\mathrm{til}}^l$ is determined via Kikuchi lines, which are generated by electron scattering in a single crystal when electrons travel along a high-symmetry direction (13, 35). In our case, when electrons travel along the [001] zone axis of our hexagonal vdW crystals (MoS₂ and graphite), i.e., ${\mathrm{\theta }}_{\mathrm{til}}^l$ = 0°, the Kikuchi lines form an evenly distributed pattern around a central point. The inset in Fig. 1E shows the Kikuchi lines generated in a graphite single crystal at ${\mathrm{\theta }}_{\mathrm{til}}^l$ = 0°. By tilting the vdW crystal away from the z axis, ${\mathrm{\theta }}_{\mathrm{til}}^l$ can be set to be a desired value for a single crystal with an accuracy better than 0.5° (35). However, for a heterostructure, the determination of ${\mathrm{\theta }}_{\mathrm{til}}^l$ is less accurate since each component layer has slightly different value of ${\mathrm{\theta }}_{\mathrm{til}}^l$ due to strain that is introduced during the preparation of vdW layers via mechanical exfoliation (using Scotch tape). Specifically, the value of ${\mathrm{\theta }}_{\mathrm{til}}^l$ for the MoS₂ and graphite layer is generally different from each other in the MoS₂/graphite heterostructure. Kikuchi lines can only determine the overall tilt angle for the heterostructure as a whole, referred to as ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$. The discrepancy can be reduced by using heterostructure layers with smoother interfaces, which can be achieved via chemical vapor deposition. In Fig. 1E, the value of ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ is measured to be 25° and the value of ${\mathrm{\theta }}_{\mathrm{til}}^l$ for the MoS₂ layer and graphite layer is determined, respectively, to be 22° (${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ − 3°) and 26° (${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ + 1°) via fitting. The accuracy and validity of this fitting is corroborated by the fact that the resulting theoretical predictions are in good agreement with experimental results for all three different values of electron energies, namely, 80, 100, and 120 keV. The dotted lines in Fig. 1E are analytical predictions of the peak photon energy by Eq. 2, where electron scattering has been ignored. The good agreement between analytical theory, Monte Carlo simulation and experimental results reveals that the impact of electron scattering on the peak photon energy is small. However, the bandwidth of the spectra is considerably affected by electron scattering (see SM section S1.2 for details).

In our experiments (Fig. 1E), the x-ray flux (obtained by summing the contribution from both the MoS₂ and graphite layers of the heterostructure) is typically about 80 photons/s for an 80-keV electron beam, which agrees with our theoretical predictions for an electron current of 1 nA. The use of a small electron current in our experiments is due to the limited measurement ability of the EDS detector. Scaling the electron beam current to 1 mA results in a photon flux of about 10⁷ photons/s, which is suitable for imaging applications (36). Compared to conventional x-ray tubes, the flux and brightness of the x-ray generation mechanism we study is enhanced over 10 times at a specific photon energy (see table S3 for details). It should be noted that although our TEM-based experiments have a fixed observation angle due to the fixed position of the EDS detector, tunable multicolor x-ray generation also occurs at all other observation angles, with angular dependences of the emitted photon energies given by Eqs. 1 and 2.

Besides being tailorable via varying the electron energy (Fig. 1E), Eq. 2 indicates that the photon energy of our multicolor x-ray source is also tailorable by varying the effective grating length. This can be achieved either by changing grating periodic d or by varying the tilt angle of the heterostructure with respect to the impinging electron beam, resulting in an effective grating length d cos θ_til. Figure 2A shows the x-ray spectra generated by an 80 keV electron beam incident on the MoS₂/graphite heterostructure for different tilt angles. The output x-ray photon energy from the MoS₂ (graphite) layer is tuned from 788 eV to 846 eV (1400 eV to 1538 eV) when the tilt angle ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ is varied from 0° to 25°. Tuning the output photon energy by varying the tilt angle of the heterostructure is a robust and practical way to manipulate the output characteristic of x-ray spectra dynamically (i.e., in real-time) since it can be achieved by simply tilting the vdW heterostructure and there is no need to realign the electron beam. The experimental spectra (solid circles) show good agreement with Monte Carlo simulations (solid curves). An additional effect we have to take into consideration for smaller ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ is the effect of shadowing, caused by the edge of the TEM sample holder partly obscuring the emitted x-rays. The shadowing effect has been taken into account in our model, with full details provided in SM section S3.

Fig. 2. Tuning the peak photon energies and controlling the relative peak intensities of multicolor x-ray emission from vdW heterostructures.

(A) Tunability of the output photon energies by tilting the heterostructure relative to the electron beam direction. The spectra are generated by an 80-keV electron beam incident on MoS₂/graphite heterostructure at three values of ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$, which label the curves. (B) The relative intensity of the x-ray peaks can be tailored by varying the position where the electron beam impinges on the heterostructure. When the electron beam mainly interacts with the graphite layer (C) a strong x-ray peak from graphite is measured whereas the x-ray peak from MoS₂ is negligible [red curve of (B)]. When the electron beam partly interacts with the pure graphite and partly with the MoS₂/graphite heterostructure, a strong (weak) x-ray peak from graphite (MoS₂) is measured [green curve of (B)]. The teal curve is generated by electrons interacting with the heterostructure [shown in (D)] and dark blue curve is generated by electrons partly interacting with the pure MoS₂ and partly with the MoS₂/graphite heterostructure. When the electron interacts with the pure MoS₂ layer (E), we obtain the purple curve of (B). The experimental results are represented by filled circles and Monte Carlo simulated spectra are represented by solid curves. The vertical dotted lines indicate the peak photon energy as predicted by Eq. 2. The SE of the photon count number is around 1%, estimated from three-time measurements.

It should be noted that the intrinsic bandwidth is in fact much smaller than the measured bandwidth we observe here. The reason for the relatively large bandwidth we measured is due to the relatively large energy resolution of the x-ray detector and the spread in observation angle of the x-ray detector. To use Fig. 1E as an example, the intrinsic bandwidth of the graphite peak is around 10 eV, whereas the energy spreads due to the x-ray detector’s energy resolution and observation angle spread are 97 and 104 eV respectively. These energy spreads have been taken into consideration via equations (4–6). To measure the actual intrinsic bandwidth of the x-rays, one could use Bragg’s law-based techniques, such as wavelength-dispersive x-ray spectroscopy. In Fig. 1E, we see that just varying the electron energy by 40 keV corresponds to a photon energy tunability range of 200 eV. To achieve an even larger photon energy tunability range for the same electron energy range, one may include the tilt angle of the heterostructure as a simultaneous degree of freedom—a method that has been shown to enhance the photon energy tunability range for single-layer vdW materials (13).

The intensities of the multicolor x-ray peaks relative to one another can be tailored by controlling the proportion of free electrons interacting with the respective material layers. Taking the two-color x-ray peaks from MoS₂/graphite for example, the intensity of x-ray peak from MoS₂ layer relative to the one from graphite layer can be increased by increasing (decreasing) the rate of free electrons incident on the MoS₂ layer (graphite layer). Similarly, the intensity of x-ray peak from graphite layer relative to the one from MoS₂ layer can also be increased by increasing (decreasing) the rate of free electrons incident on the graphite layer (MoS₂ layer). The reason for this is that a larger rate of incident electrons directly translates to a larger x-ray flux, which can be seen from Eq. 3. Controlling of the rate of free electrons incident on each material layer can be achieved simply by controlling the location of the impinging free electron beam (Fig. 2B). When the electron beam mainly impinges on the pure graphite region (Fig. 2C), the x-ray peak intensity from graphite is considerably higher than that from MoS₂, the red curve in Fig. 2B. By positioning the electron beam such that it impinges on the region where pure graphite borders the MoS₂/graphite heterostructure, we observe a relatively strong x-ray peak from graphite and a relatively weak x-ray peak from MoS₂ (the green curve in Fig. 2B). When the electron beam impinges on the heterostructure (Fig. 2D), the peak intensity from MoS₂ and graphite is equivalent. Similarly, we can obtain a relatively weak x-ray peak from graphite and a relatively strong x-ray peak from MoS₂ and by positioning the electron beam in the pure MoS₂ region (the dark blue curves in Fig. 2B). The purple curve in Fig. 2B is generated when the electron beam largely impinges on the region containing only MoS₂ (Fig. 2E). Varying the electron beam position thus allows us to smoothly tailor the intensity ratio of MoS₂ x-ray peaks to graphite x-rays across a wide range of values (from practically zero to infinity). In Fig. 2B, the experimental value of ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ is set to be 25°. For the pure graphite and pure MoS₂ regions, the value of ${\mathrm{\theta }}_{\mathrm{til}}^l$ is equal to the value of ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$. However, for the heterostructure region, the value of ${\mathrm{\theta }}_{\mathrm{til}}^l$ deviates from the value of ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ by a few degrees due to strain between the heterostructure layers. As a result, the experimental x-ray peaks match well with analytical predictions (dashed lines determined by Eq. 2 with ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ = 25°) when electrons interact with pure graphite or pure MoS₂ region, i.e., the red and purple curves in Fig. 2B. For the remaining curves in Fig. 2B where electrons interact with MoS₂/graphite heterostructure region, the experimental x-ray peaks deviate slightly from their corresponding analytical predictions because the actual tilt angle of the MoS₂ and graphite layer slightly differs from the value ${\mathrm{\theta }}_{\mathrm{til}}^{\mathrm{ov}}$ = 25° used in our theoretical predictions.

In the foregoing paragraphs, we have presented and analyzed versatile two-color x-ray generation from a two-layer vdW heterostructure. Let us now move on to present and analyze the case of three-color x-ray generation from a three-layer vdW heterostructure, namely, ZrS₃/MoS₂/graphite. As shown in Fig. 3A, an electron beam impinges on the ZrS₃/MoS₂/graphite heterostructure emitting three-color x-rays via PCB radiation. The emitted spectra are shown in Fig. 3B, where the peak around 650 eV is contributed by ZrS₃ (m = 1), the peak around 950 eV is contributed by MoS₂ (m = 2), and the peak around 1700 eV is contributed by graphite (m = 2). Different material type emits different x-ray photon via PCB radiation since different material type has different (001) interplane distance. Equation 2 shows different (001) interplane distance corresponding to different photon energy. The peak position can be tailored in photon energy by varying the tilt angle ${\mathrm{\theta }}_{\mathrm{til}}^l$, as seen from Eq. 2.

Fig. 3. Three-color x-ray emission from free electron–driven vdW heterostructures.

(A) Schematic diagram of three-color x-ray generation where a free electron beam impinges on a ZrS₃/MoS₂/graphite vdW heterostructure, generating multicolor x-rays via parametric x-ray radiation and coherent Bremsstrahlung. (B) Three-color x-ray spectra generated by an 80-keV free electron beam impinging on the ZrS₃/MoS₂/graphite heterostructure. Three x-ray peaks are observed at around 650, 950, and 1700 eV contributed by the ZrS₃, MoS₂, and graphite layers, respectively. The peak position can be tailored in photon energy by varying the tilt angle ${\mathrm{\theta }}_{\mathrm{til}}^l$, as we show by considering ${\mathrm{\theta }}_{\mathrm{til}}^l$ of 20°, 23°, and 25°. The experimental spectra are represented by filled circles and the Monte Carlo simulated spectra are represented by solid curves where electron scattering has been taken into consideration. Here, the sample thickness is 96 ± 5 nm for ZrS₃, 63 ± 2 nm for MoS₂, and 134 ± 3 nm for graphite, which is measured via convergent-beam electron diffraction. The estimated SE of the photon count number is around 1%, which is estimated using three measurements.

DISCUSSION

Because of the dangling bond–free properties of vdW materials, multiple vdW materials can be combined to form a multilayer vdW heterostructure (20). When the vdW heterostructure is excited by an electron beam, it emits multicolor x-rays via PCB mechanism. In Fig. 4, we present the concept of bespoke, tailorable x-ray sources based on the PCB mechanism in vdW heterostructures. Specifically, vdW heterostructures can be used to generate multicolor x-ray spectra with tunable photon energies and relative intensities. As shown in Fig. 4A, the output photon energy decreases with the increasing interlayer distance of the vdW materials (Eq. 2). The corresponding lattice parameters are given in SM section S4. The wide range of available vdW materials, as well as the ability to stack them to form heterostructures, provide us unprecedented versatility in the design of multicolor x-ray output. In principle, we can stack any two or more types of vdW materials to develop multicolor x-ray sources with desired output photon energies. For example, we can stack HfS₂, Graphite, GeSe, and MoS₂ to form a 4-layer vdW heterostructure (inset of Fig. 4B) and use it to generate four-color x-rays. In this sense, we can tailor the output properties of the multicolor x-ray sources by material design.

Fig. 4. Toward bespoke, tailorable x-ray sources with the ability to design arbitrary vdW heterostructures.

(A) Output x-ray photon energies from various vdW materials at three values of incident electron energies where ${\mathrm{\theta }}_{\mathrm{til}}^l$ = 0°. In principle, we can stack any two or more vdW materials to generate multicolor x-rays of user-designed output x-ray spectra. (B and C) Tunability of the output x-ray photon energies generated from a vdW heterostructure comprising HfS₂, Graphite, GeSe, and MoS₂ [the inset of (B)] by varying the electron kinetic energy and the tilt angle of the heterostructure relative to the electron beam, respectively. (D and E) Monte Carlo simulated radiation intensity from the heterostructure where the thickness of HfS₂, graphite, GeSe, and MoS₂ is 100, 100, 30, and 15 nm, respectively. The electron energy is 300 keV, beam current is 1 nA, beam diameter is 1 nm, and the color bar represents radiation brightness whose unit is photons s⁻¹ mm⁻² mrad⁻² per 0.1% BW. Details of our calculations are available in SM section S1.3.

Figure 4 (B and C) shows the prospect of tuning the constituent output photon energy peaks by varying the electron energy and the heterostructure tilt angle with respect to the electron beam respectively. We see that a relatively wide range of photon energies, spanning the soft and hard x-ray regimes can already be accessed with table-top electron sources. The radiation intensity of the x-ray source from 300-keV electrons is shown in Fig. 4D, where electron scattering has been fully taken into consideration via Monte Carlo simulations. Electron scattering, shown in fig.S5, gives rise to both angular broadening of the x-ray beam (fig. S4) and photon energy broadening (fig. S3). In Fig. 4 (D and E), the elastic electron scattering has been fully taken into consideration via Monte Carlo simulations, as described in SM section S1.3. The curves from top to bottom are contributed by HfS₂ (100 nm), graphite (100 nm), GeSe (30 nm), and MoS₂ (15 nm), respectively. The x-ray photon energy is higher in the forward direction (shown in D) than in the backward direction (shown in E) due to the Doppler effect, which compresses the radiated wavefronts emitted in the direction of electron travel, a phenomenon mathematically embodied by Eq. 2. On the other hand, the brightness is dependent on a separate physical quantity, the electronic susceptibility χ_g, which is a measure of how well the atoms scatter incident electormangetic waves, and whose value decreases rapidly with increasing photon energy (shown in fig. S2). The Monte Carlo simulated radiation intensity of the x-ray source from 100-keV electrons is given in SM section S1.4. Such an experiment is challenge in our EDS-based x-ray measurement system due to the poor energy resolution of the EDS detector (usually around 100 eV). The EDS detector cannot detect the peak from GeSe and MoS₂. However, such an experiment can be performed on a wavelength-dispersive x-ray spectroscopy based on x-ray measurement system whose energy resolution is around 5 eV.

Multicolor light sources have been intensively investigated for their potential applications in pump-probe experiments (1, 37–39). Their usefulness has also fueled the studies of many free electron–based methods of light generation in the terahertz to ultraviolet regime, via radiative mechanisms like Smith-Purcell radiation and Cherenkov radiation (40–50). Our tailorable, multicolor x-ray source could enable the extension of these applications into the x-ray regime. Our technology is highly complementary to existing research on undulator-based multicolor x-ray source (3, 4, 51), which are more intense but at the same time occupying a considerably larger footprint due to the use of much higher electron energies.

Our findings take vdW x-ray sources to the next level by introducing the use of vdW heterostructures, revealing an x-ray generation modality whereby the outgoing x-ray spectrum can be fully shaped—and not just tuned (i.e., only the peak photon energy changes)—via atomic design. To be able to fully shape x-rays requires not only that the peak photon energy (or energies) can be arbitrarily controlled, but at least two other elements: (i) that an arbitrary number of photon energy peaks can be introduced and (ii) that the relative intensity between these peaks can be controlled. We have demonstrated both of these aspects in this paper.

An exciting prospect for our compact, tailorable multicolor x-ray source is the development of laser-wakefield accelerators, which provide access to laboratory scale sources of high-energy electrons up to GeV levels of electron kinetic energy. Because the penetration depth (L_pd) and mean free path (L_mfp) of electrons increases with the increase of kinetic energy, which favors high energy electrons for thicker vdW heterostructures, see SM section S1.5 for details. A higher penetration depth results in more photon flux because it is proportional to the penetration depth (i.e., ∝L_pd). In addition, the peak brightness is proportional to the penetration depth and the mean free path (i.e., L_pd × L_mfp). Another exciting prospect is the development of chip-scale dielectric laser accelerators, which can be combined with our chip-scale vdW heterostructure to realize a chip-scale source of tailorable, multicolor x-rays. The development of ultrashort electron pulses (52–63) can be combined with vdW heterostructures to generate x-ray pulses of femtosecond and subfemtosecond time resolutions. There are currently no approaches in which multicolor x-rays have been generated using pulsed e-beam sources. However, pulsed 100-MeV electrons from a linear accelerator with sub–10-ps micropulse durations have been used to generate PCB x-rays from conventional, single-crystal materials (64). The use of ultrashort e-beam sources in both single-crystal vdW materials and heterostructures thus remains a research topic of keen interest to us and others.

The compact, versatile source of multicolor x-rays presented in this work could open up exciting frontiers in science and technology. We envision the following examples: (i) Bespoke x-ray spectral shaping: The ability to produce multicolor x-rays—having arbitrary numbers of peaks at arbitrary photon energies—ultimately implies a means to crafting an x-ray spectrum of arbitrary shape, that can be tailored to each application. This could be useful, for instance, to image materials and objects that may be particularly sensitive in some ranges of x-ray photon energies but not to others. (ii) Two-color x-ray pump-probe experiments: The ability to produce two-color x-rays could be useful for two-color pump-probe imaging at x-ray frequencies. The use of two-color x-rays for pump-probe experiments have so far mainly been performed at synchrotron and free electron laser facilities (1–3). Our compact method of generating multicolor x-rays could fulfil a set of applications where multicolor x-rays is useful, but the ultrahigh brightness of large-scale facilities is not needed. We thus expect our envisioned technology to be highly complementary to large-scale facilities in this regard. (iii) Multicolor quantum recoil: Recent experiments from our group (18) have revealed that the phenomenon of quantum recoil—theoretically predicted by Physics Nobel Laureate Vitaly Ginzburg in 1940—can be experimentally observed by measuring x-rays generated from free electron–driven single-layer vdW structures. Our current work opens up the possibility of demonstrating quantum recoil from successive photon emission events, where the classically predicted photon energies could also be different because of the emission taking place in materials with different interlayer spacings. Specifically, free electron–driven vdW heterostructures comprising two or more layers of vdW materials could enable the measurement of quantum recoil in multiple successive x-ray photon emission events by the same electron, but in different materials, which could in turn be chosen as a means of tailoring the quantum recoil (65). Besides being of fundamental significance, for instance in relation to the topic of radiation reaction (66, 67), these results are practically important in designing tunable x-ray sources in regimes where quantum recoil is considerable. We provide more details, along with feasible experimental designs, in SM section S6.

In conclusion, we have shown that vdW heterostructures are a promising platform for a compact multicolor free electron–driven x-ray source. A bespoke x-ray source emitting an arbitrary combination of output x-ray peaks can be designed by selecting the specific combination of vdW material layers in the heterostructure. The selection of the constituent vdW materials in the vdW heterostructure determines the unique correlation between the various photon energy peaks—one associated with each material, per emission order—as we tune them across the x-ray spectrum. As we theoretically predicted and experimentally demonstrated, this tunability can be achieved by varying the electron energy and/or the tilt angle of the vdW heterostructure. Furthermore, the relative intensity of the output x-ray peaks can be controlled by heterostructure design and by varying the electron beam position. Our experiments showed that the intensity ratio between the two x-ray peaks from the lowest emission order of a MoS₂/graphite heterostructure can be smoothly tailored from practically zero to infinity, just by varying the position where the electrons impinge on the heterostructure. We design and fabricate vdW heterostructures to experimentally demonstrate not only tunable two-color x-ray sources, but also tunable three-color x-ray sources. Our experimental results are in good agreement with our theoretical predictions, showing that our theory is a powerful tool for designing of vdW heterostructures even beyond our experimental findings. Our results should pave the way to the development of vdW heterostructures as platforms for compact, customizable multicolor x-ray generation, for promising applications in multicolor x-ray pump-probe spectroscopy and x-ray quantum optics.

MATERIALS AND METHODS

Material synthesis and preparation

Bulk MoS₂ crystals were synthesized via the chemical vapor transport method. The molybdenum powder and sulfur powder with the stoichiometric ratio of 1:2 was sealed in a silica tube under a high-vacuum environment (< 10⁻³ Pa), in which 30 mg of iodine was also loaded as the transport agent. The sealed tube was put in a horizontal two-zone furnace, whose cold end was heated to 900°C and another end was heated to 1000°C within 30 hours. After 2 weeks, the furnace was set to cool down to room temperature within 48 hours. Last, shiny MoS₂ bulk crystals were obtained in the cold end. The vdW heterostructures were fabricated via the dry-transfer method. First, graphite was exfoliated onto SiO₂/Si substrate (~ 285-nm SiO₂ film), and few-layer graphene was left on the substrate. Next, few-layer MoS₂ nanoflakes were exfoliated onto a polydimethylsiloxane film. The film was carefully aligned and transferred onto the surface of few-layer graphene flakes with the aid of a microscope. After that, the heterostructure was annealed at about 250°C for 2 hours in the furnace with high vacuum (< 10⁻⁴ Pa) to remove contaminants in the interfaces of the heterostructures.

X-ray measurements

The multicolor free electron driven x-ray source from vdW heterostructures (Figs. 1 and 2) was demonstrated in a TEM: JEOL 2010HR TEM, which provides a highly collimated electron beam and high level of vacuum (less than 10⁻⁵ Pa). Figure 3 was demonstrated in a TEM: JEOL EM-ARM300F. The vdW heterostructure was supported by a TEM grid. The TEM grid was held by a beryllium double-tilt sample holder that can be rotated about the x and y axes (the vdW heterostructure lies on the xy plane). The output x-ray spectra were measured by using a silicon drift EDS detector that was calibrated with an accuracy of ±2.5 eV (details in SM section S5). In the photon energy range of interest (0.7 to 1.6 keV), the energy resolution of the EDS detector was R ≈ 97 eV for JEOL 2010HR TEM and R ≈ 75 eV for JEOL EM-ARM300F. The observation angle and observation angle range of the EDS detector for JEOL 2010HR TEM were θ_obs ≈ 113.0° and Δθ_obs ≈ 8.6°; for JEOL EM-ARM300F were θ_obs ≈ 91.5° and Δθ_obs ≈ 1°. In the measurements, increasing ${\mathrm{\theta }}_{\mathrm{til}}^l$ tilted the sample toward the EDS detector, shown in Fig. 1A. The thickness of graphite and MoS₂ layers was about 138 and 29 nm, respectively. The electron beam spot size was about 10 nm, and the beam divergence was about 1 mrad. The background radiation in the experimental spectra has been subtracted using the software NIST DTSA-II (68).

Theory and simulations of multicolor x-ray generation

See SM section S1.

Supplementary Materials

This PDF file includes:

Sections S1 to S6

Figs. S1 to S12

Tables S1 to S3

References