Ultrafast Diamond Nonlinear Photonic Sensor

Diamond nonlinear photonic sensor

The diamond NV probe was fabricated using laser cutting and a Ga+ ion focused ion beam (FIB) milling technique that is described in ref. 30 (see also “Methods”). A (100)-oriented CVD-grown electronic-grade bulk diamond single crystal with initial nitrogen impurities of <5 ppb was used. Photoluminescence (PL) measurements indicated that the electronic state of the NV diamond was a mixture of negatively charged states (NV–) and neutrally charged states (NV0); however, the charge state of NV– would play a central role in the strong enhancement of the EO effect as presented in ref. 27 (see also Supplementary Note 2). The spatial resolution of the diamond NV probe is better than ≈ 660 nm and potentially ≤500 nm because of the enhancement of the EO sensitivity for the apex of the NV tip, based on scanning ion microscopy measurements and PL images (Fig. 2a–c) (Supplementary Note 3).

The fabricated diamond NV probe was successfully attached to the tip of a self-sensing cantilever (Fig. 2d–f), where atomic forces can be detected by means of a piezoelectric sensor31; the EO effect of the diamond NV probe was evaluated under this setup. The optical system around the microscope was constructed and optimized using a concave mirror to inject the excitation pulse light from a 45-degree oblique direction to the probe, while a reflective long-focus objective lens was used to inject only the probe light from the back side of the tip (Supplementary Notes 4 and 5)32. A reflective (Schwarzschild) type objective lens was selected to minimalize the dispersion of the Ti: sapphire pulse laser33, whose pulse length was ≤10 fs and whose wavelength covered the region from 660 to 940 nm (1.88 to 1.32 eV). Using an AFM system with a self-sensing cantilever, we focused the probe beam on the back of the cantilever, specifically on the diamond NV tip.

Electro-optic sampling on the surface of a semiconductor

We first evaluated the sensitivity of the nonlinear optical response of the diamond NV probe using a prototypical semiconductor bulk wafer, n-type semiconducting GaAs, as a test sample whose band-gap energy is ≈1.5 eV at room temperature34,35. Because of the high density of surface states, the Fermi level is pinned mid-gap, leading to band bending (Fig. 3a)35. In an n-type semiconductor, the bands bend upward, resulting in a depletion region near the surface (λd ∼ 100 nm depth) and a static electrical field E perpendicular to the surface34. Note that the surface electric field is determined by the potential of the surface states, enabling EO measurements with the NV tip as demonstrated below. Upon the photoexcitation of an n-type semiconductor, electron-hole pairs are generated near the surface and screen the surface electrical field, resulting in a change of E, ∆E. Here, the EO response can be measured by a change in anisotropic reflectivity, which is proportional to the surface electric field34,

$$\frac{\Delta {R}_{{eo}}(t)}{{R}_{0}}=\frac{4{r}_{{ij}}{n}_{0}^{3}}{{n}_{0}^{2}-1}\Delta E\left(t\right),$$

where \(\Delta {R}_{{eo}}(t)\) is the anisotropic reflectivity change and \({R}_{0}\) is the reflectivity without photoexcitation, \({r}_{{ij}}\) is the electro-optic (Pockels) coefficient and \({n}_{0}\) is the refractive index, both of which are material dependent (see Supplementary Note 4 in more details). In the case of GaAs36,37, for instance, \({r}_{41}=-1.6\, {{{\rm{pm}}}}\,{{{{\rm{V}}}}}^{-1}\) and n0 = 3.7. A positive EO response with a picosecond relaxation time observed under macroscopic conditions (Fig. 3b) indicates upward band bending near the surface, a characteristic phenomenon for n-type GaAs34, and indicates that the surface electric field can be accurately measured. The ≈1.1 ps relaxation dynamics is expected to be governed by the change in the surface electric field, i.e., the field is initially screened by the photogenerated carriers and later recovers after carriers relax via scattering with phonons or diffusion out of the depletion region34. Using Eq. (1), we obtain ∆E ≈ −3.1 × 106 V m−1 from the maximum experimental EO response value (\(\Delta {R}_{{eo}}/{R}_{0}=2.2\times {10}^{-4\,}\)) under macroscopic conditions, which is in good agreement with that obtained for n-GaAs by a similar technique34,38. Moreover, for the case of the EO response under the NV tip as shown in Fig. 3c, although the EO signal amplitude decreases to ≈1/42 of the macroscopic case (Fig. 3b), we still observe a positive EO signal with ≈0.5 ps relaxation time, indicating that sensing measurement is possible through the diamond NV tip (see Supplementary Note 6 for the value of the Pockels coefficient of NV diamond).

If the probing area is limited by the apex of the NV probe and this causes a decrease of the EO signal by ≈1/42 in Fig. 3, we can estimate the diameter of the NV probe to be ≈800 nm, which is consistent with the observation shown in Fig. 2 (see also Supplementary Note 3). The nearly halving of the relaxation time constant for the case of the NV tip suggests carrier scattering and diffusion in the surface region is stronger due to surface defects and/or 2D conduction39,40. Based on these observations, we performed electric field sensing for two-dimensional layered materials to further demonstrate the potential applicability of the diamond NV probe to advanced materials investigations as described below.

Electro-optic sampling on a transition metal dichalcogenide

To demonstrate that it is possible to measure the surface electric field with nanometer-resolution on a monolayer material in addition to bulk materials, micrometer-sized monolayer (1 ML) to multiple layers (bulk) of the transition metal dichalcogenide (TMDC) WSe2 on a Si substrate covered with a 100-nm SiO2 layer were prepared from a single crystal by using the Au assisted transfer method (see “Methods”)41. The regions containing both 1 ML and bulk of WSe2 were confirmed by micro-Raman measurements by the observation of characteristic phonon modes (Supplementary Note 7)42,43,44. The A-exciton direct band-gap (K-point) energy of the 1 ML WSe2 on SiO2/Si is ≈1.67 eV at room temperature, while that of the bulk is ≈1.63 eV (ref. 45). Since these energies are both covered by the broadband 10-fs laser used, electron-hole pairs are photogenerated to form A-excitons and subsequently dissociate due to the Mott transition within ∼100 fs in both 1 ML and bulk WSe2 samples46. Note that the pump fluence of 215 μJ cm−2 generates a carrier density of ≈1.35 × 1013 cm−2 per layer, being above the threshold of the expected Mott transition (≈3 × 1012 cm−2)47. Note also that bulk WSe2 has an indirect gap of ≈1.2 eV at the Λ point48, leading to a significantly different electron thermalization process.

Before the EO measurements, the morphology of the WSe2 sample was characterized under an optical microscope as well as AFM (Fig. 4a), and we focused on the interface between the 1 ML region and bulk WSe2. First, using macroscopic EO spectroscopy (without the diamond NV probe), we obtained a negative EO signal in the monolayer region and a positive EO signal from bulk WSe2 (Fig. 4b). In the bulk region, the positive EO response showed an exponential relaxation time of τ ≈ 0.8 ± 0.1 ps, whereas in the 1 ML region, the negative EO response exhibited a relaxation time of τ ≈ 0.3 ± 0.1 ps. The time constants are consistent with those of intraband and intervalley scattering obtained for WSe2 by time-resolved angle-resolved photoemission spectroscopy measurements49. The faster relaxation time in the 1 ML region suggests additional relaxation pathways of the photogenerated electrons via stronger coupling between the 1 ML WSe2 and the SiO2 substrate or scattering by surface defects50. Thus, we successfully obtained EO signals that reflect the characteristics of the carriers (see “Methods”). With macroscopic measurements (Fig. 4b), we observed the bulk region at an optical penetration depth λp ∼ 50 nm (see “Methods”), while the observation was dominated by the surface region for the case of the NV tip with the AFM. The surface of our WSe2 sample was p-type, where holes dominate the electronic properties, due to surface oxidation51,52, while the bulk region is n-type or intrinsic, where electrons dominate the electronic properties. The difference in the depth information is expected to affect the EO signal as described below.

From a line scan of topography data using a Si cantilever, the height of the bulk WSe2 was found to be ∼50 nm (Fig. 4c), matching the expected penetration depth \({\lambda }_{p}\). Furthermore, we performed nanometer-scale local EO measurements by contacting the sample with the diamond NV tip and obtained EO signals reflecting the local electric field of the sample (Fig. 4d, e). For 1 ML WSe2, we observed negative EO signals, demonstrating the p-type character of the sample nature due to surface oxidation. In contrast, for the bulk WSe2 sample, we observed negative EO signals, i.e., a p-type signal, at t ≈ 0 ps but interestingly the EO signal changed to a positive signal at t ≈ 1 ps (Fig. 4e). It is also interesting to investigate the relaxation time constant across the boundary (Fig. 4f). In the 1 ML region, the negative EO response shows a single exponential relaxation time of τ ≈ 0.2 ± 0.1 ps (P4), while in the bulk region it shows a double exponential relaxation: the initial negative signal exhibits τ1 ≈ 0.3 ± 0.1 ps while the second positive signal decay had value of τ2 ≈ 2.2 ± 0.1 ps (P9), a value much longer than that of the negative EO signal as well as that observed without the NV probe. Note that the time resolution under the NV tip can be estimated to ≈100 fs from the full width at the half maximum (FWHM) of the shortest EO response observed at the position of P9.

To further analyze the observed dynamics on the bulk WSe2, we examine the time evolution of the carrier density N based on the Boltzmann transport equation53:

$$\frac{\partial N}{\partial t}=-N/{\tau }_{{ep}}-B{N}^{2}-\gamma {N}^{3}+D{\nabla }^{2}N,$$

where \({\tau }_{{ep}}\) is the intraband and/or intervalley scattering time constant, B denotes the radiative recombination coefficient, \(\gamma\) is the Auger recombination coefficient, and D is the ambipolar diffusion coefficient. Under the assumptions that the photoexcited carrier density exceeds the threshold for the Mott transition and excitonic Auger processes can be neglected54, the right-hand side of Eq. (2) just after the photoexcitation (before radiative recombination occurs on ps ~ ns time scales46) can be simplified to \(-N/{\tau }_{{ep}}+D{\nabla }^{2}N\). Here using \(D=\left\langle \frac{{\upsilon }^{2}{\tau }_{m}}{2}\right\rangle\) with \({\tau }_{m}\) the momentum relaxation time and the Einstein’s relation \(\frac{D}{\mu }=\frac{{k}_{B}T}{e}\), with \({k}_{B}\) the Boltzmann constant, T the temperature and e the electron charge, we obtain D = 0.56 cm2 s–1 assuming the electron mobility is μ = 30 cm2 V–1 s–1 at room temperature55. We then find the electron velocity \(\left\langle \upsilon \right\rangle=3.35\times {10}^{4}\, {{{\rm{m}}}}\,{{{{\rm{s}}}}}^{-1}\) for \({\tau }_{m}\approx 100\, {{{\rm{fs}}}}\) (ref. 33). This means that the photogenerated electrons disappear from the surface region ( ≤ 1 nm) within ≈0.3 ps, a period being matched with \({\tau }_{1}\) (0.3 ± 0.1 ps).

Note that the second time constant (τ2 ≈ 2.2 ps) is nearly consistent with the average time for phonon emissions by carrier cooling in the Λ valley, i.e., the intraband scattering time \({\tau }_{{ep}}\approx {\tau }_{2}\), if we consider the emission of the optical A1g mode whose frequency is 7.5 THz; 0.133 ps × 16 emissions (Supplementary Note 8)56. The intraband scattering in the Λ valley will be, however, hindered by direct intervalley scattering from the K to Λ valleys (≤0.5 ps)49, which will contribute to the initial decay of the EO signal through population by nonequilibrium electrons at the Λ valley (\({\tau }_{1}\approx 0.3\, {{{\rm{ps}}}}\)). This path is followed by trapping by the surface defect states40 (\({\tau }_{2}\approx 2.2\, {{{\rm{ps}}}}\)). Thus, we are able to explain our observation of the dynamics of bulk WSe2 as the combination of intervalley scattering and trapping by surface defect states40 along the K-Λ valleys (Supplementary Note 8). Since the surface electric field is sensitive to the density of defects, possible targets for the measurement of local electric fields will potentially include power device materials such as SiC, as well as topological insulators and other TMDCs with mono-, bi-, and tri-layers.

In our experiment, contrary to an ODMR experiment, the laser energy (1.56 eV) was not resonant with transitions in the NV states (\({A}_{2}\to {E}_{1}\) and \({A}_{2}\to {E}_{2}\)) (Supplementary Note 1), and therefore, is not related to the conventional dc Stark effect12. However, our nonlinear optical method may be related to the “optical” Stark effect, known as the inverse Faraday effect (IFE) or inverse Cotton-Mouton effect (ICME), in which light-induced dc magnetization arises because the optical field shifts the different magnetic states of the ground manifold differently and mixes into these ground states different amounts of excited state1. We have, in fact, observed both IFE and ICME in NV diamond57, implying the “optical” Stark effect may also be realized using a diamond NV probe in the near future.

Note that the general sensitivity based on measurement time (typically 1 s at a 10 Hz scanning frequency) and the noise level of \(\Delta {R}_{{eo}}/{R}_{0}\approx 2\times {10}^{-7}\) corresponding to \(|\Delta {E|}\approx 9.6\times {10}^{-3} \, {{{\rm{V}}}}\,{{{{\rm{\mu m}}}}}^{-1}\) or 96 V cm−1 for the EO signal in n-GaAs can be used to discuss the resolution. Using the above parameters, we could estimate the sensitivity to be ∼1 × 10−2 V µm−1 Hz−1/2 or ∼100 V cm−1 Hz−1/2, which is comparable to that of the conventional NV-based electrometer by Dolde et al.11, but three-orders worse than recent work by Michl et al.58. Note also that there exist commercially available NV diamond tips from QZabre or Qnami59, with which we may improve the spatial resolution down to ∼10 nm if the sensitivity is increased down to the scale of several or an even single NV center in future experiments. In addition, the development of a diamond nonlinear photonic sensor system to be used in vacuum, and operating in non-contact mode, i.e., an oscillating tip that maintains a constant distance between the tip and sample, might also be useful for advancing EO-based electrometer technology regarding the measurement of the vertical distribution of the electric field.

To summarize, we proposed and realized spatio-temporal measurements of the surface electric field on a two-dimensional transition metal dichalcogenide by taking advantage of an electro-optic sensor based on NV centers in a diamond nanotip combined with a 10-fs pulsed laser. High sensitivity of the NV nanotip for electro-optic sampling was demonstrated on a doped semiconductor wafer. Compared with conventional macroscopic measurements, the local sensing method provides a higher sensitivity for the surface probe, resulting in an excellent information limit with respect to time (≤100 fs) and spatial (≤500 nm) resolutions and observation of the carrier screening dynamics at the surface of bulk transition metal dichalcogenide. By further developing the sensitivity of the NV probe to the single NV level, it can be surmised that sensing measurements at a spatial resolution down to ≈10 nm spatial resolution can be achieved. Since the NV probe is sensitive to both spins59 and temperature60, our approach will provide additional degrees of freedom to detect magnetic and thermal fields, in addition to the sensing of the electric field. Given the capabilities and considering the improved spatio-temporal limit, our proposed technique should find wide applications in materials science and nanotechnology.

Fabrication of nano probe