1. Introduction

Diamond is rapidly becoming one of the most promising platforms for quantum photonics [1,2]. This promise derives from its excellent material properties, especially transparency, and the fact that it hosts an array of optical centers, which are photostable at room temperature [3]. One of the most important issues for a scalable quantum platform in diamond, is the coupling of the optical centers to optical structures.

The construction of integrated diamond devices requires the development of waveguides and cavities. Conventional dielectric waveguides commonly have a core region with higher refractive index than the cladding. Ion induced refractive index modification of diamond has recently been used to demonstrate damage-induced diamond waveguides via proton implantation [4,5]. However, in that case, the core level was implanted by protons, and the undamaged pristine diamond served as cladding. Thus, light absorption in the core layer could not be neglected. Alternative approaches to creating optical waveguides in diamond include ion beam milling [6], reactive ion etching [7] and gallium hard mask [8]. In addition to optical waveguides, a design for high-Q cavities in diamond that takes advantage of ion-beam perturbation of a photonic-crystal structure was presented in Ref. [9].

The values of the optical constants of pristine diamond (i.e. refractive index and extinction coefficient) are well documented over a large spectral range [10–12]. However, the effects of ion implantation to modify these properties remain unclear. In particular, there is uncertainty in the literature about the role of ion species, especially light vs heavy ion damage, and fluence, in the modification of the optical and electrical properties of diamond. The variation of refractive index of single-crystal diamond as a function of induced structural defects has been investigated in a limited number of studies [4, 5, 13–16]. Those reports are restricted by rather small ranges of photon energies, and ion fluences. References [4], [5], and [16] report on proton, and He ion implantation respectively, Refs. [13–15] study heavier ion implantation. In these latter studies, the reported changes in refractive index were not entirely consistent. No reduction of the refractive index was observed systematically. On the other hand, proton implantation gives a monotonic increase in the refractive index with increasing fluence [4, 5]. It is evident that in the low fluence regime, the change in the refractive index to heavy ions is different from that of protons. This would suggest that the two implantation routes modify the diamond by a different set of mechanisms. Here we study the effect of shallow gallium implantation on the refractive index, absorption and conductivity of diamond over an extended energy range (0.6 – 6.5 eV, corresponding to 190 – 2100 nm) across a range of implanted fluences. An optical image of our sample is shown in Fig. 1. Our results show a non-monotonic variation in the refractive index, absorption, and conductivity of the implanted zones with fluence. In particular we show that the refractive index of diamond can be reduced below that of pristine diamond by gallium implantation. Our results show qualitative agreement with previous conductivity measurements in carbon and xenon implanted diamond [17, 18].

 

Fig. 1 A micrograph of white light reflectance measurement of the sample qualitatively indicates the changes of the optical properties of diamond induced by the implantation. Darker regions correspond to reductions in the refractive index compared with the bulk, and brighter regions indicate that the refractive index is increased. The numbers inside each square are the implanted Ga fluences in ions/cm². Note: the almost vertical black lines on the surface of the sample are polishing marks.

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2. Methodology

Three similar Sumicrystal™single crystal synthetic High Pressure High Temperature (HPHT) diamonds from Sumitomo were used in the experiments. The type Ib diamonds measured 3 × 3 × 1.6 mm³ in size, with [N] ∼ 100 ppm. Care was taken to ensure that all of the implantations were performed in the central growth sector. The front and back facets were polished and all facets were cut in the 〈100〉 crystallographic direction. The samples were implanted by a beam of 30 keV Gallium ions using a FIB2000 Focused Ion Beam (FIB) system. The ion beam was raster scanned over the scanned area of 500×500 μm² to obtain a homogeneous distribution in the central region of the implanted zone.

We used Spectroscopic Ellipsometry (SE) to obtain the optical parameters of our samples. By measuring the change in the polarization of the reflected light at oblique incidence we obtain the SE parameters Ψ and Δ, which are the amplitude ratio and phase shift, respectively, of the electric field components polarized parallel and perpendicular to the plane of incidence. By applying a physical model to account for the optical dispersion function, one can extract the optical constants precisely. In addition, surface roughness and layer thickness can also be determined [19–21]. The optical properties are characterized by the dielectric function of the material ε̃(ω) = ε₁(ω) + iε₂(ω), where ω is the angular frequency. Alternatively, the optical properties can be represented as the complex refractive index ε̃’ = ñ², which consists of the refractive index n, and extinction coefficient κ, where ñ(ω) = n(ω) + iκ(ω).

A typical sample has more than one layer to analyze. Ellipsometry gives only two independent angles at each measured photon energy, Ψ and Δ. This, however, is not sufficient to obtain all the desired information for each layer, namely: dielectric constants, refractive indices, material composition, film thicknesses, etc. Thus, it is desired to connect the measured Ψ(ω), Δ(ω) points by some law. A number of dispersion laws (formulas), were developed for describing κ(ω), most based on a quantum-mechanical approach, such that they satisfy the Kramers-Kronig relation. Each dispersion law could have as few as two parameters, with some having more than twenty four parameters. A non linear parameter fit program is then applied to derive the best fit to the measured data. The number of fitting parameters of the model should be considerably lower than that of the measured experimental points, to assure validity of the fitted dispersion law.

A relatively simple four-layer model was chosen to reproduce the ellipsometric spectra. The model comprised: air; surface roughness layer with thickness L2; implanted layer with thickness L1; and diamond substrate; the model is schematically represented in the inset to Fig. 2. L1 and L2 were optimised as parameters in the fit and compared with the expected values for 30 keV Ga implants, and found to be in good agreement. The outer surface roughness layer was assumed to consist of a 50/50 vol% mixture of the implanted-layer material and air, although this layer was not used in the pristine diamond fit. For the diamond, and the implanted diamond films, it was found that the optimal dielectric dispersion function fitting the experimental data in the NIR-UV region was determined by Forouhi and Bloomer for amorphous and crystalline materials [22, 23]. Our model employed 8 fitting parameters for each spectrum of 120 experimental points.

 

Fig. 2 Energy dependence of the refractive index of diamond from our SE measurements (line), and as found in the literature [10–12] (squares). The inset describes the layer model that was used in our SE. It consisted of four layers: (air / surface roughness layer (L2) / implanted layer (L1) / diamond): three layers only were used for diamond (see text).

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3. Experiment and results

Six areas were implanted on sample 1, with varied fluences between 1 × 10¹³ – 5 × 10¹⁴ ions/cm², as shown in the white light reflectance measurement of the sample in Fig. 1. The implanted regions were squares with side length 500 μm. The numbers inside each square indicate the fluences used in the gallium implanted regions. These fluences correspond to SRIM [24] determined vacancy concentrations of ∼ 10²¹ – 10²³ vacs/cm³, and were chosen to span the surface critical amorphization threshold [26] of diamond, D_C ∼ 10²² vacs/cm³.

The variation in the reflectivity between regions, as seen in Fig. 1, shows qualitatively the non monotonic variation in the optical properties of the sample, where a darkening of the region is indicative of a reduction of the refractive index relative to the bulk, and a brightening of the region indicates an increase in refractive index compared to the bulk. A second sample set was fabricated for the 1 × 10¹³ and 2 × 10¹³ ions/cm² fluences to confirm the results, which were identical to those of the first sample.

Ellipsometric spectra were measured by a HORIBA Jobin Yvon UVISEL™spectroscopic phase modulated ellipsometer in an energy range of 0.6 – 6.5 eV. The measurements were performed under an incident angle of 58° with respect to the surface normal. The samples were measured at room temperature.

The fitting procedure was initially applied to determine the optical parameters of the pristine diamond. The model for this fit consisted of three layers only (air / surface roughness layer / diamond). In this case, the surface roughness layer was taken as a 50/50 vol% mixture of pristine diamond and air. In Fig. 2 we compare our derived refractive index, n, of diamond (full line) with literature values (squares) [10–12]. The analysis of our experimental spectrum is shown to be in excellent agreement with the literature values. Consequently, we employed this model to determine the optical parameters for the ion-implanted diamond across the measured spectral range. The parameters of the pristine diamond substrate that were needed for the fit were those that were defined by us, as described before. Figure 3(a) presents the values of n, and κ of the implanted diamond, as a function of implantation dose at a wavelength λ = 637 nm. The quoted error bars are 95% confidence intervals based on a Monte-Carlo reconstruction from the fitting parameters. As our method assumes independence of the fitting parameters and is only performed at one wavelength, these errors are an overestimate of actual expected errors. We found that the extinction coefficient, κ, was always higher in the implanted layers than in pristine diamond, as expected. However, this extinction coefficient does not increase monotonically, showing a local maximum at around a fluence of 2 × 10¹³ ions/cm² (see Fig. 3(a)), and increasing absorption after 1 × 10¹⁴ ions/cm². The refractive index also demonstrates non-trivial variation with fluence. It is initially decreasing, following by a local maximum at 2 × 10¹³ ions/cm² (with n almost identical to that of a pristine diamond). Then it shows a local minimum at 5 × 10¹³ ions/cm² with Δn = −0.05 compared to that of pristine diamond. At higher fluences, a monotonically increasing refractive index is observed, which appears to correlate with the data from proton implanted diamond [4, 5]. These quantitative results match perfectly the observations of Fig. 1.

 

Fig. 3 (a) The optical constants n (squares) and κ (circles) of the implanted diamond as a function of fluence at λ = 637 nm. The horizontal line shows the value of n for pristine diamond, and its extinction coefficient value was κ ∼ 5 × 10⁻⁴ at this wavelength. (b) The optical resistivity, derived from the ellipsometry measurements of the implanted samples at λ = 637 nm (where the conductivity, σ, is proportional to nκω), compared with DC resistance measured on the same samples, and the resistance of diamond implanted with C, and Xe from Ref. [17, 18]. Note the qualitative agreement between the heavy ion results.

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The DC resistivity of the implanted layers was determined from the current-voltage relation (two-point probe). The results are shown in Fig. 3(b), together with the predicted optical resistivity at λ = 637 nm, derived from the real part of the computed optical conductivity, σ = 2ε₀nκω. This wavelength was chosen as it corresponds to the peak for the zero phonon line for the negatively-charged nitrogen-vacancy centre in diamond, which is the most important colour centre for quantum information applications at present [25]. Note that both the DC and optical resistivities show a local maximum around the same fluence range of 5 × 10¹³ to 2 – 3 × 10¹⁴ ions/cm². The trends in the data correlate well with each other, and the DC resistivity is in agreement with that reported in Ref. [17, 18].

4. Discussion and conclusions

At room temperature and atmospheric pressure, diamond is a metastable form of carbon, where graphite is the stable form. Ion implantation can be used to convert diamond to amorphous carbon [26]. Each implanted ion creates damage, leading to the formation of vacancies and hence swelling and strain. At a critical strain, the material converts to an amorphous form and the properties of this amorphous carbon varies with increasing sp² to sp³ ratio [27]. The conversion to amorphous material appears to be evident in the conductivity seen for high fluences (> 5 × 10¹⁴ Ga/cm²) as reported in Ref. [17, 18]. However it is clear that a simple two-component treatment using the effective medium approximation does not account for the non-monotonic changes in the optical constants and resistivity that are observed in the low fluence regime with heavy ion implantation. Therefore it is likely that extra processes, perhaps due to chemical interactions, or effects due to the nature of the damage track, dominate the properties in the low fluence region, whilst damage dominates in the high fluence region. The discrepancy in the literature implies that this low fluence mechanism is not present for proton irradiation, and a robust mechanism to explain the discrepancy between the proton induced ion beam modification of refractive index and the modifications due to heavy ions is still lacking.

In conclusion, we have demonstrated the modification of the optical constants of diamond by Ga ion implantation. In particular, the refractive index may be designed to be lower (up to Δn ∼ 0.05) or higher than that of natural diamond. This modification opens the possibilities to make waveguides and cavities where the core/cavity region is not damaged by the implantation. The refractive index changes needed [9] for ultrahigh-Q cavities are well within what can be achieved by this approach. There is another advantage of this method: postprocessing. As the index modification is post-processed it should be possible to efficiently generate optical structures around pre-characterised diamond optical centers. These optical structures can be conveniently configured by altering the fluence in multiple steps if needed.