Characterisation of thin boron-doped diamond ﬁ lms using Raman spectroscopy and chemometrics †

Diamond coatings are characterised by outstanding mechanical and chemical robustness and hence, thin diamond layers doped with boron are particularly interesting for transparent electrodes, e.g. , for spectroelectrochemical applications. In this study, we present a non-destructive chemometric method to determine thickness and boron concentration of as-deposited heavily doped diamond ﬁ lms on silicon substrates, which may be used, e.g. , as electroactive infrared transparent windows. Using partial least-squares regression, we readily predicted these parameters with high accuracy from Raman spectra after calibration with a set of diamond ﬁ lms, previously characterised by secondary ion mass spectrometry. Due to the Fano resonance caused by the boron incorporation into the diamond lattice, which is observable in the Raman spectrum, a precise determination of the boron concentration is possible. In addition, for diamond ﬁ lms below the wavelength of the used Raman laser, we were able to determine the thickness of the as-grown ﬁ lms and gain information on the underlying substrate.


Introduction
Apart from its excellent robustness and the chemical inertness, a wide optical window from the near-ultraviolet (UV) to the farinfrared (IR) makes diamond particularly attractive as a transparent functional material. 1 Nowadays, diamond is routinely synthesised using, e.g., microwave plasma enhanced chemical vapour deposition (MWCVD). 2 By incorporation of boron, electrical conductivity can be achieved and tuned. 3 Apart from the robustness, these boron-doped diamond (BDD) electrodes show excellent electrochemical properties namely a wide electrochemical window in aqueous solution, low background currents, and are less prone to fouling even under physiological conditions. 4 Thus, they are commonly used for electroanalytical applications like heavy metal detection, 5 pH sensing, 6 electrochemical conversions, 7 and other emerging areas. 8 For such applications, the boron concentration plays an important role as it inuences the electroanalytical performance. 9,10 In addition, boron incorporation into the diamond lattice largely inuences the transmission properties as observable from the dark colour of doped diamond lms.
Especially in the IR range, the conductivity plays a major role for the transmission properties. Heavily doped layers (>10 21 atoms per cm 3 ) have nearly metallic conductivity (100 S cm), and hence they are strong IR absorbers arising from the complex refractive index. 11 Nevertheless, when using nanometer-sized lms, the inuence on transmission properties can be minimized drastically which paves the way for the manufacturing of transparent contacts and electrodes, e.g., for spectroelectrochemical applications. 12 Up to now only a few studies on optically transparent electrodes (OTE) have been conducted, e.g., for spectroelectrochemical measurements on the ferrocene redox couple, 13 or a multi-analytical platform for atomic force microscopy combined with IR measurements and electrochemistry. 14 A reason for that may be the rather challenging fabrication of such OTEs, which afford well-controlled growth conditions and high reproducibility concerning uniformity, thickness, and dopant concentration.
We recently succeeded in growing ultrathin, pinhole-free diamond layers with thicknesses down to 50 nm. 15 Such lms are highly attractive for conductive coatings on optically transparent substrates. However, as they are grown within the early stages of the diamond synthesis, controlling both, the dopant concentration as well as the thickness is challenging. To ensure successful growth and reliable quality, a fast and nondestructive characterisation method is mandatory.
Commonly these parameters are obtained using secondary-ion mass spectrometry (SIMS), which even provides a depth prole of dopants in the grown diamond layer, but is destructive. 16 The boron concentration may also be determined using cathodoluminescence, which affords a sophisticated, expensive setup, 17 or Mott-Schottky analysis, where interpretation is challenging and parasitic capacitance may readily spoil the measurement. 18 Apart from that, other methods have been established including Raman spectroscopy that has been used, e.g., to study the inuence of boron incorporation on the diamond Raman line at 1332 cm À1 . The dopant concentration can be estimated using the Fano-resonance caused by the boron incorporation. 19,20 In a similar approach and in order to provide a fast, nondestructive and non-invasive method for the detection of both, the boron concentration and the thickness of thin boron doped diamond layers grown on IR transparent samples like silicon, we have developed a chemometric method based on partial least squares regression (PLSR) using Raman spectra of the as-grown diamond layers. 21,22 For this purpose, a set of diamond lms was grown and characterised by SIMS measurements. This set was used to develop and validate a chemometric model. Applying a PLSR model to a dataset in the present size, potentially decreases the number of variables by taking into account the most relevant variances for a number of features within the spectral data. Thus, the model is capable of both, predicting thickness and the dopant concentration simultaneously within a few seconds and high accuracy using the recorded Raman spectral data.
To further optimize the spectral calibration set in terms of size and avoiding collinearities, it was calculated via an experimental design. 23 Additionally, the model was found to be sensitive to characteristics of the substrate, e.g., the conductivity of underlying silicon wafer, which helps to characterise the coated element as a whole.

Sample preparation
As substrates prime grade 4 00 silicon wafers were used: lowdoped with a resistivity in the range of 10-50 U cm and heavily doped with a resistivity of 0.01-0.02 U cm, both p-type, using boron as dopant (Si-Mat, Germany). Nanodiamond seeding was carried out using 4 nm hydrogen-terminated nanodiamonds (G01 grade, Plasmachem GmbH, Germany) following a procedure described elsewhere. 24,25 Briey, asreceived nanodiamonds are hydrogen-terminated by annealing in H 2 atmosphere and then dispersed in 10 À3 M KCl aqueous solution. A pulsed ultrasonic treatment is used to break up agglomerates and the resulting solution is further centrifuged for 8 h at 40 kg RCF to separate agglomerates and obtain a seeding solution mainly consisting of individual nanodiamond particles (as conrmed via dynamic light scattering). All substrates were RCA cleaned before use, then immersed into the seeding solution and treated in an ultrasonic bath for 5 min. Aer rinsing with ultrapure water, the wafers were spin-dried and loaded into the reactor.

MWCVD growth
Diamond growth was carried out in an ellipsoidal MPCVD reactor using puried gases (hydrogen, methane, and trimethylborane (TMB)). 2 The used reactor design can load samples up to 6 00 . For all grown samples the growth conditions were identical at 9 kW microwave power, 750 C substrate temperature, 50 mbar pressure and a methane concentration of 2% in H 2 . By varying the B/C ratio (300-2000 ppm), i.e., TMB concentration and the deposition time, a set of 15 diamond lms were grown (1-11, C1-C4), of which 4 lms were grown on IR non-transparent, conductive silicon denoted as C1 to C4, as shown in Table 1.

Characterisation and data processing
The as-grown samples were characterised using SIMS measurements (Atomika 4500, Cameca, France) to obtain thickness and dopant concentration. Also the substrate resistivity was measured using a 4-point probe (MCP-T-700, Mitsubishi Chemical Analytech, Japan). These measurements served as a reference for the chemometric model. Additionally, the lms were characterised by atomic force microscopy (Nano-Wizard III, JPK Instruments, Germany) and transmission IR spectroscopy (Vertex 70, Bruker, Germany) (Fig. S1, † 2).
For the chemometric model, Raman spectra were recorded with a Raman microscope (InVia, Renishaw, UK) using a laser with a wavelength of 532 nm. All samples were measured at least 3 times (2 s exposure, 5 spectra averaged) at 3 independent spots of the individual diamond-coated samples. The PLSR was then carried out using the PLS-Toolbox (Eigenvector Research, USA) and MATLAB (MathWorks, USA). Data processing was kept at a minimum including a baseline correction (automatic weighted least squares), taking the decadic logarithm, and auto scaling as prerequisite for PLSR. Eight latent variables (LVs) were selected, which contain approx. 88% variance within the calibration data set. The number of LVs is based on the cumulative variance captured by the model in order to achieve a maximum predictability without taking artefacts and noise into account. This validation was carried out via a random data split of 41 samples out of the dataset (calibration set has 162 samples). 21 For the calibration set, an experimental design algorithm was applied via the mixexp soware package for R statistics, i.e., a x-vertices design. 23

Results and discussion
Diamond lm growth For this study, a set of diamond lms were grown, which was further characterised in detail by SIMS, AFM, IR and Raman spectroscopy. Growth parameters were optimized for the used substrates in terms of growth temperature, sp 2 -content and lm uniformity. For an IR transparent electrode, the diamond lm should show good conductivity and low absorption in the spectral window of interest. Thus, the calibration set was chosen in a range of 5 Â 10 20 to 3 Â 10 21 atoms per cm 3 (2800-17 000 ppm) for the boron concentration with a targeted lm thickness of 50-600 nm. In order to study the inuence of the underlying substrate on the chemometric model, diamond lms were also grown on 4 conductive silicon wafers (0.01-0.02 U cm). Due to the short growth times, the synthesis of thin diamond layers is challenging. Depending on the reactor type and growth parameters, constant conditions are not reached until the end of the process. This is clearly visible in the average growth rate obtained aer different growth times (Fig. 1a). For the used reactor, the rate increases in a linear manner within the rst 6 h of growth. However, signicant variations occur (R 2 ¼ 0.69), which make a fast and reliable characterisation mandatory. In our case, when using 4 00 wafers, constant growth rates are not obtained before a thickness of 2 mm, which corresponds to a growth time of approx. 24 h. Using a limited growth model, this can be tted and enables reproducible growth of diamond lms with a thickness above 1 mm with an error margin of less than 2% (Fig. S2 †). Interestingly, in our experiments the amount of the dopant gas (TMB) did not show strong inuence on the growth rate for these heavily doped diamond lms (Fig. S3 †). However, when changing conditions and dopant concentrations, this may be different. 26 The total amount of B incorporated into the diamond lattice correlates with the amount of TMB in the gas phase (Fig. 1b), but variations for the thin layers can be expected (R 2 ¼ 0.74).
All grown diamond lms used in this study and their characteristics are summarised in Table 1.

Characterisation
In order to assess the chemometric analysis for determining thickness and dopant concentration directly aer synthesis of diamond lms, the as-grown samples were used for all characterisation methods without further treatment. AFM measurements conrmed good crystallinity of the lms as well as an increasing RMS roughness with increasing thickness as expected due to the continued growth of the single crystallites ( Table 1, Fig. S1 †). IR measurements conrmed low absorbance in a wide range from 5000 to 500 cm À1 (Fig. 2).
The transmission data is homogeneous over the whole measurement range and shows a strong dependence on the thickness of the diamond lm. Plotting the absorbance of the lms at 2750 cm À1 vs. the thickness, a linear dependence can be clearly observed (Fig. S4 †), which indicates that the change in conductivity induced by the different dopant concentration is not signicant for the deposited diamond lms.
In the recorded spectra only a few bands are visible originating from the silicon substrate (611, 738, 891 cm À1 , phonon bands, 1085 cm À1 , Si-O). Samples with conductive silicon substrates (C1-C4) completely absorbed the IR light (data not shown).
Raman characterisation on the diamond lms was carried out at different locations of the samples using a laser  wavelength of 532 nm. Only negligible variations were observed for the individual spectra recorded at the different spots of the same sample. Selected spectra from Table 1 are shown in Fig. 3a.
In contrast to the IR spectra, independent from the thickness, the traces are shied to higher or lower intensity and both materials, silicon and BDD show characteristic bands. The single spectrum in Fig. 3b shows the regions of interest for the two materials. Silicon shows a sharp band at 520 cm À1 and a wide band from 920 to 1045 cm À1 , which correspond to the one-phonon peak and the two-phonon overtone, respectively. 27 The diamond single phonon line is located at 1332 cm À1 ; however, due to boron doping this line undergoes a Fano resonance, leading to a peak shi, a decrease in intensity and a broadening (D region in Fig. 3b). Apart from that, 2 wide bands at around 500 and 1200 cm À1 are observed, which can be assigned to boron-dimer vibrations and symmetry breaking of the diamond lattice. 20 Additional information on the quality of the grown diamond is obtained from the region between 1400 and 1600 cm À1 , where the G-band assigned to sp 2 -carbon impurities is observed. Depending on the thickness of the diamond lm, the signals from the underlying silicon are different in intensity, decreasing with deposited lm thickness.
For example, sample 11 with a thickness of 620 nm lacks bands from the underlying substrate. Using these spectra, the PLSR was carried out using the whole set of diamond lms. Without taking the substrate resistivity into account, it was observed that the prediction of dopant concentration reaches a root mean square error of prediction (RMSEP) of 1.74 Â 10 20 (six LVs according to variance captured). However, aer including the substrate resistivity into the model, the prediction of boron concentration can be carried out with an RMSEP of 1.46 Â 10 20 . Fig. 4 shows the predicted values from the model plotted versus the obtained results from SIMS. From the randomly selected validation set, a RMSEP for the B concentration of 1.46 Â 10 20 atoms per cm 3 and 36.57 nm for the  Table 1, 300 nm, 16.2 Â 10 20 B/cm À3 ) with highlighted regions for bands corresponding to silicon, diamond and boron-doping (note: intensity is plotted in logarithmic scale for better presentation).  thickness are obtained. Table 2 summarises the results of the PLSR. According to that, from the characteristic features in the spectrum, the B concentration for these heavily doped lms can be accurately predicted, in accordance with literature results. 28 However, for the lm thickness where no characteristic peak is present, the resulting prediction accuracy is close to the mean value of the roughness RMS (30 nm) of the diamond lm set and hence very close to the theoretical maximum.
Apart from that, taking the substrate into account, the model also predicts the resistivity with an accuracy of approx. 2 U. This can be used to determine the characteristic of the whole diamond-coated element.

Conclusions
In conclusion, we demonstrated a chemometric model, which is able to obtain boron concentration and thickness with high accuracy from Raman spectra, which reects a signicant advantage due to the short analysis times of a few seconds compared to other techniques such as SIMS. This analysis can be carried out on as-grown samples without further preparation steps. The characterisation method is non-destructive and noninvasive, leaving the diamond lm unaltered for further processing. Thus, it is ideally suited for fast and automated characterisation of as-grown lms aer diamond synthesis, which is prone to variations in the early growth stages, i.e., for thin lm growth. Additionally, substrate parameters can be included into the model to characterise a diamond-coated element as a whole. From this observation, we are condent that the described approach can be readily adapted to other materials, e.g. quartz, 12 freestanding layers, 13 or intrinsic diamond. Using Raman microscopy, also laterally resolved data on thickness and B concentration, e.g., for microstructured OTEs with thin BDD layers, can be obtained.

Conflicts of interest
There are no conicts to declare.