H-Terminated Diamond Surface Band Bending Characterization by Angle-Resolved XPS

Concerning diamond-based electronic devices, the H-terminated diamond surface is one of the most used terminations as it can be obtained directly by using H2 plasma, which also is a key step for diamond growth by chemical vapour deposition (CVD). The resultant surfaces present a p-type surface conductive layer with interest in power electronic applications. However, the mechanism for this behavior is still under discussion. Upward band bending due to surface transfer doping is the most accepted model, but has not been experimentally probed as of yet. Recently, a downward band bending very near the surface due to shallow acceptors has been proposed to coexist with surface transfer doping, explaining most of the observed phenomena. In this work, a new approach to the measurement of band bending by angle-resolved X-ray photoelectron spectroscopy (ARXPS) is proposed. Based on this new interpretation, a downward band bending of 0.67 eV extended over 0.5 nm was evidenced on a (100) H-terminated diamond surface.


Introduction
Diamond exhibits very interesting bulk properties such as a wide band-gap of 5.5 eV, a high thermal conductivity >20 W/cm, and a high breakdown field of 10 MV/cm [1,2], which makes it proper for high power and high-frequency electronic applications. Unipolar electronic devices such as diodes or transistors are awakening a great interest, but its electronic performance has been demonstrated to be very sensitive to surface terminations. Up to now, H-and O-terminated surfaces are the most frequently used for diamond power devices reported in the literature [2][3][4][5][6][7][8][9][10]. H-terminated diamond (H-diamond) has been extensively used for MOSFETs and Schottky barrier diodes. For the latter, H-diamond based diodes have been demonstrated to have lower Schottky barrier height values in comparison to that of O-diamond based Schottky diodes. Concerning MOSFETs, most of the results are obtained on H-diamond, where the device works normally in the on-state due to the surface conductive layer (SCL). The off-state can be reached by depleting the carriers by field effect. The reasons for such phenomena are that terminations affect the diamond surface band bending.
In order to obtain H-diamond, H 2 plasma is the most frequently used treatment as it forms part of the diamond CVD growth process. Thus, (100)-H-diamond surfaces present a (2 × 1) reconstruction

Materials and Methods
For this experiment, a 3 × 3 mm 2 diamond (100)-oriented type IIa substrate from the NDT company (Saint Petersburg, Russia) was used. Diamond suppliers commonly apply a polishing step that results in a surface roughness too high to be considered for this experiment. In order to get a flatter and more homogeneous surface, as received substrates were submitted to an extra polishing step. Surface morphology was evaluated by atomic force microscopy before and after this polishing process in an AFM-VEECO-NSIV system (VEECO, New York, NY, USA) working in tapping mode. Several measurements were carried out in a central region of the sample by using a 5 × 5 µm window each time. Gwyddion software has been used for data analysis [29]. From the combined analysis of all recorded measurements, surface roughness parameters R q = 0.2 nm and R a = 0.13 nm were deduced, where R q is the root mean square and R a is the arithmetical mean deviation. The surface was analogously again evaluated after H 2 plasma, showing a final R q = 0.1 nm and R a = 0.09 nm.
The cleaning process was as follows. First, it was immersed in a hot acid mixture of HClO 4 :HSO 4 :HNO 3 (1:3:4) for 2 h. The temperature of the heating platform was adjusted to 450 • C. Then, it was consecutively submitted to an acetone, ethanol, and isopropanol ultrasound bath for 5 min each. Finally, the substrate was dried by Ar gas flow and stored in room conditions. H 2 plasma was performed in a NIRIM type reactor using a microwave power of 260 W, at a pressure of 30 Torr, a gas H 2 flow of 200 sccm, and a temperature of~800 • C for 2 h.
ARXPS spectra were carried out in a Kratos Axis Ultra DLD spectrometer (Kratos analytical, Manchester, UK) at ultra high vaccum and room temperature with an Al-kα radiation source (1486.6 eV) with an accuracy of 0.1 eV and an energy pass of 20 eV. Spectra were recorded for electron polar angles of θ = 0 • , 45 • , 70 • , and 80 • with respect to the surface normal so that the higher the polar angle, the more surface sensitive the measurement is, since the depth from which the electron can escape is reduced by cosθ ( Figure 1). In this system, the stage needs to be tilted in order to achieve the required polar angle. The angle between the X-ray beam and the detection column remains constant. A charge neutralizer based on a flood gun of low-energy electrons was used in order to avoid charge effects.
Surfaces 2020, 3 FOR PEER REVIEW 3 where Rq is the root mean square and Ra is the arithmetical mean deviation. The surface was analogously again evaluated after H2 plasma, showing a final Rq = 0.1 nm and Ra = 0.09 nm. The cleaning process was as follows. First, it was immersed in a hot acid mixture of HClO4:HSO4:HNO3 (1:3:4) for 2 h. The temperature of the heating platform was adjusted to 450 °C. Then, it was consecutively submitted to an acetone, ethanol, and isopropanol ultrasound bath for 5 min each. Finally, the substrate was dried by Ar gas flow and stored in room conditions. H2 plasma was performed in a NIRIM type reactor using a microwave power of 260 W, at a pressure of 30 Torr, a gas H2 flow of 200 sccm, and a temperature of ~800 °C for 2 h.
ARXPS spectra were carried out in a Kratos Axis Ultra DLD spectrometer (Kratos analytical, Manchester, UK) at ultra high vaccum and room temperature with an Al-kα radiation source (1486.6 eV) with an accuracy of 0.1 eV and an energy pass of 20 eV. Spectra were recorded for electron polar angles of θ = 0°, 45°, 70°, and 80° with respect to the surface normal so that the higher the polar angle, the more surface sensitive the measurement is, since the depth from which the electron can escape is reduced by cosθ ( Figure 1). In this system, the stage needs to be tilted in order to achieve the required polar angle. The angle between the X-ray beam and the detection column remains constant. A charge neutralizer based on a flood gun of low-energy electrons was used in order to avoid charge effects. The angle between the X-ray beam and the detection column is constant. Polar angle θ is the angle between the sample normal and detector column and is selected by tilting the sample stage. An electron that can escape from the sample by traveling a distance λ in the detector column direction can come from the same depth λ as the maximum for θ = 0°. For different θ values, the same electron will escape from a reduced maximum depth equal to λcosθ. The region from which electrons can escape by travelling a distance λ to the detection column is dark shaded.
The background was subtracted using the Tougaard model [30]. Peak deconvolution was carried out in MATLAB R2018b software (The MathWorks, Inc., Natick, MA, USA). The angle between the X-ray beam and the detection column is constant. Polar angle θ is the angle between the sample normal and detector column and is selected by tilting the sample stage. An electron that can escape from the sample by traveling a distance λ in the detector column direction can come from the same depth λ as the maximum for θ = 0 • . For different θ values, the same electron will escape from a reduced maximum depth equal to λcosθ. The region from which electrons can escape by travelling a distance λ to the detection column is dark shaded.
The background was subtracted using the Tougaard model [30]. Peak deconvolution was carried out in MATLAB R2018b software (The MathWorks, Inc., Natick, MA, USA).

Shape Generation of a Band Bending XPS Contribution
XPS spectra represent the intensity in electron counts corresponding to each energy level. To describe the XPS contribution of electrons escaping from a fixed energy level, the Voigt distribution is commonly used. It is defined as the convolution of a mixed Gaussian-Lorentzian distribution where the Lorentzian component is related to the lifetime broadening of electrons [31]. However, when a band bending exists and hence all energy-levels bend accordingly, the contribution should be different than a Voigt distribution. In this section, a theoretical approach was obtained for the distribution of a band bending contribution in XPS. The result was applied to the H-diamond C 1s ARXPS spectra in Section 3.2.
To start, the intensity of a certain XPS contribution is commonly described theoretically as: Surfaces 2020, 3 FOR PEER REVIEW 4

Shape Generation of a Band Bending XPS Contribution
XPS spectra represent the intensity in electron counts corresponding to each energy level. To describe the XPS contribution of electrons escaping from a fixed energy level, the Voigt distribution is commonly used. It is defined as the convolution of a mixed Gaussian-Lorentzian distribution where the Lorentzian component is related to the lifetime broadening of electrons [31]. However, when a band bending exists and hence all energy-levels bend accordingly, the contribution should be different than a Voigt distribution. In this section, a theoretical approach was obtained for the distribution of a band bending contribution in XPS. The result was applied to the H-diamond C 1s ARXPS spectra in Section 3.2.
To start, the intensity of a certain XPS contribution is commonly described theoretically as: where T is the analyzer transmission; is the density of atoms per volume unity; σ is the photoionization cross-section; z is the depth measured from surface; λ is the attenuation length or inelastic mean free path; θ is the polar angle with respect to the surface normal; and K is a constant representing other factors that are supposed to remain constant during the experiment as the photon flux. The exponential term P(z) inside the integral is the Beer-Lambert law, describing the inelastic electron escape probability. In the case of a homogeneous material composed by a single type of element as diamond, Equation (1) can be simplified since T, , σ, and λ can be considered as constants for the C 1s core-level: Since λ can be considered constant for the same material, the intensity ratio NI(z) is only dependent on respective z ranges and XPS polar angle θ.
On the other hand, the band bending curvature along the z-axis, V(z), is described by a solution of Poisson's Equation: is the vacuum permittivity; and is the relative permittivity of diamond. A simple solution of this equation, known as the Schottky approximation, is possible when band bending maximum potential, Vbb, significantly exceeds kT (kT = 0.0259 eV at 300 K). Then, the z-dependence of the space charge density ρ can be approximated by a step function. Assuming that a negative charge is homogeneously distributed in the range of z∈[0, d] with a charge density , the Poisson's equation becomes: By integrating twice, V(z) is obtained as: where T is the analyzer transmission; N 1 is the density of atoms per volume unity; σ is the photoionization cross-section; z is the depth measured from surface; λ is the attenuation length or inelastic mean free path; θ is the polar angle with respect to the surface normal; and K is a constant representing other factors that are supposed to remain constant during the experiment as the photon flux. The exponential term P(z) inside the integral is the Beer-Lambert law, describing the inelastic electron escape probability. In the case of a homogeneous material composed by a single type of element as diamond, Equation (1) can be simplified since T, N 1 , σ, and λ can be considered as constants for the C 1s core-level: If two contributions are considered, one is related to the band bending region (I 1 ), for z ∈ [0, d], and the other is related to the bulk region (I 2 ), for z ∈ [d, ∞), then the intensity ratio is calculated as: Since λ can be considered constant for the same material, the intensity ratio NI(z) is only dependent on respective z ranges and XPS polar angle θ.
On the other hand, the band bending curvature along the z-axis, V(z), is described by a solution of Poisson's Equation: where ρ(z) is the charge density distribution; 0 is the vacuum permittivity; and is the relative permittivity of diamond. A simple solution of this equation, known as the Schottky approximation, is possible when band bending maximum potential, V bb , significantly exceeds kT (kT = 0.0259 eV at 300 K). Then, the z-dependence of the space charge density ρ can be approximated by a step function.
Assuming that a negative charge is homogeneously distributed in the range of z ∈ [0, d] with a charge density N, the Poisson's equation becomes: By integrating twice, V(z) is obtained as: where V 0 is the bulk potential for z ≥ d. This equation can be written in terms of maximum potential V bb by obtaining the N value from the V(0) expression, then: It must be noted that this simplification is required as a first approximation due to the absence of scientific evidence about the charge distribution in SCL. Now, P(z) and V(z) expressions can be put together, describing a curve of parametric equations: The projection of this curve on the P-V plane can be obtained by substitution: This new curve represents the dependence of the electron escape probability on its potential. Finally, the shape of a band bending contribution in XPS can be understood as the convolution of a Voigt distribution over the probability of escape P(V) in Equation (4). For this purpose, the discrete convolution is used and the numerical approximation was carried out in MATLAB R2018b. The higher the number of points of discrete signals, the better the band bending shape can be approximated. In this approximation, the presence of band bending generates an asymmetric XPS peak with a higher intensity toward the band bending direction that becomes more remarkable for higher V bb values. A representation of all the curves required for the generation of a band bending XPS contribution is shown in Figure 2.

Surface Band Bending Estimation
The measured (100) H-diamond ARXPS C 1s spectra for θ = 0 • , 45 • , 70 • , and 80 • are shown in Figure 3. By using λ, it is possible to calculate the escape probability P(z) curve for selected polar angles θ = 0 • , 45 • , 70 • , and 80 • (see Equation (1)) and, thus, the sensitivity depth can be estimated. Since P(z) follows an exponential decay with depth z, the sensitivity depth can be represented by the z value for P(z) < 99%, that is 11.05, 7.81, 3.78, and 1.91 nm for θ = 0 • , 45 • , 70 • , and 80 • , respectively. However, it must be noticed that most of the signal is due to quite lower z values. Thus, the z value for P(z) < 50% can be attributed to 1.66, 1.17, 0.56, and 0.28 nm for θ = 0 • , 45 • , 70 • and 80 • , respectively. The position of the diamond bulk contribution is expected to be at the maximum peak of the C 1s spectrum at θ = 0 • , since in that case, most of the signal should come from the fixed bulk C 1s level. Thus, the diamond C 1s bulk contribution was found at 284.05 eV, which is very similar to previous results [28]. On the other hand, C 1s spectrum at θ = 0 • appeared asymmetric with a tail toward a higher B.E. As θ increases, it is clear that this tail becomes a higher contribution with increasing intensity with respect to the bulk contribution. This indicates the surface nature of this second contribution. The position of the maximum C 1s peak moves toward a higher B.E. very slightly for increasing θ values. Very similar behavior has previously been observed by S. Kono et al. [18]. (4) This new curve represents the dependence of the electron escape probability on its potential. Finally, the shape of a band bending contribution in XPS can be understood as the convolution of a Voigt distribution over the probability of escape P(V) in Equation (4). For this purpose, the discrete convolution is used and the numerical approximation was carried out in MATLAB R2018b. The higher the number of points of discrete signals, the better the band bending shape can be approximated. In this approximation, the presence of band bending generates an asymmetric XPS peak with a higher intensity toward the band bending direction that becomes more remarkable for higher Vbb values. A representation of all the curves required for the generation of a band bending XPS contribution is shown in Figure 2.  (1)) for λ = 2.4 nm and θ = 0°, 45°, 70°, and 80°. Equation (3) is the potential curvature obtained from the Poisson's equation solution based on the Schottky approximation for V0 = 0, band bending maximum potential Vbb, and band bending width d. Equation (4) is obtained by substitution of z in Equation (3) into P(z). It must be noticed that, in the XPS spectrum, a downward band bending is seen toward higher binding energy (B.E.).

Surface Band Bending Estimation
The measured (100) H-diamond ARXPS C 1s spectra for θ = 0°, 45°, 70°, and 80° are shown in Figure 3. By using λ, it is possible to calculate the escape probability P(z) curve for selected polar  (3) into P(z). It must be noticed that, in the XPS spectrum, a downward band bending is seen toward higher binding energy (B.E.).
Since P(z) follows an exponential decay with depth z, the sensitivity depth can be represented by the z value for P(z) < 99%, that is 11.05, 7.81, 3.78, and 1.91 nm for θ = 0°, 45°, 70°, and 80°, respectively. However, it must be noticed that most of the signal is due to quite lower z values. Thus, the z value for P(z) < 50% can be attributed to 1.66, 1.17, 0.56, and 0.28 nm for θ = 0°, 45°, 70° and 80°, respectively. The position of the diamond bulk contribution is expected to be at the maximum peak of the C 1s spectrum at θ = 0°, since in that case, most of the signal should come from the fixed bulk C 1s level. Thus, the diamond C 1s bulk contribution was found at 284.05 eV, which is very similar to previous results [28]. On the other hand, C 1s spectrum at θ = 0° appeared asymmetric with a tail toward a higher B.E. As θ increases, it is clear that this tail becomes a higher contribution with increasing intensity with respect to the bulk contribution. This indicates the surface nature of this second contribution. The position of the maximum C 1s peak moves toward a higher B.E. very slightly for increasing θ values. Very similar behavior has previously been observed by S. Kono et al. [18]. As a preliminary deconvolution, the C 1s spectra were decomposed into two contributions, bulk and surface, by using Voigt distributions (not shown here). The full width at half maximum (FWHM) of the bulk contribution can be estimated in the θ = 0° spectrum since it is the dominant contribution. Then, the FWHM of the surface contribution was obtained as 30% higher than that of the bulk. Finally, all spectra were decomposed by considering the estimated bulk and surface FWHM relation. After that, the surface contribution width, d, was deduced by evaluating the bulk and surface XPS peak intensities by Equation (2). The estimated value of the ~10 monolayers (1 ML = 0.089 nm for (100)-diamond) was too high to be explained only by surface C-H. In this sense, the (100) H-diamond ARXPS C 1s spectra in [18] were very similar to that of Figure 3. The reproducibility of this peak, even for different methodologies, raises doubt about the attribution to surface contamination or defects. Additionally, in conventional XPS experiments on diamond, a tail toward higher B.E. has been routinely attributed to C-H, which somehow supports the idea about the high reproducibility and energy position of this contribution with respect to the diamond bulk contribution in As a preliminary deconvolution, the C 1s spectra were decomposed into two contributions, bulk and surface, by using Voigt distributions (not shown here). The full width at half maximum (FWHM) of the bulk contribution can be estimated in the θ = 0 • spectrum since it is the dominant contribution. Then, the FWHM of the surface contribution was obtained as 30% higher than that of the bulk. Finally, all spectra were decomposed by considering the estimated bulk and surface FWHM relation. After that, the surface contribution width, d, was deduced by evaluating the bulk and surface XPS peak intensities by Equation (2). The estimated value of the~10 monolayers (1 ML = 0.089 nm for (100)-diamond) was too high to be explained only by surface C-H. In this sense, the (100) H-diamond ARXPS C 1s spectra in [18] were very similar to that of Figure 3. The reproducibility of this peak, even for different methodologies, raises doubt about the attribution to surface contamination or defects. Additionally, in conventional XPS experiments on diamond, a tail toward higher B.E. has been routinely attributed to C-H, which somehow supports the idea about the high reproducibility and energy position of this contribution with respect to the diamond bulk contribution in H-terminated (100)-oriented diamond. On the other hand, surface contribution shifted toward higher B.E. with respect to bulk contribution with increasing θ, which makes no sense for contributions with fixed energy levels such as defects.
The presence of a downward band bending XPS contribution as described in Section 3.1. explains the observed spectra. First, because in this case, the intensity of the contribution will depend on the band bending width, explaining this~10 mL, and second, because the shape of a downward band bending XPS contribution, as shown in Section 3.1., is asymmetric toward higher B.E. and thus, a shift toward higher B.E. as θ increases is expected. Thus, it explains the observed shift of surface contribution as well as the shift of maximum of C 1s spectra.
Assuming the existence of a downward band bending contribution, the recorded spectra was decomposed based on a model consisting of a diamond bulk region (Peak bulk ), a diamond with a downward band bending region (Peak bb ), and 1 ML of C-H (Peak CH ) XPS contribution (Figure 4). The intensity ratios of the three peaks are obtained as in Equation (2). The position of the C-H x contributions has been widely reported to be at~+0.5 eV from the bulk contribution, however, the existence of a band bending near the surface makes the C-H x contribution relative to V bb . Thus, the C-H position was set to +0.5 ± 0.15 eV from V bb . The shapes of both Peak bulk and Peak CH are Voigt distributions determined by its corresponding Lorentzian and Gaussian width wL = 0.2 and wG = 0.6, respectively, and its intensity. The value of 0.2 of wL has been reported previously for a graphite sample [32] and is expected to be similar in this case. For wG, the value was estimated from the θ = 0 • spectrum as used in the preliminary deconvolution. The shape of Peak bb is generated as described in Section 3.1 with the same wL and wG.
Surfaces 2020, 3 FOR PEER REVIEW 7 Assuming the existence of a downward band bending contribution, the recorded spectra was decomposed based on a model consisting of a diamond bulk region (Peakbulk), a diamond with a downward band bending region (Peakbb), and 1 ML of C-H (PeakCH) XPS contribution (Figure 4). The intensity ratios of the three peaks are obtained as in Equation (2). The position of the C-Hx contributions has been widely reported to be at ~+0.5 eV from the bulk contribution, however, the existence of a band bending near the surface makes the C-Hx contribution relative to Vbb. Thus, the C-H position was set to +0.5 ± 0.15 eV from Vbb. The shapes of both Peakbulk and PeakCH are Voigt distributions determined by its corresponding Lorentzian and Gaussian width wL = 0.2 and wG = 0.6, respectively, and its intensity. The value of 0.2 of wL has been reported previously for a graphite sample [32] and is expected to be similar in this case. For wG, the value was estimated from the θ = 0° spectrum as used in the preliminary deconvolution. The shape of Peakbb is generated as described in Section 3.1 with the same wL and wG. and diamond surface C-Hx (DiamondCH) for zϵ [0, 1 ML]. The area ratio of XPS peaks (Peakbulk, Peakbb and PeakCH) is obtained as in Equation (2). Diamondbulk and DiamondCH XPS contributions follow Voigt distributions while the Diamondbb distribution is obtained from a convolution (see Section 3) and is defined by its band bending width, d, and maximum potential, Vbb. The peak C-H position (CHpos) is defined relative to Vbb and was set to +0.5 ± 0.15 eV.
The photoelectron refraction effect was also taken into account, as it can be significant at higher polar angles. This effect makes the detected photoelectrons come from lower angles of escape than the angle defined here as the polar angle, reducing the depth sensitivity. An angular correction is included in the algorithm based on Equation (5) [33] where θ' is the angle inside the sample, Vi is the inner potential that has been estimated to be ~18 eV elsewhere [34], and E'k is the kinetic energy of photoelectrons inside the sample.   (2). Diamond bulk and Diamond CH XPS contributions follow Voigt distributions while the Diamond bb distribution is obtained from a convolution (see Section 3) and is defined by its band bending width, d, and maximum potential, V bb . The peak C-H position (CH pos ) is defined relative to V bb and was set to +0.5 ± 0.15 eV.
The photoelectron refraction effect was also taken into account, as it can be significant at higher polar angles. This effect makes the detected photoelectrons come from lower angles of escape than the angle defined here as the polar angle, reducing the depth sensitivity. An angular correction is included in the algorithm based on Equation (5) [33] where θ' is the angle inside the sample, V i is the inner potential that has been estimated to be~18 eV elsewhere [34], and E' k is the kinetic energy of photoelectrons inside the sample.
By varying the band bending parameters d and V bb , an optimal solution was finally found for d = 0.5 nm and V bb = 0.67 eV. CH pos was finally established at V bb + 0.37 eV. The resulting spectra deconvolution is shown in Figure 5 where the peaks were normalized to maximum. The difference between the measured and fitted curves can originate from multiple reasons such as the background subtraction method, polar angle positioning accuracy, roughness effect, or the discrepancy to the used charge distribution simplification in Equation (3).
Surfaces 2020, 3 FOR PEER REVIEW 8 0.67 eV simulated here would have been estimated to be ~0.1 eV based on the maximum C 1s spectrum shift, giving an idea of the error of estimation of band bending from the shift of the maximum peaks. This work's estimation was similar to the barrier of ~1 eV observed very close to the surface between the H-diamond 2D-hole gas channel and an aluminum deposition used as a field-effect transistor gate [35]. The charge density deduced here was N = 8.6 · 10 21 cm −3 along the first 0.5 nm, which is similar to the reported hydrogen density of 1.5·10 15 cm −2 over the first 1.5 nm depth with an exponential density decay [36].
Although H-diamond surface downward band bending origin is still under discussion, shallow acceptors with very low ionization energy due to the presence of subsurface hydrogen is up to now considered the main hypothesis. However, further experimental data is still necessary to certainly know its origin as well as explore what implications H-diamond surface band bending has when it is applied in oxide-and/or metal-diamond contacts for electronic devices. The certainty is that the combined effect of surface transfer doping and the presence of shallow acceptors very near the surface can explain most of the experimental phenomena of H-diamond surface conductive layer. Figure 5. ARXPS C 1s measured spectra (black dotted) and accumulated deconvolution (red line). The deconvoluted spectra are formed by three peaks each: Peakbulk (dashed), Peakbb (dashed-dot), and PeakCH (short-dotted) corresponding to the diamond bulk region, diamond depleted region ,and 1 ML of surface C-H, respectively. For the generation of the Peakbb, band bending width, d, and band bending maximum potential, Vbb, were found to be 0.5 nm and 0.67 eV, respectively.

Conclusions
In this work, a new method to characterize the band bending by ARXPS was proposed and used for the spectra deconvolution of a (100) H-diamond. This method considers that band bending must be seen as a new contribution whose shape is defined as the deconvolution of a Voigt distribution over an expression of the probability of the escape of electrons dependent on the potential. The latter is obtained from a solution of the Poisson's equation and the XPS intensity expression. In the case of homogeneous materials like diamond, some simplifications can be considered for the intensity expression. A simple solution of the Poisson equation has been used as a first approximation to diamond surface band bending due to the absence of experimental data in this sense. Based on this method, a downward band bending of 0.67 eV along the first 0.5 nm was estimated. This band bending can be related to shallow acceptors related to subsurface hydrogen presence. The low number of ARXPS in diamond samples makes this measurement useful as a starting point for future works that could consider band bending XPS shapes for their deconvolutions. The deconvoluted spectra are formed by three peaks each: Peak bulk (dashed), Peak bb (dashed-dot), and Peak CH (short-dotted) corresponding to the diamond bulk region, diamond depleted region, and 1 ML of surface C-H, respectively. For the generation of the Peak bb , band bending width, d, and band bending maximum potential, V bb , were found to be 0.5 nm and 0.67 eV, respectively.
The maximum of the simulated accumulated C 1s spectra for θ = 45 • , 70 • and 80 • shows a shift of +0.01, +0.04, and +0.11 eV, respectively, with respect to the θ = 0 • fitting spectrum. The V bb of the 0.67 eV simulated here would have been estimated to be~0.1 eV based on the maximum C 1s spectrum shift, giving an idea of the error of estimation of band bending from the shift of the maximum peaks. This work's estimation was similar to the barrier of~1 eV observed very close to the surface between the H-diamond 2D-hole gas channel and an aluminum deposition used as a field-effect transistor gate [35]. The charge density deduced here was N = 8.6 · 10 21 cm −3 along the first 0.5 nm, which is similar to the reported hydrogen density of 1.5·10 15 cm −2 over the first 1.5 nm depth with an exponential density decay [36].
Although H-diamond surface downward band bending origin is still under discussion, shallow acceptors with very low ionization energy due to the presence of subsurface hydrogen is up to now considered the main hypothesis. However, further experimental data is still necessary to certainly know its origin as well as explore what implications H-diamond surface band bending has when it is applied in oxide-and/or metal-diamond contacts for electronic devices. The certainty is that the combined effect of surface transfer doping and the presence of shallow acceptors very near the surface can explain most of the experimental phenomena of H-diamond surface conductive layer.

Conclusions
In this work, a new method to characterize the band bending by ARXPS was proposed and used for the spectra deconvolution of a (100) H-diamond. This method considers that band bending must be seen as a new contribution whose shape is defined as the deconvolution of a Voigt distribution over an expression of the probability of the escape of electrons dependent on the potential. The latter is obtained from a solution of the Poisson's equation and the XPS intensity expression. In the case of homogeneous materials like diamond, some simplifications can be considered for the intensity expression. A simple solution of the Poisson equation has been used as a first approximation to diamond surface band bending due to the absence of experimental data in this sense. Based on this method, a downward band bending of 0.67 eV along the first 0.5 nm was estimated. This band bending can be related to shallow acceptors related to subsurface hydrogen presence. The low number of ARXPS in diamond samples makes this measurement useful as a starting point for future works that could consider band bending XPS shapes for their deconvolutions.