research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775

X-ray position-sensitive duo-lateral diamond detectors at SOLEIL

CROSSMARK_Color_square_no_text.svg

aSynchrotron SOLEIL, Saint-Aubin, 91192 Gif-sur-Yvette, France, and bCEA-LIST, Diamond Sensors Laboratory, 91191 Gif-sur-Yvette, France
*Correspondence e-mail: kewin.desjardins@synchrotron-soleil.fr

Edited by M. Yabashi, RIKEN SPring-8 Center, Japan (Received 23 June 2017; accepted 21 November 2017; online 7 February 2018)

The performance of a diamond X-ray beam position monitor is reported. This detector consists of an ionization solid-state chamber based on a thin single-crystal chemical-vapour-deposition diamond with position-sensitive resistive electrodes in a duo-lateral configuration. The detector's linearity, homogeneity and responsivity were studied on beamlines at Synchrotron SOLEIL with various beam sizes, intensities and energies. These measurements demonstrate the large and homogeneous (absorption variation of less than 0.7% over 500 µm × 500 µm) active area of the detector, with linear responses independent of the X-ray beam spatial distribution. Due to the excellent charge collection efficiency (approaching 100%) and intensity sensitivity (0.05%), the detector allows monitoring of the incident beam flux precisely. In addition, the in-beam position resolution was compared with a theoretical analysis providing an estimation of the detector's beam position resolution capability depending on the experimental conditions (X-ray flux, energy and readout acquisition time).

1. Introduction

Currently, X-ray beam position monitors are an essential element for synchrotron beamlines that focus the beam down to a few micrometres or less, like the long beamlines using a nano-size X-ray beam for large two-dimensional scan sample mapping (Somogyi et al., 2015[Somogyi, A., Medjoubi, K., Baranton, G., Le Roux, V., Ribbens, M., Polack, F., Philippot, P. & Samama, J.-P. (2015). J. Synchrotron Rad. 22, 1118-1129.]). In order to precisely monitor the intensity and adjust the position of the X-ray beams, such beamlines need a fast X-ray diagnostic inserted permanently into the beam (with low absorption and radiation hardness). Many different kinds of in-beam transparent position monitors have been used in the past: microwire devices (Heald, 1986[Heald, S. M. (1986). Nucl. Instrum. Methods Phys. Res. A, 246, 411-412.]), gaseous detectors (Schildkamp & Pradervand, 1995[Schildkamp, W. & Pradervand, C. (1995). Rev. Sci. Instrum. 66, 1956-1959.]), indirect fluorescent or scattered X-ray detection from thin foils with PIN-diodes (Alkire et al., 2000[Alkire, R. W., Rosenbaum, G. & Evans, G. (2000). J. Synchrotron Rad. 7, 61-68.]) or pixelated detectors (Rico-Alvarez et al., 2014[Rico-Alvarez, O., Kachatkou, A., Marchal, J., Willis, B., Sawhney, K., Tartoni, N. & Van Silfhout, R. G. (2014). J. Instrum. 9, C12036.]), as well as thin solid-state devices developed on silicon (Fuchs et al., 2007[Fuchs, M. R., Holldack, K., Reichardt, G. & Mueller, U. (2007). AIP Conf. Proc. 879, 1006-1009.]) or polycrystalline diamond (Bergonzo et al., 1999[Bergonzo, P., Brambilla, A., Tromson, D., Marshall, R. D., Jany, C., Foulon, F., Gauthier, C., Solé, V. A., Rogalev, A. & Goulon, J. (1999). J. Synchrotron Rad. 6, 1-5.]). In this paper, a new type of diamond X-ray beam position monitor (XBPM) is presented: the device is based on an electronic-grade single-crystal chemical-vapour-deposition (CVD) diamond material (Morse et al., 2010[Morse, J., Solar, B. & Graafsma, H. (2010). J. Synchrotron Rad. 17, 456-464.]) processed on a duo-lateral position-sensitive detector (PSD) with diamond-like carbon (DLC) resistive coating (Pomorski et al., 2009[Pomorski, M., Ciobanu, M., Mer, C., Rebisz-Pomorska, C., Tromson, D. & Bergonzo, P. (2009). Phys. Status Solidi A, 206, 2109-2114.]). In addition to the excellent physical properties of diamond (radiation hardness, low X-ray absorption, mechanical resistance, large band gap, fast speed charge propagation, etc.), this detector also has several other advantages compared with the classical quadrant XBPM design (Desjardins et al., 2013[Desjardins, K., Duran, D., Hustache, S., Pomorski, M. & Shepard, W. (2013). J. Phys. Conf. Ser. 425, 212004.]) or the strip detector (Shu et al., 1998[Shu, D., Kuzay, T. M., Fang, Y., Barraza, J. & Cundiff, T. (1998). J. Synchrotron Rad. 5, 636-638.], Zhou et al., 2015[Zhou, T., Ding, W., Gaowei, M., De Geronimo, G., Bohon, J., Smedley, J. & Muller, E. (2015). J. Synchrotron Rad. 22, 1396-1402.]): a very large active surface (usable with X-ray beams from millimetre to sub-micrometre sizes), easier to calibrate, and a simplified fabrication process. i.e. it does not need any photolithography or precise coating processes. Furthermore, the PSD is an all-carbon device; therefore it represents a good solution for low-energy applications (Desjardins et al., 2014[Desjardins, K., Pomorski, M. & Morse, J. (2014). J. Synchrotron Rad. 21, 1217-1223.]; Gaowei et al., 2015[Gaowei, M., Smedley, J., Zhou, T., Muller, E. & Sumant, A. (2015). Proceedings of the Sixth International Particle Accelerator Conference (IPAC2015), 3-8 May 2015, Richmond, VA, USA.]). However, the possible disadvantages, with respect to the quadrant detector, come from the PSD resistive coating, which generates an additional noise source and makes it slower due to the higher RC constant. In this paper, the fabrication of a PSD diamond detector is described, the advantages are presented with experimental results, and the intensity and position monitoring performances are demonstrated.

2. PSD duo-lateral design

The PSDs were made from high-quality [100]-oriented electronic-grade single-crystal CVD diamonds from Element Six Ltd (https://www.e6.com) (freestanding windows, type IIae with ∼1 p.p.m. nitro­gen, 4.50 mm × 4.50 mm) with a thickness of 50 µm down to 20 µm supplied by ALMAX easyLab (https://www.almax-easylab.com). All plates were previously controlled by cross-polarized microscopy (Hoa et al., 2014[Hoa, L. T. M., Ouisse, T., Chaussende, D., Naamoun, M., Tallaire, A. & Achard, J. (2014). Cryst. Growth Des. 14, 5761-5766.]) to check that there are no dislocations or other structural defects in the active area frequently rendering diamond devices unstable (Muller et al., 2009[Muller, E., Smedley, J., Raghothamachar, B., Gaow, M., Keister, J., Ben-Zvi, I., Dudley, M. & Wu, Q. (2009). MRS Online Proceeding Library Archive 1203.]). The thickness was measured at SOLEIL by Fourier-transform infrared spectroscopy techniques with a Raman spectroscopy microscope on the SMIS beamline (Dumas et al., 2006[Dumas, P., Polack, F., Lagarde, B., Chubar, O., Giorgetta, J. L. & Lefrançois, S. (2006). Infrared Phys. Technol. 49, 152-160.]) in order to check the homogeneity and parallelism. Additionally, the diamond thickness measurement provides information on the X-ray beam absorption for each detector (Fig. 1[link]). After hot-acid cleaning, both sides of the plates were sputtering-coated with DLC using a simple mask with an opening window of 4 mm × 4 mm, eliminating the need for photolithography. This carbon coating constitutes a resistive layer with the impedance controlled by the deposition time, approximately 100 kΩ with a thickness of ∼200 nm. The two pairs of collecting electrodes at the extremities of both sides were made by sputtering of Ti/Au (∼200 nm) layers using a shadow mask (lateral size of 4 mm × 0.25 mm by electrode). These two electrodes pairs are mutually perpendicularly positioned and the distance between the electrodes of each pair is 3.5 mm.

[Figure 1]
Figure 1
Theoretical X-ray absorption of diamond with thicknesses of 50 µm (red curve) and 20 µm (blue curve).

The free charge carriers (electron–hole pairs) generated by the X-ray beam interaction in the diamond drift under the influence of the applied electric field created by the externally biased surface electrodes, thus generating an electric current in the external circuit (Fig. 2[link]). In the DLC resistive layer, these charges are divided between the two electrodes on both surfaces; therefore the X-ray beam position (as defined by the centre of gravity of the beam) is directly obtained from the corresponding currents and the PSD dimensions as written in equation (1)[link],

[X = {K}_{x}\,{{{I}_{x1}-{I}_{x2}}\over{{I}_{x1}+{I}_{x2}}}, \quad Y = {K}_{y}\,{{{I}_{y1}-{I}_{y2}}\over{{I}_{y1}+{I}_{y2}}}, \eqno(1)]

where x and y are coordinates of the position of the X-ray beam center, Kx and Ky are the scale factors equal to L/2 with L the distance between collecting electrodes, and I (x1,2 or y1,2) is the signal collected from the horizontal (x) and vertical (y) electrode pairs, respectively.

[Figure 2]
Figure 2
Schematic diagram of the duo-lateral PSD. Inter-electrode area, L × L, with orthogonal opposed electrode on the front and back sides. Four current-to-voltage amplifier channels with bias applied to the back side. CD, RD and Iintr are, respectively, the capacitance, the impedance and the leakage current of the single-crystal CVD diamond.

The total intensity is given by the sum of the signal collected from one of the electrode pairs (i.e. It = |Ix1 + Ix2| = |Iy1 + Iy2|) and is directly proportional to the part of the absorbed X-ray beam [assuming a total charge collection efficiency equal to 100%]. It can be estimated from equation (2)[link],

[I_{\rm{t}} = q \, {{{E}_{\rm ph}}\over{{\varepsilon}_{\rm p}}} \, A\left({E}_{\rm ph}\right)\,\Phi, \eqno(2)]

where It is the total current produced by the XBPM, q is the value of the electron charge, Eph is the incident-beam energy, [\varepsilon_{\rm{p}}] = 13.25 ± 0.5 eV is the electron–hole pair creation energy (Keister & Smedley, 2009[Keister, J. W. & Smedley, J. (2009). Nucl. Instrum. Methods Phys. Res. A, 606, 774-779.]) for X-ray absorption in diamond, A is the absorption factor depending on the energy Eph and diamond thickness, and [\Phi] is the X-ray beam flux.

3. PSD diamond results

3.1. Experimental set-up and electronics

Several PSDs (Fig. 3a[link]) were mounted on specific ceramic boards where the electrodes were connected with aluminium wedge wire bondings (Figs. 3b, 3c[link]). One of these XBPMs was mounted on the GALAXIES beamline (Céolin et al., 2013[Céolin, D., Ablett, J. M., Prieur, D., Moreno, T., Rueff, J. P., Marchenko, T., Journel, L., Guillemin, R., Pilette, B., Marin, T. & Simon, M. (2013). J. Electron Spectrosc. Relat. Phenom. B, 190, 188-192.]) and tested at an energy of 6.2 keV with a high photon flux of 1.7 × 1013 photons s−1 and a small beam spot of 30 µm × 90 µm. Two other PSDs have been installed on the METROLOGIE (Idir et al., 2006[Idir, M., Mercère, P., Moreno, T. & Delmotte, A. (2006). Synchrotron Radiat. News, 19, 18-23.]) and SIRIUS beamlines (Ciatto et al., 2016[Ciatto, G., Chu, M. H., Fontaine, P., Aubert, H., Renevier, H. & Deschanvres, J. L. (2016). Thin Solid Films, 617, 48-54.]) for spatial resolution measurements with beam energies of 7 keV and 2.6 keV, respectively, and photon fluxes down to 1010 photons s−1. Finally, a micro beam position reconstruction capability has been demonstrated with an X-ray beam focused by a zone plate (1 µm × 1 µm) on the NANOSCOPIUM beamline (Somogyi et al., 2015[Somogyi, A., Medjoubi, K., Baranton, G., Le Roux, V., Ribbens, M., Polack, F., Philippot, P. & Samama, J.-P. (2015). J. Synchrotron Rad. 22, 1118-1129.]) with a beam energy of 12 keV and a flux of 1010 photons s−1.

[Figure 3]
Figure 3
(a) XBPM PSDs. (b) Active area with DLC and two electrodes wire-bounded. (c) XBPM PSD series (50 µm down to 20 µm thickness) mounted on boards.

Each pair of PSD electrodes (X and Y) were connected to the current-to-voltage amplifier (IV-amp) LOCUM-4F (ENZ, https://www.enz-de.de). This IV-amp has four channels for measuring simultaneously the four low currents (ranging from 1 mA down to 100 pA), and it is particularly adapted for PSD use with a splitter bias, which is able to apply a voltage only to one side of the PSD (X electrodes in Fig. 2[link]), while the two other channels remain connected to the main ground (0 V) potential (Y electrodes in Fig. 2[link]). However, the front-end circuit of the LOCUM is not specified in terms of noise. Finally, the IV-amp output voltages were digitized by an analog-to-digital convertor (ADC Adlink 2005, https://www.adlinktech.com) and recorded by TANGO control applications (https://www.tango-controls.org)

3.2. Detector calibration

The PSD position calibration factors (or scale factors) were determined experimentally by translating the detector linearly in the X-ray beam, recording the four currents (Fig. 4a[link]) and plotting values of difference/sum currents versus the position (Fig. 4b[link]). The results were fit by equation (1)[link] in the central region for both directions to give the two scale factors (Kx and Ky). This experimental result assures excellent position reconstruction and compensation for fabrication defects or angle misalignment. In comparision with the classical diamond quadrant XBPM, these calibration factors are stable and do not depend on the spatial X-ray beam distribution. A comparison between the vertical calibration factors obtained for the different beam sizes (as defined by slits) with the PSD device (green curve) and quadrant detector (blue line) for the same in-beam conditions is shown in Fig. 5[link]. An additional measurement has also been performed with a focused X-ray beam (1 µm × 1 µm) on the NANOSCOPIUM beamline (Fig. 6[link]). It allows demonstration of the beam position reconstruction with very small beam over a large area (1 mm) which is not a simple task with a classical quadrant detector (Bergonzo et al., 1999[Bergonzo, P., Brambilla, A., Tromson, D., Marshall, R. D., Jany, C., Foulon, F., Gauthier, C., Solé, V. A., Rogalev, A. & Goulon, J. (1999). J. Synchrotron Rad. 6, 1-5.]).

[Figure 4]
Figure 4
(a) Measured PSD currents versus XBPM displacement through the beam in the vertical direction: vertical currents (top) and horizontal currents (bottom). (b) Measured PSD difference over the sum currents versus XBPM displacement in the vertical direction and linear fit residual.
[Figure 5]
Figure 5
Comparison between the calibration factors obtained with the quadrant XBPM (blue line) and the PSD XBPM (green line) for different X-ray beam sizes. The scale factor of the quadrant XBPM depends linearly on beam size. The scale factor of the PSD is stable.
[Figure 6]
Figure 6
The PSD reconstructed position of a linear movement over 1 mm with a 1 µm X-ray beam (flux ≃ 1010 photons s−1).

Therefore, the reconstructed position could be measured independently of the experimental conditions (energy, slit gap, focused or unfocused beam, etc.).

3.3. Flux and intensity monitoring capabilities

The total charge collection efficiency was verified on the METROLOGIE beamline by measuring the X-ray beam-induced current (XBIC) as a function of the bias voltage, as shown in Fig. 7[link]. Like the other diamond XBPMs made with electronic-grade single-crystal CVD (Desjardins et al., 2013[Desjardins, K., Duran, D., Hustache, S., Pomorski, M. & Shepard, W. (2013). J. Phys. Conf. Ser. 425, 212004.]), a potential of a few Volts (>0.2 V µm−1) is enough to reach constant XBIC values. Thereby, the flux can be easily calculated as equation (2)[link].

[Figure 7]
Figure 7
Top: PSD X-ray beam-induced current (XBIC) versus detector bias. Bottom: PSD dark current versus detector bias.

The dark current depends on the PSD inter-electrode resistance (Rie), the temperature and the input voltage offsets of the operational amplifier. Its intensity is rather high with low resistance but significantly lower (<1 nA) with Rie > 100 kΩ. However, the stable dark currents do not influence the position measurement precision, due to the easily applicable corrections. On the other hand, at low X-ray fluxes, the photocurrent reaches offset levels, thereby defining a reasonable usability limit for this detector. Furthermore, these dark currents may be subtracted from each current for efficient estimation of the incident X-ray photon flux.

The XBPM intensity monitoring capability has been evaluated on the GALAXIES beamline, and the obtained sensitivity is illustrated in Fig. 8[link] with a low XBIC fluctuation. The perfect visualization of the top-up filling mode of the storage ring at SOLEIL (with 0.5% electron re-injection every few minutes) can be seen, which is in excellent agreement with silicon diode measurements (error <0.05%).

[Figure 8]
Figure 8
Time scan showing the top-up mode of operation of the SOLEIL storage ring with a re-injection at t = 30 s. XBPM PSD diamond (blue) and the corresponding downstream Si photodiode (red) current signals.

The homogeneity is determined on the METROLOGIE beamline (flux ≃ 1010 photons s−1) from a two-dimensional scan which is plotted in Fig. 9[link] with an observed signal variation below 0.7% over 500 µm × 500 µm of active area. This is clearly attributable to the thickness non-uniformity of the diamond plate corresponding here to a peak-to-peak thickness difference of 300 nm at an X-ray energy of 7 keV.

[Figure 9]
Figure 9
Total current, It, map made over the central area (500 µm × 500 µm) of the PSD (X-ray energy of 7 keV and flux ≃ 1010 photons s−1).

Hence, the intensity and flux can be easily measured independently of the X-ray beam characteristics (energy, spatial distribution, focused or unfocused beam, etc.).

3.4. Beam position monitoring capabilities

A first and simple demonstration of the PSD position measurement capability consisted of the reconstruction of the position for small PSD displacements with a high beam flux (>1013 photons s−1) on the GALAXIES beamline (Fig. 10[link]). Beam displacements of 5 µm, 1 µm, 500 nm and 100 nm could be reconstructed under these conditions (ADC integration time of 100 ms, LOCUM-4F bandwidth = 2.5 kHz, total XBIC = 140 µA) with a standard deviation of 50 nm r.m.s. (when the beam is assumed to be stable).

[Figure 10]
Figure 10
Diamond PSD reconstructed position for very small displacements: 5 µm, 1 µm, 0.5 µm and 0.1 µm (X-ray energy of 6.2 keV and flux ≃ 1013 photons s−1).

To understand the noise contributions associated with a beam position measurement, a model is proposed where the instrumental noise is distinguished from the photonic noise and X-ray beam noise. Also, this model is compared with the measurement from a large range of X-ray beam currents.

In equation (1)[link], the position P on an axis (X or Y) is defined by the ratio of the difference over the sum of currents. In equation (3)[link], we denote D for the differential current (I1 − I2) and C for the common-mode current (I1 + I2) crossing the detector; the scale factor is now denoted K,

[P = K \, {D \over C}.\eqno(3)]

In the following text, μ refers to a mean and σ to a standard deviation. For instance, the position P has a mean, [{\mu_{\rm p}}], and a variance, [\sigma_{\rm p}^2], given in equation (4)[link]. The latter derives from the variance of the ratio D/C (Seltman, 2017[Seltman, H. (2017). Approximations for Mean and Variance of a Ratio. Department of Statistics at Carnegie Mellon University, USA.]). It is further shown that the covariance, [\sigma_{\rm dc}^2], is small,

[\sigma_{\rm p}^2 = {{\mu_{\rm d}^2} \over {\mu_{\rm c}^2}} \left[\,{{{\sigma _{\rm d}^2} \over {\mu_{\rm d}^2}} + {{\sigma_{\rm c}^2} \over {\mu_{\rm c}^2}} - 2{{\sigma_{\rm dc}^2} \over {{\mu_{\rm d}}{\mu_{\rm c}}}}}\,\right]. \eqno(4)]

[\sigma_{\rm d}^2] and [\sigma_{\rm c}^2] are, respectively, the difference and the sum noises and are given in equations (7)[link] and (9)[link]; [\sigma_{\rm dc}^2] is the covariance between D and C.

Also, each PSD current has a noise, which is the sum of the correlated and independent noise, and is written as

[\sigma_{I1}^2 = \sigma_{0I1}^2 + \sigma_{\rm co}^2 + \sigma_{\rm ac}^2, \quad \sigma_{I2}^2 = \sigma_{0I2}^2 + \sigma_{\rm co}^2 + \sigma_{\rm ac}^2,\eqno(5)]

where the different types of noise are described in Table 1[link].

Table 1
Sources of noise for each PSD current and their correlation

Independent noise [\sigma_{0I1}^2], [\sigma_{0I2}^2] are composed of the low amplifier self-noise, [\sigma_{\rm amp}^2], and the ADC noise, [\sigma _{\rm adc}^2].
Correlated noise [\sigma_{\rm co}^2] results from the X-ray beam flux noise (unmodelled), the eddy currents (unmodelled) and the shot noise [\sigma_{\rm id}^2] and [\sigma_{\rm ic}^2] of the difference and sum currents, respectively.
Anti-correlated noise [\sigma_{\rm ac}^2] is a combination of the unmodelled noise from the X-ray beam vibration ([\sigma_{\rm bv}^2]) and the dominant noise ([\sigma_{{\rm{i}}R{\rm{ie}}}^2]) caused by the resistive (Rie) coupling of the IV-amp's inputs. This noise has not been analyzed here (Van Esch et al., 2004[Van Esch, P., Gahl, T. & Guérard, B. (2004). Nucl. Instrum. Methods Phys. Res. A, 526, 493-500.]).

In practice, each electronic channel is similar ([\sigma_{0I1}^2] = [\sigma_{0I2}^2] = [\sigma_0^2]) and the associated electronic noise is very low (<1 pA Hz−1/2) compared with the other noise sources, which implies that the covariance [(\sigma_{\rm dc}^2] = [\sigma_{0I1}^2 - \sigma _{0I2}^2]) is negligible. Furthermore, if the beam is centred ([{{{{\mu}}_{\rm{p}}}=0}]), the term [{\sigma}_{\rm{c}}^2] in equation (4)[link] vanishes, and the expression of the position noise reduces to equation (6)[link],

[{\sigma}_{\rm p} = K\,{{{\sigma }_{\rm d}}\over{{\mu}_{\rm c}}}. \eqno(6)]

Hence, the centred position noise is proportional to the differential noise, and inversely proportional to the detector current. The differential noise, [{{\sigma}}_{\rm{d}}^2], is modelled according to equation (7)[link],

[{\sigma}_{\rm d}^{2} = \left[{\sigma }_{\rm id}^{2}+4{\sigma}_{\rm ac}^{2}\right] \,H1(\,f\,)^{2}+{\sigma}_{\rm adc}^{2}, \eqno(7)]

where [\sigma_{\rm id}^2] is the current noise, [\sigma_{\rm ac}^2] is the anti-correlated noise (Table 1[link]), [{\sigma}_{\rm adc}^{2}] = 11 fA Hz−1/2 is the ADC quantization noise, which appears to be partially correlated, likely due to some clock jitter, and H1( f ) is the module of the trans-impedance amplifier frequency response [equation (8)[link]],

[H1\left(\,f\,\right) = {\Big\{\left[1+ {\left(\,f/F1\right)}^{2}\right]\left[1+ {\left(\,f/F2\right)}^{2}\right]\Big\}}^{-1/2}.\eqno(8)]

As we wanted to consider the sum noise [(\sigma_{\rm c}^2]) in this study, we give it in equation (9)[link],

[{\sigma}_{\rm c}^{2} = \left[{\sigma}_{\rm ic}^{2}\right]\, {H1(\,f\,)}^{2} + 2{\sigma}_{\rm adc}^{2}. \eqno(9)]

The shot noise (Spear, 2005[Spear, J. D. (2005). Rev. Sci. Instrum. 76, 076101.]) difference, [{\rm{\sigma}}_{{\rm{id}}}^2], and sum, [{\rm{\sigma }}_{{\rm{ic}}}^2], remain to be defined in equations (10)[link] and (11)[link] to complete this noise model,

[{\sigma}_{\rm id}^{2} = 2q{\mu}_{\rm d} \left({\rm{FF}}+{E}_{\rm ph}/{\varepsilon}_{\rm p}\right), \eqno(10)]

[{\sigma}_{\rm{ic}}^{2} = 2q{\mu}_{\rm c} \left({\rm{FF}}+{E}_{\rm ph}/{\varepsilon}_{\rm p}\right), \eqno(11)]

where q is the value of the electron charge, Eph is the energy of the incident beam, [{\varepsilon_{\rm p}}] = 13.25 ± 0.5 eV is the electron–hole pair creation energy for X-ray absorption in diamond, and FF = 0.08 is the Fano factor of diamond.

This established model was compared with a series of noise density measurements performed on the METROLOGIE beamline. A diamond PSD was irradiated with different X-ray fluxes (108 photons s−1 to 1011 photons s−1) by insertion of various metallic absorbers into the beam. The ADC sampling frequency was 200 kHz with an integration time of 1 s which allows the acquisition of 200000 samples per measurement. The LOCUM current range (Irange) was adapted to the XBIC level. At every flux level, varying the corresponding total PSD current between 4 nA and 130 nA, 20 spectra corresponding to the fast Fourier transfer of the ADC data were successively acquired. Table 2[link] summarizes the detector characteristics, the experimental conditions and the parameters of the noise model used.

Table 2
Detector characteristics, beamline experimental conditions, acquisition characteristics and the parameters of the noise model used

PSD Diamond thickness 26 µm, Rie(X) = 25 kΩ and Rie(Y) = 45 kΩ
X-ray beam METROLOGIE beamline (bending magnet), 108 photons s−1 to 1010 photons s−1 and Eph = 7 keV
IV-amp LOCUM-4F with Irange = 100 nA [i.e. RF = 100 MΩ, output = 1 V nA−1 and BP(3dB) = 360 Hz]
IV-amp filter parameters [equation (8)[link]] F1 = 230 Hz and F2 = 2800 Hz
ADC ADC Adlink 2005 with sampling frequency Fs = 200 kHz (FNyq = 100 kHz), 16 bit with noise of2 bit (dynamic 14 bit)
ADC noise [{\sigma}_{\rm adc} = {I}_{\rm Range}/\left[{2}^{14}({12 {F}_{\rm Nyq}})^{1/2}\right]] = 10 fA Hz−1/2
Anti-correlated noise model fitted [{\sigma}_{\rm ac}] = 1.8 pA Hz−1/2 + (10 pA Hz−1/2/f−1/2).

Figs. 11(a) and 11(b)[link] give examples of two acquired spectra for a total photocurrent of μc = 88.1 nA for the sum and difference, respectively, in comparison with the models given by equations (7)[link] and (9)[link].

[Figure 11]
Figure 11
(a) Measured and model of the sum of the current density spectrum. (b) Measured and model of the difference of the current density spectrum. The blue lines are the measurement, the red lines are the models of [\sigma_{\rm c}^2] and [\sigma_{\rm d}^2]. The green dashed line is [\sigma_{\rm adc}^2] and the magenta dashed line is the shot noise, [\sigma_{\rm ic}^2] and [\sigma_{\rm id}^2]. The total current is μc = 88 nA and μd = 0.6 nA.

Excess noise appears in the sum noise (Fig. 11a[link]) as peaks (50 Hz and 70 Hz). This noise does not come from the amplifier, because its variance is proportional to the total current. This is a flux noise, which will not be converted as position noise [equation (6)[link]]. Similarly, in the difference noise (Fig. 11b[link]), the harmonic frequencies from the local electrical supply network are present. This defect comes from the amplifier. This noise will be converted as position noise.

With these observations, and knowing that the current difference shot noise ([\sigma_{\rm id}^2]) and the beam vibration noise ([\sigma_{\rm bv}^2]) are both low, the difference noise is considered constant. The position noise is then calculated from equations (6)[link] and (7)[link] and compared in Fig. 12[link] for two incident X-ray fluxes. The position noise is always the same shape, with the intensity proportional to the total current, as stated in equation (6)[link].

[Figure 12]
Figure 12
Two measured position noise density spectra compared with their models with total currents of μc = 88.1 nA (blue and red) and μc = 5 nA (green and purple).

Finally, it is possible to trace a complete diagram giving the theoretical PSD limit of the position resolution as a function of the X-ray beam-induced current (depending on the diamond thickness, the beam flux and energy used) and the acquisition bandwidth. In Fig. 13[link] we have compiled the measurement results obtained for a bandwidth of 40 Hz at the METROLOGIE and SIRUS beamlines obtained with two different PSD devices and compare it with the presented model. The corresponding result obtained at the GALAXIES beamline and presented in Fig. 10[link] is also included. All of these demonstrate excellent accordance with the theoretical model.

[Figure 13]
Figure 13
Position resolution measured versus the theoretical model for different PSD and X-ray beam fluxes. The blue, red and violet dots represent the measured PSD resolution (sum of position noise density between 10 Hz to 40 Hz) obtained on the METROLOGIE and SIRIUS beamlines, respectively, for different incident fluxes. The green dot shows a similar measurement obtained on the GALAXIES beamline corresponding to the measurement standard deviation when the beam is stable (Fig. 10[link]). The lines are the calculated theoretical limits of the reconstructed position for these PSDs, the beamline configurations and the acquisition bandwidth.

4. Conclusion

The feasibility of building a duo-lateral position-sensitive detector based on CVD diamond has been demonstrated in this paper. Its excellent capabilities of intensity and flux monitoring on the same level as the more common diamond quadrant XBPMs have been confirmed. Additionally, the various advantages of PSDs have been shown, such as their simpler position calibration, and the large active area for both large and very small beam dimensions. The PSDs are particularly adapted to beamlines where the X-ray beam spatial distribution could be modified during the experiment (i.e. during energy scans and monochromator movements) or for synchrotron beamlines which do not use a position feedback device. The principal drawbacks linked to the noise sources have been discussed and a theoretical model has been compared with measured data, which permit the optimization of the diamond PSD knowing the experimental beamline conditions (i.e. energy, incident flux and especially the beam position precision measurement needed in the sample) with a compromise between the expected generated X-ray beam current, the XBPM absorption and desired readout acquisition speed.

Finally, PSD damond XBPMs have been installed on 12 beamlines at Synchrotron SOLEIL and at two other synchrotrons (NSLSII and SSRF). Additionally, a very thin device has been made (CVD diamond of 4 µm thickness) for the SIRIUS beamline at SOLEIL for use in the tender X-ray range in order to upgrade the previously installed thin quadrant diamond detector.

Acknowledgements

We would like to thank the GALAXIES, SIRIUS, NANO­SCOPIUM and particularly the METROLOGY beamline teams for their support and beam time necessary for the characterization of the PSD XBPM.

References

First citationAlkire, R. W., Rosenbaum, G. & Evans, G. (2000). J. Synchrotron Rad. 7, 61–68.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationBergonzo, P., Brambilla, A., Tromson, D., Marshall, R. D., Jany, C., Foulon, F., Gauthier, C., Solé, V. A., Rogalev, A. & Goulon, J. (1999). J. Synchrotron Rad. 6, 1–5.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationCéolin, D., Ablett, J. M., Prieur, D., Moreno, T., Rueff, J. P., Marchenko, T., Journel, L., Guillemin, R., Pilette, B., Marin, T. & Simon, M. (2013). J. Electron Spectrosc. Relat. Phenom. B, 190, 188–192.  Google Scholar
First citationCiatto, G., Chu, M. H., Fontaine, P., Aubert, H., Renevier, H. & Deschanvres, J. L. (2016). Thin Solid Films, 617, 48–54.  Web of Science CrossRef CAS Google Scholar
First citationDesjardins, K., Duran, D., Hustache, S., Pomorski, M. & Shepard, W. (2013). J. Phys. Conf. Ser. 425, 212004.  CrossRef Google Scholar
First citationDesjardins, K., Pomorski, M. & Morse, J. (2014). J. Synchrotron Rad. 21, 1217–1223.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationDumas, P., Polack, F., Lagarde, B., Chubar, O., Giorgetta, J. L. & Lefrançois, S. (2006). Infrared Phys. Technol. 49, 152–160.  Web of Science CrossRef CAS Google Scholar
First citationFuchs, M. R., Holldack, K., Reichardt, G. & Mueller, U. (2007). AIP Conf. Proc. 879, 1006–1009.  CrossRef CAS Google Scholar
First citationHeald, S. M. (1986). Nucl. Instrum. Methods Phys. Res. A, 246, 411–412.  CrossRef Google Scholar
First citationHoa, L. T. M., Ouisse, T., Chaussende, D., Naamoun, M., Tallaire, A. & Achard, J. (2014). Cryst. Growth Des. 14, 5761–5766.  Web of Science CrossRef CAS Google Scholar
First citationIdir, M., Mercère, P., Moreno, T. & Delmotte, A. (2006). Synchrotron Radiat. News, 19, 18–23.  CrossRef Google Scholar
First citationKeister, J. W. & Smedley, J. (2009). Nucl. Instrum. Methods Phys. Res. A, 606, 774–779.  Web of Science CrossRef CAS Google Scholar
First citationGaowei, M., Smedley, J., Zhou, T., Muller, E. & Sumant, A. (2015). Proceedings of the Sixth International Particle Accelerator Conference (IPAC2015), 3–8 May 2015, Richmond, VA, USA.  Google Scholar
First citationMorse, J., Solar, B. & Graafsma, H. (2010). J. Synchrotron Rad. 17, 456–464.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationMuller, E., Smedley, J., Raghothamachar, B., Gaow, M., Keister, J., Ben-Zvi, I., Dudley, M. & Wu, Q. (2009). MRS Online Proceeding Library Archive 1203.  Google Scholar
First citationPomorski, M., Ciobanu, M., Mer, C., Rebisz-Pomorska, C., Tromson, D. & Bergonzo, P. (2009). Phys. Status Solidi A, 206, 2109–2114.  Web of Science CrossRef CAS Google Scholar
First citationRico-Alvarez, O., Kachatkou, A., Marchal, J., Willis, B., Sawhney, K., Tartoni, N. & Van Silfhout, R. G. (2014). J. Instrum. 9, C12036.  Google Scholar
First citationSchildkamp, W. & Pradervand, C. (1995). Rev. Sci. Instrum. 66, 1956–1959.  CrossRef CAS Web of Science Google Scholar
First citationSeltman, H. (2017). Approximations for Mean and Variance of a Ratio. Department of Statistics at Carnegie Mellon University, USA.  Google Scholar
First citationShu, D., Kuzay, T. M., Fang, Y., Barraza, J. & Cundiff, T. (1998). J. Synchrotron Rad. 5, 636–638.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationSomogyi, A., Medjoubi, K., Baranton, G., Le Roux, V., Ribbens, M., Polack, F., Philippot, P. & Samama, J.-P. (2015). J. Synchrotron Rad. 22, 1118–1129.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationSpear, J. D. (2005). Rev. Sci. Instrum. 76, 076101.  Web of Science CrossRef Google Scholar
First citationVan Esch, P., Gahl, T. & Guérard, B. (2004). Nucl. Instrum. Methods Phys. Res. A, 526, 493–500.  Web of Science CrossRef CAS Google Scholar
First citationZhou, T., Ding, W., Gaowei, M., De Geronimo, G., Bohon, J., Smedley, J. & Muller, E. (2015). J. Synchrotron Rad. 22, 1396–1402.  Web of Science CrossRef IUCr Journals Google Scholar

© International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Follow J. Synchrotron Rad.
Sign up for e-alerts
Follow J. Synchrotron Rad. on Twitter
Follow us on facebook
Sign up for RSS feeds