Performance of a four-element Si drift detector for X-ray absorption fine-structure spectroscopy: resolution, maximum count rate, and dead-time correction with incorporation into the ATHENA data analysis software

The performance of a four-element Si drift detector for energy-dispersive fluorescence-yield X-ray absorption fine-structure measurements is reported, operating at the National Institute of Standards and Technology beamline X23A2 at the National Synchrotron Light Source. The detector can acquire X-ray absorption fine-structure spectra with a throughput exceeding 4 × 10⁵ counts per second per detector element (>1.6 × 10⁶ total counts per second summed over all four channels). At this count rate the resolution at 6 keV is approximately 220 eV, which adequately resolves the Mn Kα and Kβ fluorescence lines. Accurate dead-time correction is demonstrated, and it has been incorporated into the ATHENA data analysis program. To maintain counting efficiency and high signal to background, it is suggested that the incoming count rate should not exceed ∼70% of the maximum throughput.

1. Introduction

In 1984, Gatti & Rehak described a novel charge-transport scheme in semiconductors that led to the development of the silicon drift detector (SDD) (Gatti & Rehak, 1984). It is based on the full depletion of a silicon wafer by a virtual electrode. A secondary electric field is then used to transport charge. As Gatti & Rehak explained, it is the small charge-collecting capacitance of the device that has the advantage of shorter rise times and higher gains over other charge-collecting devices. For X-ray absorption fine-structure (XAFS) spectroscopy applications, this development translates to a detector that can operate at faster count rates and higher temperatures than standard silicon or germanium lithium drifted detectors (SiLi or GeLi). In addition, the capacitance of the SDD is independent of its active area, thereby affording the production of large area detectors without the loss of resolution suffered by SiLi and GeLi detectors. For these reasons the SDD has become an attractive solution for cost effective, high-resolution and high-count-rate energy-dispersive fluorescence-yield XAFS measurements (Strüder et al., 1998; Welter et al., 2009; Letard et al., 2006), and this trend is likely to continue with the increasing flux afforded by the next-generation synchrotron sources.

In this work we demonstrate the energy resolution and high-count-rate performance of a newly commissioned commercially available four-element SDD operating at the National Institute of Standards and Technology (NIST) XAFS beamline X23A2 at the National Synchrotron Light Source (NSLS). In addition to characterizing the performance of the detector, we carefully studied and report on its dead-time and the corrections necessary to obtain accurate XAFS spectra in the high-count-rate limit. This dead-time correction has been incorporated into the ATHENA (Ravel & Newville, 2005) XAFS data analysis program that should facilitate use by the synchrotron community not only for the SDD but also for standard SiLi and GeLi detectors.

2. Experimental

The detector was procured from SII Nanotechnology¹. It is composed of four circular SDD elements, each with an active area of approximately 50 mm². The detector is Peltier cooled (thus it does not require the use of liquid nitrogen) with a cool-down time of less than 2 min. The detector was supplied by the manufacturer with electronics that include a power supply, cooling control, and four charge-sensitive pre-amplifiers (one for each element). In order to energy-discriminate the pulses from the pre-amplifiers, four Canberra 2026x spectroscopy amplifiers are utilized. The amplifiers have been modified to operate at faster shaping times, down to 0.1 µs, compared with the standard Canberra 2026 amplifiers that operate down to only 0.5 µs. Each filtered output from the shaping amplifiers is fed to its own Ortec 850 quad single-channel analyzer (SCA) for pulse-height energy discrimination. To facilitate cabling, the SCAs have been internally hard wired to receive only one amplifier input per quad unit. Pulse outputs from the SCAs as well as the incoming count rate (ICR) outputs of the Canberra amplifiers are recorded by a National Instruments PXI-1042 crate controlled by LabVIEW data acquisition software (Furenlid et al., 1997) that is in wide use at the NSLS for XAFS spectroscopy. In addition, the ICR outputs are directly monitored by four Ortec 449 rate meters. Spectra are acquired by step-scanning a motor (typically either a sample stage or the monochromator) and recording the total number of counts for each output channel of the four detector elements acquired in a specified integration time. Modification for slew scanning would be straight forward. To record the entire energy spectrum, four (one for each detector element) Canberra Multiport II multi-channel analyzers (MCAs) with Genie software are utilized. To facilitate setting the SCA windows to detect a particular energy region of interest (ROI), the MCAs are gated by the SCAs. XAFS spectra for a given element are thereby recorded by scanning the monochromator and recording the intensity of a fluorescence line so selected and normalizing to the incidence flux as determined by the current from an I₀ ion chamber upstream of the sample.

3. Results and discussion

Fig. 1 compares an MCA trace from detector element #1 of the SDD with a similar MCA trace from a Canberra single-element SiLi detector with 30 mm² active area operating at liquid-nitrogen temperature for the Mn Kα and Kβ fluorescence lines (∼6 keV) from a Mn₂O₃ sample. The shaping time of the amplifier was set at 0.1 µs for the SDD and 2 µs for the SiLi detector. Even with the shorter shaping time and larger detector area, the resolution of the SDD exceeds the resolution of the SiLi detector, and it is good enough to resolve the Mn Kα and Kβ lines. This energy resolution is therefore sufficient to collect high signal-to-background XAFS spectra in the low-energy X-ray range of a typical high-energy XAFS beamline where overlap between the fluorescence lines and the elastic and Compton scattering peaks of the incident X-ray beam pose the most challenge. The SDD therefore offers a significant improvement (by a factor of approximately ten) in count rate over the smaller area and liquid-nitrogen-cooled SiLi detector.

Figure 1 Comparison of an MCA trace for element #1 of the SDD operating at 0.1 µs shaping time with an MCA trace for the single-element SiLi detector operating at 2 µs shaping time for the Mn Kα and Kβ fluorescence lines. The curves have been scaled by a constant to make their peak height equal.

To characterize the counting efficiency of the SDD, we fabricated an aluminium wedge that was stepped in 2 mm-tall steps each with a depth of 0.25 mm. By step scanning the wedge vertically through the X-ray beam, discrete photon fluxes are produced in accordance with Beer's law with no change in beam geometry relative to the four elements of the SDD. The experimental set-up is shown in Fig. 2, along with a picture of the Al wedge. In addition to the SDD that was placed in front of a GeO₂ sample, the set-up consists of an upstream I₀₀ ion chamber used in a feedback loop to tune the monochromator, an I₀ ion chamber downstream of the wedge to record the flux incident on the sample, and an I_t ion chamber downstream of the sample to record the flux transmitted through it. The I_t chamber was used to verify the linearity of the I₀ chamber over the full 10⁶ dynamic range of the SDD. `Wedge scans' were recorded at a photon energy of 2.8 × 10⁴ eV to allow transmission of the photon beam through the Al wedge and to minimize the presence of harmonics from the NSLS and the Si(311) monochromator operating at X23A2. All ion chambers were filled with N₂ gas to further insure that the measurements were free of harmonics.

Figure 2 Experimental geometry used to measure detector intensity versus I0 (see text). Also shown is a photograph of the stepped wedge used to vary the photon intensity.

Fig. 3 shows wedge scans for element #1 of the SDD for different shaping-time settings of the Canberra 2026x amplifier. The observed count rate (OCR) output that is determined by setting an SCA window from just above the detector/amplifier noise threshold to its upper limit (approximately equal to 60 keV photon energy) is plotted versus I₀. Also plotted is the ICR output of the Canberra amplifier itself that has a factory-set shaping- or filter-time constant of 0.043 µs. Note the strong dependence of the maximum attainable count rate (or throughput) on the amplifier shaping time.² Assuming Poisson statistics and paralyzable dead-time for a solid-state detector, the OCR output from the SCA should follow the dead-time equation (Knoll, 1989),

Here ICR_t is the true incoming count rate, and τ_d is the dead-time parameter associated with the SDD element, its pre-amplifier, the Canberra shaping amplifier, and any additional dead-time effects introduced by the pulse-counting electronics. Note that the ICR output will always be less than the true ICR_t count rate owing to its own dead time. Taking the derivative of (1) with respect to ICR_t and setting it equal to zero yields the maximum attainable count rate or throughput for each detector element,

As we cannot measure ICR_t directly, we assume that it is proportional to I₀: ICR_t = PI₀. This assumption allows us to fit the OCR output versus I₀ curves of Fig. 3 using only the linear parameter P and the non-linear parameter τ_d for each shaping time,

The results of the fits are plotted in Fig. 3, and the fitted values of τ_d are given in the legend for each amplifier shaping time.³ Also plotted is a fit to the ICR output of the amplifier itself and its dead-time parameter .

Figure 3 Intensity versus I0 scans measured by scanning the stepped wedge of Fig. 2 vertically through the X-ray beam for element #1 of the SDD as a function of amplifier shaping time. Also shown are the best fits to the data points. The fitted dead-time parameters τd are given in the legend (see text).

Despite the roll-off of both the OCR and ICR outputs at high count rate, the response of the OCR and ICR outputs should be linear at low count rates given a fast enough shaping time. Fig. 4 shows OCR, ICR and ICR_t plotted versus ICR_t for our fastest shaping time of 0.1 µs. In the plot we have taken ICR_t = PI₀. Note that the detector response deviates from linearity by 1% for an incoming count rate of 1.2 × 10⁴ counts per second per detector element, and this non-linearity grows to 10% for an incoming count rate of 1.25 × 10⁵ counts per second per detector element. Consequently, although the detector is capable of energy-discriminating photons in excess of 4 × 10⁵ counts per second per detector element (OCR_m = 4.38 × 10⁵ counts per second per detector element for shaping time equal to 0.1 µs), in order to record accurate XAFS spectra it appears necessary to apply a dead-time correction for count rates as low as 1 × 10⁴ counts per second per detector element.

Figure 4 OCR, ICR and ICRt plotted versus ICRt for low incoming count rate and detector element #1 (see text) operating at 0.1 µs shaping time. Note the non-linearity of the count rate.

To correct XAFS spectra for dead-time, we follow the suggestions given by Cramer et al. (1988), Nomura (1998), Ciatto et al. (2004a,b) and Warburton (2004). As discussed, in addition to collecting the energy-discriminated fluorescence ROI for each detector element, it is also necessary to record both the OCR and ICR outputs for each detector element.

Because the entire energy spectrum of an OCR output is affected uniformly by dead-time,⁴ the dead-time-corrected ROI_corr count rate for each element may be approximated by

As emphasized by Warburton (2004), it is necessary to use the true incoming count rate ICR_t in (4) because the ICR itself also suffers from dead-time loss. This is especially true when the shaping time of the amplifier is close to the shaping or filter-response time of the ICR channel, as is the case for our SDD. Each ICR_t then is obtained by measuring as in Figs. 2 and 3 for each detector element and numerically inverting,

This inversion is evaluated point-by-point and for each detector element using an iterative algorithm, expressed here in pseudocode:

dead time, do a simple ICR/OCR} \cr&\hbox{\tt correction //}\cr& \hbox{\tt if (DeadTime} = \hbox{\tt 0)\semi}\,\,\hbox{\tt do:}\cr& \hbox{\tt CorrectedROI }{:\!\,=} \hbox{ \tt ROI * ICR / OCR}\cr& \hbox{\tt return}\cr&\hbox{\tt end if}\cr&\hbox{\tt // given a value for dead time, iteratively correct} \cr&\hbox{\tt the ICR //}\cr&\hbox{\tt Test}:\!\,= \hbox{\tt 10**8}\cr& \hbox{\tt TestICR}:\!\,= \hbox{\tt ICR}\cr& \hbox{\tt while (Test} > \hbox{\tt DeadTime)\semi}\,\,\hbox{\tt do:}\cr& \hbox{\tt TrueICR}:\!\,= \hbox{\tt ICR * exp(TestICR * DeadTime)}\cr& \hbox{\tt Test}:\!\,= \hbox{\tt (TrueICR}-\hbox{\tt TestICR) / TestICR}\cr& \hbox{\tt TestICR}:\!\,= \hbox{\tt TrueICR}\cr& \hbox{\tt end while}\cr& \hbox{\tt CorrectedROI}:\!\,= \hbox{\tt ROI * TrueICR / OCR}\cr& \hbox{\tt return}}]" src="teximages/hf5175fd6.gif" style="max-width: 100%; height: auto; width: 417px;" />

Care must be taken to normalize the measured ICR and OCR by the integration time, to terminate the loop if it fails to converge in a reasonable number of steps [as the loop will not terminate if OCR is greater than the OCR_m value defined in (2)], and not to perform the iteration if the measured ICR is zero or less (as might happen in the event of a beam dump).

This dead-time correction scheme has been incorporated into the ATHENA XAFS data analysis program (Ravel & Newville, 2005). Given a data file containing the three data channels for each detector element (ROI, OCR, and ICR) together with the total integration time and I₀ intensity as a function of photon energy, knowledge of for each detector element allows ATHENA to transparently produce corrected XAFS spectra. When is not known, inputting a value of zero for into ATHENA simplifies the correction to

i.e., it is assumed that the ICR channel does not suffer dead-time loss. For slower SiLi or GeLi detectors that require longer shaping times than the SDD, this may be an adequate approximation.

To demonstrate the dead-time correction as implemented in ATHENA, Fig. 5 shows the ATHENA dead-time dialogue window, and Fig. 6 shows Mn K-edge XAFS spectra from SrMnO₃ recorded with an ICR count rate of approximately 7 × 10⁵ counts per second per detector element at 0.1 µs shaping time. At this count rate the detector is operating close to its maximum throughput, OCR_m. Clearly, dead-time correction of both the ROI and ICR outputs is necessary. Once the total correction has been made, data from the SDD and an ion chamber (Stern & Heald, 1979) that do not suffer from dead-time loss are indistinguishable.

Figure 5 ATHENA dead-time dialogue window implemented to correct XAFS spectra for dead-time. The dialogue may be modified for an arbitrary number of channels.

Figure 6 Illustration of the ATHENA XAFS dead-time correction. Shown is the SDD spectrum from SrMnO3 uncorrected for dead-time, the SDD spectrum corrected for dead-time assuming = 0 (simple correction), and the SDD spectrum corrected for dead-time using the experimentally determined values for (full correction). The SDD spectra are compared with the spectrum acquired by an ion chamber that suffers no dead-time loss. Note that in the latter case the two spectra are indistinguishable. The inset shows an expanded view of the Mn pre-edge feature.

As a final note, although the algorithm is capable of correcting XAFS spectra at count rates approximating the maximum throughput of each detector element, as seen from Fig. 3, at the maximum throughput the collection efficiency of the detector is equal to zero; i.e., d(OCR)/d(ICR_t) = 0, and the detector is no longer able to energy-discriminate photons. The detector therefore performs not as an energy-discriminating detector but rather as a total fluorescence-yield detector through the faster amplifier ICR outputs. This situation will lead to XAFS spectra with significantly reduced signal-to-background ratios and inferior performance compared with an ion chamber (Stern & Heald, 1979). To avoid such inefficient use of the detector, we suggest that the true incoming count rate should not exceed the maximum throughput of the detector,

It can then be shown that d(OCR)/d(ICR_t) ≥ 0.44, and the detector therefore will be operating near to or better than 50% of its maximum collection efficiency. At this count rate, OCR = 0.69OCR_m, and a relatively high count rate (3 × 10⁵ counts per second per detector element or 1.2 × 10⁶ total counts per second for all four elements summed) for our SDD operating at 0.1 µs shaping time is still preserved. Note that the value of should be determined from a fit of the ICR versus I₀ data that are also limited to this maximum counting rate, because the extreme high-count-rate performance of the detector may be affected by the timing structure of the synchrotron (Walko et al., 2008). When the detector is operated at count rates exceeding 70% of its maximum throughput, then the extent of photon pile-up will depend on the details of the fill pattern, and the dead-time parameter τ_d should be determined independently for each timing structure. Fig. 7 shows a graph of the OCR and ICR outputs for detector element #1 plotted versus ICR_t along with our maximum suggested incoming count rate OCR_m.

Figure 7 OCR and ICR versus ICRt for detector element #1. Shown is our suggested maximum count rate, i.e., ICRt ≤ OCRm (see text). Note that when ICRt = OCRm, the detector is operating close to 50% of its maximum counting efficiency.

4. Conclusion

We have described the performance of a four-element SDD operating at the NIST beamline X23A2 at the NSLS. The detector is capable of acquiring accurate high signal-to-background dead-time-corrected EXAFS spectra at count rates exceeding 1.2 × 10⁶ counts per second for all four channels summed. The dead-time algorithm has been implemented into the ATHENA data analysis software that should benefit the EXAFS community.

Footnotes

¹The inclusion of company names is for completeness and does not represent an endorsement by the National Institute of Standards and Technology.

²We also tested the performance of the detector with digital XIA electronics. The maximum throughput of the detector when operating with digital electronics was within 10% of the maximum throughput when operating with analog electronics for similar energy resolution.

³P depends strongly on the experimental conditions (photon energy, detector/sample geometry, gain, length, and gas of ion chamber etc.), whereas τ_d should depend only on the amplifier shaping time. For the data plotted in Figs. 3, 4 and 7, P was equal to 4.05. Note that it should be verified that the P values are equal for the OCR and ICR channels.

⁴We verified this experimentally by placing a Mn₂O₃ sample in front of the GeO₂ sample of Fig. 2 and recording wedge scans. ROIs set to monitor the Mn Kα and Ge Kα fluorescence lines as well as the OCR output differed by only constant scale factors for each element over the entire photon intensity range.