Improving the Sensitivity of Electron Beam Microanalytical Techniques by Enhanced X-ray Spectrometry: X-ray Microcalorimetry, Silicon Drift Detector Energy Dispersive X-ray Spectrometry, and Polycapillary X-ray Optics

The microcalorimeter energy dispersive x-ray spectrometer, the silicon drift detector (SDD), and polycapillary x-ray optics are recent developments that have significantly advanced analytical x-ray spectrometry for electron beam instruments. The microcalorimeter EDS is capable of high resolution operation (∼ 5 eV wide peaks) over a wide range of photon energies (250 eV ∼ 10 keV). The microcalorimeter EDS can be successfully applied to peak interference problems that are not accessible with the conventional semiconductor EDS such as TiN and BaTiO3. Polycapillary x-ray optics can augment the collection angle of the microcalorimeter EDS to increase its sensitivity. The SDD is capable of extremely high count rates, up to 1 MHz, and is especially useful for high speed x-ray mapping. [DOI: 10.1380/ejssnt.2003.130]


I. INTRODUCTION
Chemical characterization by electron-excited x-ray microanalysis frequently involves challenging problems that require determination of trace level constituents under measurement conditions that approach the limit of detection [1]. For a spectral situation in which peak interference is not an issue and only the variance in the background sets a limit on the determination of the peak intensity, the classic formula for the instrumental limit of detection, C MMF , contains two critical spectrometry terms: P, the peak counting rate (characteristic xray peak, counts/second) and P/B, the spectral peak-tobackground [2]: 3.29a [nτ P (P/B)] 0. 5 (1) In equation (1), n is the number of measurements and τ is the integration time in seconds for a single measurement. The term 'a' is the factor in the hyperbolic relation [3] between the concentration, C, and the experimentallymeasured 'k-value' (defined as k = I UNK /I ST D , where 'UNK' is the unknown, 'STD' is the standard, and I is the peak intensity for the same x-ray peak measured under the same beam and spectrometer conditions [4]): Extraordinary advances have recently been made in instrumentation for x-ray spectrometry suitable for exploitation in the electron probe microanalyzer (EPMA)/analytical scanning electron microscope (ASEM) and the analytical electron microscope (AEM). The microcalorimeter energy dispersive x-ray spectrometer, the silicon drift detector (SDD), and polycapillary FIG. 1: Spectrometer energy resolution versus photon energy for various spectrometers: (1) solid lines = Si-EDS, upper = 50 mm 2 detector and lower = 10 mm 2 optimum resolution; (2) dashed lines = WDS with various crystal diffractors; (3) open circles, open squares = WDS with various synthetic layered material diffractors; (4) x = first generation microcalorimeter EDS with Ag absorber and Al-Ag transition edge sensor; (5) + = second generation microcalorimeter EDS with Bi absorber and Cu-Mo transition edge sensor; (6) filled triangle = third generation microcalorimeter EDS with Bi absorber, thinned to limit photon energies to approximately 2.5 keV and Cu-Mo transition edge sensor; (7) boxes with internal crosses: natural peak FWHM of Kα1 peaks for various elements.
x-ray optics are recent developments that have significantly advanced analytical x-ray spectrometry for electron beam instruments. These advances directly impact the sensitivity, spectral specificity, and spatial resolution of these methods, leading to improved limits-of-detection both in the fractional concentration and in the minimum mass that can be effectively measured. These advances are particularly important for the newly emerging area of interest in low beam energy microanalysis (incident beam e-Journal of Surface Science and Nanotechnology Volume 1 (2003) FIG. 2: Microcalorimeter EDS: illustration of basic measurement principle and absorber temperature thermal history; schematic of electrothermal thermometry circuit.
To fully appreciate the new advances, it is useful to first consider the classic x-ray spectrometry methods currently in use in the EPMA, ASEM, and AEM: wavelength dispersive spectrometry (WDS) and semiconductor energy dispersive spectrometry (EDS) [1]. WDS and EDS have strengths and weaknesses that are mutually supportive, as listed in Table 1, and are often combined in analytical systems for EPMA and ASEM. The great strength of the semiconductor EDS is that it can measure the entire excited x-ray spectrum (0.1 keV to 25 keV for silicon EDS and 0.1 keV to 100 keV for germanium EDS). The weakness of semiconductor EDS is that its best peak resolution is typically 125 eV at MnK α (5890 eV), which can be compared with a natural peak width of 1.3 eV for MnK α . The resolution over a range of photon energy is plotted in Figure 1 for two sizes of semiconductor EDS: 10 mm 2 for 'optimum resolution' and 50 mm 2 to maximize the solid angle for optimum counting rate. The severe degradation of the measured characteristic x-ray peak is due to the limited counting statistics of the discrete charge carriers created by the scattering of the photoelectron emitted after photoelectric absorption of the x-ray. A broad x-ray peak inevitably degrades the P/B ratio. The maximum throughput count rate for a semiconductor EDS with a long processing time constant to optimize resolution is about 5 kHz, but this rate is necessarily distributed across the full spectrum, so that the maximum peak counting for a pure element rate is ∼3 kHz (e.g., FeK α from pure iron excited at 20 keV). WDS has much better resolution, 12 eV at MnK α with a LiF diffractor, as a result of the narrow angular response of the diffraction phenomenon. The WDS detector is the gas ionization counter, operated in the energy-proportional response mode, yielding a maximum throughput of approximately 150 kHz, which moreover is restricted by the diffraction process entirely to the narrow instantaneous energy bandpass, about half the peak width. However, the inevitable consequence of the angular response of diffraction is that WDS can only detect x-rays within the narrow energy bandpass so that the rest of the excited spectrum is lost. The simplest peak intensity measurement involves sequentially tuning the WDS to the peak position and then to background positions on either side of the peak. To view more of the spectrum, the WDS must be mechanically scanned to access different peaks. To span the entire region of analytical interest in EPMA/ASEM, 0.1 to 15 keV, requires a suite of at least five diffractors as shown in Figure 1, so that a complete WDS spectrum scan incurs a significant time penalty as well as a dose penalty, if the material under study is sensitive to radiation damage. As a result, it is not common analytical practice to perform a complete WDS qualitative analysis at every specimen location to be characterized. Naturally, the EDS is used to fulfill the qualitative analysis function in combined EDS/WDS systems.

II. INCREASING SENSITIVITY BY IMPROVING P/B: HIGH SPECTRAL RESOLUTION WITH THE MICROCALORIMETER EDS
The NIST microcalorimeter EDS operates by measuring the temperature rise of a metal target (normal conducting state) when it absorbs an x-ray photon [5]. The electro-thermal thermometry circuit, illustrated in Figure  2, is cooled externally (with liquefied N 2 and He gases and an adiabatic demagnetization refrigerator) until it reaches an equilibrium established when the input Joule heating from the internal current source is balanced by the heat losses. This operating point is sharply defined at the superconducting transition temperature of a transition edge sensor (TES, a thin film bilayer of Al-Ag or Cu-Mo) through which heat is exhausted to a low temperature reservoir. After equilibrium is established at approximately 100 mK, the absorption of an x-ray in the target of the quiescent circuit deposits extra heat in the electrothermal circuit, which responds by lowering the internal current. This changing current induces a changing magnetic field in the inductor, which is detected by the SQUID. The measure of the x-ray energy is thus the time integral of the magnetic field history. This process can respond to any x-ray energy and is thus energy dispersive in character. The resolution response over a wide photon range is shown in Figure 1. The first generation microcalorimeter EDS used an Ag absorber and Al-Ag TES which achieved a resolution of 8.9 eV at MnK α (5890 eV) [5]. The best resolution performance of the NIST microcalorimeter EDS to date has been 4.5 eV at MnK α (5890 eV) for a second-generation broad energy range spectrometer (Bi absorber, Cu-Mo TES, 250 eV∼10 keV [6]) and 2.0 eV at AlK α (1487 eV) for a thirdgeneration narrow range spectrometer (thin Bi absorber,  Cu-Mo TES, 250 eV∼2.5 keV [7]). The maximum count rate (full spectrum) is approximately 500∼1000 cps, limited by the long time constant necessary to accurately measure the pulse history to achieve high spectral resolution.
The range of problems that can be solved with the NIST microcalorimeter EDS is demonstrated in the examples presented in Figures 3∼7 [8][9][10].

A. Resolution of classic Si-EDS spectral interferences
There exist a number of technologically interesting materials for which the x-ray spectra measured with Si(EDS) contain such severe peak interferences that peak stripping, such as the multiple linear least squares method, is inadequate to separate the components, especially when the spectral quality is limited by poor counting statis- tics. Figure 3 shows an example for the optoelectronic material BaTiO 3 analyzed under conventional beam energy conditions (E 0 ≥10 keV). The interferences of TiK α and TiK β with the Ba L-family peaks are unresolved by Si-EDS, whereas the same spectral region is completely resolved with the microcalorimeter EDS. Figure 4 shows a similar problem for the compound WSi 2 , used in semiconductor manufacturing, where the Si-K family peaks suffer severe interference from the W M-family peaks in Si-EDS spectra, while the NIST microcalorimeter EDS completely resolves the major peaks.

B. Low beam energy microanalysis
Low beam energy microanalysis, where the incident beam energy E 0 ≤5 keV, is hampered by the low fluorescence yield of the low ionization energy shells, especially for L-and M-family shells compared to K-shell x-rays of similar photon energy. This situation is illustrated in Figure 5(a), where the spectrum of BaTiO 3 (where C Ba = 0.589 mass fraction; C T i = 0.205; C O = 0.206) excited with E 0 = 3 keV and measured with a conventional Si-EDS (FWHM = 129 eV at MnK α ) reveals only the prominent oxygen peak. The Ti-L family peaks are unresolved on the non-Gaussian, low energy shoulder (due to incomplete charge collection) of the O-K peak, while the Ba-M family peaks are barely detected above the continuum background (note also the lack of correspondence to the reference relative peak abundances for the Ba-M family). Under the same excitation conditions but measured with the NIST microcalorimeter EDS, Figure 5(b), the TiL α and TiL l peaks are clearly resolved (note the large difference in yield for two elements that are present at the same weight fraction), and there is sufficient resolution to observe a suite of Ba-M family members, several of which appear with much higher relative weight than the reference relative peak abundances.

C. Low photon energy microanalysis
Low photon energy microanalysis is encountered with the K-shell x-rays of the light elements, Be, B, C, N, O, and F, for which there is no alternative x-ray family of higher photon energy available. Frequently L-and Mshell x-rays from heavier elements that are also present will interfere with the low atomic number element Kpeaks, requiring high spectral resolution for separation. The layered synthetic materials (e.g, W-C, Mo-C, etc.) that have become the preferred diffractors for WDS in the low energy photon region (E p <1 keV) are noted for their high efficiency but limited resolution (FWHM 10 to 20 eV), as shown in Figure 1. A further complication occurs because of hemical effects in which the peak position and shape are dependent on the chemical state of the element, since the electron transitions involved in the emission of the x-ray are modified by the chemical bonding states. It is thus necessary to view the entire peak and adjacent background to make an accurate measurement of the x-ray intensity, which requires WDS scanning at a considerable time penalty. The usual WDS practice of measuring the intensity at the peak and background positions determined on a pure element standard may be subject to serious errors if the peak shape and position shift due to variations in the local chemical state, which itself may depend upon position within the specimen if the cation is multivalent and the composition is heterogeneous. Figure 6(a) shows a comparison between Si-EDS and microcalorimeter EDS spectra of the N-K region in TiN excited with E 0 = 2 keV. The full complexity can only be appreciated with the high resolution of the microcalorimeter EDS, but even with a spectrometer resolution performance of 2 eV at AlK α , the N-K peak suffers interference from the TiL l and TiL η peaks, as seen in Figure 6(b). To correct the N-K peak for the Ti-L contribution, a reasonable strategy might be to use the TiL α1,2 and TiL β1 peaks from a Ti-metal spectrum (obtained by scraping under inert gas before insertion in the vacuum) to scale the TiL l and TiL η peaks. However, close examination of the TiL α1,2 and TiL β1 in TiN and Ti shows a dramatic change in the peak shape which would introduce a severe error in such a peak scaling procedure on N-K. Interestingly, this chemical effect is not seen in TiO 2 compared to Ti metal in Figure 6(c), where the peak shapes are virtually identical for the TiL l and TiL η peaks as well as the TiL α1,2 and TiL β1 peaks.

III. POLYCAPILLARY X-RAY OPTICS
Because the resolution of the microcalorimeter EDS depends inversely upon the mass of the detector, to achieve the best possible resolution the detector area is minimized. The detector heavy metal (Bi) absorber dimensions are typically 0.5 mm×0.5 mm. This small detector area (0.25 mm 2 ) and the large specimen-to-detector distance needed to accommodate the extended detector snout, needed to shield the detector so that it can operate at 100 mK, result in an extremely small detector solid angle. The small solid angle places the microcalorimeter EDS at a distinct disadvantage when absolute efficiency is important. A case in point is low beam energy microanalysis where the beam current is limited to 1 nA or less by the diminished brightness of the electron source and the desire to focus a small diameter probe to take advantage of the much reduced range of low energy electrons. Polycapillary x-ray optics have been used to increase the solid angle of the microcalorimeter EDS. The principle of the polycapillary or Kumakhov x-ray optic is total external x-ray reflection at the inside surface of a tube, shown schematically in Figure 7(a) [11]. X-rays that approach a surface at an angle below a critical angle are efficiently reflected, while x-rays above the critical angle penetrate into the wall material and are absorbed. Multiple shallow angle reflections along the length of the tube can conduct x-rays over centimeter or greater distances.
To maximize the efficiency, the available surface area for reflection must be maximized, which can be accomplished by combining many thin-walled, fine diameter capillaries into a bundle. By gradually tapering this bundle, a converging optic is created. The converging optic has the effect of focusing a parallel source of x-rays that is incident on the untapered end of the optic. Alternatively, if a point source of x-rays, such as that effectively produced by the focused electron beam, is placed at the focus of the tapered end of the polycapillary optic, then a large solid angle is collected and rendered into a nearly parallel beam of x-rays. Finally, if the other end of the optic is also tapered, that near-parallel beam can be converged to a small area crossover. A double-tapered polycapillary optic is used to more efficiently couple the electron-excited source of x-rays at the specimen to the detector of the microcalorimeter EDS, Figure 7(b) [12]. The performance of this optic is demonstrated in Figure 8, which shows the effective increase in detector solid angle for TiL α and TiK α as a function of the lateral position of the x-ray source. For a centrally located source, the improvement is nearly a factor of 300 for the low energy TiL α radiation at 452 eV. Because the critical angle for x-ray reflection varies inversely with x-ray energy, the improvement in efficiency is reduced by e-Journal of Surface Science and Nanotechnology approximately 30% for the more energetic TiK α radiation at 4510 eV.
With the double-tapered polycapillary x-ray optic in place, the NIST microcalorimeter EDS becomes a practical device for analytical spectrometry even with the reduced excitation encountered in low beam energy microanalysis.

A. Limits of detection with no peak interference
It is illuminating to compare the concentration minimum mass fraction, C MMF , that can be detected under low beam energy conditions with the Si-EDS, WDS, and microcalorimeter EDS. Using equation (1) for the calculation of C MMF , consider the problem of measuring low levels of aluminum in a matrix of SiO 2 with the Si-EDS, WDS, and the microcalorimeter EDS. This is a case in which the characteristic x-ray peaks are sufficiently well resolved with conventional semiconductor-EDS to permit easy separation with multiple linear least squares fitting, so that only P and P/B are being compared among the three spectrometry methods. Moreover, for elements like Al and Si with similar atomic numbers, critical ionization energies, and x-ray energies, the 'a factor in equation (1) is close to unity, especially for low beam energy analysis conditions that limit beam penetration and reduce x-ray absorption. For typical low measurement conditions (E 0 = 5 keV; I B = 1 nA; τ = 100 s; n = 1), Table 2 compares the performance characteristics as implemented on an SEM platform of the first generation NIST microcalorimeter EDS augmented with polycapillary optics compared with WDS and Si-EDS. Typical values of detector solid angle, efficiency, and other performance characteristics have been used in preparing this table. The C MMF calculated for Al in SiO 2 for the WDS (TAP crystal) considers the WDS measurement sequence of on-peak and off-peak background measurements needed to extract the peak intensity. Surprisingly, the values of C MMF span a range of only 1.5 for the three very different types of spectrometers. This unexpected behavior can be understood by considering the relative contributions of the key factors, P and (P/B), in equation (1). Note that both the peak counting rate, P, and the spectral peak-to-background, P/B, enter equation (1) with equal weight. The WDS is a high resolution spectrometer with very high P/B but with poor absolute efficiency, so when the beam current limited to 1 nA, the resulting peak counting rate, P, is low, yielding a P * (P/B) product that limits C MMF to the value listed. For the Si-EDS, the P/B is low compared to WDS, but the geometric efficiency is very high, so that the peak count rate for a 1 nA beam current is high compared to WDS, resulting in a similar product P * (P/B) that yields a similar value of C MMF . Finally, the microcalorimeter EDS equipped with a polycapillary optic has a P/B approaching the WDS while having a better geometric efficiency than the WDS, giving a higher P for a 1 nA beam current. However, P is not as good as that of the Si-EDS because of geometric factors, so that again the C MMF is comparable. The results in Table 2 reveal that both P and P/B must be optimized if the lowest possible values of C MMF are to be obtained under practical measurement conditions.

B. Limits of detection with peak interference
Another approach to estimating the minimum mass fraction, C MMF , can be applied when a constituent is present as a known minor constituent (0.01≤C ≤ 0.1 mass fraction) or a trace constituent (C<0.01 mass fraction) or has been determined as a result of a quantitative analysis procedure. C MMF can then be estimated from the assumption that the working curve of x-ray counts versus concentration is linear. That is, the slope of the working curve N vs C is controlled by the interelement effects due to the major constituents of the matrix with no significant change as the concentration of the minor or trace constituent varies. With these assumptions and the usual convention that the limit of detection is defined when N-N B = 3N 1/2 B , the concentration limit of detection C MMF (minimum mass fraction) is given by Ref. (Goldstein et al., 2003): where C s is the known (or measured) concentration of the dilute constituent, N s is the gross peak count, N B is the background under the peak, and n is the number of replicate measurements. Figure 9 shows a comparison of various spectra of Al-GaAs, where the Al peak suffers some interference from the As L-family x-rays. Applying equation (3) to determine the limit of detection for Al in AlGaAs gives a value of C MMF = 0.000870 (870 parts per million) with Si-EDS spectrometry for a specific set of primary electron dose and detector solid angle. The improved spectral quality achieved with the microcalorimeter EDS (8.6 eV at MnK α , augmented with polycapillary x-ray optics) for the same electron beam dose at 5 keV gives C MMF = 0.000060 (60 parts per million).
The AlGaAs example provides a simple demonstration of the improved trace performance of the microcalorimeter EDS compared to Si-EDS where limited interference occurs. A much more challenging example is shown in Figure 10, where the interference occurs between two trace constituents, SiK (0.00126 mass fraction) and TaM (0.00803 mass fraction). In the Si-EDS spectrum in Figure 10(a), these peaks are completely unresolved (resolution 129 eV at MnKα) and cannot be distinguished as peaks above the background. These trace constituents are effectively lost to the analyst if there is no prior knowledge suggesting their presence. With the microcalorimeter EDS, Figure 10(b), the resolution of the peaks is complete, and the limit of detection is at least a factor of 10 lower than the trace concentration level analyzed in the material, e.g., C MMF = 0.00013 mass fraction for Si and 0.00080 mass fraction for Ta.

V. INCREASING SENSITIVITY BY IMPROVING P: HIGH COUNT RATE SPECTROMETRY WITH THE SILICON DRIFT DETECTOR
The conventional Si-EDS is based on a large Si crystal, ranging in area from 10 mm 2 for a 'high resolution' (129 eV at MnK α ) version to 60 mm 2 or larger for a large solid angle detector (145 eV at MnK α ). The crystal has a thickness of 3 mm and thin (∼10 nm) uniform gold electrodes on both the entrance and exit surfaces. To minimize thermal noise, the Si-EDS operates at a temperature of ∼80 K, achieved with a liquid nitrogen reservoir. The limiting throughput is typically 25 kHz with reduced resolution, and 5 kHz at optimum resolution.
The silicon drift detector (SDD) represents an important advancement on the classic Si-EDS design [13,14]. The physical principle of x-ray photon detection is the same as in the familiar semiconductor EDS: photoelectric absorption and subsequent inelastic scattering of the photoelectron to create electron-hole pairs that are separated by an applied bias field and collected at the respective electrodes. The nature of this applied bias field is the key distinction of the SDD operation. The SDD is based upon a thin Si crystal wafer (0.3 mm) with an area of 10 mm 2 to 100 mm 2 . The entrance surface electrode is uniform, but the back surface electrode is applied lithographically in the form of a concentric set of electrode rings separated by a series of resistors that permit application of a graded potential, as shown schematically in Figure 11. This graded potential has the effect of placing a lateral displacement on the free electrons, focusing their collection onto a central anode only 100 micrometers in diameter, or about 1/10,000 of the area of the anode on a conventional Si-EDS. This design significantly reduces one of the major noise sources of the Si-EDS detector. The SDD is also operated at much higher temperature, about 250 K, achieved with a Peltier cooler, so that the drift velocities of the electrons and holes are substantially higher than at liquid nitrogen temperature. The combination of detector thickness, the focusing effect of the graded potential, and the higher drift velocities enable the SDD to operate at much higher count rate for a given resolution, e.g., 250 kHz (measured throughput count rate at 59% deadtime) at 220 eV FWMH (MnK α ) for a 50 mm 2 detector, as shown in Figure 12, which also shows the constancy of the resolution with input count rate (proportional to beam current). Equally interesting is the capability of the SDD, when operating with a long time constant comparable to the conventional Si-EDS, to achieve a resolution of 127 eV (MnK α ) for a 10 mm2 detector, comparable to the best performance of the Si-EDS despite the much higher operating temperature of the SDD.
The SDD offers the prospect for EDS operation with count rates of 500 kHz or higher, as shown in Figure 13. Thus, the possibility exists for recording very short duration 'flash' EDS spectra with much higher integrated counts in the peaks than has ever been possible with the conventional Si-EDS. Through equation (1) this will lead to improved limits of detection by increasing P for equivalent values of the P/B. However, the major contribution of the SDD is that it enables a previously unobtainable level of speed for x-ray mapping, including mapping by spectrum imaging, where a complete x-ray spectrum is recorded at each picture element (pixel). Even with a dwell as short as 10 ms, which gives a total mapping time of 650 seconds for 256×256 pixels, each pixel spectrum will contain about 5,000 x-ray counts for an throughput count rate of 500 kHz. Figure 14 shows mapping results obtained with 10 milliseconds spent per pixel, giving a complete map in 164 seconds at a spectrum throughput count rate of 200 kHz. The backscattered electron image of the mapped field of Raney nickel alloy is shown in Figure 14(a) with maps for the major constituents Al in Figure 14 (b) and Ni in Figure 14 (c). Single pixel spectra for the three distinct phases recognizable in Figure  14(a) are shown in Figures 15(a), 15(b), and 15(c). These figures show that the spectrum quality at such very high count rates is still reasonable.
The high count rates achievable with the silicon drift detector make possible the recording of very short duration spectra, 10 seconds or less, that can still provide useful limits of detection. Figure 16 (a) shows a spectrum of copper integrated over 10 seconds at an output count rate of about 160 kHz. Expanding the vertical sensitivity of the plot in Figure 16(b) shows the detection of a trace level of iron at C = 0.0040 mass fraction and the establishment of a limit of detection for manganese of C MMF = 0.00092 under these dose conditions.

VI. MAXIMIZING BOTH P/B AND P
From the comparison of trace measurement performance listed in Table 1, it is clear that the best possible x-ray spectrometry for trace level characterization would be EDS operation with both the peak counting rate, P, and the peak-to-background, P/B, optimized. While SDD offers pure element peak counting rates of 250 kHz or higher (and total spectrum counting rates approaching 1 MHz), the peak-to-background is limited by the consid-erable peak degradation imposed by the SDD resolution function as a consequence of the extremely short pulse processing times that must be employed (500 ns or less). Given that EDS operation is desired, advanced development of the microcalorimeter EDS is the most promising route to a truly advanced x-ray spectrometry system. Recent microcalorimeter EDS detector research has indicated that it will be possible to create an n×n array of microcalorimeter detectors, each of which has an area of approximately 0.25 mm 2 [15,16]. A 16×16 array would therefore have a total area of 64 mm 2 which would provide a large solid angle of collection even without the use of polycapillary optics, thus raising the limiting value of the peak counting rate. (If desired, a single-taper polycapillary bundle could be used to more efficiently couple the array detector to the specimen x-ray source.) Since each independent detector in the array should be capa-ble of processing at a count rate of 500 to 1,000 Hz, the overall detector array count rate would be in excess of 100 kHz. The individual detectors should be capable of a resolution of 5 eV at MnK α (wide photon energy range). Multiplexing the signals from the independent detectors will likely result in a degradation of resolution in the composite spectrum, but it is hoped the resolution will be in the range 10∼15 eV. Thus, it should be possible with a microcalorimeter array to realize high values for both P and P/B in a full EDS operational mode so as to achieve trace level performance at the limits of performance: low beam energy analysis, low photon energy analysis, etc.
Another possible route for future development of analytical x-ray spectrometry is to extend the work that has already been demonstrated on augmenting the solid angle of collection of the WDS by using single-taper polycapillary optics. A single-taper polycapillary collects xrays over a large solid angle and the low angle reflection through the straight portion of the polycapillary acts to present a nearly parallel x-ray beam to a large flat diffractor. As in the conventional WDS, to view the peak and its immediate spectral background, the diffractor must be scanned. A more efficient measurement schedule could be accomplished if the diffracted peak could be imaged, including a section of background on either side of the peak. This can be done in principle by using a curved focusing diffractor and placing an imaging detector nearer to the diffractor than the focus crossover on the Rowland circle [17]. Such an imaging WDS would be especially useful for peaks that shift and change shape due to chemical effects, such as the situation for TiN shown in Figure 6.

VII. SUMMARY
Trace sensitivity with analytical x-ray spectrometry performed in electron beam instruments depends on both the peak counting rate, P, and the peak-to-background, P/B. Recent advances in analytical electron spectrometry with the microcalorimeter EDS and the silicon drift detector have increased the number of effective tools available to the analyst. In its current form, the microcalorimeter EDS augmented with polycapillary x-ray optics can effectively attack problems involving peak interferences which arise in low beam energy microanalysis and low photon energy microanalysis that the conventional Si-EDS cannot solve. Under low beam energy microanalysis conditions, the microcalorimeter EDS, Si-EDS, and conventional WDS show very similar limits of detection because of the interplay of P and P/B. The silicon drift detector can operate at extremely high count rates, 10 5 to 10 6 Hz (full spectrum), which can achieve extraordinary improvements in x-ray mapping. Future developments to produce arrays of microcalorimeter detectors may achieve optimization of both P and P/B in full EDS operation. A polycapillary optic augmented WDS with imaging of the diffracted peak may also significantly advance analytical x-ray spectrometry.