Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 7.1, pp. 622-623

Section 7.1.5. Energy-dispersive detectors

B. Burasf and L. Gerward d

7.1.5. Energy-dispersive detectors

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In white-beam energy-dispersive X-ray diffraction, the spectral distribution of the diffracted beam is measured either with a semiconductor detector (low-momentum resolution) or with a scanning-crystal monochromator (high-momentum resolution) (see Subsection[link] ). Commercially available detectors are made of lithium-drifted silicon or germanium [denoted Si(Li) and Ge(Li), respectively], or high-purity germanium (HPGe). There are, however, other materials that are good candidates for making energy-dispersive detectors.

The semiconductor detector can be regarded as the solid-state analogue of the ionization chamber. Charge carriers of opposite sign (electrons and holes) are produced by the X-ray photons. They drift in the applied electric field of the electrodes and are converted to a voltage pulse by a charge-sensitive preamplifier. The energy required for creating an electron–hole pair is 3.9 eV in silicon and 3.0 eV in germanium. The number of electron–hole pairs is proportional to the energy of the absorbed photon (the intrinsic efficiency is discussed below). There is no intrinsic gain and one has to rely on external amplification. The preamplifier employs an input field-effect transistor (FET), cooled in an integral assembly with the detector crystal in order to reduce thermal noise. Usually the detector is operated at liquid-nitrogen temperature. However, Peltier-cooled silicon detectors are available, removing the maintenance concerns of cryostat cooling. The basic counting system consists further of an amplifier, producing a near-Gaussian pulse shape, and a multichannel pulse-height analyser. It is common to use an additional circuit to reject pileup pulses that can distort the spectrum at high count rates.

The intrinsic efficiency, defined as the ratio of the number of pulses produced to the number of photons striking the detector, is close to 100% in a large energy range. Because of the penetrating power of high-energy X-rays, the efficiency declines at high energies. The low-energy limit is set mainly by the absorption in the beryllium entrance window of the detector. Fig.[link] shows the intrinsic efficiency for an Si(Li) detector and HPGe detector with typical crystal size and window thickness. It is seen that the useful photo-energy range is about 1–40 keV for the Si(Li) detector and 2–150 keV for the HPGe detector. Some minor complications of the HPGe detector are a dip in efficiency around the germanium K absorption edge at 11 keV and the presence of Ge Kα and Kβ escape peaks in the measured spectrum.


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Intrinsic efficiency of semiconductor detectors. The dimensions are selected to give typical best values of the energy resolution. (a) Si(Li), detector thickness 3 mm, Be-window thickness 25 µm. (b) HPGe, detector thickness 5 mm, Be-window thickness 50 µm.

The energy resolution is commonly expressed as the full width at half-maximum (FWHM) of a peak in an energy spectrum. For a spectral peak with Gaussian shape, ΔE(FWHM) corresponds to 2.355 times the root mean square of the energy spread. The energy resolution, including both the detector and the associated electronics, is given by [\Delta E_{\rm FWHM} = \{e^2_n+[2.355(F\varepsilon E)^{1/2}]^2\}^{1/2}, \eqno (]where en is the electronic noise contribution, F the Fano factor (about 0.1 for both silicon and germanium), and [\varepsilon] the energy required for creating an electron–hole pair.

The energy resolution is generally specified at 5.9 keV (Mn Kα) as a reference energy. Typical best values for a detector with 25 mm2 area are 145 eV (2.5%) for an HPGe detector and 165 eV (2.7%) for an Si(Li) detector. The resolution is degraded for larger detector areas.

Count-rate limitations are particularly obvious in synchrotron-radiation applications, where high photon fluxes are encountered (Worgan, 1982[link]). The count rate is limited to below 105 counts s−1, mainly by the pulse processing system.

Cadmium telluride, mercury iodide and other wide-band-gap semiconductors could be good candidates for energy-dispersive room-temperature X-ray detectors. Until now, the best energy resolution of the Hg2I spectrometer with both the detector and the preamplifier operating at room temperature is 295 eV (FWHM) for the 5.9 keV Mn Kα line, corresponding to a relative resolution of 5.0%. By lowering the noise level of the preamplifier FET with cryogenic techniques, a resolution of about 200 eV (3.4%) has been achieved (Warburton, Iwanczyk, Dabrowski, Hedman, Penner-Hahn, Roe & Hodgson, 1986[link]).


Warburton, W. K., Iwanczyk, J. S., Dabrowski, A. J., Hedman, B., Penner-Hahn, J. E., Roe, A. L. & Hodgson, K. O. (1986). Development of mercuric iodide detectors for XAS and XRD measurements. Nucl. Instrum. Methods, A246, 558–560.
Worgan, J. S. (1982). Energy-dispersive detectors for synchrotron radiation. Nucl. Instrum. Methods, 201, 85–91.

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