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Energy resolution

The X-ray energy required to liberate a charge pair in a semiconductor is approximately an order of magnitude lower than in gas detectors, hence the potential spectroscopic advantage of CCD detectors. In a silicon device the FWHM energy resolution in eV is given by

where E is the photon energy, =3.68eVper electron is the charge conversion factor, r the system noise in electrons (which may include readout and dark current noise), and F the Fano factor for silicon (0.115 [Alig et al]).

Examination of equation 1 reveals that the CCD readout noise must be minimized in order to exploit the potential for X-ray spectroscopy offered by the silicon properties. For a number of years, good scientific CCDs attained noise performance of electrons rms, but this limited the energy resolution for X-ray energies 3keV. Nevertheless, this noise performance would have allowed CCDs to be able to discriminate between H- and He-like emission lines of light metallic elements, which occur in the kilovolt region of X-ray spectra. Reducing read noise to 1 electron results in Fano noise limited performance down to energies of 0.1keV.

Such a requirement for extremely low noise is almost unique to X-ray CCDs, as images taken for ground-based astronomy have a shot noise on sky background which will usually be significantly higher than the read noise (although applications such as narrow filter imaging and dispersive spectroscopy might benefit from such improvements in noise performance).

CCD read noise performance is limited by that of the MOSFET amplifiers used as the CCD output stage. Typically these are one or two stage source follower designs, and by careful attention to geometric design their node capacitance can be reduced to 0.1pF. The equivalent charge noise is then determined by the MOSFET white and flicker noise components. For a MOSFET with white noise of nVHz and sampling rates of secs per pixel, the noise is limited to 2 electrons rms.

There is an implicit trade-off in that this sampling rate determines a readout time of the order seconds for an entire CCD. For bright sources (eg. 100mCrabs) and high collecting area telescopes, this is not fast enough to prevent pulse pile-up. While there has been much attention paid to theory of different sampling schemes which optimize this trade-off [Hopkinson and Lumb], the limits are usually practical ones concerned with clock feedthroughs, grounding etc..

The most promising recent development is that of the skipper amplifier [Chandler et al], which promises to offer sub-electron noise, by resurrecting the idea of multiple reading of signals first implemented by [Wen]. However the same trade-off problem remains - to obtain the lowest noise requires many samples, which increases the readout time and reduces the maximum X-ray count rate limit. Only the development of lower noise with high speed amplifiers with multiple sampling can circumvent this problem.

Another important approach is to improve the intrinsic noise performance of MOSFETs. Changes to circuit design and silicon processing may in future reduce the flicker (1/f or 1/f ) noise produced in MOSFET devices to levels comparable with JFET or bipolar devices [Kandiah]. In MOSFETs the 1/f corner frequency may be 20kHz, whereas in the other technologies it may be 1kHz.

While the skipper technologies have demonstrated 1 electron noise imaging, at present, the best X-ray energy resolution data have been obtained with devices with a noise performance of 3 electrons, and typical data are shown in Figure 2.

CCD energy resolution predicted by equation 1, plotted for three values of readout noise r. The points represent measured energy resolution for an MIT Lincoln Laboratories CCID7 framestore device, operated at a temperature of -70 C at a readout rate of approximately 50 kpixels/s. }

For completeness, the readout noise term in equation 1 should also contain terms such as the spatially varying charge transfer efficiency, and effects of energy dependent efficiency of signal charge collection. The best practical CCDs have finite readout noise, imperfect charge transfer, and the photo-electron charge packets may split between pixels or partially recombine before collection.

Immense efforts have been expended to decrease the noise and enhance CTE performance for all scientific applications of CCDs, but the effects of charge splitting have been a peculiar concern for X-ray applications. The splitting of charge between pixels can occur when the signal charge packet diffuses radially in a plane parallel with the silicon surface, before collection in the potential well of a single pixel. This is most likely to happen when the photon is absorbed deep in the silicon where the electric field is small. Charge may split between 2 or more pixels or even partially recombine in the silicon. Even when charge is conserved, the summation of charge split between pixels is subject to the corresponding quadrature summation of readout noise, and the precision of charge (and hence energy) measurement is degraded. Therefore recognition of X-ray events which split between pixels places a greater premium on obtaining low noise than the simple shot noise fluctuation considerations alone would require.

Figure 3 illustrates the effect of event selection algorithms on detection efficiency and spectral resolution. Each of the histograms shown was obtained from a single data set. The data were obtained with a low resistivity MIT Lincoln Laboratories CCID7 CCD using a radioactive source that produces the Mn K (5.9 keV) and K (6.4 keV) X-rays.

The upper line shows the result of binning all pixel amplitudes in the data set, without any event selection or processing. The two peaks from well-collected X-ray events are evident, but a significant low-energy tail is evident (note the suppressed zero of the energy scale). This tail is produced by the events which lost charge in the collection process and/or spplit between two or more pixels.

The hatched histogram shows the effect of simple event selection and processing algorithms on both spectral resolution and quantum efficiency. These data were obtained by selecting only those events in which the charge is very well-collected. The actual selection criterion is that no pixel in an eight-pixel neighborhood surrounding the event centroid may exceed a fixed threshold. This single pixel selection criterion essentially removes the low energy tail, and makes visible a small Si K escape peak at 4.1 keV. This improvement in the shape of the spectral response function comes at the cost of some detection efficiency: the single pixel event histogram peak contains less than 50% as many events as does the peak in the unprocessed histogram.

However the energy resolution is improved, for example the FWHM resolution is 170eV in the raw data, but 125eV in the selected data set. In this particular device the depletion depth comprises a small fraction of the total active silicon, so a large fraction of events fall outside the depleted volume, and hence are split between several pixels.

The parameter used to select events (ie. the maximum acceptable amount of charge in any pixel neighboring an event centroid) can be adjusted to trade detection efficiency for resolution. This relationship is illustrated for a standard low resistivity MIT Lincoln Laboratories CCD in Figure 4. The data were again obtained at an X-ray energy of 5.9 keV. It should be noted that for a given selection threshold (eg. 5 read noise 's above the nominal zero energy level) the fraction of a split charge packet which is undetectable increases with decreasing X-ray energy.