Limitations of the CCD Performance

The performance of the CCDs is subject to several limitations: physical and technical. We will treat some of the limitations:

7.3.2.1 Quantum Efficiency

The quantum efficiency at the lowest energies from several tens of electron volts to slightly above the Si-K edge at 2 keV is determined by the transmission through insensitive or partially insensitive layers. This directly leads to incomplete charge collection resulting in an asymmetric signal peak with a "shoulder" on the low energetic side of the spectrum and a shift of the peak position. The remedy for this effect pixel pixel

Fig. 7.7 The focal plane of the pnCCD camera on XMM-Newton and ABRIXAS consists of 12 independent, monolithically integrated pnCCDs with a total image area of approximately 60 x 60 mm2. In total 768 on-chip amplifiers process the signals and transfer them to a VLSI JFET-CMOS amplifier array. The 12 output nodes of the CAMEX arrays are fed into 4 ADCs, i.e., one ADC is dedicated to a quadrant [22]

Fig. 7.7 The focal plane of the pnCCD camera on XMM-Newton and ABRIXAS consists of 12 independent, monolithically integrated pnCCDs with a total image area of approximately 60 x 60 mm2. In total 768 on-chip amplifiers process the signals and transfer them to a VLSI JFET-CMOS amplifier array. The 12 output nodes of the CAMEX arrays are fed into 4 ADCs, i.e., one ADC is dedicated to a quadrant [22]

is to avoid lattice perturbations, which could lead to charge trapping and recombination. Additionally, electrons from the ionization process in the insensitive layers may reach the partially or totally sensitive regions and leave their remaining energy there. Both effects reduce the proper detection of the X-ray energy and worsen the peak-to-valley ratio of an energy spectrum.

The detector response to high X-ray energies is simply given by the depleted and thus sensitive thickness d:

12£0 £r (Na + Nd) 12£0 £r Vbias , ,r ^ ,r „ ,, d =\ -- ■ Vbias --^ for Na > Nd (7.1)

The depleted device thickness d can be increased by using silicon with higher resistivity, i.e., with small donor concentration ND in the case of «-type material. Or the reverse bias Vbias must be increased. But for long term stable operation Vbias should be kept below e.g., 500 V. with given resistivity that limits the achievable sensitive thickness. With 4.5 kQcm «-type silicon (ND = 1012 donors per cm3) a depletion width of 800 |im can be achieved at a reverse bias of 500 V. In the above equation, £o £r is the dielectric constant of silicon, q the charge of one electron and NA the high acceptor concentration of the boron implant.

7.3.2.2 Ionization Statistics

Once above 50 eV of photon energy, UV and X-rays need approximately w = 3.7 eV (average) of energy to generate an electron-hole pair, despite of the fact that the band gap of silicon is only 1.1 eV. Most of the incident energy is converted into phonons, only about 30% goes into the creation of electron-hole pairs. In addition the ionization cascade is not an uncorrelated process; therefore, straightforward Poisson statistics does not apply. The energy response of incident monochromatic X-rays is broadened by the competing relaxation processes in silicon. The resultant equivalent noise charge contribution ENCfano is given by:

E is the photon energy, F the Fano factor, and w the electron-hole pair creation energy. Assuming a material dependent Fano factor F of 0.12 for silicon and a pair creation energy of 3.7 eV, the intrinsic line width of a photon of 5.9 keV cannot be better than 121 eV (FWHM). According to Fig. 7.8, the Fano noise is dominant for energies above 1 keV if the electronic noise contribution (ENCel) amounts to 5 electrons. For 1 electron noise (ENCel) this threshold is lowered to 50 eV only.

Eano Noise

Eano Noise

1000

10000

Energy [eV]

Fig. 7.8 Energy resolution as a function of the photon energy. The Fano noise is taken into account as well as a 5 e- and 1 e- electronic equivalent noise charge (ENCel), respectively [22]

7.3.2.3 Charge Transfer Noise

In CCDs, where the signal electrons are transferred over many pixels, the charge shifting mechanism from pixel to pixel must be excellent. Leaving charges behind during the transfer means a reduction in signal amplitude. This loss can be corrected, but adds noise to the signal amplitude measurement.

In a simple model the lost charges can be parametrized according to (3), where the left behinds can be considered as a backward flow loss of electrons. As the loss process is of statistical nature, it is treated similar to a signal leakage current. Ntrans denotes the number of pixel transfers of the signal in the CCD to the anode and CTE is the charge transfer efficiency-a number close to one, so that (1-CTE) is in the order of 10-5, depending on CCD type, radiation damage, temperature, etc.

7.3.2.4 Electronic Noise

The origin of electronic noise and the processing of signals is described in ref. [14] in detail. We simply summarize the result:

ENC2

series noise

low frequency noise parallel noise

Ctot is the total input capacitance, kT Boltzmann's constant times absolute temperature, t is the shaping time constant, ¡l the leakage current and Rf the feedback resistor of the charge sensitive amplifier, af and bf parameterize the low frequency 1 / f noise. A1, A2, and A3 are constants depending on the shaper's filter function.

For the pnCCD (as any other silicon drift detector type system) the electronic noise can be reduced by reducing the read node capacitance, by lowering the leakage current and the 1/ f noise constants and by optimizing the shaping time constant t. The total read noise, if not correlated, can be added quadratically and delivers the total equivalent noise charge ENCtot:

State of the art pnCCD systems of today exhibit electronic noise figures around two electrons and a readout speed of several pixels per microsecond and operating temperatures warmer than -60° C.

In pixellated detectors, the signal charges of one single X-ray photon will not always be collected in a single pixel, so the electronic content of several pixels must be added. This increases for the so called split events the electronic noise floor by the factor VN, with N as the number of pixels involved.

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