Degradation of the Energy Resolution due to the Non-Uniform CTE

1. Non-Uniform CTE

It is known that the charge transfer efficiency (CTE) of the CCDs in SIS is gradually decreasing due to the radiation damage. Radiation damage produces charge traps in the CCD. When the charge packet encounters an empty trap, an electron in the packet will be captured in the trap. Because the charge packet is typically transfered through several hundreds pixels before read-out, many electrons may be lost from the packet. This means that size of the charge packet is slightly reduced from the original size at the time of read-out. This effect artificially reduce the apparent X-ray photon energy. The photon energy may be recovered in the course of ground data analysis if we know the average loss rate of the electrons.

The average rate of the CTE decrease was almost as expected before the launch of ASCA, but it was unexpected that CTE decrease was quite non-uniform over the chip. CTE was found to vary largely from column to column in a chip. This can be seen as the difference of the energy spectra created from the single column data (see figure). The large difference of the apparent line centers indicates column-to-column variations of the CTE.

2. Degradation of the Energy Resolution

Non-uniform CTE degrades the energy resolution. We show the Cas A energy spectra obtained in 1993 and 1998 with the same pointing position and the observation mode (1 ccd faint mode) in the figure. Degradation of the energy resolution is very clear. Because the RDD effect is corrected in the calculation of the energy spectra, the change of the energy resolution is solely due to the non-uniform CTE.

We traced the history of the apparent line widths of Cas A. Because Cas A is a stable X-ray source, change of the apparent line width should be attributed to the instrumental effects. This figure shows the histories of the apparent line widths. It is found that only the parallel and frame-store transfer contribute the degradation of the energy resolution.

3. Empirical Model of the Resolution Degradation

Because it is practically impossible to measure the CTE for each column, degradation of the energy resolution cannot be corrected in the data. Thus the degradation needs to be incorporated in the response matrices of SIS. We found that the degradation of the energy resolution can be reasonably well described as a time variation of the fano factor, f:

f = f0 + f1t.

Here, f0 is a fano factor at the time of launch, f1 an increase rate of the fano factor, and t is the elapsed time after the launch of ASCA. Note that f1 is a function of the position in a chip. With this empirical model of the fano factor, an apparent line width, sigma, can be described as follows:

sigma = sqrt( sigma02 + 3.65 f1 t E )

This model function is fitted to the observed Cas A line widths. The results are shown in the figure. Because the line widths are almost same for positions O and V (positions H and X), the data are combined to fit a single model function. The best-fit parameters are tabulated below.

Chip s0c1 s1c3
Position O,V H,X O,V H,X
V-address (RAWY) 345 100 340 100
f1 (x10-9 s-1) 3.3 1.8 2.9 1.4

As seen from the table, f1 is a function of the V-address (RAWY) of the chip. For simplicity, we assume that f1 is a linear function of the V-address. Thus the final functional form of the fano factor is:

f = f0 + ( fa + fb V ) t,

where V is the V-address on the chip, and t is the elapsed seconds after the launch of ASCA. The best-fit model parameters are:

Chip s0c1 s1c3
fa (x10-9 s-1) 1.188 0.775
fb (x10-12 s-1) 6.12 6.25

This empirical model of energy resolution degradation due to the non-uniform CTE will be included in the SIS response generator, sisrmg.

Although we have analyzed only the standard chip in each sensor, the formula will be applied to all the chips in the sensor.
1998/12/27 T. Dotani