X-ray CCD Detection Efficiency: Processes,Models and Parameters

A cross-section of a generic, front-illuminated CCD is shown in Figure  4.2. In this figure, X-rays incident from the top must pass through a number of ``dead'' layers which make up the so-called gate structure before entering the photosensitive volume of the device. The function of the gate structure is to allow charge collected in the device to be moved (transferred) from the vicinity of the photon interaction site to an output amplifier which converts the charge to a measurable electrical signal. The direction of charge transfer is indicated in the figure. The gate structure consists of overlapping strips of highly-doped, conductive polysilicon, interlarded with insulating silicon dioxide, and undergirded by relative thin, uniform insulating layers of silicon nitride and silicon dioxide. Although the gate structure is not completely insensitive to X-rays, (see section  4.10 below) for present purposes we assume it to be so.

  

Figure 4.2: Cross-section through front-illuminated and back-illuminated CCDs. X-rays are incident from the top. The gate structure poses a deadlayer; only the depletion region volume is effectively photosenstive. Calibration data must constrain the physical dimensions of these and other regions shown in the figure.

A section of the CCD in a plane orthogonal to that shown in figure  4.2, would reveal a set of structures called the channel stops. (The channel stops are illustrated and discussed in great detail in section  4.5 below). The channel stops function to isolate adjacent CCD columns from one another, and present additional dead layers which affect CCD detection efficiency.

Back-illuminated CCDs differ from the front-illuminated devices in two crucial ways. First, back-illuminated devices are thinned; essentially all of the material shown ``below'' the depletion region in Figure  4.2 is removed during device fabrication. In fact, to ensure a sufficiently strong electric field at the back surface, some of the putative depletion region is removed during the thinning. Therefore, a back-illuminated device is thinner than the depleted region of a front-illuminated device. Second, the device is mounted so that the X-rays are incident from the bottom in Figure  4.2. As a result, the gate structure does not function as a deadlayer in a back-illuminated device. A very thin deadlayer of silicon dioxide (of order $\sim 500$ Angstroms thick) does exist on the back (illuminated) surface of the back-illuminated devices.

The total thickness of the gate structure is of order 0.5 microns. Deadlayers associated with the channel stops are somewhat thicker, but cover a relatively small fraction of the device (see section  4.5, below). In any event, the scale of the deadlayer thicknessses (rather than, say, electronic noise) largely determines the low-energy limit of the useful bandpass of a front-illuminated CCD. By construction the gate structures and channel stops are not deadlayers for the back-illuminated CCD., and the ``low-energy limit'' of these devices is much lower than that of the front-illuminated detectors.

X-rays penetrating the gate structure may be absorbed photoelectrically by the silicon below. If the X-ray is absorbed, the resulting primary photoelectron produces secondary ionization within a volume which is very small compared to the scale of 1 CCD pixel (generally much less than 1 micron in radius for X-rays in the 0.1- 10 keV bandpass of interest). Auger relaxation of the absorbing silicon atom will also contribute to the charge produced. The volume immediately below the gates (for the first 60 - 75 $\mu$m) is depleted of free charge carriers. The residual negative fixed charge provided by the ionized acceptor impurities (the substrate is very lightly doped p-type), together with the charge induced on the gates when they are biased, produces a relatively strong electric field in the depletion region. This field sweeps photo-liberated electrons up to the charge transfer channel very rapidly (on timescales of nsec or less). Once in the transfer channel, the charge may be transferred to the CCD output node by application of proper voltage waveforms to the various gates, and meausured.

The depletion region of a typical front-illuminated ACIS flight device is between 65 and 75 microns thick; the back-illuminated devices have photosensitive volumes which are about 40 microns thick. These thicknesses essentially determine the high-energy detection efficiency limit.

In simplest terms, then, the CCD detection efficiency is the probability than an incident X-ray will interact (photoelectrically) in the depletion region, rather than being absorbed in the gate structure or passing entirely through the depletion region without interaction. This is in principle a straightforward problem requring that one find the spatially averaged transmission of the gate structure, and the transmission of the (assumed uniformly thick) depletion region as functions of incident X-ray energy. If the relevant mass absorption coefficients are known, (except near edges, where, as discussed in section  4.6.3, below, we have measured the mass absorbtion coefficients, we adopt the values published by Henke in 1993) the problem reduces to one of determining dimensions.

In practice, even this simple model is rather more complex than we have yet attempted to fit to the data. Specifically, all analysis presented in this report will assume that each gate structure layer is uniform along the charge transfer direction shown in Figure  4.2, and piecewise uniform in the direction normal to the page of the figure. The quantum efficiency model then has only the seven gate structure parameters listed in Table  4.2; the thickness of the depletion region is the eighth and final model parameter.

 

$$\mu$$ Parameter/Description

Pixel Width 24.0

Silicon Gate Thickness 0.28

SiO₂ Insulator Thickness 0.2- 0.3

Si₃N₄ Insulator Thickness 0.02 - 0.03

Channel Stop Width 4.1

Channel Stop Silicon Implant Thickness 0.35

Channel Stop SiO₂ Thickness 0.45

 

While this model oversimplifies the three-dimensional gate structure, it is worth noting that it is exactly correct to first order in the gate structure optical depth. Thus it may be expected to be least accurate at energies where the gate optical depth is large (e.g., at energies immediately above those of the K abosorption edges of oxygen and, to a lesser extent, of nitrogen and silicon). Our detection efficiency model also neglects the influence of charge collection efficiency (described below) on detection efficiency; fortunately, we have found that by judicious choice of event selection criteria, that the latter effects are independent of energy. We discuss this point further in the following paragraphs. Finally, it is worth stressing that the depletion approximation is just that; in adopting this approximation by fitting for the ``depletion depth'' parameter (see section  4.6.2), we have ignored the fact that the electric field does not drop linearly to zero in the substrate. The remarkable accuracy of this approximation is a consequence of the fact that the depletion region is quite large compared to the amount the initial charge cloud diameter changes over the energy band.