Description of Mesh Experiments

One possible method for determining the sub-pixel structure is illuminating a pixel with a very narrow beam of monochromatic X-ray and observing how the CCD response changes as the beam is rastered across the pixel. Unfortunately, obtaining a well focused X-ray beam is difficult, and even if it were trivial, the experiment would require too much time to acquire enough data to make the results statistically significant. One possible solution to both of these problems is using a metal film with relatively small holes (4 $\mu m$ holes compared to the 24 $\mu m$ size of a pixel) placed in a regular fashion [Tsunemi et al.1997]. When this mesh is placed close to the CCD surface and rotated with respect to the axes defined by the gate structure and channel stops, a moiré pattern is formed when the device/mesh combination is illuminated with X-rays. Below, we summarize the experimental technique and our initial results. Interested readers are referred to the paper by Pivovaroff et al. for details [Pivovaroff et al.1998].

Figure 4.47 shows a section of the mesh, and Figure 4.48 shows the fixture used to hold the mesh tight and close to the surface of the CCD. The resulting moiré pattern contains the CCD's response to a 4 $\mu m$ X-ray beam that was uniformly rastered across the pixel area. The smaller the relative angle between the mesh's orientation and the CCD axes, the more pixels are required to make a moiré cell, and the finer resolution of the CCD's response^4.2. Typical measurements were performed with angles on order of $5^{\circ}$, and moiré cell dimensions of 61 pixels.
 
 

Figure 4.47: Schematic of the mesh showing its orientation to the CCD

 
 

Figure 4.48: Fixture used to hold the mesh close to the CCD surface

Analysis of the data begins with selecting suitable grade events (single pixel and horizontally or vertically split events) from the photo-peak of the monochromatic line to build the moiré cells, rotating the moiré cells, and summing individual cells into one representative pixel (hereafter RP) for the entire CCD. Figure 4.49 shows a sample of the unrotated, raw moiré cells that are a direct output of the illumination of the mesh/CCD system and the RP, repeated in a $3 \times 3$ array to make it easy to see the boundary regions of the pixel. With the RP generated, determination of the sub-pixel structure can proceed. By compressing the RP in one direction, the attenuating affect of the channel stops or the gates can be modeled. For the rest of this review, we concentrate only on the channel stops, although the same techniques can be applied to measure the gates.
 

Figure 4.49: Left: Raw data showing the moire cells. Right: The representative pixel (RP) repeated in a 3 x 3 array.

The approach for determining the channel stop dimensions is quite straightforward. The attenuation in detected photons expected from the channel stop (recall that the Slab and Stop Model assumes that any photon interacting in the sub-pixel structure will not be detected) is convolved with the PSF of the mesh holes. The resultant convolution is compared to the experimental data, and the channel stop model parameters are allowed to vary, using a $\chi ^{2}$ fit statistic to determine the best-fit parameters. Figure 4.50 shows the five parameters used to describe the channel stop. Compare the model to the SEM photo of an actual channel stop in Figure 4.46.
 
 

Figure 4.50: Five parameter channel stop model.

In addition to constructing a realistic channel stop model, the success of this technique depends on providing an accurate PSF for the mesh and accounting for additional processes that effectively broadens the PSF (i.e. diffraction, diffusion of the charge cloud, distortions to the PSF caused by using a non-parallel X-ray source). Producing such an analytic aperture function (hereafter AF) is a daunting task. Fortunately, the AF can be ascertained from the mesh data itself. Horizontal and vertical split events come from photons that interact within an electron cloud size diameter of the pixel boundary. Analysis of BESSY KMC data performed by Jones and Prigozhin [Jones et al.1997] indicate that cloud sizes range between 10 and 100 nm. The distribution of the horizontal and vertical split events ($\Delta_{split \: events}$), then, is the convolution of a 10-100 nm step function ($\Theta$) with the AF.

$$AF \otimes \Theta = \Delta_{split \: events}$$ (4.23)

The projection of the mesh holes on the surface of the CCD are at least 4.5 $\mu m$ in diameter, so $\Theta$ can be approximated as a $\delta$ function. Equation 4.23 then becomes

$$AF \otimes \Theta \approx AF \otimes \delta = AF = \Delta_{split \:events}$$ (4.24)