First Results

Two different X-ray sources were used to perform measurements at six different energies. A monochromator produced photons corresponding to the O $K_{\alpha}$line, and the HEXS electron impact source [Jones et al.1996] produced Al, Si, P, Cl and K $K_{\alpha}$ lines. Table 4.12 shows the number of photons collected at each of the energies. Figure 4.40 shows the relative amount of attenuation caused by the channel stops, modulated with the mesh AF. The amount of attenuation is governed entirely by the characteristic attenuation lengths of the $K_{\alpha}$ photons in Si, SiO₂, and Si₃N₄ and does not simply monotonically decrease with increasing photon energy.

 

$$K_{\alpha}$$ Energy (eV) total counts

O 525 4.5 x 10⁵

Al 1487 8.4 x 10⁴

Si 1740 6.8 x 10⁴

P 2035 2.2 x 10⁵

Cl 2622 5.5 x 10⁴

K 3312 7.7 x 10⁴

 

  

Figure 4.40: Variation in detection efficiency due to the channel stop

Fitting the channel stop model to data from only one $K_{\alpha}$ line results in degeneracies in the model. Effectively, the five parameters reduce to two: the total width of the stop and the total attenuation. These are given by:

Width_Total = 2 x Width_wing + Width_box

Atten_Total = Atten_Si x Atten_SiO<<1800>>2 x Atten_{Si<<1801>>3N<<1802>>4}

The upper two panels of figure 4.41 show the $\chi^{2}$ confidence plots for the O $K_{\alpha}$ data set and the P $K_{\alpha}$ data sets. The contours are for the 68 %, 90 % and 99 % confidence levels. The box and wing parameters have great uncertainty, but the constant slope of the contours does indicate some bound to the total width. The situation is similar for the thicknesses of the Si P⁺ channel and the insulating SiO₂. By simultaneous fitting multiple data sets, a tighter constraint can be placed on the model. The bottom panels of figure 4.41 show the $\chi^{2}$ contours for the five HEXS data sets (Al,Si,P,Cl, and K). Taken together, these data still do not tightly constrain the width parameters, but do provide estimations for thicknesses of the P⁺ and SiO₂. Table 4.13 lists the parameter, the range of parameter space and grid sized used, and the derived best fit-value (90 % confidence levels) from the simultaneous fitting.

 

Parameter Parameter Space Data Best Fit - Value

search range step size

$$\mu m \mu m \mu m$$ box width

$$\mu m \mu m \mu m$$ wing width

$$\mu m \mu m \mu m$$ Si thickness

$$\mu m \mu m \mu m$$ SiO₂ thickness

$$\mu m \mu m$$ Si₃N₄ thickness insensitive

 

Unfortunately, the O $K_{\alpha}$ $\chi^{2}$ contours do not overlap the the HEXS data $\chi^{2}$ contours. Figure 4.42 shows the experimental data and the model with the best-fit values derived from combining all five HEXS measurements. The difference between the oxygen data and the model is quite severe, and no set of acceptable HEXS parameters yield a reasonable fit to the oxygen data. A number of possibilities have been explored to explain the discrepancy. The oxygen data was obtained with a different X-ray/vacuum system than the HEXS data and scattering may have been present. Scattering would have the effect of introducing a false background to the system and thus influence the measure of relative attenuation. The monochromator data also had a steep position dependent intensity gradient. In order to add the moiré cell data to produce the RP, a correction had to be applied to the raw data to normalize the flux across the CCD imaging area. This correction also could have introduced an error into the data.

  

Figure 4.41: $\chi^{2}$ contour plots for box width vs. wing width and Si P⁺ depth vs. SiO₂ depth. Contours are the 68 %, 90 %, and 99 % confidence levels.

  

Figure 4.42: Best-fit HEXS channel stop model compared to experimental data.

In addition to the suspected problems with O $K_{\alpha}$ data, there is a disagreement between the best-fit parameters and other, independent measures of the channel stop dimensions. The manufacturers of the CCDs, MIT Lincoln Laboratories, reports that about one $\mu m$ of P⁺ dopant is implanted to make the channels, not .35 $\mu m$as determined by the mesh experiments. Many SEM measurements were performed on chips identical to the CCDs. These photos, exactly like Figure 4.35, show that the SiO₂ thickness is about .45 $\mu m$, not .70 $\mu m$.The same SEM studies, however, do show that the box and wing parameters obtained by the mesh studies agree with physical reality.

The discrepancy between the dimensions obtained from the experiments and those known either from the fabrication process or from direct measurement indicate flaws in the experimental technique or an incorrect model. As discussed above, the quality of some data sets is suspect. Additional experiments are planned, and attempts will be made to minimize the amount of scatter and source non-uniformities. A mesh with 2 $\mu m$ holes has been obtained, and once the mesh is characterized, new data will be taken at multiple energies. The smaller hole size will reduce the width of the AF and decrease the broadening of the attenuation caused by convolution of the signal with the AF. This increase in the contrast should make the model even more sensitive and will remove some of the degeneracy in the best-fit parameters.

There also exists the distinct possibility that the Slab-and-Stop model is too simplistic and not entirely correct. In their analysis of the KMC data, Jones and Prigozhin have synthesized a model to explain the low energy spectral redistribution tail associated with low penetrating X-ray events [Jones and Prigozhin1997]. The model accounts for the incomplete charge collection from photons that interact close to the gate oxide and nitride layers. Similar processes may be occurring for photons that land close to the SiO₂ region of the channel stop. A larger unknown is the exact physical processes that occur in the doped P⁺ channel. The dopant concentration decreases non-linearly as a function of distance from the insulating oxide layer. More than likely, the charge from photons that interact in low P+ concentration regions is fully collected. But there is no model for where (if at all) the transition to a region of partial collection begins. Work is on-going to better model the photo-absorption process in boundary regions between the depleted Si and other structures.