  Future high-resolution imaging X-ray observatories may require detectors with
both fine spatial resolution and high quantum efficiency at relatively high
X-ray energies (>5keV). A silicon imaging detector meeting these requirements
will have a ratio of detector thickness to pixel size of six or more, roughly
twice that of legacy imaging sensors. This implies greater diffusion of X-ray
charge packets. We investigate consequences for sensor performance, reporting
charge diffusion measurements in a fully-depleted, 50um thick, back-illuminated
CCD with 8um pixels. We are able to measure the size distributions of charge
packets produced by 5.9 keV and 1.25 keV X-rays in this device. We find that
individual charge packets exhibit a gaussian spatial distribution, and
determine the frequency distribution of event widths for a range of internal
electric field strength levels. We find a standard deviation for the largest
charge packets, which occur near the entrance window, of 3.9um. We show that
the shape of the event width distribution provides a clear indicator of full
depletion and infer the relationship between event width and interaction depth.
We compare measured width distributions to simulations. We compare traditional,
'sum-above-threshold' algorithms for event amplitude determination to 2D
gaussian fitting of events and find better spectroscopic performance with the
former for 5.9 keV events and comparable results at 1.25 keV. The reasons for
this difference are discussed. We point out the importance of read noise driven
detection thresholds in spectral resolution, and note that the derived read
noise requirements for mission concepts such as AXIS and Lynx may be too lax to
meet spectral resolution requirements. While we report measurements made with a
CCD, we note that they have implications for the performance of high
aspect-ratio silicon active pixel sensors as well.
