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This technique makes use of the following idea. Let us assume that
CCD is illuminated with a monochromatic source of X-ray photons whose

characteristic absorption length is smaller than, but comparable to the depletion depth. If an interaction of the photon with

Depending on where relative to pixel boundaries the photon landed the resulting event can be either a single-pixel or a split one (can be either horizontally or vertically split, or grade 6), but the sum of the amplitudes of the pixels containing a signal charge should account for all the charge generated by the photon, and, hence, be part of the main peak in the response histogram. On the other hand, if an interaction occurred in an undepleted bulk of the semiconductor, the charge cloud diffuses more or less uniformly in all directions. Part of the cloud drifting towards the back side of the device will be lost. Electrons moving towards the front surface enter the depletion region and being pulled by an electric field end up in the potential wells of the CCD. Due to initial diffusion of charge the registered event in this case is a widespread multipixel cloud. According to the ASCA grading scheme this is a grade 7 event and, since part of the initial charge is lost to the backside junction, the amplitude is lower than the peak energy even if all the pixels of the event are summed together.

If we denote *N*_{d} the number of interactions in the depleted region and
*N*_{und} the number of events in the undepleted bulk, then, due to
exponential distribution of the of the number of interacting photons as
as a function of depth, a simple equation holds (see Fig. 4.52 for
a better understanding):

(30) |

This implies the following algorithm of the depletion depth calculation.

1. Sum the the intensities of the grades 0,1,2,3,4,6 and determine what is the
number of
events *N*_{d} in the main peak. Find the peak center *E*_{c} and
width ,and then count how many events are within the interval from
the peak center.

2. Count what is the total number of events *N*_{und} in the grade 7 below
.

3. Calculate the depletion depth *d*_{d} according to the formula derived from
(4.19):

(31) |

The logarithmic function in the above equation makes the result very
insensitive to small changes in both *N*_{d} and *N*_{und} caused by
statistical uncertainties or, say, choosing different set of grades
for the peak counts calculation. At the same time, small changes
of the depletion depth cause changes in the *N*_{d} and *N*_{und} to
go in the opposite directions (because the sum *N*_{d} + *N*_{und} = *const*,
see Fig. 4.52),
thus amplifying the change in the result. Sharp sensitivity of the result
to the changes of the depletion depth has been confirmed by
experiment where the gate voltage was stepped from 0 to +10 Volts.

11/20/1997