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Thermal excitation of charge carriers from the valence to the conduction band creates a dark current signal which may vary with position in the array, and also has temporal shot noise variation. Therefore CCDs must be cooled to ensure this dark current and associated noise is small compared with the noise of the readout amplifier. The temperature dependence of dark current is of the form
where 
is in general the bandgap energy, but for individual generation sites
E may be a trapping state energy. In a device devoid of localized defects which
give rise to individual dark current spikes, most dark current arises from
electrons generated at interface states at the surface. This surface component
of dark current is described by an equation of the form
The first terms are silicon material constants whose
magnitudes are usually related to the quality of silicon processing.
is the trap capture cross-section, 
is the thermal velocity
of the charge carriers and
the surface state trap density.
In the case of a depleted condition at the surface, the free charge carrier
densities, 
and 
are 
(the intrinsic carrier density), but if the surface is forced into
inversion then 
and 
. The inverted surface
case offers a reduction in dark current by a factor 
, or
in principle.
By adjusting the surface potential to a sufficiently low level compared with
the substrate, free holes from surface implants may populate the surface,
changing the dominant carriers from n- to p-type, and as can be seen above,
the dark current decreases by orders of magnitude. This feature has been
exploited in technologies such as Open Pinned Phase, Multi Pinned Phase
and Virtual Phase. In
practice, a conventional CCD operates at room temperature with a dark current
density of 
nA cm 
, but a a device operating with a pinned
inverted surface has 
pA cm [Janesick et al 1989a]. This allows a
temperature advantage for a given dark current performance.
Integration times for X-ray astronomy are short compared with optical applications,
and less emphasis is placed on dark current performance.
Besides using special CCD architectures, dark current may be minimized by
appropriate choice of clocking schemes. For example, during integration of images
some of the clocks may be biased to place a large fraction of the surface into
the inverted state. However, this implies a reduced surface potential and
hence a lower depletion depth, such that there is a trade-off between ease of
cooling the CCD and hard X-ray sensitivity.
A recent discovery [Thorne et al] shows that rapidly switching the clocks between on and
off states, so that stored charge moves from one electrode to the next and
back, should produce a factor reduction in dark current. The physical
principle behind this technique is that dark charge generation
is a time dependent phenomenon, and takes msec to reach steady state. The
so-called ``Dithering'' or ``wobbling'' of the clocks at a 
sec rate therefore prevents the equilibrium generation rate from being
reached.
The choice of operating temperature is complicated by the trade-off of CTE,
readout noise and dark current performance. Optimum performance can be obtained
with a temperature typically in the range -100 
C to -70 C,
depending on the details of the application.
Such temperatures allow cooling without consumable cryogens. In low earth orbit a Peltier effect cooler can be employed, but with a penalty of substantial power requirements. In the cases of XMM and JET-X a highly eccentric orbit, with minimal thermal load from earthshine, permits the use of passive radiators.