  A closed-form approximate expression is presented for the short time-frame
development of silicon diode sensor signals in the context of high frame-rate
detection of incident X-ray fluxes, in the limit that the X-ray absorption
profile generates a longitudinally-uniform distribution of electron-hole pairs
in the detector bulk. The expression represents the immediate time development
of signals from diode sensors both with (LGAD) and without (PIN) gain, and
presents a temporal scale associated with the onset of gain. Principles
limiting the detection frame rate in the presence of electronic readout noise
are discussed. Making use of an elemental simulation, the relative advantage of
LGAD vs. PIN diode sensors is explored as a function of the effective
electronic collection time. It is found that for an idealized LGAD sensor with
a gain of 30, the gain provided by impact ionization yields an advantage
relative to PIN diode sensors for frame rates as high as 10 GHz.
