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A closed-form approximate expression is presented for the short time-framedevelopment of silicon diode sensor signals in the context of high frame-ratedetection of incident X-ray fluxes, in the limit that the X-ray absorptionprofile generates a longitudinally-uniform distribution of electron-hole pairsin the detector bulk. The expression represents the immediate time developmentof signals from diode sensors both with (LGAD) and without (PIN) gain, andpresents a temporal scale associated with the onset of gain. Principleslimiting the detection frame rate in the presence of electronic readout noiseare discussed. Making use of an elemental simulation, the relative advantage ofLGAD vs. PIN diode sensors is explored as a function of the effectiveelectronic collection time. It is found that for an idealized LGAD sensor witha gain of 30, the gain provided by impact ionization yields an advantagerelative to PIN diode sensors for frame rates as high as 10 GHz.

Signal Development for Saturated Ultrafast Sensors with Impact Ionization Gain