Incomplete charge transfer in IGFET bucket-brigade shift registers

The time evolution of the charge transfer during one half-cycle of operation of an IGFET bucket-brigade dynamic shift register is calculated analytically for a smooth but otherwise arbitrary voltage driving function. Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) solutions to the charge transfer equation are matched to Airy-function solutions in the current cutoff region to determine the charge transferred as a function of initial charge. This directly gives several contributions to the incomplete transfer parameter α, the rate of change of the charge left behind on transfer with the initial charge. Although the increment of charge not completely transferred is less than 1 percent of the charge comprising the signal, the calculation is done so that no subtraction of nearly equal large numbers is necessary. We do not evaluate the actual loss of charge due to leakage, traps, recombination, etc. It is found that the finite dynamic drain conductance of an IGFET makes a major contribution to the parameter α, and that under many experimental conditions it will limit shift-register performance. It is also found that all contributions to α depend on the clock-voltage wave-form. Comparison is made with the results of preliminary experiments, and good qualitative and reasonable quantitative agreement is obtained.