Fowler-Nordheim erasing time prediction in flash memory

Programming of a flash memory cell used two different mechanisms: a fast channel hot electrons injection in programming mode (with programming time of about mus) and a slow Fowler-Nordheim injection in erasing mode (with erasing time of about ms). In order to pre-evaluate the necessary time needed to write a flash cell memory (programming or erasing), we use a simplified expression for the Fowler-Nordheim injecting current during the erase mode which is the longer one. This allows us to find a relationship between the applied voltages and the resulting threshold voltage. We show in this study that the absolute value of the derivative of the threshold voltage is equal to the positive signal slope applied on the control gate. We validate this assumption by measurements on samples provided by STMicroelectronics with different slope and with samples with different coupling ratios. In order to reduce this erasing time, we need a better modeling of the Fowler-Nordheim injecting current, especially during the establishment of the current