In order to pre-evaluate the necessary time needed to write a flash cell memory, we use a simplified expression for the Fowler Nordheim injecting current during the erase mode, which 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