Reconcile the two problems. Problem 1 and Problem 2, by estimating a oxide trap concentration for Problem 1 and a trapping efficiency for problem 2.

Problem 1

Electrons are slowly injected by tunneling Into the SiO₂ from Si in a MOS transistor when a high electric field appears across the oxide. A small but significant fraction, about 10^-4, of the injected electrons will be captured by oxide electron traps in the SiO₂. The transistor will age and the MOS integrated circuit will fail when -10¹¹q/cm² charges are trapped in the oxide. Calculate the time to failure when 10V is applied to a 100A VLSI oxide. What is the maximum applied voltage to the oxide film for 10-year life?

Problem 2:-

The electron binding energy at an oxide trap is found to be leV and the potential barrier height between the Si and the SiO₂ film grown on Si is 3.1eV. Electrons are slowly injected by tunneling from Si into a trap in the gate oxide of a MOS transistor when +1V is applied to a 100A-thick oxide film on the Si substrate. Suppose that the integrated circuit using this MOS transistor will fail when 10¹¹ electron/cm² are trapped at the oxide electron trap. How long does it take to fail if there are 10¹² cm^-2 unoccupied traps initially? What is the maximum applied voltage to the oxide for 10-year life?