ELEG 867 Nanotechnology
Homework #3 - due Thursday, 27 September 2001

1. Consider the 3 types of tunneling mentioned in class for insulators: direct, Fowler- Nordheim and Frenkel-Poole. Consider a sample of oxide insulator such that all 3 mechanisms have the same current density of 1mA-mm^-2 at the particular thickness 10 nm and the electric field strength E_ox = 10 MV/cm (note: 1 MV = 10⁶ V). Using this common starting point, plot on a single graph the different trends of tunnel current densities versus oxide thickness t_ox as it varies from 1 nm to 10 nm, assuming that the applied field is held constant at 10MV/cm. Note that these plots will be slightly similar to Fig. 12 on p. 41 in G. Timp. Hint; obtain your plots from the relative dependence of current on thickness and field - do not independently re-calculate each current from first principles. Repeat for 2 additional plots of current densities versus oxide thickness for the applied fields of 5 MV/cm, and 20 MV/cm, but maintain the original starting point of 1mA-mm^-2 at t_ox = 10 nm and E_ox = 10 MV/cm.

2. From the above analysis, describe which tunneling mechanisms contribute more leakage currents in ultra-thin oxides.

For proper credit, include the course number, assignment number, and
due date on your submission.