Ultimate Limits of Pattern Stability Due to Thermal Vibrations

The analysis of the thermal vibrations of nanoscale features due to random thermal noise shows that given a high enough aspect ratio, features will vibrate far enough that their ends can touch. Depending on the balance of elastic forces and van der Waals forces one of three possible results can occur: the tips release after contact, the tips stay in contact, or the sides of the two features fall into each other causing total collapse. Analytical formulas for calculating the probability of failure for simple geometric structures are shown, and a methodology for determining the same for more complex structures is explained.