Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures

Abstract

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. CitationLe, Jia-Liang, Zdene#k P. Baz#ant, and Martin Z. Bazant. "Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures.The two-parameter Weibull distribution has been widely adopted to model the lifetime statistics of dielectric breakdown under constant voltage, but recent lifetime testing for high-k gate dielectrics has revealed a systematic departure from Weibull statistics, evocative of lifetime statistics for small quasibrittle structures under constant stress. Here we identify a mathematical analogy between the dielectric breakdown in semiconductor electronic devices and the finite-size weakest-link model for mechanical strength of quasibrittle structures and adapt a recently developed probabilistic theory of structural failure to gate dielectrics. Although the theory is general and does not rely on any particular model of local breakdown events, we show how its key assumptions can be derived from the classical dielectric breakdown model, which predicts certain scaling exponents. The theory accurately fits the observed kinked shape of the histograms of lifetime plotted in Weibull scale, as well as the measured dependence of the median lifetime on the gate area ͑or size͒, including its deviation from a power law. The theory also predicts that the Weibull modulus for breakdown lifetime increases in proportion to the thickness of the oxide layer and suggests new ideas for more effective reliability testing.

Theory of nanoscale pattern formation produced by oblique-incidence ion bombardment of binary compounds

“…A number of experiments have been carried out to date in which GaSb was subjected to oblique-incidence bombardment with a single ion beam [25,[32][33][34]. For θ = 80 • , ripples with their wave vector perpendicular to the projected ion direction (i.e., perpendicular mode ripples) were observed [33,34].…”

“…In contrast, for smaller angles of incidence, experiments have shown that disordered arrays of nanoscale cones can form. These "nanocones" are tilted in the direction of the incoming ion beam [25,32,34].…”

“…Le Roy et al have argued that phase separation is responsible for the formation of nanodots on GaSb [25,26]. In their view, preferential sputtering of antimony leads to segregated regions of gallium at the surface of the solid; these in turn shield the underlying gallium antimonide from the incident ions, leading to the development of cones with gallium dots at their apices.…”

“…One obvious way to test the theories is to work out their predictions for oblique-incidence bombardment and then compare with experimental results. In fact, preliminary experimental studies of the patterns formed during OIIB of GaSb have already been performed [25,[32][33][34].…”

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

“…If the buildup of residual stresses in the microstructure can be successfully introduced into the formulation, a comprehensive unified theory encompassing also fatigue under cyclic loading is in sight. Finally, note that a mathematically analogous formulation can describe the lifetime statistics of electrical breakdown of gate dielectrics (41).…”