Modelling of Layers and Traps in High-Κ Gate Stacks and Energy Band and Equivalent Circuit Representations

Abstract

Five layers - two bulk and three chemically graded layers - have been identified to constitute the high-K gate stack; the bulk layers being the intermediate oxide and the high-K layers; the three chemically graded layers being the silicon/intermediate-oxide, the intermediate-oxide/high-K, and the high-K/metal-oxide interfacial layers. Energy band diagrams across the silicon space-charge, the five gate stack, and the metal layers, have been modeled, in which graded band-gap in the chemically graded layer, and the effects of the electric fields and image force barrier lowering have been considered. Response of traps in all the five layers of the gate stack to an applied small signal has been modeled, including the profile of the quasi-Fermi function in the gate stack. Relations for the potentials across the five gate stack layers have been formulated. Finally, small-signal equivalent circuit representations have been developed for the entire gate stack and the silicon space-charge layer.