Efficient Calculation of Quasi-Bound StateTunneling through Stacked Dielectrics

The continuous progress in the development of MOS field-effect transistors by down-scaling of the device feature size leads to high gate leakage currents. State-of-the-art devices deal with an Equivalent Oxide Thickness (EOT) of 1.5nm and below, and thus high-k dielectrics are a hot research topic[1]. However, quantum mechanical tunneling significantly affects the device characteristics and thus accurate, but still efficient analysis methods are of high interest. This is especially true for material characterization, in order to extract relevant parameters like effective masses of new high-k materials form measurements. Quasi-bound states (QBS) represent the major source of tunneling electrons in the inversion layers of MOS-structures as displayed in Fig. 1. Thus, the estimation of tunneling current is based on the accurate calculation of the QBS, which follows from the Schrödinger equation. The QBS are determined by the eigenstates of the Hamiltonian where lifetimes are related to the imaginary parts of the eigenvalues: τi = /2Ei.