Efficient calculation of lifetime based direct tunneling through stacked dielectrics

We present the efficient simulation of lifetime based tunneling in CMOS devices through layers of high-κ dielectrics which relies on the precise determination of quasi-bound states (QBS). The QBS are calculated using the perfectly matched layer (PML) method. Introducing a complex coordinate stretching allows artifical absorbing layers to be applied at the boundaries. The QBS appear as the eigenvalues of a linear, non-Hermitian Hamiltonian where the QBS lifetimes are directly related to the imaginary part of the eigenvalues. The PML method turns out to be an elegant, numerically stable, and efficient method to calculate QBS lifetimes for the investigation of direct tunneling through stacked gate dielectrics.