The continuous progress in the development of MOS field-effect transistors within the last years goes hand in hand with down-scaling the device feature size. Therefore, the featured gate oxide thicknesses has reached two nanometers and below. Thus, quantum mechanical tunneling has significant effects on the characteristics of state-of-the-art electrical devices. We study the calculation of quasi-bound states (QBS) in MOS inversion layers, which represent the major source of tunneling electrons.
A variety of computational approaches has been presented to calculate the energetic position and lifetime broadening of these states, but there is still no generally accepted and efficient algorithm for QBS lifetimes available.
Here, the calculation of QBS is performed by the perfectly matched layer (PML) method. Introducing a complex coordinate stretching enables us to apply artifical absorbing layers at the boundaries. This allows us to determine the QBS 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 formalism has been compared to other established methods, and it has been proven as an efficient and numerically stable method to determine the QBS, which seems to be appropriate for integration in a device simulator for the investigation of direct tunneling phenomena.