Fermi’s golden rule provides one way to calculate the transition rate between two certain quantum mechanically defined states. Due to its generality, it has various applications in the field of atomic, nuclear, and solid-state physics. In the case of NBTI, it is of most interest for charge transfer reactions and electron tunneling in particular. In the following, Fermi’s golden rule is derived for electron tunneling from the substrate into an oxide defect as illustrated in Fig. A.1.
The system is divided into three separate regions, namely the channel, the insulator barrier, and the trap region. The electron wavefunctions and extend into the classically forbidden barrier region. Their overlap actually leads to a mutual influence between the channel and the trap system. However, this influence is assumed to be negligible so that both systems can be treated independently to first order. This justifies the assumption that in a first approximation the channel and the trap system can be described by their own Hamiltonians and . For the derivation of the tunneling rate, the Hamiltonian of the common system is taken as a starting point.