Quantum-mechanical modeling towards trap-assisted tunneling in semiconductor devices

For the last few decades, the persistent downscaling of the metal oxide semiconductor field-effect transistor (MOSFET) has been the main reason for the enormous increase in the computational performance of everyday electronics. Currently, the fundamental 60 mV/decade subthreshold swing (SS) limits the downscaling of the MOSFET supply voltage which in turn makes it difficult to further downscale the dimensions, because the power density of integrated circuits can not be kept constant or lowered. Of all novel solutions to replace the MOSFET, the tunnel field-effect transistor (TFET) promises to surmount the SS limitation, because of its inherent band-to-band tunneling (BTBT) mechanism for carrier transport. However, there is a substantial discrepancy in theoretical predictions and experimental results of TFET performance. In particular, the latter exhibits a degraded SS and considers trap-assisted tunneling (TAT) as one of the probable reasons for SS degradation. Simultaneously, the TAT increases the unwanted stress-induced leakage current and gate-induced drain leakage current in the MOSFET. Owing to such importance, the accurate modeling of TAT in semiconductor devices is essential to assess the device performance. We therefore present an approach towards an all-inclusive, fully quantum-mechanical simulator of TAT in semiconductor devices. In the first part of the thesis, we investigate the electric field effects on the traps in semiconductors and oxides, with as aim to present the significance of quantum effects in determining TAT and to justify the need for a quantummechanical based TAT model. In particular, we determine the impact of high electric field on the characteristic trap energy level. We find that the traps in semiconductors exhibit a field-induced level shift and broadening at TFETrelevant electric fields. We further find that the field-effects of traps in oxides depend on the trap position, trap charge state, tunneling barrier type and the host material parameters. We study the impact of electric field on the TAT-relevant emission rates in semiconductors by including the field-induced level shift and broadening in the existing semi-classical emission rate formalism. To determine the implications of field-effects on the oxides emission rates, we formulate a semi-classical based emission rate based on the standard Wenzel-Kramer-Brillouin approximation for the tunneling probability through a finite barrier. We find that the field-induced quantum effects can increase the emission rates of a semiconductor trap level at high electric field, while the impact for the oxide traps is much smaller due to the higher effective mass and barrier heights. Since the fundamental mechanism underlying TAT in a semiconductor device is phonon-assisted tunneling (PAT), we present a formalism to calculate the PAT current for bi-dimensional semiconductor devices. We formulate the PAT current equation by revising an existing approach of calculating Zener tunneling in indirect-bandgap devices. We apply a quantum transmitting boundary method approximation and calculate the electron-phonon coupling (EPC) strength for homostructure and heterostructure devices, while using the envelope function approximation of electron wavefunctions. To allow for a faster calculation of PAT current, we use the physics based lattice approach and apply the low phonon wavevector approximation to eliminate the basis functions in the overlap integrals of the EPC strengths. To allow for simulations of the PAT current in homostructure III-V devices, we implement the PAT current formalism in an existing direct-BTBT simulator (Pharos) and study the PAT in In0.53Ga0.47As p-n diodes with a 2 and 15-band implementation of the formalism. We find that there is a limited difference for the calculated PAT current densities between the 2 and 15-band model of our formalism. We discover that the electron-phonon coupling strength is inefficient across the tunneling junction due to the phase-shift between the envelope functions injected from bands corresponding to basis function with different parity. We find that the PAT current densities depend on the minimum allowed phonon wavevector and on the device length along the transport direction because of the PAT contributions in the near-tunneling regions. We also find that the combined effects of the near-tunneling region length and the effective tunneling-energy interval determine the observed doping dependence of the PAT current density. Finally, we present the future framework to calculate multiphonon assisted tunneling to enable the accurate predictions of TAT currents in semiconductor devices.status: publishe