With the advent of strain engineering in CMOS technology, the modeling of carrier transport in anisotropic media has gained considerably in importance. Today's TCAD tools widely employ the Scharfetter-Gummel (SG) discretization scheme for the convection-diffusion equation. This scheme is derived assuming current conservation along the edges of a mesh. However, for certain applications, such as magnetotransport and transport in anisotropic media, the one-dimensional treatment of the edge currents is no longer sufficient and two-dimensional extensions of the SG scheme have to be sought. An established solution to this problem is the so-called edge-pair method, which attempts to reconstruct a current density vector for a triangular element from three projections on the edges, whereby these projections are again determined by the one-dimensional SG expression. In this project an alternative method of extending the SG scheme to higher dimensions has been pursued. Exponential shape functions have been derived from an analytical solution of the two-dimensional carrier continuity equation. The shape functions have been defined for triangular elements and vary exponentially in the direction of the element field vector and linearly in the direction orthogonal to the element drift velocity vector. A conservative discretization scheme has been constructed by means of the box method and implemented in Minimos-NT.
Quantum effects determine transport in emerging nano-electronic devices. The importance of inter-subband coupling in single- and double-gate silicon-on-insulator MOSFETs has been further investigated. It has been demonstrated that in a double-gate MOSFET, degeneracy effects lead to a higher occupation of upper subbands due to a carrier concentration twice as large as in a single-gate structure for the same gate voltage. This leads to an increase in inter-subband scattering, which explains the mobility lowering observed experimentally. Higher substrate occupation of higher subbands due to degeneracy effects is responsible for the mobility degradation in ultra-thin body double-gate MOSFETs with (100) body orientation. A Monte Carlo simulator was used to study the mobility in MOSFETs under general stress conditions. It has been shown that the effective mass change due to shear strain results in a substantial mobility enhancement in the direction of tensile strain. To explore the physics of carbon nanotube (CNT) FETs and to optimize their characteristics, self-consistent quantum mechanical simulations based on the Non-Equilibrium Green's Functions (NEGF) formalism have been performed. Numerical methods to reduce computational cost and memory requirements have been developed in order to enable large-scale applications, such as device optimizations. The effect of electron-phonon interactions on the device characteristics has been studied in detail. In agreement with experimental data, our results indicate that scattering with high energy phonons reduces the on-current only weakly but can increase the switching time considerably, due to charge pileup in the channel.
The aim of the next project was the simulation of complete organic devices based on amorphous semi-conducting hydrocarbons. Attention was paid both to electric currents in the bulk and to the injection and extraction of charges at the electrodes. A three-dimensional kinetic Monte Carlo simulator covering heterojunctions, molecular doping, metal interfaces, image charge effects at metals, interband transitions, and arbitrary space charge accumulations has been developed, tested, and optimized with regard to computational issues. For calibration, the dark current characteristics of zinc phthalocyanine has been used. Organic devices most frequently show contact-dominated behavior. So do the simulations performed. The physics of organo-metallic heterojunctions is far from being elucidated in detail. Therefore, the simulations performed focused on the charge dynamics at the interface, testing various models for the interfacial structure suggested in the literature, like wave function decays and densities of states depending on the distance to the contact. The comparison with the empirical data of zinc phthalocyanine shows, however, that for this compound, tunneling has to be enhanced significantly in the simulator, since the latter reproduces thermionic emissive behavior, analogous to that predicted by the Richardson-Schottky model.
Research on analytical modeling of charge transport and contact characteristics in organic devices has continued. A diffusion-controlled injection model has been developed, assuming drift-diffusion and multiple-trapping transport theory. This model can explain the dependence of injection current on temperature, electric field, and the energy barrier between metal and organic semiconductors. Good agreement between model and experimental data has been found. Finally, a model describing Space-Charge-Limited Current (SCLC) has been developed, based on hopping transport and a Gaussian Density of States (DOS) function. By treating the states at the center of DOS as transport sites and those in the tail as trapping sites, the model predicts an essentially quadratic dependence of the SCLC on voltage.