Crystallization and Thermoelectric Transport in Semiconductor Micro- and Nanostructures Under Extreme Conditions
This project focused on thermoelectric transport in semiconductor micro and nanostructures where moderate and typical operating voltages and currents lead to extreme thermal gradients and current densities. Models that describe behavior of semiconducting materials typically assume an equilibrium condition or slight deviations from it. In these cases the generation-recombination processes are assumed to have reached a local equilibrium for a given temperature. Hence, free carrier concentrations and their mobilities, band-gap, thermal conductivity, thermoelectric properties, mobility of atoms and mechanical properties of the material, can be described as a function of temperature. In the case of PN junctions under electrical bias, carrier concentrations can change up to ~ 1020 cm-3 and a drift-diffusion approximation is typically used to obtain the carrier concentrations while assuming that the material properties do not change. In non-equilibrium conditions, the assumption that the material properties remain the same may not be valid. While the increased conduction-band electron concentration may not have a drastic effect on the material, large hole concentration is expected to soften the material as ‘a hole’ comes into existence as a broken bond in the lattice. As the hole density approaches 1022 cm-3, the number of bonds holding the lattice together is significantly reduced, making it easier to break additional bonds, reduce band-gap and inhibit phonon transport. As these holes move away from where they were generated, local properties are expected to deviate significantly from the equilibrium case. Hence, temperature alone is not sufficient to describe the behavior of the material. The behavior of the solid material close to a molten region (liquid-solid interfaces) is also expected to deviate from the equilibrium case as a function of hole injection rate, which can be drastically increased or decreased in the presence of an electric field. In the past years we have investigated the possible thermoelectric explanation of asymmetric melting of self-heated Si micro-structures using equilibrium materials’ properties that exist in the literature. We have analyzed the contribution of the electrons and the holes and identified the generation-transport-recombination of minority carriers (GTR) as the reason for an extreme change in the thermal profile in presence of strong generation and electric field. A more complete analysis required construction of models that capture the individual generation and recombination processes to understand the thermal profile as well as the possibility of electronic softening and non-equilibrium melting of the structure below melting temperature. The possibility of melting a material at a lower temperature breaks the correlation between the atomic mobility and the kinetic energy in the system for a given temperature and may allow alternative growth processes. This may also be the mechanism behind ‘amorphization-without-melting in layered structures heated with laser pulses’ that has been reported earlier. The conventional models for semiconductors are constructed for low temperature operation and their projections to higher temperatures do not yield reasonable carrier concentrations. Using these models, the free hole concentrations are calculated to be on the order of 1019 cm-3 at melting, which also do not correlate well with the latent heat of fusion. The melt is expected to correspond to broken bond concentrations on the order of the atomic density (~5x1022 cm-3 for Silicon). Hence, using conventional models the thermoelectric contribution expected from the GTR process is estimated to be much smaller than it likely is. Our work focused on improving the computational models and electrical characterization of materials and devices to better understand thermoelectric trabsport under extremen thermal gradients and current densities. Specifically, during this project, we have - Expanded our computational models to include self-consistent solution of Poisson charge equation (together with current and heat equations currently solved) for improved accuracy of role of bipolar conduction, - Developed a crystallization model incorporating experimentally determined nucleation rates and growth velocities to enable simulation of grain growth, growth-from-melt, filament formation and retention, - Performed high-temperature characterization of relevant materials (including metal contacts, interfacial and insulation layers); electrical and thermal conductivities, Seebeck coefficient, carrier mobility and concentration, - Performed High-speed device-level characterization of metastable amorphous and crystalline phases, crystallization and amorphization dynamics, melting and crystalline growth-from-melt, - Observed and characterized formation of microplasmas in electrically stressed ZnO nanoforests.