Advanced thermal analysis of microelectronics using spreading resistance models

Thermal analysis of electronic devices is one of the most important steps for designing of modern devices. Precise thermal analysis is essential for designing an effective thermal management system of modern electronic devices such as batteries, LEDs, microelectronics, ICs, circuit boards, semiconductors and heat spreaders. For having a precise thermal analysis, the temperature profile and thermal spreading resistance of the device should be calculated by considering the geometry, property and boundary conditions. Thermal spreading resistance occurs when heat enters through a portion of a surface and flows by conduction. It is the primary source of thermal resistance when heat flows from a tiny heat source to a thin and wide heat spreader. In this thesis, analytical models for modeling the temperature behavior and thermal resistance in some common geometries of microelectronic devices such as heat channels and heat tubes are investigated. Different boundary conditions for the system are considered. Along the source plane, a combination of discretely specified heat flux, specified temperatures and adiabatic condition are studied. Along the walls of the system, adiabatic or convective cooling boundary conditions are assumed. Along the sink plane, convective cooling with constant or variable heat transfer coefficient are considered. Also, the effect of orthotropic properties is discussed. This thesis contains nine chapters. Chapter one is the introduction and shows the concepts of thermal spreading resistance besides the originality and importance of the work. Chapter two reviews the literatures on the thermal spreading resistance in the past fifty years with a focus on the recent advances. In chapters three and four, thermal resistance of a twodimensional flux channel with non-uniform convection coefficient in the heat sink plane is studied. The non-uniform convection is modeled by using two functions than can simulate a wide variety of different heat sink configurations. In chapter five, a non-symmetrical flux channel with different heat transfer coefficient along the right and left edges and sink plane is analytically modeled. Due to the edge cooling and non-symmetry, the eigenvalues of the system are defined using the heat transfer coefficient on both edges and for satisfying the orthogonality condition, a normalized function is calculated. In chapter six, thermal behavior of two-dimensional rectangular flux channel with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). The proposed solution can be used for modeling the flux channels with numerous different source plane boundary conditions without any limitations in the number and position of heat sources. In chapter seven, temperature profile of a circular flux tube with discretely specified boundary conditions along the source plane is presented. Also, the effect of orthotropic properties are discussed. In chapter 8, a three-dimensional rectangular flux channel with a non-uniform heat convection along the heat sink plane is analytically modeled. In chapter nine, a summary of the achievements is presented and some systems are proposed for the future studies. It is worth mentioning that all the models and case studies in the thesis are compared with the Finite Element Method (FEM).

The mosses of Terra Nova National Park, Eastern Newfoundland, a bryofloristic analysis and interpretation

The known moss flora of Terra Nova National Park, eastern Newfoundland, comp~ises 210 species. Eighty-two percent of the moss species occurring in Terra Nova are widespread or widespread-sporadic in Newfoundland. Other Newfoundland distributional elements present in the Terra Nova moss flora are the northwestern, southern, southeastern, and disjunct elements, but four of the mosses occurring in Terra Nova appear to belong to a previously unrecognized northeastern element of the Newfoundland flora. The majority (70.9%) of Terra Nova's mosses are of boreal affinity and are widely distributed in the North American coniferous forest belt. An additional 10.5 percent of the Terra Nova mosses are cosmopolitan while 9.5 percent are temperate and 4.8 percent are arctic-montane species. The remaining 4.3 percent of the mosses are of montane affinity, and disjunct between eastern and western North America. In Terra Nova, temperate species at their northern limit are concentrated in balsam fir stands, while arctic-montane species are restricted to exposed cliffs, scree slopes, and coastal exposures. Montane species are largely confined to exposed or freshwater habitats. Inability to tolerate high summer temperatures limits the distributions of both arctic-montane and montane species. In Terra Nova, species of differing phytogeographic affinities co-occur on cliffs and scree slopes. The microhabitat relationships of five selected species from such habitats were evaluated by Discriminant Functions Analysis and Multiple Regression Analysis. The five mosses have distinct and different microhabitats on cliffs and scree slopes in Terra Nova, and abundance of all but one is associated with variation in at least one microhabitat variable. Micro-distribution of Grimmia torquata, an arctic-montane species at its southern limit, appears to be deterJ]lined by sensitivity to high summer temperatures. Both southern mosses at their northern limit (Aulacomnium androgynum, Isothecium myosuroides) appear to be limited by water availability and, possibly, by low winter temperatures. The two species whose distributions extend both north and south or the study area (Encalypta procera, Eurhynchium pulchellum) show no clear relationship with microclimate. Dispersal factors have played a significant role in the development of the Terra Nova moss flora. Compared to the most likely colonizing source (i .e. the rest of the island of Newfoundland), species with small diaspores have colonized the study area to a proportionately much greater extent than have species with large diaspores. Hierarchical log-linear analysis indicates that this is so for all affinity groups present in Terra Nova. The apparent dispersal effects emphasize the comparatively recent glaciation of the area, and may also have been enhanced by anthropogenic influences. The restriction of some species to specific habitats, or to narrowly defined microhabitats, appears to strengthen selection for easily dispersed taxa.