Gallium nitride and its alloys with aluminium and indium are hard, thermally and mechanically stable direct band gap semiconductors used for a wide range of applications. A recent application is the high electron mobility transistor which is the result of the high two-dimensional electron gas density and the large breakdown field exhibited by using these materials.
Due to a lack of a suitable native lattice matched substrate, gallium nitride based devices are grown upon a foreign substrate causing the development of a high density of defects which damage the performance of the device. A particular class of defects called dislocations has a deleterious effect on high electron mobility transistors. In order to achieve desired specifications, it is necessary to reduce the dislocation density by using multilayered structures with varying geometry and composition.
The goal of this work is to define design rules to improve the crystalline quality, i.e., to reduce the dislocation density, of gallium nitrided based structures. Continuum theory of dislocations treated within the linear elasticity theory and the laws of thermodynamics are used for gaining understanding and modeling the dislocation development in these structures.
This work is structured in six chapters. Chapter 1 describes the reasons why GaN and its alloys are widely used in electronics, and further introduces the dislocations as a primary factor for damage of the device performance. Chapter 2 introduces the elements of linear elasticity theory useful to model dislocations. In Chapter 3, general elasticity theory is applied to evaluate the dislocation energy and their equilibrium configuration. In Chapter 4, theoretical studies of the critical thickness are extended for GaN based alloys. Subsequently (Chapter 5) the reaction-kinetic approach is used to evaluate the dislocation density in different multilayered structures. The main results and conclusions are summarized in Chapter 6.