We are rapidly approaching the end of the semiconductor roadmap with respect to silicon. To continue its growth, the semiconductor industry is therefore looking into new materials. Two primary materials that are of interest for continuing semiconductor development are germanium (Ge) and gallium nitride (GaN). Ge is of interest as a replacement for silicon, in an effort to improve electronics performances because of its high mobility and its ability to grow a native oxide. In addition, Ge is of interest because of its potential use for economical CMOS-based short wave infrared (SWIR) imaging systems. GaN is a nascent wide bandgap semiconductor and has many potential applications in high power electronics and ultraviolet imaging systems. In this thesis, the key material properties and applications of these two ”end of the roadmap” semiconductors are explored.

Ge is a semiconductor material with an indirect bandgap of 0.66eV. This bandgap value corresponds to a wavelength of 1.88μm, which lies in the infrared range. The Ge material itself is also compatible with the standard Si CMOS process technology. Because of these advantages, Ge is considered a candidate for the application of photo detecting in the SWIR range. Apart from the indirect bandgap of 0.66eV, Ge also has a direct bandgap of 0.8eV. From early research, the relatively small offset between the indirect and direct bandgaps can be inverted either by applying strain[1, 9, 10, 11] or alloying with tin.

GaN is a binary direct wide bandgap material with a direct bandgap of 3.4eV. It has a high breakdown field, and relatively high saturation velocity and carrier mobility. These properties give GaN an advantage in the realm of high power application. GaN can also form a heterostructure with AlGaN, which can give rise to a 2D electron gas (2DEG) layer at the interface without intentionally doping either material. The 2DEG layer has an even higher mobility when compared to the mobility of the bulk GaN, which allows the heterostructure to be utilized for the design of high electron mobility transistors (HEMTs). The formation of the 2DEG layer also gives rise to potential well confinement at the heterostructure interface. The width of the potential well is only a few nanometers, making the interface electron gas subject to quantum confinement along the direction perpendicular to the interface. The detailed shape of the potential well is determined by the configuration of the heterostructure, as well as the applied voltage across the heterostructure.

The first set of goals for this research is to investigate how the bandstructure of Ge changes: Part (1) with the applied strain, and Part (2) with alloyed tin (Sn). The empirical pseudopotential method (EPM) was utilized for the band structure calculation, together with the rules for strain translation for the investigation of Part (1). In Part (1), simulation results give the optimal orientation for different types of applied strain and also thoroughly map the influence of strain applied on any arbitrary orientations. It also reveals that for biaxial strain, there exists another orientation that is more robust against misalignment with respect to the originally desired orientation than the optimal plane, with little compromise of bandgap and slightly higher requirements for the sufficient strain. For Part (2), EPM is combined with perturbation theory for the inclusion of the influence of the Sn atoms in the Ge lattice. A new and computationally inexpensive method is developed during the research. Simulation results agree significantly when compared to reported

experimental measurements, indicating the capability of the method.

The second set of goals is to investigate the electron transport properties of the 2DEG layer at the interface of GaN HEMT and related power transistors. The potential well is approximated and quantified by a triangular potential well and the carrier sheet density is kept the same during the approximation. Thorough simulations are conducted by calculating the band alignment of the heterostructure with

different structural configurations. A fixed correlation between the carrier sheet

density and the shape of the potential well (slope of the triangular potential well

and the height of the well) is revealed. This correlation is used as an input for the

Monte Carlo (MC) simulation. The changes to the mobility of the electrons at the

2DEG layer with changing interface potential well shape are investigated and statis-

tics of drift velocity, electron energy, and valley occupation are collected. Mobility

information is also extracted and compares favorably with reported experimental

measurements. The simulation results are used in the device simulations, which

compares the performances of two GaN/AlGaN heterostructure based devices: a

lateral HEMT and a current aperture vertical electron transistor (CAVET).