Calculations of energy band structure and mobility in critical bandgap strained Ge1-xSnx based on Sn component and biaxial tensile stress modulation

Abstract

Optoelectronic integration technology which utilizes CMOS process to achieve the integration of photonic devices has the advantages of high integration, high speed and low power consumption. The Ge1-xSnx alloys have been widely used in photodetectors, light-emitting diodes, lasers and other optoelectronic integration areas because they can be converted into direct bandgap semiconductors as the Sn component increases. However, the solid solubility of Sn in Ge as well as the large lattice mismatch between Ge and Sn resulting from the Sn composition cannot be increased arbitrarily:it is limited, thereby bringing a lot of challenges to the preparation and application of direct bandgap Ge1-xSnx. Strain engineering can also modulate the band structure to convert Ge from an indirect bandgap into a direct bandgap, where the required stress is minimal under biaxial tensile strain on the (001) plane. Moreover, the carrier mobility, especially the hole mobility, is significantly enhanced. Therefore, considering the combined effect of alloying and biaxial strain on Ge, it is possible not only to reduce the required Sn composition or stress for direct bandgap transition, but also to further enhance the optical and electrical properties of Ge1-xSnx alloys. The energy band structure is the theoretical basis for studying the optical and electrical properties of strained Ge1-xSnx alloys. In this paper, according to the theory of deformation potential, the relationship between Sn component and stress at the critical point of bandgap transition is given by analyzing the bandgap transition condition of biaxial tensile strained Ge1-xSnx on the (001) plane. The energy band structure of strained Ge1-xSnx with direct bandgap at the critical state is obtained through diagonalizing an 8-level kp Hamiltonian matrix which includes the spin-orbit coupling interaction and strain effect. According to the energy band structure and scattering model, the effective mass and mobility of carriers are quantitatively calculated. The calculation results indicate that the combination of lower Sn component and stress can also obtain the direct bandgap Ge1-xSnx, and its bandgap width decreases with the increase of stress. The strained Ge1-xSnx with direct bandgap has a very high electron mobility due to the small electron effective mass, and the hole mobility is significantly improved under the effect of stress. Considering both the process realization and the material properties, a combination of 4% Sn component and 1.2 GPa stress or 3% Sn component and 1.5 GPa stress can be selected for designing the high speed devices and optoelectronic devices.