Direct and indirect band gaps in Ge under biaxial tensile strain investigated by photoluminescence and photoreflectance studies

Germanium is an indirect semiconductor which attracts a particular interest as an electronics and photonics material due to low indirect to direct band separation. In this work we bend the bands of Ge by means of biaxial tensile strain in order to achieve a direct bandgap. Strain is applied by growth of Ge on a lattice mismatched InGaAs buffer layer with variable In content. Band structure is studied by photoluminescence and photoreflectance, giving the indirect and direct bands of the material. Obtained experimental energy band values are compared with a k·p simulation. Photoreflectance spectra are also simulated and compared with the experiment. The obtained results indicate direct band structure obtained for a Ge sample with 1.94 % strain applied, with preferable Г-valley to heavy hole transition. Introduction In recent years there has been extensive on-going research in the field of optical interconnects. However an integrated laser-on-a-chip still faces the bottleneck of different substrate materials typically used in current industrial processes for lasers and transistor structures. There are different approaches proposed to combine these substrates such as flip-chip or wafer bonding. Other approaches propose growth of both the laser and transistor structures on a single chip. Some success was reported on InP substrates, but the high cost of InP wafers is discouraging for broader applications. Growth of a laser directly on a Si substrate encounters challenges given by the lattice mismatch between common laser materials and Si. However there are a number of interesting results in this field obtained by growth of a buffer GaAs layer on a Si substrate and by growth of materials with similar lattice parameters, such as GeSn. Germanium is a promising material for both photonic and electronic applications. It is an indirect gap semiconductor, but has a direct band valley merely 0.14 eV above the conduction band. This band can be lowered in energy by applying tensile strain to Ge, turning it into a direct gap semiconductor. This method can also be applied to boost charge carrier mobility, which has a profound effect on transistor switch rate and is critical for electronic applications. When attempting to increase power density on a chip through miniaturization of the next generation of transistors, heat dissipation becomes challenging in standard MOSFETs. Heat is generated not only by transistors, but also by the connection wires. Instead, increasing the transistor switch rate allows keeping the same wiring with an increase of overall processor clock rate. Also Ge FETs are candidates for low voltage stage gap transistors. These properties of Ge will provide low energy consumption with easier heat dissipation than existing Si technology. In this paper, we study the band of Ge under biaxial tensile strain, applied by growth of Ge on a lattice mismatched InxGa1xAs layer, by means of photoluminescence (PL) and photoreflectance (PR) studies. In the beginning we describe the theoretical model of Ge crystal used to calculate energy levels and electron-hole wavefunctions coupling in the crystal under various strain and temperatures. In the next section we describe growth conditions of the studied samples. This is followed by the experimental methods, PL and PR in particular, including the theory used for spectra interpretation. The main section presents and discusses the results obtained from the experiment and the theoretical modelling, with a short summary in the conclusion section. Theoretical model of strained Ge The quantum well energy levels and optical coupling between conduction and valence bands were calculated as follows: We used the 30 band k·p approach that includes the effects of strain from D. Rideau et al, which is based on experiment and GW calculations. We added the temperature dependence of the L and Г bands to this model from experiments. The quantum confinement was solved using the envelope approximation numerically, using the k·p Hamiltonian mentioned above. The boundary conditions were given by the experimental values of the band gap and effective masses of InGaAs and the calculated band-offsets from Ref. We used the boundary matching conditions from W.A. Harrison. The temperature dependence of the energy gaps in InGaAs is taken from Ref. The latter approach gives permitted crystal momentum k values for the k·p model. The optical coupling constants are extracted from the momentum operator between the wave-function of the permitted states in the k·p model: ( ) ( ) * 0 k . . i f i f i f k k k k k k m u H u dz z z = p ò ò (1.1) Where and u are the envelope and Bloch functions, respectively. The generation rate of direct band gap photons goes as: ( ) 2 2 . i f dir k k f i R E E = − p ò (1.2) The generation rate of indirect phonons is given by: