Energy band structures of strained GaInAsP membrane quantum wire lasers considering anisotropic strain relaxation

Abstract

Electronic band structures of compressively strained (CS) GaInAsP /InP membrane quantum wire (QWR) are studied using 8 band k.p method considering anisotropic strain relaxation. Strain distribution is determined by solving Navier equations. Finite element method (FEM) using commercial software FEMLAB is used to solveNavier equations. Strain distribution is calculated for a variety of conventional and membrane structures with different values of wire width, thickness of top and bottom InP layers (t) of membrane structure, number of wire layers stacked vertically and tensile strain (TS) in barriers. Change in the transition energy Eg due to strain relaxation in each type of structure is then estimated which allows a comparison between the lasing frequencies of the two types of structures. The performance in these structures is compared by comparing the transition matrix elements. Numerical results show that the difference between isotropic and anisotropic result increases when strain compensation by barriers is stronger and this effect is more pronounced in the barrier regions. Strain redistribution occurs in membrane structure due to etching away of the top and the bottom cladding layers and normal strain component E:zz along the crystal growth direction is affected more than other components due to etching. In multiple QWR stack, strain relaxation is stronger and can be suppressed using TS in barriers. With increase in wire width, the difference between the strain distribution between conventional and membrane structures increases. For low value of t, strain relaxation between membrane and conventional structure differs significantly. In membrane structure effective band gap Eg is increased relative to a similar conventional structure which will contribute to blue shift of emission frequency. To observe these effects, we calculate the difference in effective bandgap energy !'>Eg with and without quantum mechanical (QM) and bandmixing effects. It can be concluded that bulk-like calculation of Eg neglecting QM and band-mixing effects leads to over-estimation of !'>Eg• Variation of !'>Eg with various parameters is attributed to the different strain relaxation in conventional and membrane structures. By observing the transition matrix elements, it is found that the optical gain in membrane structure is slightly reduced.