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.
