  The fractional quantized Hall state (FQHS) at the filling factor {\nu} = 5/2
is of special interest due to its possible application for quantum computing.
Here we report on the optimization of growth parameters that allowed us to
produce two-dimensional electron gases (2DEGs) with a 5/2 gap energy up to 135
mK. We concentrated on optimizing the MBE growth to provide high 5/2 gap
energies in "as-grown" samples, without the need to enhance the 2DEGs
properties by illumination or gating techniques. Our findings allow us to
analyse the impact of doping in narrow quantum wells with respect to
conventional DX-doping in AlxGa1-xAs. The impact of the setback distance
between doping layer and 2DEG was investigated as well. Additionally, we found
a considerable increase in gap energy by reducing the amount of background
impurities. To this end growth techniques like temperature reductions for
substrate and effusion cells and the reduction of the Al mole fraction in the
2DEG region were applied.
