  Controlling the strain level in nanowire heterostructures is critical for
obtaining coherent interfaces of high crystalline quality and for the setting
of functional properties such as photon emission, carrier mobility or
piezoelectricity. In a nanowire axial heterostructure featuring a sharp
interface, strain is set by the materials lattice mismatch and the nanowire
radius. Here, we show that introducing a graded interface in nanowire
heterostructures offers an additional parameter to control strain. For a given
interface length and lattice mismatch, we first derive theoretically the
maximum nanowire radius below which coherent growth is possible. We validate
these findings by growing and characterizing various In(Ga)As/GaAs nanowire
heterostructures with graded interfaces. Furthermore, we perform a complete
chemical and structural characterization of the interface by combining
energy-dispersive X-ray spectroscopy and high resolution transmission electron
microscopy. In the case of coherent growth, we directly observe that the
mismatch strain relaxes elastically on the side walls of the nanowire around
the interface area, while the core of the nanowire remains partially strained.
Moreover, our experimental data show good agreement with finite element
calculations. This analysis confirms in particular that mechanical strain is
largely reduced by interface grading. Overall, our work extends the parameter
space for the design of nanowire heterostructures, thus opening new
opportunities for nanowire optoelectronics.
