Semiconductor nanowires are often regarded as having potential to be building blocks for novel applications. Their geometry allows defect-free combinations of materials that have a high degree of lattice mismatch. III-V semiconductor nanowires can also be grown in the wurtzite crystal phase, which is not stable in bulk material or thin films. The atomic arrangement differs between wurtzite and zinc blende polytypes, resulting in different optical and electrical properties. This thesis focuses on studies of the wurtzite GaAs polytype and on understanding the optical behaviour of polytypic heterostructures in GaAs nanowires. Optical techniques such as photoluminescence, photoluminescence excitation, Raman scattering and resonant Raman scattering spectroscopy are contactless and versatile tools for studying semiconductor nanowires. They are capable of providing information about emission, absorption and scattering of light that are directly linked to the electronic band structure of semiconductors. In this work, combining these spectroscopic techniques with transmission electron microscopy performed on the same single nanowires allowed the exraction of various fundamental parameters of wurtzite GaAs. The thesis demonstrates strong quantum confinement effects in zinc blende and wurtzite quantum structures embedded in nanowires of the dissimilar polytype, as well as in thin (down to 9.7 nm in diameter) wurtzite GaAs nanowires. The results obtained in this work show good agreement with theoretical theoretical predictions and will be of importance in future studies of wurtzite GaAs, and in designing potential novel devices
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