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While it is widely appreciated that disorder is intricately related to observed sample-to-sample variation in property values, outside of very specialized cases, analysis is often qualitative in nature. One well-understood quantitative approach is based on the 1930s work of Bragg and Williams, who established an order parameter S, which ranges from unity in the case of a perfectly ordered structure to zero in the case of a completely randomized lattice. Here, we demonstrate that this order parameter is directly related to charge carrier mobility in undoped GaN. Extrapolating experimental points yields a value of 1640 cm2/Vs for the maximum room temperature mobility in stoichiometric material, with higher values potentially accessible for Ga-rich material. Additionally, we present a model for observed trends in carrier concentration based on the occurrence of distinct structural motifs, which underpin S. The result is an alternative perspective for the interplay between lattice structure and charge carriers that enables a predictive model for tuning mobility and carrier concentration in undoped material. 

Movies showing the nucleation of WSe2 on Al2O2 with mixed (Se/O) and single (Se) steps.