Size-dependent electron chemical potential in nanostructures derived from statistical configuration

We rederived the fermion distribution function by considering the effect of assembly size. We did not use Stirling approximation to avoid the deviation generated by this approximation for a small number of constituents and small assembly size. Furthermore, we identified that in small systems, the chemical potential should also depend on the assembly size. We also rederived a general expression for the size-dependent chemical potential from a statistical configuration and showed that it is consistent with the results from previously reported theoretical or simulation methods. Finally, we applied the model to derive a size-dependent thermoelectric power factor of nanostructured materials. One important finding is that the power factor initially increases when reducing the particle size; however, it then reduces to approach zero when further reducing the material size, due to a dramatic change in the material behaviors.