Modeling miniband for realistic silicon nanocrystal array

Within the envelop-function framework, we developed the finite element method to calculate the minibands in the realist Silicon nanocrystal array. This method clearly reveals the miniband formation and accurately calculates the E–KE–K dispersion relationship. In the simple 1D array, the deduced miniband structure matches well with the analytic Kronig–Penney method. More importantly, it can better simulate the 2D and 3D nanocrystal array, which avoids approximations of the quantum cubic box and the independent periodic potential of the multi-dimension Kronig–Penney method. Further, this model is utilized to calculate miniband structure of realistic 2D-array Silicon nanodisk array for guiding quantum dot solar cell design.