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In the last years, electron density profile functions characterized by a linear dependence on the scale height showed good results when approximating the topside ionosphere. The performance above 800 km, however, is not yet well investigated. This study investigates the capability of the semi-Epstein functions to represent electron density profiles from the peak height up to 20,000 km. Electron density observations recorded by the Van Allen Probes were used to resolve the scale height dependence in the plasmasphere. It was found that the linear dependence of the scale height in the topside ionosphere cannot be directly used to extrapolate profiles above 800 km. We find that the dependence of scale heights on altitude is quadratic in the plasmasphere. A statistical model of the scale heights is therefore proposed. After combining the topside ionosphere and plasmasphere by a unified model, we have obtained good estimations not only in the profile shapes, but also in the Total Electron Content magnitude and distributions when compared to actual measurements from 2013, 2014, 2016 and 2017. Our investigation shows that Van Allen Probes can be merged to radio-occultation data to properly represent the upper ionosphere and plasmasphere by means of a semi-Epstein function.