In this paper, electrical characterizations by C(V$_G$) and I$_D$(V$_G$) and comparison with 1D Schrödinger-Poisson simulations are carried out to investigate the effects of AlN layer thickness and n-type AlGaN barrier doping on the two-dimensional electron gas resistance (R$_{2DEG}$). Specifically, these impacts are related to either the electron sheet density (n$_s$) effects or the mobility (μ) effects. In this study, we show that varying the AlN thickness from 0.7nm (n$_s$=7.8cm$^{-2}$) to 1.5nm (n$_s$=9.0 cm$^{-2}$) leads to a linear increase of ns. However, simultaneous degradation of the transport properties due to intensifying roughness mechanism at high ns tend to limit the improvement of the device properties. Furthermore, we show that the heavily doped AlGaN barrier slightly increases ns and drops the 2DEG mobility to ~1770 cm$^2$.V$^{-1}$.s$^{-1}$ leading to a degraded 2DEG resistance. However, the overall resistance is improved (R=323Ω/□) compared to the undoped case (R=380Ω/□) due to the simultaneous contribution of two conducting channels at V$_G$=0V. To go further, the polarization charges at the AlGaN/AlN and AlN/GaN interfaces are computed in the 1D Schrödinger-Poisson simulations to account for the presence of the AlN layer. A reduced polarization for very thin AlN layers is considered to account for the experimental results. A very simple empirical model is proposed that predicts the enhancement of polarization charges (σ) as a function of AlN thickness.