This work describes the strain-relaxation--dependent carrier concentration ($n_{s})$ profile model using spontaneous and piezoelectric polarization for AlN/Al$_{x}$Ga$_{1 - x}$N/AlN HEMTs in all mole fraction ($x)$ interpolations. As $x$ varies, the Aluminum Gallium Nitride (AlGaN) channel shows strain relaxation with the Aluminum Nitride (AlN) barrier. The degree of relaxation is modeled from AlN to GaN regions in the channel. It shows that the AlN barrier and buffer relaxation and strain recovery occurs due to the gradual crystal quality degradation from barrier/buffer to the channel interface. These combination devices show less drain current degradation with temperature variation from 300 K to 573 K. This model shows a good agreement with experimental data with a carrier density of $n_{s}$ = 2.8 $\times $ 10$^{13}$/cm$^{2}$.