Si in your HEMT structure is a doping. Doping atoms are added to the host material (AlGaAs or InAlAs). The concentration o fthe doping atoms are many orders of magnitude (2-3-4-5) lower than the host atom concentration. That's why the material properties of the semiconductor (bandgap, mobility, etc.) are still determined by the host material (these properties may be modified by doping - for example, mobility usually decreases as doping increases), and not by the doping species.
Placing a silicon delta-doped layer into AlGaAs does not make that region silicon. It is silicon-doped AlGaAs.
it is the same situation as when you put boron or arsenic doping to silicon - the semiconductor is still silicon, it does not become boron or arsenic.