Modulation-doping influence on the photoluminescence from the two-dimensional electron gas of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructures

A photoluminescence (PL) investigation is carried out on an undoped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructure and several modulation-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructures with different doping levels at low temperature. The emission peaks of the first and second levels related to a two-dimensional electron gas (2DEG) are first observed in heavily modulation-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructures, which is supported by a calculation based on a self-consistent solution of one-dimensional Poisson and Schrödinger equations and an excitation-power dependent PL measurement. However, such emission peaks do not appear in undoped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructure, in which the 2DEG is confirmed by the observation of a clear Shubnikov–de Hass oscillation and quantum Hall plateaus. The formation of a 2DEG in an undoped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructure generally results from a strong piezoelectric field, which results in a rapid diffusion of photoexcited holes into the flatband region of GaN. Consequently, the recombination probability between the 2DEG and photoexcited holes becomes very low, which is the reason that the emission peaks related to the 2DEG become difficult to observe. In the case of heavily modulation-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructures, the piezoelectric field is screened out by silicon doping in the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ layer, and the 2DEG formation is due to the electron transfer from ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ to GaN, which is the same as that happening in the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ system. Therefore, the emission peaks related to the 2DEG can be observed. The difference of the 2DEG formation mechanism between undoped and modulation-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructures is observed.