We have investigated the photoluminescence (PL) characteristics of AlGaN/GaN heterostructure with an extremely high two-dimensional electron gas (2DEG) density. A very high 2DEG density was obtained by controlling the tensile stress during the growth of the heterostructure on silicon substrate. Strong PL emission peaks corresponding to both the band edge and the 2DEG were observed in the highly tensile-stressed heterostructure. Furthermore, the strong longitudinal optical (LO) phonon replicas (1-LO2DEG and 2-LO2DEG) of the 2DEG peak were also observed in the heterostructure. (C) 2011 American Institute of Physics. [doi:10.1063/1.3578399]