Emission spectrum of a single quantum dot embedded in a $p-n$ junction

We present theoretical studies of the spontaneous emission spectrum of an isolated self-assembled quantum dot (SAQD) embedded in a $p-n$ junction under bias. Keldysh’s nonequilibrium Green’s function approach is used to derive a set of nonlinear coupled rate equations, which are then solved to obtain the steady-state electron and hole occupation numbers. Combining this approach with a simple but realistic effective mass model, we calculate the emission spectrum of a SAQD and examine the relative peak strengths of exciton, positive and negative trions, and biexciton as functions of carrier tunneling rate. Our theoretical studies provide satisfactory explanation for the behavior of the emission spectrum observed in many recent experiments.