Figure 30.

In a standard “inverted” LED, a QD is excited by the injection of an electron, followed by the injection of a hole. The latter process is facilitated by Coulombic attraction that favors the injection of a positive charge (energy downhill process). Simultaneously, Coulombic repulsion impedes the injection of the second negative charge (energy uphill process). The net result of these two injection steps is the creation of an exciton. It recombines to emit a photon, which brings the QD back to the ground state. Then, this cycle (shown by blue shading) repeats again. Labels |0⟩, |e^–⟩, and |X⟩ denote the ground, single-electron, and single-exciton states; g_e and g_h are the rates of electron and hole injection, respectively. The vertical axis shows electrostatic energies of different QD states computed using a model of a charged sphere.¹⁵ In this model, the electrostatic energy of a doubly charge QD is 4 times greater than the energy of the singly charged dot (E_c,1). In order to realize optical gain, a QD must be excited with a biexciton. This requires a different excitation/relaxation cycle (red shading) in which the QD is circulated between the single-exciton, negatively charged-exciton (|X^–⟩, negative trion), and biexciton (|XX⟩) states. The lifetimes of these states are τ_X, τ_X^– and τ_XX. “QLD” is the abbreviation for “QD laser diode”. Reproduced with permission from ref (15). Copyright 2021 Springer Nature Limited.