Lasing in the space charge limited current regime

We introduce an analytical model for ideal organic laser diodes based on the argument that their intrinsic active layers necessitate operation in the bipolar space charge-limited current regime. Expressions for the threshold current and voltage agree well with drift-diffusion modeling of complete p-i-n devices and an analytical bound is established for laser operation in the presence of annihilation and excited-state absorption losses. These results establish a foundation for the development of organic laser diode technology.

Figure 1

Normalized carrier concentration, electric field, and $np$ product as a function of position for bipolar space charge-limited current with a Langevin recombination rate, equal charge carrier mobilities, and Ohmic electron and hole injection.

Figure 2

Drift-diffusion simulations of the current-voltage relationship for a BSBCz-like active layer with Ohmic majority carrier injection and equal electron and hole mobilities that are either constant (blue line) or given by the EGDM for disordered organic semiconductors (red). The black dashed line shows the analytical SCL current prediction and solid circles denote the lasing threshold in each case.

Figure 3

Contours showing the relative increase in threshold current due to parasitic absorption and singlet exciton annihilation caused by (a) triplet excitons and (b) hole polarons. Lasing is forbidden in the shaded region at any current density. The solid lines are calculated using Eq. (8) and are compared in (b) with the results of the Setfos numerical modeling (solid circles). The ${\mathrm{Alq}}_3$:DCM material system marked by the red dot in (a) lies in the forbidden region for the $t_{\mathrm{rise}}=10$ ns case shown. All of the calculations are based on the BSBCz parameters given in the main text along with ${\sigma }_{\mathrm{st}}=2\times {10}^{-16} {\mathrm{cm}}^2$ [19].