# Two-State Lasing in Microdisk Laser Diodes with Quantum Dot Active Region
## 3 Results and Discussion
### Threshold Current Density of Microdisk Lasers  
Next, the current densities of the laser thresholds were studied as a function of the microdisk diameter. Several microdisks of each diameter were studied. The obtained data are presented in Figure 4. The observed scatter of the current density can be associated with the influence of the dispersion of microcavity parameters caused by the roughness of the side walls and a possible deviation from the expected size and shape (see also the discussion of the data presented in Figure 6). Nevertheless, the trends on the plot are very distinct.  
An increase in the current density for the GS lasing threshold, \(J_{\mathrm{th}}\)GS, is observed with a decrease in the cavity diameter \(D\). This can be attributed to several physical mechanisms, such as non-radiative recombination at microdisk sidewalls or rise of optical loss in smaller disks. The former effect becomes significant if the device size is comparable to the carrier diffusion length \(L_{\mathrm{d}}\)[28]. However, this is not the case for the QD microlasers under study, since \(L_{\mathrm{d}}\) (which is about 0.1 \(\upmu\)m [29]) is expected to be much smaller than the diameter. Another possible reason, which we believe to be the most important, is the growth in optical loss in smaller microdisks. In particular, light scattering by the sidewall roughness [30] and light absorption in the near-surface depleted region [31] depends on the diameter as \(1/D\).  
Meanwhile, the current density for the onset of ES1 lasing, \(J_{\mathrm{th}}\)ES1, decreases. This can be attributed to the fact that higher optical loss in smaller cavities causes higher charge carrier concentrations to occupy all excited-state quantum levels, including the ES1 one, which facilitates earlier lasing through the ES1 optical transition. This can be explained in terms of the Pauli blocking, which slows down the carrier relaxation rate from the ES1 level  
Figure 4: Dependences of threshold current densities on microdisk diameter for lasing through different optical transitions: GS (circles), ESI (squares), or ES2 (triangles). Lines are guides to the eye. Arrow indicates critical diameter for GS lasing.  
Figure 3: Electroluminescence spectra of the 9 \(\upmu\)m microdisk measured at different injection currents (**a**) and dependences of the integrated intensity of lasing modes for ES1 (squares) and ES2 (triangles) optical transitions on the injection current (**b**). Several spectra in figure (**a**) are vertically shifted for better clarity with the appropriate coefficients shown in figure.  
to the GS one when the latter is partly occupied [32]. Thus, the current density interval between \(J_{\text{th}}\text{{}^{GS}}\) and \(J_{\text{th}}\text{{}^{ESI}}\), where pure GS-lasing occurs, shrinks as the diameter gets smaller up to complete collapse at a certain critical diameter \(D_{\text{ES1}}\). Once the microdisk becomes smaller than \(D_{\text{ES1}}\), no GS lasing can be observed, and the first lasing threshold represents the onset of ESI-lasing, as discussed for the 9 \(\upmu\)m microdisk. According to the extrapolation of the experimental data presented in Figure 4, the critical diameter is about 14 \(\upmu\)m (at room temperature).