# Modulation Characteristics of High-Speed Transistor Lasers
## 2 Inherent Advantages of TL
### Drastically Reduced Effective Carrier Recombination Lifetime  
Figure 3a,b show the energy band structure and carrier density distribution of double-heterojunction DML and TL [23]. For DML, due to the double- heterojunction structure, a large number of electrons injected from the N region cannot reach the P region within the recombination time. Consequently, they accumulate in the active region and increase the recombination lifetime. Meanwhile, the injected holes also accumulate in the valence band. This situation results in a uniform distribution of carriers, which induces relaxation oscillations and transport delays. For TL, because of the base transition in the transistor, the carriers that are not recombined within the base transition time are collected by the collector. Therefore, the recombination lifetime of TL is not higher than the transit time of the base region, and the long-lived carriers leave the active region in time to greatly alleviate the carrier accumulation of TL. The carrier distribution of NPN-type TL can be simply drawn if the charge at the boundary between the collector and base is assumed to be zero, which is shown in Figure 3b. Note that although this unique slanted distribution defines the fast characteristics of TL, it is evident that the number of carriers involved in recombination to emit photons is much less than that of DML. However, for a device applied to high-speed modulation, high power is the goal that needs to be pursued because it means longer transmission distance and higher modulation bandwidth. Achieving this is the main challenge for TL. Figure 3: (**a**) Energy band structure and carrier population distribution of PIN-type double heterojunction DML; it is uniformly distributed, which induces accumulation. (**b**) Energy band structure and carrier density distribution of TL; it has a skewed distribution of carriers due to base transition [23]. Reproduced from Ref. [23], with the permission of AIP Publishing. Figure 2: Structure diagram of traditional (**a**) directly modulated laser and (**b**) transistor laser. Assuming that the amount of recombination in the active region is much greater than that in other regions of the base region, the charge distribution of the base can be approximated as a superposition of two triangular charge groups represented by \(\mathbf{Q_{1}}\) and \(\mathbf{Q_{2}}\)[24; 25]. \(\mathbf{Q_{1}}=\mathbf{\delta}\pi n_{1}\mathbf{A}W_{\text{EGW}}\mathbf{/2}\) represents the carrier transported from the emitter to the QW, and \(\mathbf{Q_{2}}=\mathbf{q}\Delta n_{2}AW_{\text{EC}}\mathbf{/2}\) represents the carrier transported from the emitter to the collector. \(\Delta\mathbf{n_{1}}\) and \(\Delta\mathbf{n_{2}}\) are the electron concentrations to the QW and collector, and the integral values for \(\Delta\mathbf{n_{1}}\) and \(\Delta\mathbf{n_{2}}\) along the electron transfer direction are \(\mathbf{Q_{1}}\) and \(\mathbf{Q_{2}}\), respectively. \(\text{W}_{\text{EGW}}\) is the distance from the emitter to the QW and \(\text{W}_{\text{EC}}\) is the distance from the emitter to the collector. The carrier model of TL was reported by [PERSON] et al. [26], which is simplified in Figure 4b. Assuming that the carriers passing through the left separation confinement heterostructure (SCH) layer are trapped by the first QW and the remaining carriers continue to diffuse through the barrier to the next well until they are trapped by other wells, the carrier transport model in the base region can be established when hot-electron escape and QW tunneling are considered. It can be seen in Figure 4a that the carrier density gradually decreases from the E region to the C region, and the amount of reduction also decreases, which indicates that the QW closer to the C region has a weaker capture ability for electrons.