# Modulation Characteristics of High-Speed Transistor Lasers
## 3 Modulation Characteristics of TL
### Optimizations of QW
#### 3.1.2 Location of QW  
According to the carrier density distribution model in Figure 4a, regulating \(\mathrm{W_{EQW}}\) changes the relative values of \(\mathrm{Q_{1}}\) and \(\mathrm{Q_{2}}\). The value of \(\mathrm{Q_{1}}\) determines the number of carriers injected into the QW; therefore, it affects the photon density. Moreover, different locations of the QW in the base region affect the transport process and recombination rate of carriers. Therefore, the relationship between QW locations and optical bandwidth involves various factors [27; 28; 29; 30; 31; 32]. In a simulation study of TL, [PERSON] et al. found that the closer the QW is to the collector, the larger the bandwidth [32]. They provided an explanation stating that more carriers are distributed to the current gain \(\mathrm{Q_{2}}\) when the QW is closer to the collector, and the number of carriers for recombination emission decreases. This phenomenon is defined as a \"trade-off\" between current gain \(\beta\) and optical bandwidth f.3 dB [33]. Simultaneously, the study found that a large \(\mathrm{W_{EQW}}\) corresponds to a high recombination lifetime. However, another study found that the closer the QW is to the emitter, the larger the bandwidth [34]. The reasoning provided was that moving the QW closer to the emitter increases the carrier group velocity [35]. This reduces the spontaneous  
Figure 5: (**a**) Variation in bandwidth with base current at different cavity lengths. (**b**) Variation in bandwidth with cavity length under different QW numbers [31].  
recombination lifetime while increasing the damping factor of the relaxation oscillations, which leads to an increase in bandwidth.  
In the process of studying the \"trade-off\" between \(\beta\) and f\({}_{\text{3 dB}}\), [PERSON] et al. found that the larger the W\({}_{\text{EGW}}\), the higher the recombination lifetime and bandwidth [33]. This phenomenon of the parallel growth of the carrier recombination lifetime and the optical modulation bandwidth can be explained by the spontaneous recombination lifetime as a function of the optical cut-off frequency [36,37]. This function indicates that the size of the spontaneous recombination lifetime increases gradually as the QW moves to the collector, but the modulation bandwidth varies with the spontaneous recombination lifetime in a parabolic manner. There is an optimal carrier recombination lifetime such that the TL has a maximum optical cut-off frequency (modulation bandwidth). When the QW is near the emitter, the number of carriers in the QW increases because the QW is closer to the collector; further, the optical bandwidth is significantly enhanced (up to 51 GHz). The carrier lifetime has been increased in this process, but it is the number of carriers and photons that mainly affect the light intensity and bandwidth. After reaching the maximum bandwidth, it continues to move to the collector, and the transport delay of the carriers gradually dominates the bandwidth; thus, the recombination lifetime and bandwidth no longer increase in parallel.  
In addition to the location in the base, the distribution of the QW affects the bandwidth [38]. The asymmetric multiple quantum well (MQW) structure has a higher optical confinement factor than that of symmetric MQW. This results in the bandwidth of the asymmetric MQW being higher than that of the symmetric MQW structure; however, the output power of the asymmetric MQW is slightly lower.