# Modulation Characteristics of High-Speed Transistor Lasers
## 3 Modulation Characteristics of TL
### Optimization of Each Layer in the Base Region
#### 3.2.1 Base Thickness and Number of QWs  
In more than a decade of research, owing to the differences in the material of TL devices and the number of QWs, the relationship between the tuning characteristics and the width of the base may be non-trivial.  
[PERSON] et al. (University of Illinois at Urbana-Champaign) conducted a detailed study on the effects of base variation in GaAs based TL [30]. For the MQW structure, the larger the \(\text{W}_{\text{QW}}\), the larger the transit time \(\tau_{\text{c}}\) between wells, which is unfavorable for carrier transport. The wider the L\({}_{\text{b}}\), the larger the \(\tau_{\text{c}}\) (until saturation); the reason why \(\tau_{\text{c}}\) reaches saturation is that reaching a certain width diffusion completely replaces tunneling as the transport mode between wells. For different numbers of QWs, there exists an optimal W\({}_{\text{SCH}}\) that maximizes the modulation bandwidth. [PERSON] et al. reported that this was due to the competition between the optical confinement factor and carrier transport [30]. At the SCH layer, tunneling gradually replaces diffusion as the main carrier injection method. Therefore, the transmission efficiency of the base region was significantly improved, the carrier lifetime was reduced, and the bandwidth was increased. However, the reduced photon confinement ability of the SCH layer results in a reduced photon concentration and bandwidth within the QW. The two variations compete with each other in the process of deriving the largest modulation bandwidth. The sudden decrease in bandwidth when the SCH layer reaches a certain thickness confirms the assumptions established in the previous analysis of the carrier transport model: because the increase in W\({}_{\text{B}}\) decreases the carrier transport rate and increases the radiative recombination lifetime, the competition between spontaneous emission and stimulated emission leads to a sudden decrease in bandwidth when the radiative lifetime exceeds a certain threshold. Further, in studying the modulation properties of GaAs based single QW-TL, [PERSON] et al. came to similar conclusions as [PERSON] et al., which means that there is a W\({}_{\text{B}}\) corresponding to the maximum modulation bandwidth [42]. The maximum bandwidth occurred at approximately W\({}_{\text{B}}\) = 100 nm. The optimal W\({}_{\text{B}}\) values reported by [PERSON] et al. [47] and [PERSON] et al. [30] were not identical possibly because of the differences in the material and structure of the device.  
Subsequently, [PERSON] et al. studied the modulation properties of InP based TL [48; 49; 50]. The effect of the W\({}_{\text{QW}}\) of InP based TL on the bandwidth was reported to be different from that of GaAs TL. The obvious difference is that the frequency of the InP based TL does not increase to the maximum peak with increasing W\({}_{\text{B}}\) but reachessaturation [49; 50]. Besides, with increasing W\({}_{\rm B}\), the response curve reaches -3 dB before the relaxation peak. This results in a sudden cutoff of the response frequency at WB = 300 nm, which is similar to that reported by [PERSON] et al. [30].