# Modulation Characteristics of High-Speed Transistor Lasers
## 3 Modulation Characteristics of TL
### Optimizations of QW
#### 3.1.3 Main Excited State of QW as a Function of Current and Temperature  
Different energy levels in the QW under different currents contribute differently to the optical gain due to their different gains [39]. Figure 6a presents the spectrum of the GaAs based TL current, lasing wavelength, and modulation bandwidth [40]. The lasing wavelength is blue-shifted with increasing external current. This is because under small implantation, the ground state energy level \(\lambda_{0}\) of GaAs based TL dominates the carrier recombination process. As shown in Figure 6b, the bandwidth growth trend of this device at low current is mainly determined by \(\lambda_{0}\). Although base current I\({}_{\text{B}}\) keeps increasing, \(\lambda_{0}\) binds the carriers more strongly and thus has a greater impact on the carrier transport. This leads to the gradual saturation of the modulation bandwidth controlled by \(\lambda_{0}\). Under a large injection, the main excitation energy level becomes the first excited state \(\lambda_{1}\), which has a weak ability to bind carriers; thus, the carrier transport process is further accelerated, the carrier recombination lifetime is further reduced, and a higher modulation bandwidth is obtained [41]. Figure 6: (**a**) Radiative recombination spectrum of I\({}_{\text{B}}\) and wavelength. (**b**) Curve of TL bandwidth under different currents, ground state energy level (blue), and first excited state energy level (red) [40]. According to the report by [PERSON] et al., as I\({}_{\text{B}}\) increases to 75 mA, the modulation bandwidth of a single QW-TL increases by 1.5 GHz. Further, the device achieved a no-error modulation signal transmission of 13.5 Gb/s at room temperature under this condition [42]. On a better bit error rate test equipment, the device achieved I\({}_{\text{B}}\) = 85 mA and 22 Gb/s no-error data transmission under the conditions of T = 15 \({}^{\circ}\)C and f\({}_{\text{3}}\) dB = 10.4 GHz [43]. In addition to the current, changes in the operating temperature also affect the lasing wavelength [44]. Figure 7a shows a temperature change I-V characteristics diagram of a GaAs based TL. With increasing temperature, the main excitation energy level changes (i.e., \(\lambda_{0}\) to \(\lambda_{1}\)) and the electrical gain I\({}_{\text{C}}\) increases, which is manifested by the stretched I\({}_{\text{C}}\)-V\({}_{\text{CE}}\) characteristic curve shown in Figure 7a. With the injection unchanged, the increase in electrical gain indicates a decrease in optical gain (see Figure 7b). After the main excitation energy level was changed by heating, the light intensity was significantly reduced. For InP based lasers, which are more commonly used in optical fiber communication, the variation law is different from that of GaAs lasers in terms of the excitation energy level with current and temperature. However, for InP based TLs, both the base current and the operating temperature red-shift the lasing wavelength--but for different reasons. The red-shift caused by the current change is due to the change in the excited state, and the main excited state gradually shifts from the first excited state to the ground state when the current increases [45]. In contrast, the red-shift caused by temperature changes is due to the power reduction resulting from the increase in the threshold current after the temperature rise [46]. Figure 7: **(a)** TL collector I-V characteristics curve at various temperatures. When the temperature rises, the I-V characteristics curve rises and compresses in the negative direction of V\({}_{\text{CE}}\), which is the same as the increase in the power gain (I\({}_{\text{B}}\)) of V\({}_{\text{CE}}\), and the corresponding optical gain decreases. **(b)** TL collector L-IV characteristics curve at various temperatures. The single-facet optical power varies with temperature, the power decreases at high temperature, and the main excitation energy level changes [44]. Reproduced from Ref. [44], with the permission of AIP Publishing.