Studies On The Influence Of Transverse Motion Of An Electron On The Performance Of Terahertz Quantum Cascade Laser

Quantum cascade laser (QCL) is one of the main devices emitting THz electromagnetic, and it becomes one of the main terahertz radiation sources. Quantum cascade lasers are semiconductor devices which are based on transitions between subbands. Getting accurate subband levels is one of the key issues in the design of the active region. The influence of the coupling between the transverse and longitudinal components of an electron on the transmission spectrum, subbands of the active region, the main dispersions of an electron that has the longitudinal energy E₁, E₂ and E₃ and the dwell time is discussed in this article using the transfer matrix method in the quantum cascade laser of GaAs/Al_0.3Ga_0.7As. It is helpful to understand the tunneling progress of an electron, and the aspect of designing transition radiation. Some major conclusions of the content are as follows:1. Considering the effect of transverse motion of an electron, we calculated the transmission coefficient of electrons tunneling the active region, and the three lowest resonant energies as a function of the transverse wave number are calculated, finally, we give the main dispersions of an electron that has the longitudinal energy E₁, E₂ and E₃, the relations between location and the probability with several different transverse wave numbers are shown using the transfer matrix method in Sec II. The results show that the resonant peaks in the transmission spectrum shift toward the low-energy region and are accompanied by the broadening of resonant peaks and the reducing of the peak-to-valley ratio with the increase of the transverse wave number; The three lowest resonant energies decrease monotonically with the increase of kxy. The decrease of the first excited state E₂ is faster than that of the second excited state E₃. At zero bias, the decrease of the ground state E₁ even faster than that of the second excited state E₃, but when the active region is under an applied electric field, the decrease of the second excited state E₃ is faster than that of the ground state E₁. We can say that when an applied electric field is given, the influence of the transverse motion is more significant, and the influence on higher-lying resonant states is more remarkable than the lower resonant states; In addition, when the active region is worked with an external electric field, the overlap of the wave functions of the first excited state and the second excited state begins to increase with the increase of transverse wave number kxy, thus, this is helpful to the radiation of THz wave.2. The dwell time of an electron tunneling through the active region of one period of the terahertz quantum cascade laser is calculated in Sec. III. The influences of the transverse motion on the dwell time follows the similar rules as the transmission coefficient, that is, with or without electic field, as kxy increases, the peaks of the dwell time shift to low-energy region with larger peaks width. The height of the resonant peaks of the transmission coefficient increases while the rule of dwell time is reverse. At zero bias, the dwell time of the low resonant state is longer than that of the high resonant state. While under an external bias, the dwell time of the low reaonant energy is shorter than that of the high resonant energy.