Modeling of semiconductor devices based on quantum wells: quantum cascade laser as an example

It has been two decades since the quantum-cascade lasers (QCLs) have emerged in 1994 for the first time. As time goes on, QCLs reach to higher points scientifically and economically and the usage of QCLs devices continually grows in optoelectronic device market because of their potential applications in various areas in mid- and far-infrared regions. Moreover, their performance is still improving. QCLs lase based on electron transition between intersubbands and tunneling through potential barriers where electron transition causes photon emission. This takes place in conduction band; that is why QCLs are considered as unipolar semiconductor lasers. The frequencies of emitted photons depend on the location of the allowed energy levels which can be controlled by carefully choosing consecutive wells and barriers with suitable widths. In the present thesis, the transfer matrix method is employed to obtain transmission coe cient and wave functions of electron inside an arbitrary potential profile which is crucial for characterizing semiconductor devices based on quantum well. The obtained wave functions are used to get quantities necessary for characterizing QCL resulted from the potential profile.