Candidate: Jiarun Bai
Date: August 11, 2025
Time: 10:00am
Place: EIT 3141
Supervisor: Dr. Dayan Ban
All are welcome!
Abstract:
Accurate modeling of electron scattering is critical for understanding and optimizing carrier transport in semiconductor heterostructures such as quantum wells (QWs) and quantum cascade lasers (QCLs). In this thesis, we present a comprehensive study of scattering rate calculations using an advanced 8-band k.p formalism that incorporates non-parabolic band dispersion, multiband coupling, and k-dependent wavefunctions. This approach allows for precise modeling of sub-band structures and associated scattering mechanisms, such as longitudinal optical (LO) phonon, impurity, interface roughness (IFR), and alloy disorder (AD) scattering, which strongly influence electron lifetimes and optical transition rates in QCLs.
There are mainly two parts of this work. The primary objective of the first part work is to determine the interface roughness (IFR) and alloy disorder (AD) scattering parameters (, , VAD) by fitting simulated electron sub-band scattering rates using the 8-band k.p model to pump-probe measurements for three InGaAs/AlGaAs quantum well samples. This fitting process, although is not sufficient to uniquely determine the AD, IFR parameters, gives a narrow range of those parameters, and serves to validate the accuracy of the 8-band k.p formalism. By only using 1-band model, the scattering rate is overestimated by 66% in a QW tuned at 215 m, while using the 8-band model, a good agreement with the experimental data is obtained by properly choosing the aforementioned parameters. The reason this fitting is insufficient to narrow down those parameters to single value is due to the inherent time resolution of the pump-probe experiments, and the fact that alloy disorder and interface roughness scattering are processes of the same nature. To find the exact value of those parameters, one possible way would be associating this method with other material characterization techniques, such as ultra-high vacuum scanning tunneling microscope or electron tomography. Above all, this analysis confirmed the cruciality to consider not only the correct dispersion but also the k-dependent band-mixing effect.
The second part then extended to InAs/AlSb-based QCL structures to investigate the k-dependent confinement effect. When the wavevector k increases from zero, the shape of the wavefunctions will become more concentrated in one quantum well. This phenomenon, neglected in previous studies, directly affect the form factor in Fermi’s Golden Rule and consequently has a significant impact on the transition rate. Two QCL structures are simulated with the same model in the first part. The wavefunctions and dispersion relations for each sub-band are calculated using 8-band k.p formalism. The primary focus is placed on the photon transition levels, with the higher energy state referred as the Upper Lasing State (ULS) and the lower energy state as the Lower Lasing State (LLS). In the simulation, the pair of sub-bands whose energy separation most closely matches the experimental photon energy is selected as the ULS and LLS. The ULS is fixed at k = 0, while the LLS is evaluated at various wavevector values k. The qualitative change of the LLS wavefunction with increasing k directly demonstrate the confinement of wavefunction caused by the higher k value. The corresponding quantitative change is also shown by a defined parameter called static dipole, which measures the spatial separation between the expectation values of the ULS and LLS wavefunctions. Since the ULS remains fixed at k = 0, the separation change is caused by the LLS alone, therefore, is an effective indicator for the LLS confinement effect. This study further underscores the necessity of incorporating both k-dependent wavefunctions and nonparabolicity when calculating scattering rates. What’s more, it further underscores the importance of incorporating k-dependent wavefunctions in accurate scattering rate calculations.