Abstract
In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.
Highlights
Semiconductor nano-structures can operate at their potential if they can be grown with high degree of purity and if any introduced impurities and defects are controlled
The binding energy is a nonmonotonic function of the well width and peaks at a relatively small width value. This is because where the electron distribution is more localized, the probability of finding the electrons around the impurity is increased the energy levels are pulled down because of the attractive coulomb potential of the hydrogenic donor impurity while at larger dot length where the electrons feels less attractive effect of the hydrogenic donor impurity, the binding energy becomes small
The results show that photoionization crosssection is much larger for donor impurities located close to the centre of the quantum well dot than for those farther away from the quantum well dot centre
Summary
Semiconductor nano-structures can operate at their potential if they can be grown with high degree of purity and if any introduced impurities and defects are controlled. One of the ways of controlling the un-intentional impurities that are introduced to a semiconductor device is by photoionization This makes photoionization cross-section an important optical property needed for characterization of a hydrogenic donor impurity in a semiconductor device. This is of great significance due to its numerous applications in laser design [1], astrophysics, radiation detection among others. El-Said and Tomak [6, 7] have investigated the photon energy dependence of the photoionization cross-section of hydrogenic impurities in quantum wells [QW] using infinite barrier model They found out that the photoionization cross-section depended on the polarization of the incident light relative to the direction of carrier confinement.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
