In the present paper, energy eigenvalues of core–shell (normal and inverted) quantum dots of cubic and spherical geometries are calculated using finite-difference technique. Accuracy and computational time depends heavily on the dimension of discretization. By making sparse, structured Hamiltonian matrices, grid dimension can be made smaller than the size of the actual device. This technique has a number of very good absorbing boundary conditions to choose from, which simulates the effect of free space beyond the boundary forever. It is a very intuitive and versatile modeling technique, which allows the user to specify the material at all points within the computational domain by employing grid structures. Among these different methods, finite-difference technique is capable of simulating the arbitrary nanostructure profiles. Researchers computed ground state energy using FD technique which matches with earlier result for larger base width, but deviates for lower values. Several methods have already been considered by theoretical researchers e.g., variational method, finite-element method, shooting method and finite-difference method. Therefore, numerical procedure is an alternative choice for solving such problems. Therefore, a systematic investigation of electron states of core–shell quantum dot is very essential.Įnergy is obtained by solving time-independent Schrödinger equation, but, in many cases, because of complex geometry, it is very difficult to solve the equation using analytical method. Properties of these electronic and optoelectronic devices are dependent on their confinement levels, which in turn, is dependent on geometry, dimension and material composition of the structure. It is recently reported that inverted core–shell structure show better lasing performance, than other quantum dots. Position-controlled doping in CSQD helps in biomedical diagnosis. This property along with tuning ability of eigenenergy provides a wider range of absorption and emission spectra. These core–shell structures have the potential of higher absorption cross-sections and lower Auger recombination coefficient. It also improves quantum yield due to the localization of carriers in the core area from all possible dimensions and, thus, reduces the interaction with interface trap states. Recently, it is reported that core–shell nanostructures exhibit much higher photoluminescence than single-layered geometries. In a normal CSQD, lower bandgap ‘core’ is surrounded by higher bandgap ‘shell’ material, while in an inverted CSQD, core layer is made of higher bandgap material and shell is made of lower bandgap material. Recently, core–shell quantum dots (CSQDs) have emerged as potential candidates for electronic and photonic devices due to their tailorable intersubband transition energy. Energy quantization due to complete carrier confinement in a quantum dot (QD) introduces remarkable novelty in the performance of QD-based transistors, optical transmitters, modulators, receivers, etc. In a nanostructure, dimension is comparable to or less than the de-Broglie wavelength of electrons, and so the carriers are confined due to the restricted motion along the reduced dimensions, resulting in quantization of states. Thanks to the advancement of technology, , it has become possible to fabricate new devices of various geometries and controllable dimensions. In recent years, there has been increasing interest in semiconductor nanostructures because of their key roles in novel electronic, and photonic, devices. Wide tuning range for intersubband transition by tailoring dot dimensions indicates important applications for optical emitters/detectors. Also, in inverted configuration, transition energy decreases for a cubic dot while increases for a spherical dot as core size is increased. When compared, spherical CSQDs show higher transition energy between two subbands than cubic CSQDs of similar size and same material composition. Transition energy decreases with increase in core thickness. Computed results for the lowest three eigenstates and intersubband transitions are shown for different structural parameters taking GaAs/Al xGa 1− xAs based CSQD as example. The matrices are diagonalized to obtain eigenstates for electrons. Sparse, structured Hamiltonian matrices of order N 3 × N 3 for cubic and N × N for spherical dots are produced considering N discrete points in spatial direction. In this paper, intersubband transition energy is computed for core–shell (normal and inverted) quantum dots (CSQD) of cubic and spherical geometries by solving time-independent Schrödinger equation using finite-difference technique.
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