| Summary: | 博士 === 國立成功大學 === 電機工程學系碩博士班 === 90 === Abstract
The bond orbital model (BOM) is a very powerful method for theoretical calculating on the semiconductors and their heterostructures. This method is a link of the tight-binding and k•p method, while it combines the merit above two methods. The BOM contains many virtues of the empirical tight-binding method, while avoiding the tedious fitting procedure. The computational effort required to the BOM is comparable to the k•p method involving the same number of bands. Unlike the envelope-function (k•p) method, the boundary conditions of the BOM are straight-forward. The another advantage of the BOM is its flexibility to accommodate otherwise awkward geometries of the device structure.
The (001)-oriented BOM had published in detail by Chang. To obtain the (hkl)-oriented BOM Hamiltonian, we rotate the above-mentioned (001) Hamiltonian by the orthogonal transform matrix. The (11N)-oriented bandstructres of bulks quantum wells, and superlattices have been finished in this dissertation. To fit the high-symmetry points, not only the -point and the X-point, the second-neighbor interaction is included into the BOM framework.
The BOM is a tight-binding-like form with s- and p-like basis functions. Due to the unit-cell-scale basis set, the microscopic interface perturbation (intracell effect) is neglected by the BOM. To improve this problem, we expand the BOM basis in terms of the tetrahedral (anti)bonding orbitals and use the potential operator instead of the scalar potential for the extraction of the microscopic information, this is a so-called modified bond orbital model (MBOM). For the no-common-atom quantum wells or superlattices, such as InAs/GaSb and (InGa)As/InP, the heterobonds exist at the interfaces, which result in the symmetry reduction. According to our MBOM calculation, the unusual potential matrix emerges at the interfaces, but not a scalar potential. The MBOM provides the direct insinght into the microscopic symmetry of the crystal chemical bonds in the vicinity of the heterostructure interfaces.
In the past, Chang has calculated the (10,10) InAs/GaSb superlattice with the BOM and tight-binding method. He pointed out the sizable differences of the bandstructure between these two methods. These differences originate from the interface perturbation, which is neglected by the BOM but can solved by the MBOM. Therefore, the MBOM can regarded as a link between the BOM and tight-binding method. For the no-common-atom (InGa)As/InP quantum wells grown on the (001)-, (111)-, (110)-substrates, the interface inversion asymmetry effects are analyzed in detail on this dissertation, which result in the zero-field spin splitting and in-plane anisotropy. Based on the MBOM calculation on the (11N)-oriented InAs/GaSb superlattices, the new phenomenon of zero-field spin splitting is discovered. This spin splitting happens on the growth direction of the (hkl)-oriented no-common-atom superlattices other than the (001) and (111). Moreover, this spin splitting is based on a similar phenomenon of the Dresselhaus effect, so we term it as Dresselhaus-like spin splitting. In the semimetal regime, the bandstructures of (001)-, (111)-, and (110)-oriented InAs/GaSb superlattices are studied by the MBOM. The semimetal phenomenon (a negative band gap) may originates from three possible contributions: the band anisotropy, the spin splitting, and the multiband coupling, which is strongly growth-direction dependent. The crossing behavior (a zero gap) between the conduction and valence subbands is also discussed.
In the second topic of this dissertation, we take the Taylor-expansion on the BOM Hamiltonian up to the second order in k and then obtain the same k•p Hamiltonian as usual. The usual k•p Hamiltonian makes the k-dependent terms for each matrix elements lumped together (all-in-one). However, the k-dependent terms of our k•p matrix are discrete with the different interaction neighbors, which are easily used by the k•p finite difference method to obtain the most accurate result. With the optimum step length in the differential calculation, it is so surprisingly found that the k•p bandstructure in the longitudinal direction can yield as same as that of the BOM. Taking the same process depicted above on the BOM with more bands and more interaction neighbors, we can obtain a more accurate k•p formalism which can fit not only the -point but also other high-symmetry points.
In addition, the optical matrix elements of interband transistion in quantum wells are estimated. Apart from the (001) and (111) quantum wells, the optical anisotropy can be seen, which is in accordance with the zone-center mixing effect. The (11N) Hamiltonian other than the (001) and (111) has the zone-center mixing effect between the heavy-hole and light-hole states. Due to the low symmetry, this mixing effect and in-plane anisotropy exist on the semiconductors and their heterostructures.
|
|---|
