Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations
Two methods for calculating transport parameters in semiconductor superlattices by applying Green’s functions are compared in the paper. For one of the methods, the Wannier functions method, where computations in the complex space and Wannier functions base are required, the Hamiltonian matrix is sm...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2019-06-01
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| Series: | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/113175/PDF/20_631-642_00910_Bpast.No.67-3_06.02.20.pdf |
| _version_ | 1828152526817460224 |
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| author | M. Mączka G. Hałdaś |
| author_facet | M. Mączka G. Hałdaś |
| author_sort | M. Mączka |
| collection | DOAJ |
| description | Two methods for calculating transport parameters in semiconductor superlattices by applying Green’s functions are compared in the paper. For one of the methods, the Wannier functions method, where computations in the complex space and Wannier functions base are required, the Hamiltonian matrix is small in size and its elements depend solely on the energy. For the real space method, as it operates in the floating point domain and uses the Hamiltonian containing the elements dependent both on energy and position, the Hamiltonian matrix is larger in size. The size makes the method computationally challenging. To find the consequences of choosing one of the methods, a direct comparison between the computations, obtained for both methods with the same input parameters, was undertaken. The differences between the results are shown and explained. Selected simulations allowed us to discuss advantages and disadvantages of both methods. The calculations include transport parameters such as the density of states and the occupation functions, with regard to scattering processes where the self-consistent Born approximation was used, as well as the spatial distribution of electron concentration for two superlattices structures. The numerical results are obtained within the non-equilibrium Green’s functions formalism by solving the Dyson and the Keldysh equations. |
| first_indexed | 2024-04-11T22:11:30Z |
| format | Article |
| id | doaj.art-2a9402d8a9fe475ea7a9c60cd9744e0b |
| institution | Directory Open Access Journal |
| issn | 2300-1917 |
| language | English |
| last_indexed | 2024-04-11T22:11:30Z |
| publishDate | 2019-06-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| spelling | doaj.art-2a9402d8a9fe475ea7a9c60cd9744e0b2022-12-22T04:00:32ZengPolish Academy of SciencesBulletin of the Polish Academy of Sciences: Technical Sciences2300-19172019-06-0167No. 3631641https://doi.org/10.24425/bpasts.2019.129661Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representationsM. MączkaG. HałdaśTwo methods for calculating transport parameters in semiconductor superlattices by applying Green’s functions are compared in the paper. For one of the methods, the Wannier functions method, where computations in the complex space and Wannier functions base are required, the Hamiltonian matrix is small in size and its elements depend solely on the energy. For the real space method, as it operates in the floating point domain and uses the Hamiltonian containing the elements dependent both on energy and position, the Hamiltonian matrix is larger in size. The size makes the method computationally challenging. To find the consequences of choosing one of the methods, a direct comparison between the computations, obtained for both methods with the same input parameters, was undertaken. The differences between the results are shown and explained. Selected simulations allowed us to discuss advantages and disadvantages of both methods. The calculations include transport parameters such as the density of states and the occupation functions, with regard to scattering processes where the self-consistent Born approximation was used, as well as the spatial distribution of electron concentration for two superlattices structures. The numerical results are obtained within the non-equilibrium Green’s functions formalism by solving the Dyson and the Keldysh equations.https://journals.pan.pl/Content/113175/PDF/20_631-642_00910_Bpast.No.67-3_06.02.20.pdfsemiconductor superlatticenegf formalismwannier functions |
| spellingShingle | M. Mączka G. Hałdaś Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations Bulletin of the Polish Academy of Sciences: Technical Sciences semiconductor superlattice negf formalism wannier functions |
| title | Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations |
| title_full | Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations |
| title_fullStr | Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations |
| title_full_unstemmed | Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations |
| title_short | Calculations of transport parameters in semiconductor superlattices based on the Greens’ functions method in different Hamiltonian representations |
| title_sort | calculations of transport parameters in semiconductor superlattices based on the greens functions method in different hamiltonian representations |
| topic | semiconductor superlattice negf formalism wannier functions |
| url | https://journals.pan.pl/Content/113175/PDF/20_631-642_00910_Bpast.No.67-3_06.02.20.pdf |
| work_keys_str_mv | AT mmaczka calculationsoftransportparametersinsemiconductorsuperlatticesbasedonthegreensfunctionsmethodindifferenthamiltonianrepresentations AT ghałdas calculationsoftransportparametersinsemiconductorsuperlatticesbasedonthegreensfunctionsmethodindifferenthamiltonianrepresentations |