Quantum Point Contact simulations on ISIS structure

In the work a numerical method of dissolving the Poisson equation in an electrostatically formed Quantum Point Contact (QPC) is described. Such a device is based on the structure called ISIS (Inverted Semiconductor Insulator Semiconductor). This structure was proposed in 1991 by Kastner [1] who made single electron transistor in it. In this paper the Poisson equation is solved by means of boundary elements method [2] with functions of the single layer potential [3] whose result provides potential distributions of the QPC device. The electronic properties of the QPC model are found by the use of Green functions method [4]. The interaction between structure and two leads is described by self-energy method [5]. The QPC conductance is calculated with the help of Landauer formula, after the Green’s function corresponding to device Hamiltonian is evaluated

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 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