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Efficient computational algorithm for calculating the electrical characteristics of nanoscale heterostructures based on the formalism of Landauer-Buttiker

DOI 10.18127/j22250980-201901-05


V.D. Shashurin – Dr.Sc. (Eng.), Professor, Head of the Department “Technology of instrumentation”, Bauman Mos-cow State Technical University (National Research University)
N.A. Vetrova – Ph.D. (Eng.), Associate Professor, Department “Technology of instrumentation”, Bauman Moscow State Technical University (National Research University)
K.P. Pchelintsev – Assistant, Department “Technology of instrumentation”, Bauman Moscow State Technical University (National Research University)
E.V. Kuimov – Post-graduate Student, Department “Technology of instrumentation” Bauman Moscow State Technical University (National Research University)
A.A. Koziy – Student, Bauman Moscow State Technical University (National Research University)

In the design of modern electronic devices based on nanoscale semiconductor structures an important task is to predict their operating parameters, taking into account technological factors and gerontological processes.On the one hand, such devices have attractive, as it was previously thought – unattainable due to the "fundamental physical limit" – properties that allow them to be attributed to the class of ultra-fast devices.On the other hand, the capabilities of the modern quantum-mechanical device allow to develop effective models of current transfer in channels of low-dimensional structures and, as a result, not only to predict the electrical properties of devices based on them, but also to design optimal devices according to the criterion of complex indicators that take into account the functional parameters and indicators of their reliability even in hard conditions.The most important advantage of modern ultra-fast electronics devices based on low – dimensional heterostructures, which allows to develop such optimization models, is "an additional degree of freedom" for the control of quantum mechanical effects in the structures of its topological and stoichiometric parameters.However, despite the high practical orientation of such models, the problem of widespread implementation and commercialization of software systems for the design and technological optimization of nanoelectronic devices on semiconductor heterostructures due to the complexity of algorithms and the task of improving their performance is extremely important. For example, the calculation of the current-voltage characteristic for a given topology of a heterostructure is a complex multi-iterative problem, the speed of which is significantly affected by the speed of the most frequently executed program blocks that solve various subtasks. The results on the development and implementation of an optimal from the point of view of resource intensity of the model is shown in the present work authors.
The presented mathematical model is developed on the basis of the numerical method of calculating the transparency block, taking into account the time complexity of the various ways of its implementation, has a time complexity O(2n*m) and provides a gain in performance of about 50% compared to the model based on the widely used to date conditional analytical method of transfer matrices. As a solution to the problem of reducing the order of accuracy of the finite-difference scheme, it is proposed to use a special kind of approximation based on the Integro-interpolation method. In order to minimize the operating time of the numerical model for calculating transparency, it is proposed to use sparse matrices as a basis for the formation of SLAE, the solution of which is carried out by the LU – decomposition method. Based on the results of verification and validation of the developed model, it is concluded that the efficiency of the algorithm is improved while maintaining the accuracy of forecasting the current-voltage characteristics of the device.

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