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Faculty of Electrical Engineering and In­for­ma­ti­on Technology
A detail shot of a laser in the lab in green colors. © Nikolas Golsch​/​TU Dortmund

Analysis and modeling of quantum components in THz technology and photonics

In analogy to microelectronics, efficient methods for analyzing the transport behavior within quantum components (quantum films, quantum wires, quantum dots) have to be developed in nanoelectronics and photonics. Existing methods for the numerical solution of the Wigner equation using the finite difference method or the Dyson equation using non-equilibrium Green functions are very complex and afflicted with a large number of problems, especially with regard to time-dependent simulations. The numerical approximation in the momentum space based on the Wigner equation also causes problems, since strongly oscillating integral kernels occur, coherent effects are not included and the bound states, which are important for many applications (lasers, modulators), cannot be recorded in principle.

On the basis of the von Neumann equation in centroid coordinates, the DFG project (Schu 1016/8-1) aims to develop fast algorithms for the stationary and transient case based on finite volume technology that avoid these problems. For this purpose, knowledge of the approximation of propagators for the calculation of wave propagation in electrodynamics should be used to solve the Von Neumann equation. With these measures, the inclusion of coherent effects as well as a reduction of the computing time and the integration of open boundary conditions succeed. In addition, an improved description of the electronic interaction mechanisms can be expected.

  • Development of numerical methods based on the finite volume technique to solve the von Neumann equation
  • On the basis of the results obtained, new methods for solving the Wigner equation are developed
  • Extension of the methods for the integration of electronic interaction mechanisms.
  • L. Schulz, B. Inci, M. Pech, D. Schulz, "Subdomain based Exponential Integrators for Quantum Liouville-type Equations", eingereicht bei J. Comput. Electron. 2021
  • L. Schulz, M. Pech, D. Schulz, "Dynamic Modelling of Quantum Transport within MGFETs", International Workshop on Computational Nanotechnology (Webkonferenz), Daejeon, South Korea, May 2021
  • L. Schulz and D. Schulz, "Approximation of Multiband Hamiltonians for the Wigner Equation", International Wigner Workshop (Webkonferenz), Daejeon, South Korea, May 2021
  • L. Schulz and D. Schulz, "Formulation of a phase space exponential operator for the Wigner transport equation accounting for the spatial variation of the effective mass", J. Comput Electron., doi.org/10.1007/s10825-020-01551-0, 2020
  • L. Schulz and D. Schulz, "Transient Mode Space based Quantum Liouville-type Equations applied onto DGFETs, International Conference on Simulation of Semiconductor Processes and Devices", Kobe, Japan, September 2020
  • L. Schulz and D. Schulz, "Multiband Phase Space Operator for Narrow Bandgap Semiconductor Devices, International Conference on Simulation of Semiconductor Processes and Devices", Kobe, Japan, September 2020
  • L. Schulz and D. Schulz, "Complex Absorbing Potential Formalism accounting for Open Boundary Conditions within the Wigner Transport Equation", IEEE Trans. Nanotechnology, vol. 18, pp. 830-838, doi: 10.1109/TNANO.2019.2933307, 2019
  • L. Schulz and D. Schulz, "Formulation of a Complex Absorbing Potential for the transient numerical solution of the Wigner Transport Equation", International Wigner Workshop, Chicago, USA, 2019
  • L. Schulz and D. Schulz, "Subdomain Algorithm for the Numerical Solution of the Liouville-von Neumann Equation", International Workshop on Computational Nanotechnology, Chicago, USA, 2019
  • L. Schulz and D. Schulz, "Numerical Analysis of the transient behavior of the nonequilibrium Quantum Liouville Equation", IEEE Trans. Nanotechnology, pp. 1197 - 1205, vol. 17, no. 6, 2018
  • L. Schulz and D. Schulz, "Boundary Concepts for an Improvement of the Numerical Solution with regard to the Wigner Transport Equation", International Conference on Simulation of Semiconductor Processes and Devices, Austin, Texas, USA, Sept. 2018
  • M. Pech, A, Abdi, D. Schulz, "Time-resolved analysis of DGFETs with non-parabolic energy dispersion for THz applications", Journal of Applied Physics, Nov. 2023, submitted
     
  • M. Pech, D. Schulz, "Investigating the impact of quantum confinement on the THz behavior of Nanoscale FinFETs", https://doi.org/10.1016/j.sse.2023.108808, Solid-State Electronics, vol. 210, Oct. 2023
     
  • A. Abdi, D. Schulz,  "Application of the Tight Binding Method onto the von-Neumann Equation", https://doi.org/10.21203/rs.3.rs-3255819/v1 , Journal of Computational Electronics, August 2023, preprint
     
  • A. Abdi and D. Schulz, "Resolving Inconsistencies between Discretizations for the Density Operator and the Wigner Function," 2023 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), Kobe, Japan, pp. 313-316, doi: 10.23919/SISPAD57422.2023.10319556. Sep. 2023
      
  • V. Ganiu and D. Schulz, "Application of a Hybrid Discontinuous Galerkin Scheme onto Quantum-Liouville-type Equations for Heterostructure Devices," 2023 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), Kobe, Japan, pp. 261-264, doi: 10.23919/SISPAD57422.2023.10319502., Sep. 2023
      
  • M. Pech and D. Schulz, "Transient Effects of Band Non-Parabolicity in DGFETs for RF Applications," 2023 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), Kobe, Japan, pp. 253-256, doi: 10.23919/SISPAD57422.2023.10319483., Sep. 2023
      
  • M. Pech, A. Abdi, D. Schulz, "Investigation of a Staggered Grid Formulation of the Wigner Transport Equation for Complex Band Structures ", IWW Book of Abstracts, International Wigner Workshop (IWW), Barcelona, Spain, Jun. 2023
     
  • A. Abdi, M. Pech, D. Schulz, "Incorporation of the Tight Binding Hamiltonian into Quantum Liouville-type Equations", IWCN Abstract ,International Workshop on Computational Nanotechnology (IWCN), Barcelona Spain, Jun. 2023
     
  • M. Pech, D. Schulz, "Investigating the impact of quantum confinement on the THz behavior of Nanoscale FinFETs", International Conference on Simulation of Semiconductor Processes and Devices (SISPAD) 2022 Special Issue, Granada, Spain, Feb. 2023 
     
  • Mathias Pech, Dirk Schulz, "THz gain compression in nanoscale FinFETs", Solid-State Electronics, vol. 199,  https://doi.org/10.1016/j.sse.2022.108485 , Oct. 2022
     
  • Mathias Pech, Dirk Schulz, "THz Gain compression in nanoscale FinFETs", International Conference on Si­mu­la­tion of Semiconductor Pro­cess­es and Devices, Granada, Spain, Sep. 2022
  • V. Ganiu and D. Schulz, "Efficiency Analysis of Discontinuous Galerkin Approaches for the Application onto Quantum-Liouville Type Equations", Journal of Computational Electronics, doi.org/10.21203/rs.3.rs-3744467/v1, Dec. 2023, preprint
     
  • V. Ganiu and D. Schulz, "Application of a Hybrid Discontinuous Galerkin Scheme onto Quantum-Liouville-type Equations for Heterostructure Devices," 2023 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), Kobe, Japan, pp. 261-264, doi: 10.23919/SISPAD57422.2023.10319502., Sep. 2023
      
  • V. Ganiu, D. Schulz, "Application of Discontinuous Galerkin Methods onto Quantum-Liouville type Equations", IWCN Abstract ,International Workshop on Computational Nanotechnology (IWCN), Barcelona, Spain, Jun. 2023
     
  • V. Ganiu, M. Jäger and D. Schulz, "Hybrid Discontinuous Galerkin Approach for the Solution of Quantum Liouville-Type Equations," in IEEE Transactions on Nanotechnology, vol. 22, pp. 696-705, doi: 10.1109/TNANO.2023.3322541, 2023
     
  • V. Ganiu, D. Schulz, "Hybrid Discontinuous Galerkin Approach for the Solution of Quantum Liouville-type Equations", International Conference on Si­mu­la­tion of Semiconductor Pro­cess­es and Devices, Granada, Spain, Nov. 2022
     
  • Valmir Ganiu, Dirk Schulz, "Discontinuous Galerkin concept for Quantum-Liouville type equations", Solid-State Electronics, doi.org/10.1016/j.sse.2022.108536 , Nov. 2022
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