10.26165/JUELICH-DATA/8WA9I7Wittberg, ClemensClemensWittbergPGI-7, Forschungszentrum Jülich GmbHJülich DATA2026EngineeringMathematical SciencesPhysicsBand-alignmentReRAMMemristive DeviceWittberg, ClemensClemensWittbergPGI-7, Forschungszentrum Jülich GmbHDeckers, MalteMalteDeckersPGI-7, Forschungszentrum Jülich GmbHDittmann, ReginaReginaDittmannPGI-7, Forschungszentrum Jülich GmbH2026-07-282026-07-30source code1325185377717373943498127181117679661027564application/x-ipynb+jsontext/x-pythonapplication/x-ipynb+jsontext/x-pythonapplication/ziptext/plain; charset=UTF-8text/markdowntext/markdowntext/plain1.0MIT License Copyright (c) 2026 Clemens J. Wittberg / Peter Grünberg Institut 7 for electronic materials Forschungszentrum Jülich Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.The corresponding git repository can be found at: https://iffgit.fz-juelich.de/pgi-7/band-alignment-calculations This repository contains the numerical model used to calculate the equilibrium and bias-dependent electrostatic potential, electric field, charge density, and conduction/valence band profiles across arbitrarily complex, multi-layer (metal–insulator–semiconductor) heterostructures. The model self-consistently solves the Poisson equation as a two-point boundary value problem (BVP), including: Position-dependent doping/trap concentrations, permittivities, effective masses, and electron affinities across an arbitrary number of layers. A Gaussian-distributed trap density of states (DOS) per material, with configurable mean depth, standard deviation, and relative weight for multiple trap species. Fermi–Dirac occupation statistics (with spin degeneracy for donor-like traps) for both trapped charge and free carriers in the conduction band (parabolic band approximation). Externally applied bias, including additional voltage-drop terms to capture non-ideal voltage division across the stack (e.g., due to interface dipoles or series resistances). The output of the model is the spatial profile of the conduction and valence band edges, which can be used to interpret band alignment, barrier formation, and accumulation/depletion behavior at oxide interfaces relevant to resistive-switching (memristive) devices.Deutsche Forschungsgemeinschaft528378584Federal Ministry of Research Technology and Space16ME0398KFederal Ministry of Research Technology and Space03ZU1106ABFederal Ministry of Research Technology and Space03ZU1106AAFederal Ministry of Research Technology and Space16ES1133K