AA2 – Materials, Light, Devices



Electro-Mechanical Coupling for Semiconductor Devices

Project Heads

Patricio Farrell, Annegret Glitzky, Matthias Liero, Barbara Zwicknagl

Project Members

Petr Vágner (from 01/22 on), Grigor Nika (until 12/21)

Project Duration

01.01.2021 − 31.12.2022

Located at



Mechanical strain has a strong impact on the electronic and optical properties of semiconductor materials. Therefore, strain engineering is crucial in novel optoelectronic device designs e.g. for Germanium microbridges or quantum dots. Also elastomeric polymer LEDs emit significant light if they are exposed to strains in the range of 120%.


Considerable strain is reached in quasi lower-dimensional structures like nano- and microwires or thin-film (organic) LEDs and solar cells. Our partners at Paul-Drude Institute (PDI) observe a strong influence of strain on the mobility in nanowires [4]. Whereas in practice such phenomena are often described by small-strain elasticity as input for charge-carrier transport and no backward coupling is taken into account, in this project we consider the full coupling in the finite-strain setting.


The project follows three main topics: (i) We derive nonlinear PDE models for the coupling of charge-carrier transport and finite-strain elasticity. We plan a consistent modeling using the GENERIC framework (see [1,6,7]) and want to seek the consistency with the small-strain setting. (ii) Our analytical investigations concern the isothermal situation with realistic mixed boundary conditions. For different temporal regimes we study the existence of solutions and their properties. Analytical tools are time discretization, Galerkin approximation, and Schauder’s fixed-point theorem. Moreover, we assume second-grade non-simple materials as in [8,9]. Additionally, we derive effective models for thin wires, where the elasticity is reduced to a 1D rod model, see [2], and the charge transport remains fully 3D. (iii) The final aim is develop and approve new numerical techniques for specific applications. We derive structure preserving discretizations based on finite-volume methods and generalized Scharfetter-Gummel schemes that include mechanical (small-) strain. Here, we combine the existing ddfermi solver for charge-transport with a linear elasticity solver. Additionally, we include the backward coupling to elasticity and perform simulations for single nanowire investigated at our partners at PDI.

External Website


The Workshop Applied Mathematics and Simulation for Semiconductors and Electrochemical Systems AMaSiS 2021 took place from September 6-9, 2021

Project Publications

  1. F. Agnelli, G. Nika, and A. Constantinescu. Design of thin micro-architectured panels with extension-bending coupling effects using topology optimization. Computer Methods in Applied Mechanics and Engineering, 391:114496, 2022.
  2. A. Glitzky, M. Liero, and G. Nika. Analysis of a bulk-surface thermistor model for large-area organic light-emitting diodes. Portugaliae Mathematica, 78:187–210, 2021.
  3. A. Glitzky, M. Liero, and G. Nika. Dimension reduction of thermistor models for large-area organic light-emitting diodes. DCDS-S, 14:3953–3971, 2021.
  4. A. Glitzky, M. Liero, and G. Nika. Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures. J. Math. Anal. Appl., 507:125815, 2022.
  5. A. Glitzky, M. Liero, and G. Nika. A coarse-grained electrothermal model for organic semiconductor devices. Math. Meth. Appl. Sci., 45:4809–4833, 2022.
  6. A. Kirch, A. Fischer, M. Liero, J. Fuhrmann, A. Glitzky, and S. Reineke. Electrothermal tristability causes sudden burn-in phenomena in organic LEDs. Adv. Funct. Mater., 31:2106716, 2021.
  7. P. Vágner, M. Pavelka, J. Fuhrmann, and V. Klika. A multiscale thermodynamic generalization of Maxwell–Stefan diffusion equations, and of the dusty gas model. Int. J. Heat Mass Transf., 199:123405, 2022.
  8. M. Heida, M. Landstorfer, and M. Liero. Homogenization of a porous intercalation electrode with phase separation. WIAS Preprint 2905, Berlin, 2021.

  9. M. Liero, A. Mielke, and G. Savaré. Fine properties of geodesics and geodesic λ-convexity for the Hellinger–Kantorovich distance. WIAS Preprint 2956, Berlin, 2022.

  10. P. Farrell. Drift-diffusion models for innovative semiconductor devices and their numerical solution. Habilitation thesis, Freie Universität Berlin, 2023.

  11. M. Liero. Mathematical analysis of charge and heat flow in organic semiconductor devices. Habilitation thesis, Humboldt-Universität zu Berlin, 2022.

  12. G. Nika. Derivation of effective models from heterogeneous Cosserat media via periodic unfold- ing. Ric. Mat., DOI 10.1007/s11587-021-00610-3, published online on 01.07.2021, 2021.

  13. G. Nika and B. Vernescu. Micro-geometry effects on the nonlinear effective yield strength re- sponse of magnetorheological fluids. In P. Donato and M. Luna-Laynez, editors, Emerging problems in the Homogenization of Partial Differential Equations. SEMA SIMAI Springer Series, 2021.


Related Publications

  1. M. Grmela and H. Chr. Öttinger: Dynamics and thermodynamics of complex fluids. I. Development of a general formalism, Phys. Rev. E (3) 56.6 (1997), pp. 6620–6632.
  2. R. V. Kohn and E. O’Brien: On the bending and twisting of rods with misfit, Journal of Elasticity, 130 (2018) pp. 115–143.
  3. M. Kružík and T. Roubíček: Mathematical methods in continuum mechanics of solids, Cham: Springer, 2019.
  4. R. B. Lewis, P. Corfdir, H. Küpers, T. Flissikowski, O. Brandt, and L. Geelhaar: Nanowires bending over backward from strain partitioning in asymmetric core-shell heterostructures, Nano Letters, 18 (2018) pp. 2343–2350.
  5. A. Mielke: A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, Nonlinearity 24.4 (Mar. 2011), pp. 1329–1346.
  6. A. Mielke: Formulation of thermoelastic dissipative material behavior using GENERIC, Contin. Mech. Thermodyn. 23.3 (2011), pp. 233–256.
  7. H. Chr. Öttinger and M. Grmela: Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism, Phys. Rev. E (3) 56.6 (1997), pp. 6633–6655.
  8. T. Roubíček and A. Mielke: Thermoviscoelasticity in Kelvin–Voigt rheology at large strains, Arch. Ration. Mech. Anal., 238 (2020)
  9. T. Roubíček and G. Tomassetti: Dynamics of charged elastic bodies under diffusion at large strains, DCDS-B 25.4 (2020) pp. 1415–437.
  10. P. Vágner, M. Pavelka, O. Esen, Multiscale thermodynamics of charged mixtures, Contin. Mech. Thermodyn., (2020), DOI 10.1007/s00161-020-00900-5.
  11. M. Heida, M. Landstorfer, M. Liero, Homogenization of a porous intercalation electrode with phase separation, WIAS Preprint No. 2905, (2021), DOI 10.20347/WIAS.PREPRINT.2905
  12. V. Miloš, P. Vágner, D. Budáč, M. Carda, M. Paidar, J. Fuhrmann, K. Bouzek, Generalized Poisson-Nernst-Planck-Based Physical Model of the O2| LSM| YSZ, Electrode. Journal of The Electrochemical Society (2022), DOI 10.1149/1945-7111/ac4a51

Related Pictures

Simulation picture by Y. Hadjimichael (WIAS Berlin)