Predictive modelling of structure formation in semiconductor films produced by meniscus-guided coating

A Publisher Correction to this article was published on 01 October 2020

A Publisher Correction to this article was published on 22 September 2020

An Author Correction to this article was published on 28 August 2020

This article has been updated


Meniscus-guided coating methods, such as zone casting, dip coating and solution shearing, are scalable laboratory models for large-area solution coating of functional materials for thin-film electronics. Unfortunately, the general lack of understanding of how the coating parameters affect the dry-film morphology upholds trial-and-error experimentation and delays lab-to-fab translation. We present herein a model that predicts dry-film morphologies produced by meniscus-guided coating of a crystallizing solute. Our model reveals how the interplay between coating velocity and evaporation rate determines the crystalline domain size, shape anisotropy and regularity. If coating is fast, evaporation drives the system quickly past supersaturation, giving isotropic domain structures. If coating is slow, depletion due to crystallization stretches domains in the coating direction. The predicted morphologies have been experimentally confirmed by zone-casting experiments of the organic semiconductor 4-tolyl-bithiophenyl-diketopyrrolopyrrole. Although here we considered a small molecular solute, our model can be applied broadly to polymers and organic–inorganic hybrids such as perovskites.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Schematic representation of the computational domain and coating process.
Fig. 2: Computational and experimental morphologies.
Fig. 3: Order parameter profiles and approach to steady state.
Fig. 4: Mapping of the parameter space determined by coating speed and evaporation rate.
Fig. 5: Film thickness, initial concentration and simulated crystalline morphology as a function of coating speed and evaporation rate.
Fig. 6: Overview of the numerical simulations: domain statistics, order parameter profiles, parameter space mapping and aligned morphologies.

Data availability

The data represented in Figs. 2c,d, 3, 5a–c and 6a,b are available online at Other data from the current study are available from the corresponding author upon reasonable request.

Code availability

The code that support the findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 21 August 2020

    In the PDF version of this Article originally published, some of the equations in the Methods section were incorrect. The HTML version, however, was correct. The PDF has now been updated.

  • 28 August 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

  • 22 September 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

  • 01 October 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


  1. 1.

    Diao, Y., Shaw, L., Bao, Z. & Mannsfeld, S. C. B. Morphology control strategies for solution-processed organic semiconductor thin films. Energy Environ. Sci. 7, 2145–2159 (2014).

    CAS  Google Scholar 

  2. 2.

    Gu, X., Shaw, L., Gu, K., Toney, M. F. & Bao, Z. The meniscus-guided deposition of semiconducting polymers. Nat. Commun. 9, 534–549 (2018).

    Google Scholar 

  3. 3.

    Patel, B. B. & Diao, Y. Multiscale assembly of solution-processed organic electronics: the critical roles of confinement, fluid flow, and interfaces. Nanotechnology 29, 044004 (2018).

    Google Scholar 

  4. 4.

    Sele, C. W. et al. Controlled deposition of highly ordered soluble acene thin films: effect of morphology and crystal orientation on transistor performance. Adv. Mater. 21, 4926–4931 (2009).

    CAS  Google Scholar 

  5. 5.

    Rogowski, R. Z. & Darhuber, A. A. Crystal growth near moving contact lines on homogeneous and chemically patterned surfaces. Langmuir 26, 11485–11493 (2010).

    CAS  Google Scholar 

  6. 6.

    Zhang, K. et al. Crystallization control of organic semiconductors during meniscus-guided coating by blending with polymer binder. Adv. Funct. Mater. 28, 1805594 (2018).

    Google Scholar 

  7. 7.

    Gans, A. et al. Dip-coating of suspensions. Soft Matter 15, 252–261 (2019).

    CAS  Google Scholar 

  8. 8.

    Grosso, D. How to exploit the full potential of the dip-coating process to better control film formation. J. Mater. Chem. 21, 17033–17038 (2011).

    CAS  Google Scholar 

  9. 9.

    Giri, G. et al. Tuning charge transport in solution-sheared organic semiconductors using lattice strain. Nature 480, 504–508 (2011).

    CAS  Google Scholar 

  10. 10.

    Gsänger, M. et al. High-performance organic thin-film transistors of J-stacked squaraine dyes. J. Am. Chem. Soc. 136, 2351–2362 (2014).

    Google Scholar 

  11. 11.

    Galindo, S., Tamayo, A., Leonardi, F. & Mas-Torrent, M. Control of polymorphism and morphology in solution sheared organic field-effect transistors. Adv. Funct. Mater. 27, 1700526 (2017).

    Google Scholar 

  12. 12.

    Haase, K. et al. Solution shearing of a high‐capacitance polymer dielectric for low‐voltage organic transistors. Adv. Electron. Mater. 5, 1900067 (2019).

    Google Scholar 

  13. 13.

    Tamayo, A., Riera-Galindo, S., Jones, A. O. F., Resel, R. & Mas-Torrent, M. Impact of the ink formulation and coating speed on the polymorphism and morphology of a solution‐sheared thin film of a blended organic semiconductor. Adv. Mater. Interfaces 6, 1900950 (2019).

    CAS  Google Scholar 

  14. 14.

    Pisula, W. et al. A zone‐casting technique for device fabrication of field‐effect transistors based on discotic hexa‐peri‐hexabenzocoronene. Adv. Mater. 17, 684–689 (2005).

    CAS  Google Scholar 

  15. 15.

    Tang, C., Wu, W., Smilgies, D.-M., Matyjaszewski, K. & Kowalewski, T. Robust control of microdomain orientation in thin films of block copolymers by zone casting. J. Am. Chem. Soc. 133, 11802–11809 (2011).

    CAS  Google Scholar 

  16. 16.

    Su, Y. et al. Uniaxial alignment of triisopropylsilylethynyl pentacene via zone-casting technique. Phys. Chem. Chem. Phys. 15, 14396–14404 (2013).

    CAS  Google Scholar 

  17. 17.

    Janneck, R., Vercesi, F., Heremans, P., Genoe, J. & Rolin, C. Predictive model for the meniscus-guided coating of high-quality organic single-crystalline thin films. Adv. Mater. 28, 8007–8013 (2016).

    CAS  Google Scholar 

  18. 18.

    Xie, Y.-M. et al. Solution processable small molecule based organic light-emitting devices prepared by dip-coating method. Org. Electron. 55, 1–5 (2018).

    CAS  Google Scholar 

  19. 19.

    Dörling, B. et al. Uniaxial macroscopic alignment of conjugated polymer systems by directional crystallization during blade coating. J. Mater. Chem. C. 2, 3303–3310 (2014).

    Google Scholar 

  20. 20.

    He, M. et al. Meniscus-assisted solution printing of large-grained perovskite films for high-efficiency solar cells. Nat. Commun. 8, 16045 (2017).

    CAS  Google Scholar 

  21. 21.

    Lee, J.-C., Kim, J.-O., Lee, H.-J., Shin, B. & Park, S. Meniscus-guided control of supersaturation for the crystallization of high quality metal organic framework thin films. Chem. Mater. 31, 7377–7385 (2019).

    CAS  Google Scholar 

  22. 22.

    Dimitrov, A. S. & Nagayama, K. Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces. Langmuir 13, 1303–1311 (1996).

    Google Scholar 

  23. 23.

    Jing, G., Bodiguel, H., Doumenc, F., Sultan, E. & Guerrier, B. Drying of colloidal suspensions and polymer solutions near the contact line: deposit thickness at low capillary number. Langmuir 26, 2288–2293 (2010).

    CAS  Google Scholar 

  24. 24.

    Berteloot, G., Pham, C.-T., Daerr, A., Lequeux, F. & Limat, L. Evaporation-induced flow near a contact line: consequences on coating and contact angle. Europhys. Lett. 83, 14003 (2008).

    Google Scholar 

  25. 25.

    Doumenc, F. & Guerrier, B. Drying of a solution in a meniscus: a model coupling the liquid and the gas phases. Langmuir 26, 13959–13967 (2010).

    CAS  Google Scholar 

  26. 26.

    Doumenc, F. & Guerrier, B. Self-patterning induced by a solutal Marangoni effect in a receding drying meniscus. EPL 103, 14001 (2013).

    Google Scholar 

  27. 27.

    Dey, M., Doumenc, F. & Guerrier, B. Numerical simulation of dip-coating in the evaporative regime. Eur. Phys. J. E 39, 19 (2016).

    Google Scholar 

  28. 28.

    Le Berre, M., Chen, Y. & Baigl, D. From convective assembly to Landau–Levich deposition of multilayered phospholipid films of controlled thickness. Langmuir 25, 2554–2557 (2009).

    Google Scholar 

  29. 29.

    Doumenc, F., Salmon, J.-B. & Guerrier, B. Modeling flow coating of colloidal dispersions in the evaporative regime: prediction of deposit thickness. Langmuir 32, 13657–13668 (2016).

    CAS  Google Scholar 

  30. 30.

    Landau, L. & Levich, B. G. Dragging of a liquid by a moving plate. Acta Physicochim. U.R.S.S 17, 42–54 (1942).

    Google Scholar 

  31. 31.

    Deryaguin, B. C. R. Thickness of liquid layer adhering to walls of vessels on their emptying and the theory of photo- and motion-picture film coating. Acad. Sci. USSR 39, 13–16 (1943).

    Google Scholar 

  32. 32.

    Peng, B., Wang, Z. & Chan, P. K. L. A simulation-assisted solution-processing method for a large-area, high-performance C10-DNTT organic semiconductor crystal. J. Mater. Chem. C. 4, 8628–8633 (2016).

    CAS  Google Scholar 

  33. 33.

    Zhang, Z., Peng, B., Ji, X., Pei, K. & Chan, P. K. L. Marangoni‐effect‐assisted bar‐coating method for high‐quality organic crystals with compressive and tensile strains. Adv. Funct. Mater. 27, 1703443 (2017).

    Google Scholar 

  34. 34.

    Janneck, R., Karagiannis, D., Heremans, P., Genoe, J. & Rolin, C. Influence of solute concentration on meniscus-guided coating of highly crystalline organic thin films. Adv. Mater. Interfaces 6, 1900614 (2019).

    CAS  Google Scholar 

  35. 35.

    Provatas, N. & Elder, K. Phase-Field Methods in Materials Science and Engineering (Wiley, 2010).

  36. 36.

    Eres, M. H., Weidner, D. E. & Schwartz, L. W. Three-dimensional direct numerical simulation of surface-tension-gradient effects on the leveling of an evaporating multicomponent fluid. Langmuir 15, 1859–1871 (1999).

    CAS  Google Scholar 

  37. 37.

    Vieyra Salas, J. A., van der Veen, J. M., Michels, J. J. & Darhuber, A. A. Active control of evaporative solution deposition by modulated infrared illumination. J. Phys. Chem. C. 116, 12038–12047 (2012).

    CAS  Google Scholar 

  38. 38.

    van Franeker, J. J. et al. Controlling the dominant length scale of liquid–liquid phase separation in spin‐coated organic semiconductor films. Adv. Funct. Mater. 25, 855–863 (2015).

    Google Scholar 

  39. 39.

    Sharifi Dehsari, H., Michels, J. J. & Asadi, K. Processing of ferroelectric polymers for microelectronics: from morphological analysis to functional devices. J. Mater. Chem. C. 5, 10490–10497 (2017).

    Google Scholar 

  40. 40.

    Abolhasani, M. M. et al. Thermodynamic approach to tailor porosity in piezoelectric polymer fibers for application in nanogenerators. Nano Energy 62, 594–600 (2019).

    CAS  Google Scholar 

  41. 41.

    Allen, S. M. & Cahn, J. W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27, 1085–1095 (1979).

    CAS  Google Scholar 

  42. 42.

    Schaefer, C., Michels, J. J. & van der Schoot, P. Structuring of thin-film polymer mixtures upon solvent evaporation. Macromolecules 49, 6858–6870 (2016).

    CAS  Google Scholar 

  43. 43.

    Schaefer, C., Michels, J. J. & van der Schoot, P. Dynamic surface enrichment in drying thin-film binary polymer solutions. Macromolecules 50, 5914–5919 (2017).

    CAS  Google Scholar 

  44. 44.

    Fan, D., Chen, S. P., Chen, L.-Q. & Voorhees, P. W. Phase-field simulation of 2-D Ostwald ripening in the high volume fraction regime. Acta Mater. 50, 1895–1907 (2002).

    CAS  Google Scholar 

  45. 45.

    Cogswell, D. A. & Carter, W. C. Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases. Phys. Rev. E 83, 061602 (2011).

    Google Scholar 

  46. 46.

    Li, M. et al. Ferroelectric phase diagram of PVDF: PMMA. Macromolecules 45, 7477–7485 (2012).

    CAS  Google Scholar 

  47. 47.

    Gránásy, L., Börzsönyi, T. & Pusztai, T. Nucleation and bulk crystallization in binary phase field theory. Phys. Rev. Lett. 88, 206105 (2002).

    Google Scholar 

  48. 48.

    Gránásy, L., Pusztai, T. & Warren, J. A. Modelling polycrystalline solidification using phase field theory. J. Phys.: Condens. Matter 16, R1205 (2004).

    Google Scholar 

  49. 49.

    Gránásy, L., Pusztai, T., Tegze, G., Warren, J. A. & Douglas, J. F. Growth and form of spherulites. Phys. Rev. E 72, 011605 (2005).

    Google Scholar 

  50. 50.

    Dai, X., Deng, Y., Van Brackle, C. H. & Huang, J. Meniscus fabrication of halide perovskite thin films at high throughput for large area and low-cost solar panels. Int. J. Extrem. Manuf. 1, 022004 (2019).

    Google Scholar 

  51. 51.

    Yang, M. et al. Facile fabrication of large-grain CH3NH3PbI3xBrx films for high-efficiency solar cells via CH3NH3Br-selective Ostwald ripening. Nat. Commun. 7, 12305 (2016).

    CAS  Google Scholar 

  52. 52.

    Wheeler, A. A., Boettinger, W. J. & McFadden, G. B. Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45, 7424–7439 (1992).

    CAS  Google Scholar 

  53. 53.

    Wang, S.-L. et al. Thermodynamically-consistent phase-field models for solidification. Physica D 69, 189–200 (1993).

    CAS  Google Scholar 

  54. 54.

    Egry, I., Ricci, E., Novakovic, R. & Ozawa, S. Surface tension of liquid metals and alloys—recent developments. Adv. Colloid Interface Sci. 159, 198–212 (2010).

    CAS  Google Scholar 

  55. 55.

    de Gennes, P. G. Dynamics of fluctuations and spinodal decomposition in polymer blends. J. Chem. Phys. 72, 4756–4763 (1980).

    Google Scholar 

  56. 56.

    Nagele, G., Dhont, J. K. G. & Meier, G. in Diffusion in Condensed Matter: Methods, Materials, Models (eds Heitjans, P. & Kärger, J.) 706 (Springer, 2005).

  57. 57.

    Kramer, E. J., Green, P. & Palmstrøm, C. J. Interdiffusion and marker movements in concentrated polymer-polymer diffusion couples. Polymer 25, 473–480 (1984).

    CAS  Google Scholar 

  58. 58.

    Ronsin, O. J. J. & Harting, J. Strict equivalence between Maxwell–Stefan and fast-mode theory for multicomponent polymer mixtures. Macromolecules 52, 6035–6044 (2019).

    CAS  Google Scholar 

  59. 59.

    Michels, J. J. & Moons, E. Simulation of surface-directed phase separation in a solution-processed polymer/PCBM blend. Macromolecules 46, 8693–8701 (2013).

    CAS  Google Scholar 

  60. 60.

    Wedershoven, H. M. J. M., Zeegers, J. C. H. & Darhuber, A. A. Polymer film deposition from a receding solution meniscus: the effect of laminar forced air convection. Chem. Eng. Sci. 181, 92–100 (2018).

    CAS  Google Scholar 

  61. 61.

    Saylor, D. M., Kim, C.-S., Patwardhan, D. V. & Warren, J. A. Diffuse-interface theory for structure formation and release behavior in controlled drug release systems. Acta Biomater. 3, 851–864 (2007).

    CAS  Google Scholar 

Download references


The authors acknowledge P. W. M. Blom for stimulating discussions. K.Z. acknowledges the China Scholarship Council (CSC) for financial support. T.M. acknowledges the Foundation for Polish Science financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-3ED8/17-01).

Author information




J.J.M. developed the model, performed numerical simulations and analysed the results of calculations; K.Z. performed zone-casting experiments and morphological analysis; P.W. and P.M.B. synthesized and characterized DPP(Th2Bn)2; W.P. and T.M. assisted in the interpretation of the results of calculations; J.J.M., K.Z., W.P. and T.M. contributed to the writing of this manuscript.

Corresponding author

Correspondence to Jasper J. Michels.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Synthesis details and spectra, supplementary discussion, Figs. S1–S13 and Tables S1–S5.

Supplementary Video 1

Video of coating of aligned domains.

Supplementary Video 2

Video of coating of stretched domains.

Supplementary Video 3

Video of coating of isotropic domains.

Supplementary Video 4

Video of coating of isotropic domains for a large field-of-view.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Michels, J.J., Zhang, K., Wucher, P. et al. Predictive modelling of structure formation in semiconductor films produced by meniscus-guided coating. Nat. Mater. (2020).

Download citation


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing