Spatial modeling of the 3D morphology of hybrid polymer-ZnO solar cells, based on electron tomography data

Abstract

A spatial stochastic model is developed which describes the 3D nanomorphology of composite materials, being blends of two different (organic and inorganic) solid phases. Such materials are used, for example, in photoactive layers of hybrid polymer zinc oxide solar cells. The model is based on ideas from stochastic geometry and spatial statistics. Its parameters are fitted to image data gained by electron tomography (ET), where adaptive thresholding and stochastic segmentation have been used to represent morphological features of the considered ET data by unions of overlapping spheres. Their midpoints are modeled by a stack of 2D point processes with a suitably chosen correlation structure, whereas a moving-average procedure is used to add the radii of spheres. The model is validated by comparing physically relevant characteristics of real and simulated data, like the efficiency of exciton quenching, which is important for the generation of charges and their transport toward the electrodes.

A Multiscale Approach to the Representation of 3d Images, With Application to Polymer Solar Cells

“…The locations of the spheres are the points and the corresponding radii the marks. This representation allows us to analyse and model the set B ′′′ using tools from point-process theory; see Stenzel et al (2011).…”

“…Spatial stochastic models as considered in Stenzel et al (2011), which are based on the results derived in the present paper, can be used to identify morphologies with improved efficiency by generating virtual morphologies and investigating the transport processes of electrons and excitons, respectively.…”

“…On the other hand, the functionality of the solar cells heavily depends on the fine structures, which are removed by morphological smoothing. Thus, these 'misspecified' voxels are also included into stochastic simulation models considered in Stenzel et al (2011). They are interpreted as the 'micro-scale' nanostructure of the binarized ET images, whereas the morphologically smoothed images represented by unions of overlapping spheres describe the nanostructure on a 'macro-scale'.…”

“…The advantage of this off-grid representation of the macro-scale part of the nanostructure is that it can be modeled relatively easily, independent of any given resolution or grid structure of the underlying ET images. This is the subject of a forthcoming paper where we develop a stochastic simulation model of the 3D nanostructure; see Stenzel et al (2011). This model is based on the multiscale approach to the description of image data with geometrically complex structure considered in the present paper.…”

Simulating charge transport in organic semiconductors and devices: a review

“…Stenzel et al [461] used this method to first determine the statistical properties of a P3HT-Zinc Oxide (ZnO) blend from transmission electron microscope images and then use this information to generate equivalent morphologies. The equivalence of experimental and generated morphologies was then tested by simulating exciton dissociation efficiencies [461], as well as connectivity and mobility of the P3HT and ZnO phases [462], and good agreement was observed in all cases. Westhoff et al [463] demonstrated that parameterising the statistical properties of a range of polymer-fullerene blend with respect to a process variable (spin speed in this case) could accurately predict the morphology of a blend which was not used to train the stochastic model.…”