# Thin film photonic crystals: synthesis and characterisation

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## General Information

Authors: M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.

Publication: Journal of Materials Chemistry, 14:144–150, 2004.

Keywords: Thin film, colloids, photonic crystal, self-assembly

## Summary

This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals. The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals. There are many diverse applications and methods to create photonic crystals such as synthetic opals. One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study. The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate. While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution. The crystals are then characterized using various microscopy and spectroscopy methods.

## Experimental methods

The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1]. Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed. The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).

The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C). The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚. The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air. Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator. The size of the sample grown was 10 x 40 mm $^2$ for all temperatures and RH. Depending on the conditions, the growth times ranged from < 4 to 40 days. The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.

For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached. This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).

Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker is 200 µm. From [1].

The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples. This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.

For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm $^2$ spot on the sample at controlled angles. The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm). Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1]. As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.

Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].

In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of $n_{eff}^2$, the square of the effective refractive index and a slope of $1/(4d)^2$, where $d$ is the interplanar spacing in the (111) direction.

Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].

This arises form Bragg's law: $n \lambda = 2 d \sin \theta$ and Snells law: $n_1 \sin \theta_1 = n_2 \sin \theta _2$ to produce [1]:

$\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2}$.

This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information. For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis. SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of growth.

Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.

## Results and discussion

These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films. Temperature, T was found to have the largest effect on the growth quality of the crystals. Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C. Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 $\times$ 300 µm at 65 ˚C). FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process. The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.

Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects. In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%. Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate. Hence, the results suggest that low RH is better for growing these types of crystals. For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚. However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.

The authors also found that higher concentrations of the PS spheres produced thicker thin films. However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate. Hence, they determined that 1% was optimal for fabrication. Sphere diameter was found to have little effect on the growth properties of the crystals.

Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings. They also used it to determine that temperature was most significant for optimizing the domain size. Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was. It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.

As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks. They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.

## References

[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.

Entry by: Xingyu Zhang, AP225, Fall 2012