Mechanism of hollow nanopyramid growth

Figure 5-6 Schematic diagrams to describe the formation mechanism of the hollow nanopyramidal arrays at the Ta/Al interface

Schematic illustration of the formation process of the hollow tantalum oxide nanostructure has been showed in Figure 5-6. In the earlier stage, the upper Al layer was anodized to Al2O3, accompanied by the outward migration of Al³⁺ and inward diffusion of O^2- driven by the applied electric field, leading to the vertical pore channel growth. As the oxide barrier layer at the bottom of the pore approaches the Ta/Al interface, anodization of the underlying tantalum can be initiated. The O 2-migrating inward through the alumina barrier layer is injected into the Ta layer and the tantalum oxide nucleus is formed. (see Figure 5-6(b)). The growth of the tantalum oxide nanostructure resulting from the continuously injecting O^2- accompanies the volume expansion of tantalum oxide formation. The barrier layer was thinned by

dissolution of H3PO4 etching and more O^2-/ OH^- ions passed through it readily. The excess O^2-/ OH^- ions were too many to oxidize limited tantalum ions and combined with themselves. Thus, O^2-/ OH^- ions combined and released O2 gas at the anode. The formation of the gaseous oxygen, acting as porogen, producing a great pressure, expand the tantalum oxide hillock and leave a void inside between tantalum oxide hillock and underlying substrate. In fact, the similar phenomenon has been observed at the pore bottom of anodized alumina on silicon substrate without metal interlayer.

Although previous reports indicated that these voids may be formed by dissolution of the alumina near the silicon surface because of a localized-temperature-enhanced or electric-field-enhanced dissolution near the interface ^[1], tantalum oxide, such anti-corrosive and thermal-stable material, is difficult to be dissolved in this condition.

Besides, the integral hollow hillocks grew up continuously instead of shrinking by etching. This result suggests that the dissolution of the tantalum oxide hillock is not the cause of the void formation since physical stress of gaseous pressure has been demonstrated ^[2]. As the voids expanded by gaseous oxygen, the barrier layers were dissolved entirely, and hollow hillocks grew upward. Finally, a pyramid-like hollow nanostructure array appeared. Note that the alumina layer and hollow nanostructures were peeled off the substrate at redundant anodizing time.

Figure 5-7 (a) SEM image of the inverted and reduced barrier layer. Anodization for

this structure was performed at 100 V, yet the same barrier layer features were observed at lower anodizing voltages on n-type Si. The white bar is 200 nm long.^[1] (b) Field-emission scanning electron microscope (FESEM) images of fracture sections where alumina film full off the substrate. ^[2]

5.3 Antireflective Properties

To demonstrate the tunable optical properties with various thicknesses of hollow nanostructure, three species with different thicknesses of initial tantalum films were applied. The experimental optical reflectivity of nanopyramidal arrays on AlN substrate is shown as a function of wavelength in Figure 5-8. An integrating sphere was used in measurement, which collects the diffuse and specular reflectance from all directions. In the meantime, the reflectance data were compared with calculations of the reflectance from nonstructured alumina nitride substrate over a spectral range from 200 to 900 nm. The results clearly show that there are distinct differences on the reflectance of three samples. The hemispherical reflectance of nanopyramid-arrays coated on AlN will increase because of the increase in the hollow portion of pyramidal nanostructure. The graded index, which is observed for 200 nm solid pyramid, changes from air to substrate gradually since the bulk tantalum oxide has an approximate refractive index to alumina nitride. However, the hollow portion of the nanostructure, which comprises low refractive index of nair=1, reduces the effective refractive index of the whole nanostructure. Therefore, a distinct gap of refractive indexes between hollow nanostructure and substrate results in much higher reflectivity than solid nanostructure.

Figure 5-8 The experimental reflectance of nanopyramidal arrays on AlN substrate

A multilayer rigorous coupled wave analysis (RCWA) has also been developed to complement the optical measurement. Firstly, we divide the pyramid array into 20 horizontal layers with equal thickness. We used different H/B ratio which was defined by hollow length/base length of pyramidal geometry as simulated conditions with hexagonal array (Figure 5-9). Based on the effective medium theory ^[3], the effective refractive index neff(z) of the layer at level z can be approximated by

( ) ( [ ( )

(

( ) )

] )

eff z f z N f z n

n = X + −

where f(z) is the fraction of tantalum oxide contained in the layer, NTaOx=n+ik is the complex refractive index of tantalum oxide (n and k are optical constants), and nair =1.

The optical constants of tantalum oxide and AlN which are functions of wavelengths are obtained from ellipsometry measurement.

Figure 5-9 Schematic diagrams of effective medium theory for rigorous coupled wave analysis

Spectroscopic ellipsometry data were taken for the samples of 200nm anodic tantalum oxide film on AlN substrate and polished blank AlN substrate, wedged to prevent reflection from back surface entering the light collection. The results of tanΨ and cosΔ are shown in Figure 5-10 and Figure 5-11 as a function of wavelength. To determine the refractive index and absorption coefficient from the individual data point, the Cauchy’s equation was used for a material by fitting the equation to measured refractive indices at known wavelengths ^[4]. From the software inside the spectroscopic ellipsometry, tanΨ and cosΔ were converted into refractive index (n) and extinction coefficient (k) shown in Figure 5-12 and Figure 5-13. Clearly ∣k∣<

0.001 for all wavelengths, and the fact that k is so small over such a wide-wavelength region gives us confidence that this fitting procedure is realistic.

Figure 5-10 The results of tanΨ and cosΔ of AlN

Figure 5-11 The results of tanΨ and cosΔ of TaOx

Figure 5-12 The refractive index (n) and extinction coefficient (k) of AlN.

Figure 5-13 The refractive index (n) and extinction coefficient (k) of TaOx.

Since refractive index (n) and extinction coefficient (k) were obtained, we calculate the reflectance of the whole system by solving the Maxwell equation to

express the electromagnetic (EM) field in each layer and then match EM boundary conditions between neighboring layers for the determination of the reflectance of the system. The RCWA-simulated reflection for a bare AlN substrate and nanopyramid-array coating with 200 nm base length are shown in Figure 5-14. It is apparent that the theoretical prediction for bare AlN substrate is close to the experimental spectrum, while for the solid nanopyramid structure of the subwavelength gratings, the modeling results match nearly with experimental data.

The difference of the reflectance between experimental and theoretical solid nanopyramid coating may be due to the non-homogeneous composition of tantalum oxide as mentioned above (Chapter 4.3). Meanwhile, the theoretical reflectance of hollow nanopyramid coating agrees reasonably well with experiments in Figure 5-8 and 5-14. The experimental reflectance of hollow nanopyramid structure is in common with the theoretical reflectance of H/B=0.9. The result indicates that hollow portion of nanopyramid occupies about 72% of the whole structure which was confirmed by TEM observation in Figure 5-x in substance. Moreover, the RCWA simulation can effectively predict the reflectivity, and it’s useful for customization of various antireflective coating on different substrates.

Figure 5-14 The RCWA-simulated reflection for a bare AlN substrate and nanopyramid-array coating with 200 nm base length