Hybrid Generalized Ellipsometry and Quartz Crystal Microbalance

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Hybrid Generalized Ellipsometry and Quartz Crystal Microbalance Nanogravimetry for the Determination of Adsorption Isotherms on Biaxial Metal Oxide Films R. Alan May,† David W. Flaherty,‡ C. Buddie Mullins,†,‡ and Keith J. Stevenson*,† †

Departments of Chemistry and Biochemistry and ‡Department of Chemical Engineering, Center for Electrochemistry, Texas Materials Institute, The University of Texas at Austin, 1 University Station, MC A5300, Austin, Texas 78712

ABSTRACT Generalized ellipsometry and quartz crystal nanogravimetry are combined to determine adsorption isotherms and changes in the optical properties of biaxial TiO2 thin films by monitoring changes in the Mueller matrix. Individual Mueller matrix elements, corresponding to a variety of polarization states, exhibit dramatically different sensitivities to the adsorption of toluene. While some elements are sensitive to structural anisotropy and orientation, others report uniquely on the refractive index. The fast (na) optical axis reflects the greatest change in refractive index due to the adsorption, leading to a decrease from Δn800nm =0.4 to 0.1. This change is discussed in terms of the Bragg-Pippard (B-P) effective medium approximation, which is shown to accurately describe changes in optical behavior in response to adsorption. The integration of generalized ellipsometry with quartz crystal nanogravimetry establishes a highly sensitive technique for acquiring adsorption isotherms and for chemical optical sensing of structurally anisotropic thin films. SECTION Nanoparticles and Nanostructures

(ellipsometry,13 X-ray reflectivity,14 diffraction15), each of which introduces uncertainty based on assumptions and technique limitations. GE/QCNP determines a material's interaction with light as a function of structural orientation and chemical environment while at the same time providing the mass adsorbed, affording three distinct advantages. The first is that GE/QCNP allows for direct visualization of how parameters measured by ellipsometry, the Mueller matrix elements, respond to adsorption without the modeling typically necessary to extract physically meaningful parameters, potentially leading to direct ellipsometry sensing schemes. Second, the simultaneous acquisition helps to verify assumptions for each individual GE and QCN technique while minimizing concerns over sample variations that can complicate the analysis of experiments performed separately. Third, GE/ QCNP has been utilized to show that the conceptually and mathematically straightforward Bragg-Pippard (B-P) effective medium approximation is a valid predictive model for changes in the optical properties of anisotropic thin films following gas adsorption, useful for the design of anisotropic coatings for varying ambient conditions. Reactive ballistic deposition (RBD) was utilized to deposit porous TiO216 films directly on quartz crystals. This method, often referred to as glancing angle deposition (GLAD), takes

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ighly structured, columnar thin films deposited via oblique or glancing angle deposition (GLAD) possess unique optical, electrical, and magnetic properties not found in bulk structures.1,2 Exquisite control over these properties is achieved by adjusting the deposition angle, resulting in columnar structures with tailored anisotropic optical and electronic properties for applications such as antireflective coatings,3,4 sensors,5,6 and catalysts.7,8 The optical anisotropy of these films originates from contrast between the refractive indices of the solid columnar structure and the surrounding void volume, and therefore, the optical response is dependent on a variety of parameters such as orientation, angle of incidence, and the ambient environment. These aspects make it difficult to not only characterize anisotropic dielectric thin films but also to optimize structure and morphology (e.g., crystallinity, surface area, porosity) for emerging applications of anisotropic thin films such as surfaceenhanced Raman spectroscopy (SERS) substrates,5,6 Bragg reflectors,9 and photovoltaic devices.10,11 Consequently, it is vital to develop new optical diagnostic techniques for characterizing anisotropic dielectric thin films which can completely probe complex optical properties. In this regard, we present a hybrid approach using both generalized ellipsometry and quartz crystal nanogravimetric porosimetry(GE/QCNP) to simultaneously obtain optical- and mass-based adsorption isotherms in an effort to discern how the anisotropic optical response is influenced by gas adsorption. The current state of the art in characterizing porous thin films, as reviewed by Sanchez et al.,12 relies on single methods of detection

r 2010 American Chemical Society

Received Date: February 19, 2010 Accepted Date: March 22, 2010 Published on Web Date: March 29, 2010

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DOI: 10.1021/jz1002428 |J. Phys. Chem. Lett. 2010, 1, 1264–1268

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Figure 1. SEM image of TiO2 deposited via RBD at 75°. This is a biaxial orthorhombic system; the three principle axes are labeled with c being parallel to the column direction (column angle θ), b coming out of the image, and a perpendicular to c.

Figure 2. Toluene adsorption isotherms on nonporous TiO2 determined simultaneously by both ellipsometry and QCN. The presented data are the average of four isotherms, and the error bars are one standard deviation.

advantage of the initial deposition stochastically “templating” or self-shadowing the surface combined with limited adatom diffusion to produce samples with deposition-angle-dependent properties (e.g., surface area and porosity). For instance, when the vapor flux is incident at 75° with respect to the substrate normal, columnar thin films (Figure 1) are produced with three major optical axes in an orthorhombic structure with the c axis aligned along the column direction at angle θ from the surface and the refractive indices (n) of the three axes decreasing in the order nc > nb > na).17 Due to the anisotropy of these films, standard ellipsometric measurements of Ψ and Δ are insufficient to uniquely determine the refractive indices. In prior work, an isotropic approximation was used to characterize columnar TiC18 films prepared by RBD. Good agreement between ellipsometric13,19 and quartz crystal nanogravimetry20 (QCN) porosimetry was achieved with this approach. However, this method could not determine the absolute porosity or the volume adsorbed from ellipsometric measurements without first using QCN for calibration. This isotropic approximation was also inadequate for understanding how the optical anisotropy evolves with adsorption. To resolve these shortcomings, generalized ellipsometry was applied to determine the three axial-dependent refractive indices, na, nb, and nc, at varying levels of vapor adsorption. This is achieved by utilizing the Stokes vector system and measuring the first three rows of the Mueller matrix (normalized to M11). In the Stokes regime, light is described by one unpolarized (S0) and three polarized (S1, S2, S3) components. Optical interactions with the sample are represented by a 4 4 matrix (eq 1), known as the Mueller matrix, which acts to modify the four input Stokes parameters.21,22 2 3 2 3 2 3 S0 S0 M11 M12 M13 M14 6 6 M21 M22 M23 M24 7 7 6 6 S1 7 7 ¼6 6 S1 7 7 ð1Þ 4M 4S 5 M32 M33 M34 5 3 4 S2 5 31 2 M41 M42 M43 M44 S3 IN S3 OUT

are sensitive to changes in both intrinsic (ncolumns, nsurroundings, column angle θ) and extrinsic (angle of incident light, azimuthal orientation) properties.23 The dependence of the Mueller matrix on the extrinsic properties has been demonstrated by Schmidt et al.,24,25 who showed the off-block diagonal Mueller matrix elements approach zero (pseudoisotropic response) when the incident beam is approximately parallel to the plane formed by the a and c axes (ac plane) and reach a maximum when the incident light is perpendicular to the ac plane. However, until now, the relationship(s) between the responses of Mueller matrix elements to intrinsic and extrinsic properties has not been understood because methods to directly determine the volume adsorbed along with the Mueller matrix elements were unavailable. Now, utilizing GE/ QCNP, the interaction between intrinsic and extrinsic factors can be directly visualized. Understanding this relationship is important because the unique response of individual elements may be used to improve the selectivity of optical sensing schemes (i.e., a single measurement can break correlation between multiple parameters). The average of four adsorption and desorption isotherms on nonporous TiO2 is shown in Figure 2 to illustrate the agreement between the two techniques and the incredible sensitivity of both ellipsometric porosimetry (EP) and quartz crystal nanogravimetric porosimetry (QCNP). The mass of toluene, which readily physisorbs on TiO2 at room temperature,13 adsorbed on nonporous TiO2 was determined via EP by fitting the thickness of a toluene layer (assuming bulk toluene optical constants) and multiplying the thickness by the density of toluene (0.8669 g/cm3). The mass of toluene adsorbed was determined by QCNP directly from the Sauerbrey equation. Excellent agreement between QCNP and EP results is achieved with high precision as evidenced by a maximum standard deviation of 6 and 3 ng/cm2, respectively. The optical responses of the anisotropic TiO2 films were modeled using two layers, a Au substrate and an orthorhombic biaxial layer, with each axis parametrized using the Cauchy equation (n=A þ B/λ2, k=0). The optical axis was

Isotropic materials are represented by nonzero values for the block diagonal matrix elements (bold) with the off-block diagonal elements (italic) being equal to zero. For anisotropic materials, these off block diagonal elements are nonzero and


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Figure 4. Refractive indices of the three principal axes na (b), nb (9), and nc (2) at 800 nm during toluene adsorption (solid) and desorption (hollow) on TiO2 deposited at 75°. The sensitivity of na to toluene adsorption is much greater than the other axes, and the anisotropy is dramatically reduced. Corresponding black lines are estimated isotherms using the B-P EMA.

Figure 3. Block diagonal Mueller matrix elements (a) M12 (b) M22 and off-block diagonal elements (c) M14 and (d) M23 at 800 nm versus the mass of toluene adsorbed as determined by QCNP. Measurements taken with the column direction oriented perpendicular (2) and parallel (b) to the incident probe beam. All graphs have the same adsorbed mass range.

rectified to the lab axis by manipulating the Euler angles j and θ, which were set to the known azimuthal orientation and column angle (determined via SEM), respectively. Adsorption of toluene on the anisotropic TiO2 film causes the refractive index13 of the film to increase due to the void volume (n ≈ 1) being displaced by toluene (n800nm = 1.49), while the anisotropy of the film decreases because the refractive index contrast between the columns (ncolumns) and the surroundings (nsurroundings) is reduced.26 Both of these changes are directly observed through specific Mueller matrix elements. Representative Mueller matrix values determined by probing at a 60° angle of incidence at a wavelength of 800 nm have been plotted against the mass of adsorbed toluene derived from QCN measurements (Figure 3). The absolute value of the slope of the best-fit line through these points provides the sensitivity of each element to toluene adsorption (greater absolute values indicate greater sensitivity). Adsorption isotherms were recorded with the incident light parallel (pseudoisotropic point) and perpendicular (maximizes sensitivity to anisotropy) to the ac plane. In general, the sensitivities of block diagonal Mueller matrix elements are independent of sample orientation, while offblock diagonal elements exhibit strong orientation dependence. For example, the sensitivity of block diagonal element M12 to toluene adsorption (Figure 3a) is 1.3 cm3/g in both parallel and perpendicular orientations, implying that this element is insensitive to anisotropy and primarily dependent on increases in the refractive index caused by toluene adsorption. Interestingly, diagonal element M22 is insensitive to toluene adsorption at either orientation. However, this element is known to be sensitive to scattering.27 Therefore, the fact that M22 ≈ 1 (Figure 3b) indicates that these samples do not strongly scatter light, an observation also supported by the fact that M12 ≈ M21 (not shown). In contrast to block diagonal elements, the sensitivity of off-block diagonal elements such as M14 and M23 (Figure 3c


and d) is orientation-dependent. Both elements are near zero in the parallel configuration and are insensitive to toluene adsorption. In the perpendicular orientation, M14 and M23 are nonzero but trend toward zero with increasing toluene adsorption, a direct indicator of decreasing anisotropy due to adsorption. Note that some anisotropy persists following saturation of the film with toluene (P/Po > 0.85 with ∼0.23 g/cm3 adsorbed) as M14 and M23 level out. Block diagonal elements M13 and M24 (not shown) behave in a similar manner, further confirming the observed trend. Clearly, the individual Mueller matrix elements have very different sensitivities that report on specific aspects of the anisotropic film. Specifically, the increase in the film refractive index, independent of orientation, is reported on by M12 as nitrogen (n = 1) is displaced by toluene (n = 1.49), whereas, decreases in anisotropy are directly correlated with orientation sensitive elements M14 and M23. The extracted refractive index for each of the major axes is shown versus P/Po of toluene (Figure 4). As expected from observation of M14 and M23, the anisotropy between axis c and axis a decreases from Δnca = 0.4 to 0.1 with na approaching nc. The difference in sensitivity of nc and na is explained by the B-P17,28 effective medium approximation, which, while not rigorous, is instructive. In the B-P formalism, anisotropy arises from each axis having different depolarization factors (Lj), a measure of the tendency to oppose the applied field (eq 2). n2j ¼ n2v þ

pðn2col: - n2v Þ 1 þ ð1 - pÞðn2col: - n2v ÞLj =n2v

j ¼ a, b, c ð2Þ

where nj is the principle refractive index, nv is the refractive index between the columns, p is the packing fraction, ncol. is the column refractive index, and Lj is the depolarization factor. Equation 2 indicates that na is an order of magnitude more sensitive to toluene adsorption than nc, based on values

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given in Figure 4. This difference in sensitivity is heavily influenced by the depolarization factors (La > Lb > Lc ≈ 0) and is consistent with the experimentally observed sensitivities. Equation 2 was used to simulate optical isotherms (black lines in Figure 4) using as inputs only the refractive indices at P/Po= 0 (na = 1.50, nb = 1.65, nc = 1.89, nv = 1) and the volume adsorbed as determined by QCN. These initial values were used to solve for the remaining parameters in eq 2 with p = 0.62, ncol. = 2.27, La = 0.68, and Lb = 0.32. Given these values, eq 2 directly relates each of the primary refractive indices to the void refractive index, nv. The void refractive index can be determined using QCN measurements of the volume adsorbed and the Bruggeman effective medium approximation (BEMA), combining the refractive index of air (n800nm =1.00) and that of toluene (n800nm =1.49) according to the fraction of each component determined via QCN. This value is independent of the toluene adsorption mechanism as the pore size is much smaller than the wavelength of light and is being considered as an effective medium. The use of this model is verified by the generally good agreement between simulated isotherms and values determined using ellipsometry. However, agreement between the two is not perfect; notably, na is overestimated by ∼2% through the middle of the isotherm, and the simulated values for nc diverge from the measured values at high partial pressures. As discussed previously, high partial pressures of toluene lead to saturation of the mesopores and multilayer adsorption, which act to decrease the refractive index contrast between the TiO2 film and the void space surrounding the columns.17 Therefore, with increasing toluene adsorption, the off-block diagonal elements vanish, increasing fit parameter correlation and leading to the nonphysical result observed in Figure 4 for values of nc above P/Po = 0.70. In summary, the anisotropic optical response of columnar TiO2 films to changes in the ambient environment has been determined using GE/QCNP. The unique response of individual Mueller matrix elements to both intrinsic and extrinsic factors improves our understanding of how light interacts with structurally anisotropic materials. The optical response of the fast axis (na) is shown to be an order of magnitude more sensitive to adsorption with respect to the slow axis (nc) due to column depolarization. The integration of generalized ellipsometry with quartz crystal nanogravimetry establishes a highly sensitive technique for acquiring adsorption isotherms and for chemical optical sensing using structurally anisotropic thin films. Future work seeks to extend this hybrid GE/ QCNP technique to understand the influence of film growth parameters on film structure in order to elucidate how resultant structural, optical, and electronic properties of anisotropic thin films can be harnessed to create advanced nanostructured materials for wide-ranging use in optics, energy conversion and storage, and chemical sensor applications.

Ti-coated quartz crystals with an electron beam evaporator (Omicron EFM3) at 35 °C with a base pressure of ∼7 10-9 mbar in an oxygen atmosphere of ∼2 10-7 mbar.16 Porosimetry measurements were conducted by mounting the TiO2/Au/Ti-coated quartz crystal inside of a hemispherical quartz tube flow cell through which varying concentrations of toluene were flowed at 2.5 L/min (using two Inficon Model P8a mass flow controllers) in a temperature-controlled, 19.8 ( 0.2 °C, class 1000 clean room. The QCN was monitored with a Maxtek RQCM controller, and the frequency change was converted to mass using the Sauerbrey equation;29 ellipsometry measurements were taken at 50 and 60° angles of incidence with a M2000 spectroscopic ellipsometer (J. A. Woollam Co.) and modeled from 500-1000 nm.

AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: stevenson@ cm.utexas.edu.

ACKNOWLEDGMENT K.J.S. acknowledges the Welch Foundation

(F-1529) and the National Science Foundation (CHE-0809770) for their generous support. C.B.M. acknowledges the Army Research Office (W911NF-09-1-0130), the National Science Foundation (CTS0553243 and CHE-0934450), and the Welch Foundation (F-1436). D.W.F. would like to acknowledge the Bruce B. Jackson Endowed Graduate Fellowship in Engineering.

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Hybrid Generalized Ellipsometry and Quartz Crystal Microbalance

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