Journal of Sol-Gel Science and Technology 13, 707 712 (1998) c 1998 Kluwer Academic Publishers. Manufactured in The Netherlands. Optical Viscometry of Spinning Sol Coatings F. HOROWITZ AND A.F. MICHELS Instituto de Fisica, UFRGS, Campus do Vale CP15051, 91501-970 Porto Alegre, RS, Brasil flavio@if.ufrgs.br E.M. YEATMAN Department of Electrical and Electronic Engineering, Imperial College of Science, Technology and Medicine, London SW7 2BT, UK Abstract. Optical interferometric monitoring of spin coating (optospinography) has allowed close observation of the temporal evolution of a thin silicate sol film (typically at 2000 rpm, 100 Hz data acquisition). The kinematic viscosity data obtained, using a simple analytical model, are validated with those from a mineral oil standard, with agreement well within the experimental uncertainties. For spin coating in open air, the influence of variations in refractive index, rheological properties and air flow are discussed. Inflections in the temporal evolution of the optical thickness of silicate sol films are analyzed, which indicate the usefulness of optospinography, particularly when applied in the proximity of the rotation axis and evaporation is minimized, to monitor time variations in the kinematic viscosity of these sols during spin coating. Keywords: spin coating, kinematic viscosity, optical viscometry, monitoring of spin coating 1. Introduction Sol-gel coatings, due to their wide flexibility in composition and microstructure, have increasingly been used in magnetic, opto- and microelectronics applications. The viscosity of the coatings during formation is a key parameter for process control and reproducibility. In addition, valuable information on the solution structure of a sol, and on its subsequent transition to a gel, is provided by determination of its viscosity dependence on time [1, 2]. When a sol is spin cast in open air, the optospinography technique, where an interferometric representation is obtained for the temporal variation of the optical thickness of the film during the process, has allowed us to distinguish four main stages of evolution: (I) prespinning oscillations in the sol, (II) ultrafast convective mass flow, (III) convection-evaporation, and (IV) limited evaporation [3], as can be seen in Fig. 1. We have recently proposed use of this technique for the measurement of viscosities during spin coating, and considered its potential and validity for spinning sols [4]. In this study, we examine temporal variation of the optical thickness, and its relationship with kinematic viscosity of the film of silicate sol. 2. Experimental Analysis is made of a HeNe laser beam reflected from the liquid film on a silicon wafer or glass substrate, spinning at speeds in the range of 700 3000 rpm, in the experimental setup described in [3]. The ratio between the reflected and reference signals is computed after processing by an A/D converter, and readings are taken every 10 ms. Alignment of the system is critical, to ensure that the illuminated spot remains at the center of the substrate at all spinning times, which are typically up to 60 s. Conversion from optical to physical thickness was performed by index measurement using a commercial Abbe refractometer. For three different sets of process parameters, Fig. 2 shows the temporal evolution of the sol optical thickness, as inferred from the optospinogram data [3].
708 Horowitz, Michels and Yeatman Figure 1. A typical optospinogram of a spinning sol (tetraethylorthosilicate precursor, 1 : 1 vol dilution in ethanol, ph = 1.0, 12 days old) at 2000 rpm: (a) saturated solvent atmosphere; (b) open-air.
Optical Viscometry 709 Figure 2. Optical thickness variation with time, in quarterwave units for a spinning sol at three different sets of process parameters. Counting of quarterwaves starts from the last reference extreme in each optospinogram. 3. Theoretical Assuming an infinitely extended horizontal, rotating plane disk, and a thin liquid film with negligible Coriolis forces and Newtonian behavior, the Emslie, Bonner and Pack (EBP) model [5] predicts a thickness time dependence of the form: d = d 0 [1 + ( d0 b ) 2 t] 1 2 ; b 2 = 3ν 4ω 2 where d 0 is the initial thickness, ω the angular speed, and ν the kinematic viscosity. For times t b d 0, d bt 1 2. It should be also pointed out that no mass loss is considered in this model, which therefore cannot be applied to situations where there is significant evaporation to the surrounding atmosphere. 4. Validation and Results In order to validate the results obtained from optospinography [3], we applied our method to an oil standard with kinematic viscosity value ν 0 1 = 0.37±0.01 S (mineral oil OP20) at 22 C. This value was obtained from interpolation, with a second degree polynomial fitting, starting from the supplier specifications at a set of temperatures; the uncertainties correspond to a temperature fluctuation of ±0.5 C in our experimental conditions. The measured and linear fitting for the temporal evolution of the oil optical thickness at 2000 rpm is shown in Fig. 3. The fact that a straight line is obtained, corresponding to a constant ν, implies that the liquid is Newtonian and that the EBP model is valid in all measured ranges.
710 Horowitz, Michels and Yeatman Figure 3. Optical thickness variation vs. t 1/2, where the minus sign was used to plot variation with increasing time. Linear fitting corresponds to the EBP model prediction for a Newtonian fluid with v 1 = 0.361 S. Conversion from optical to physical thickness is made possible by a direct measurement with an Abbe refractometer, giving n 1 = 1.46 ± 0.01 (OP20). From this procedure, the experimental result for the oil standard is ν 1 = 0.361 ± 0.001 S, where the uncertainties correspond to the observed angular speed fluctuation of ±5 rpm. The agreement between the known kinematic viscosity of the oil standard and the result obtained by optospinography, within the experimental uncertainties, indicates the validity of the method. Application to our typical spinning sol at 2000 rpm, produced the optical thickness variation vs. t 1/2, in saturated solvent and open air atmospheres, shown in Fig. 4. 5. Discussion and Concluding Remarks For open-air sol-gel processing, application of this method could generally be useful as an alternative kinematic viscosity measurement, without need of additional instrumentation, and whose result is applicable to initial sol conditions. In terms of viscometry of the sols during spinning sols in open air, possible changes in refractive index and rheological properties need to be considered, as well as the influence of air flow. For the sol composition we used in this work, (which gives silica films after subsequent heat treatment) the refractive index values of the initial sol, as measured by Abbe refractometry, were the same, up to the second decimal place, as those measured by ellipsometry right after spinning. Although this does not apply for all sol compositions (as opposed to the case of a saturated solvent atmosphere, where negligible loss by evaporation allows the refractive index to remain constant), it does indicate that the index contrast between the solvent and the partially dried porous medium was very small. As to the implications of the rheological evolution of the sol during the process in open air, we rely on present models and the available experimental evidence. For resist and spin-on glass materials, Sukanek has shown that non-newtonian effects are always accompanied by a variation of thickness with radial position, and that the film remains uniform up to a critical value of the radius, ξ, corresponding to the critical value of shear up to which the liquid viscosity is independent of shear rate [6]. In agreement with published data [7], silicate sol-gel films spun at 2000 rpm have shown nearly uniform thickness up to a radius larger than 10 mm; the radius of the spot illuminated by the laser beam was of the order of 0.1 mm. Taking into account the influence of the air flow dynamics, Bornside and collaborators have identified a central region in the spinning disk where, for radii less than a critical value (corresponding to a Reynolds
Optical Viscometry 711 Figure 4. Optical thickness variation (in quarterwaves, at 632.8 nm and 2000 rpm) vs. inverse square root of spinning time (s 1/2 ) for the sol described in Fig. 1, for open air and saturated solvent atmosphere. The latter case corresponds to a kinematic viscosity in the range 3 21 cs. number of the order of 10 5 ), the flow is laminar, axisymmetric and steady state, and the mass transfer coefficient is independent of radial position [8]. Specifically for a colloidal system (polystyrene latex spheres suspended in water), Rehg and Higgins showed experimentally, by measuring the film thickness dependence on the inverse square root of the angular velocity, that shear rate thinning effects are unimportant in a region with radius up to 2.5 cm around the axis of rotation (the variation in film thickness was less than 0.3% at 1930 rpm) [9]. In Fig. 4, at the initial spin-off stage the slope is constant, and therefore the kinetic viscosity of the sol is essentially constant a behavior similar to that of the oil standard. As the sol thins further, on the contrary, the kinematic viscosity of the sol changes significantly. In the case of saturated solvent atmosphere, if we assume that the evaporation of solvent is insufficient to account for this behavior, a possible explanation for the increase in viscosity (from 3 to 21 cs) is an attractive interaction with the substrate, which is consistent with the EBP boundary condition of zero fluid velocity with respect to the rotating disk in the limit of zero film height. The open-air film shows the opposite final behavior, with the thinning rate increasing beyond that predicted by the EBP model. This can be explained directly by mass loss through evaporation, which although continuous, only becomes significant as the spin-off decreases. We therefore have good theoretical and experimental indications that, despite the simplifying assumptions in this study, useful measurements of viscosity evolution during spin coating of sols can be obtained, particularly for the case where mass loss through evaporation is minimized. Acknowledgments We are grateful to Eng. Leandro Galuska and Ms. Vanessa Dutra for their assistance, as well as to Ms. Lizette Peters for providing us the oil standard, under the supervision of Eng. Rogerio Auad at TINTAS RENNER S.A. This work was partially supported by CNPq, PADCT/FINEP and CAPES programs. References 1. C.J. Brinker and G.W. Scherer, Sol-gel science: the physics and chemistry of sol-gel processing, (Academic Press, San Diego, 1990), chap. 3. 2. R. Xu, E.J.A. Pope, and J.D. Mackenzie, J. Non-Cryst. Sol. 106, 242 (1988).
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