The index profiles of the yttrium oxide films in this study were determined using_the above method. Needless to say, it is imperative that the optical monitor for determining R be accurate (in this case transmission was measured and R was found using R = 1 - T). Considerable effort was made to insure that the optical monitor gave stable and accurate data. An absorption filter was used in the input slit of the monochromator to reduce the effect of scattered stray light from the grating. The monitor wavelength, 340 nm is close to the absorption edge of standard viewport materials and can be seen in the optical monitor as the absorption band of the glass moved up and back down the spectrum. So, fused silicon dioxide viewports were substituted for the original glass viewports. The viewports were carefully shielded to prevent an accumulation of coating which also would lead to inaccuracy.

There is a question of the validity of allowing the absorption to be zero for these measurements. In fact, post-deposition measurements did show that some of the films had significant absorption in the UV. A series of simulated depositions were made using existing programs, and the "optical monitor" data was extracted from the simulations. The model predicted the index profile of the nonabsorbing films as expected. However, in absorbing films, after the steep drop in index, there was often a gradual increase in index. The model with absorption also displayed this increase in index. Since a drop in index can only be caused by inhomogeneity, the initial drop is likely to be real, but the gradual increase may well be an artifact caused by absorption in the layer.

Manuscript received 1-24-86 SAR

Self-Consistent Dependence of Porosity and Refractive Index on Composition in

Zirconia: silica films grown by e-beam coevaporation show a decreased porosity compared to pure zirconia films. This decreased porosity causes an anomalous dependence of refractive index on composition. A maximum in refractive index occurs at about 20 percent by volume of silica, the concentration at which the films appear to become amorphous. A simple model which derives the porosity as a function of composition from the deposition parameters predicts the general compositional behavior of the refractive index. The results agree best with the Drude model of refractive index for mixed component systems.

Key words: coevaporation; porosity; refractive index; thin films; Zr02; Si02.

1. Introduction

One approach suggested for obtaining optical coatings resistant to laser damage is to produce films that possess a bulk-like glassy structure. E-beam deposited films generally are not bulk-like in that they exhibit a columnar structure and a significant porosity. Because of this porosity, water is adsorbed and desorbed from the film depending upon the ambient atmospheric humidity. The net effect is an unstable refractive index. In addition water can seep between film layers leading to delamination. One method shown to decrease porosity is ion-assisted e-beam deposition [1]. In this work we show a similar decrease in porosity by e-beam coevaporation and without the need for an ion gun. This result is important because manufacturers of thin film coatings can use the current e-beam technology to produce bulk-like films without investing in the newer ion-beam technology.

Recent work has shown that mixed zirconia: silica films have varying structures depending on composition [2]. Pure zirconia films are polycrystalline with two crystalline phases present. Films with a silica content of up to 20 % by volume have a single crystalline phase. At volume fractions of silica >20 % the films show an amorphous structure as determined by x-ray diffraction.

In this work we show that some of these films appear to exhibit bulk-like densities. A simple model derives the porosity of the films as a function of composition. The model also is consistent with the observed anomalous compositional dependence of the refractive indices of the films. We find that the addition of silica to zirconia can produce films with larger refractive indices than pure zirconia films. The compositional dependence of the refractive index agrees best with the Drude model.

**

"This work was supported in part by the Air Force Office of Scientific Research under Grant Nos. AFOSR-84-00060 and AFOSR-ISSA-85-0006.

Guest worker from Instituto Tecnologico de Aeronautica, Brazil with partial support from CNPq.

Films in the system (ZrO2)x: (Si02) (1-x) were produced by e-beam coevaporation from two independent sources onto fused silica substrates at a substrate temperature of 300 °C. The deposition system has been described elsewhere [3]. Each source was monitored by a separate quartz-crystal thickness monitor. Films were produced varying in composition from pure ZrO2 to pure Si02. The thickness monitors were calibrated on the basis of stylus measurements on the pure films. The target deposition rate for the sum of the constituents was 0.5 nm/s, however, a higher rate was used on the deposition of some of the films with a low fraction of one constituent because the monitors had to operate near the lower limit of their sensitivity range. Thicknesses were in the range 0.7 to 1.1 μm.

Two sets of films were produced. In the first set, the deposition rates were controlled manually; in the second set, the rates were controlled by a commercial controller. The results reported were similar for both sets of films.

The thickness of each film was measured by stylus profiling at several points around the film border. The reported results are based on the average value. The refractive index was obtained from a combination of channel spectra measurements [4] and the thickness measurements. Thickness and refractive index were also obtained by the method of m-line spectroscopy [5]. Although there appears to be some discrepancy between the two methods of obtaining refractive index, the agreement is sufficient to sustain our principal conclusions.

In order to expedite the discussion we introduce the following symbols and nomenclature: = measured film thickness,

t

Figure 1 shows a plot of refractive index as a function of the thickness fraction of silica, t1/(t1+t2), for film set one. If it is assumed that the volume fraction is proportional to the thickness fraction, then the behavior of the refractive index with composition is anomalous. On the basis of all theories of mixed component systems, the refractive index of the composite should have a value that falls between the values of the pure constituents. Thus, the addition of silica, a low index material, to zirconia, a high index material, would be expected to lower n. Instead, we find that initially n increases. A decrease in film porosity would account for this behavior.

In order to test

this hypothesis, we have compared t1 + t2 with t for each film. In every case we find t1 + t2 > t. This is clearly demonstrated in figure 2 where we observe Dn > 1 for all mixed films. On the basis of a simple model, we are able to calculate the pore fraction of the coevaporated films as a function of composition. We can also model the compositional dependence of the refractive index.

5. Porosity Model

We make the following assumptions: 1) The sticking coefficient is independent of composition. This implies that the quantity of material deposited is proportional to the monitored thickness. 2) A given volume is associated with each type of molecular unit [6]. This implies that the deviations of t1 + t2 from t are due to porosity.

From these assumptions several relationships can be derived:

Α

From eq (3) we see that the packing fraction of a film can be obtained from the measured quantities t, tq, t2 and assumed values for the pore fractions in pure films p1 and p2. theoretical expression for Dn can be obtained if we can assume a relationship between the pore fraction in the film and the fractions of the two constituents, f1 and f2. The following expression was chosen as an empirical fit to simulate the experimental data:

p = P2 exp[-(f1/A1)]2 + P1 exp[-(f2/A2)]2

(4)

(5)

The parameters A, and A2 are chosen so that the porosities of the pure films are obtained, that is A1 << 1, A2 <<1. The expression implies that a small increasing fraction of one constituent acts to reduce the porosity. If we solve equations (1), (2), and (4) in a self-consistent manner we can obtain a curve for comparison with one set of experimental data. Figure 3 shows such a comparison with the experimental data of film set two. The values for P1, P2, A1, and A2 are chosen so that the packing fraction did not exceed unity. We see that a reasonable fit is obtained with p1 =0.10, P2-0.25, A1-0.15, and A2-0.25.

These results were used to calculate values of refractive index as a function of film composition on the basis of three different models, the Drude model, the Lorentz-Lorenz model, and the linear model. The Bruggeman effective media model agrees approximately with the linear model so it has not been used. Each of the models average the refractive indices in a different

Linear:

n =

i ni

(8)

In Figure 4, the results for each of the models are superposed on the experimental data of film set two. All of the models show the same general compositional behavior as the experimental data. Two data points are shown for each specimen; one point is obtained by m-line spectroscopy (x's), the other point by the method of channel spectra and stylus thickness measurements (dots). We believe the discrepancies are due to the different sensitivities of the measurement methods to compositional inhomogeneity. However, in spite of this difference, the two sets of data still display the same behavior and do not alter our conclusions. The best quantitative agreement appears to be provided by the Drude model.

6. Conclusions

The pore fractions in e-beam coevaporated zirconia: silica films are significantly smaller than in pure zirconia films. This results in an anomalous dependence of refractive index on composition. A porosity model, which requires estimates of porosity in pure films only, predicts the compositional dependence of the pore fractions in the films. This result is in reasonable agreement with the experimentally determined nominal densification of the films. Calculations of the compositional dependence of the refractive index agree with the behavior of the experimental data. Of the different models of refractive index in mixed component systems examined, the Drude model appears to agree best with the experimental data.

We thank T. Vorburger and C. Giauque of the Micro and Optical Technology Group for the diamond stylus measurements of specimen thicknesses.

[1] Martin, P.J., Macleod, H.A., Netterfield, R.P., Pacey, C.G., and Sainty, W.G., Appl. Opt. 22, 178 (1983).

[2] Farabaugh, E.N. and Sanders, D.M., J. Vac. Sci. Technol. A1, 356 (1983).

[3] Sanders, D.M., Farabaugh, E.N., Hurst, W.S., and Haller, W.K., J. Vac. Sci. Technol. 18, 1308 (1981).

[4] Feldman, A., Appl. Opt. 23, 1193 (1984).

[5] Tien, P.K., Ulrich, R., and Martin, R.J., Appl. Phys. Lett. 14, 291 (1969).

[6] Jacobsson, R., in Physics of Thin Films, 8, Hass, G., Francombe, M.H., and Hoffman, R.W., editors (Academic Press, New York, NY, 1975).