Technical Issues - ZrO2 case study
A FilmStar user developing a new method for depositing ZrO2 found that it impossible to fit measured data with a single layer. As shown below, the inhomogeneity of ZrO2 results in transmission higher than the uncoated substrate. According to the user, 150nm of ZrO2 was deposited.
A table of ZrO2 indices was supplied. Although inspection of the above curve indicates that the index of ZrO2 is not as expected, it provided a starting point.
In order to analyze this in DESIGN, we first use INDEX to fit the dispersion curve with a smooth function over the measured range. This is accomplished in Functions...Fit Index. Going through the FTG-supplied index files, we note that LOREN fits Ta2O5 fairly well ((A=3.825, B=0.603, C=246.2), so it seemed to be a reasonable starting guess for ZrO2. Using the fitting routine, we quickly obtain A=2.993581, B=0.8116322, C=236.2361. As shown on the plot above (green line), the fit is excellent. In fact, most non-absorbing dielectrics can be fit quite well with this function.
Resaving index table 5ZR02A also saves the coefficients. In DESIGN we access the Film Indices editor and click Insert Function to replace the dispersive file name with associated LOREN function.
Our goal is to fit the measured spectrum with a 2-component film. In order to do this we copy the LOREN function to new film material J.
Our next task is to convert the measured spectrum to optimization targets. This is accomplished in the Optimization Targets dialog by first clearing any current targets (click box at grid upper left and hit <Delete>) and then clicking the Generate button with Reverse Synthesis mode checked.
Observing a glitch in the measured data, we manually deleted values from 1375 to 1470.
The original design (150H) is replaced by 75J 75H (the educated guess of Ron Willey). While we could try three or more layers, we are ultimately limited by measurement accuracy. Accessing the Optimization Variables dialog, we specify both layers (1, 2) and both indices (-3, -4) as optimization variables.
Our final design is SUB 60.32J 90.5H AIR with the indices shown above. Are these values reasonable? Exporting the functions to INDEX results in the curves shown below. The upper plot is J, the lower one H.
While these results seem reasonable, there may be insufficient data for a unique solution. Multiple angle data might be useful. Without a reflectance spectrum we are not certain that absorption can be discounted. Indices seem rather lower than expected, but that is obvious from the measured curves. Further experiments with thinner and thicker films might be revealing.