In this paper, we focus on the metrological aspects of spectroscopic Mueller ellipsometry—i.e. on the uncertainty estimation of the measurement results. With the help of simulated Mueller matrices, we demonstrate that the commonly used merit functions do not return the correct uncertainty for the measurand under consideration (here shown for the relatively simple case of the geometrical parameter layer thickness for the example system of a SiO2 layer on a Si substrate). We identify the non-optimal treatment of measured and sample- induced depolarization as a reason of this discrepancy. Since depolarization results from sample properties in combination with experimental parameters, it must not be minimized during the parameter fit. Therefore, we propose a new merit function treating this issue differently: It implicitly uses the measured depolarization as a weighting parameter. It is very simple and computationally cheap. It compares for each wavelength the measured Jones matrix elements to Cloude’s covariance matrix: ∼ ∑ λ j sim, λ † H meas, λ  +  j sim, λ . Moreover, an extension will be presented which allows us to include the measurement noise into this merit function. With this, reliable statistical uncertainties can be calculated. Except for some pre-processing of the raw data, there is no additional computational cost.

In situ real-time ellipsometry (irtE) with a very high time resolution of 24 ms was applied to monitor the inductively coupled plasma enhanced atomic layer deposition (ALD) process of Al2O3 thin films to precisely resolve each step of the ALD process and its complete cycle. The influence of plasma power, plasma pulse duration, and deposition temperature on the film growth characteristics was investigated. Ex situ ellipsometry [UV-VIS-NIR-SE (ultraviolet-visible-nearinfrared-spectroscopic ellipsometry) and IR-SE (infrared spectroscopic ellipsometry)] and x-ray photoelectron spectroscopy revealed the bulk properties (thickness, refractive index, chemical composition, and carbon incorporation) of the films, which together with the in situ results are compared to those of the films prepared by thermal ALD (T-ALD). The ICPEALD (inductively coupled plasma enhanced ALD) films were deposited at substrate temperatures between 80 and 250 °C and the role of plasma power (50–300 W) and its pulse duration (1–20 s) was investigated at 250 °C. The reference T-ALD layers were prepared at 200 °C. The ICPEALD process of Al2O3 shows an increased growth rate, and the produced films exhibit higher carbon contaminations than the T-ALD Al2O3 films. Plasma pulse times of up to 15 s further increase the content of carbon and CH species; at the same time, the refractive index decreases. The optical properties of ICPEALD deposited Al2O3 films are comparable with those of the T-ALD films for low plasma power and short plasma pulse durations. For the ICPEALD films, UV absorption is found and it is dependent on the deposition parameters. irtE resolves process effects that correlate with the bulk properties of Al2O3, such as impurities and oxygen deficiencies.

There are some commonly-used optimization techniques for the analysis of measured data in spectroscopic Mueller matrix ellipsometry (MME) used, for example, to calculate the layer thicknesses of samples under test. Concentrating on the metrological aspects of MME, we identified a non-optimal treatment of depolarization in all these techniques. We therefore recently developed an improved optimization method to adequately take depolarization in MME into account. In a further step, we also included statistical measurement noise and derived a likelihood function, which enabled us to apply both the maximum likelihood method and Bayesian statistics as well as the Bayesian information criterion for data evaluation. In this paper we concentrate on the application of this new method to measurements of SiO2-layer thicknesses on silicon. With a state-of-the-art SENTECH SENresearch 4.0 Mueller ellipsometer, we measured standard samples of different SiO2-layer thicknesses, whose calibrated thicknesses were between about 6 nm and 1000 nm. The MME results were compared to the calibration data. For all samples, an SiO2-SiO double-layer model turned out to be optimal. The measured total oxide layer thicknesses matched excellently with the calibration values, within the estimated range of uncertainties. All the results are presented here. This is the first comparison with traceable reference measurements demonstrating the validity of our novel MME analysis method.

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