New Approach for Analyzing Wafer Roughness
It is an interesting question how the formation of thermal oxide is influenced by wafer roughness. Typical roughness of planarized silicon wafer is about 2nm (P-V). A set of irregular roughness often forms higher structure called step or terrace. Their scale factors are about 100nm. Since deposition is a thermal process, it increases entropy, and, thereby, these higher structures are gradually decreased as the process progresses.
Since surface roughness is a stochastic concept, it is necessary to measure a whole surface two-dimensionally. Sub nm resolution may be necessary for vertical accuracy. As the unevenness of a model becomes visible by mirrored unevenness of its plaster, it might be possible to obtain information about higher structure of interfacial layer between wafer and oxide by recognizing a distribution of oxide thickness. However, it is a question if definite information about micro structure can be obtained from a measurement by two-dimensional ellipsometer. The reason for this question is that its surface resolution is either 1 or 100Κand is very coarse for morphology of the surface so that a result of measurement comes out as an average of many micro structures. 1 unit of a surface resolution is consisted of about 100 to 10000 micro structures. Measuring a whole wafer means that it operates an actual coarse observation of an ensemble which is consisted of a set of these micro structures with various initial conditions.1) How does a distribution of the ensemble represent the characteristic of the wafer? The purpose of this report is to give an experimental answer to above questions.
As an experiment, we measured an oxide of 25nm and 50nm thickness which had been deposited on wafers with different roughness (wafer roughness of substrate is 0.3, 0.5, 1.0nm RMS) by our two-dimensional ellipsometer QR120K (surface resolution is 300Κ). A data of oxide of 25nm thickness is explained in the following.
1) To say this, it is necessary to measure sufficient numbers of units compared to the numbers of microstructures included within one unit.
FIG 1:Display of distribution of thickness of oxide of 25nm thickness. The upper row is a representation of whole wafer, and the lower row is a three-dimensional representation of the center portion of sample. Roughness of a substrate is 0.3, 0.5, 1.0nm RMS from the left.
FIG 1 is the display of distribution of thickness of oxide of 25nm thickness. The upper row is a representation of whole wafer, and the lower row is a three-dimensional representation of the center portion of sample. The color resolution is 1 angstrom (256 colors are used in the display). Roughness of a substrate is 0.3, 0.5, 1.0nm RMS from the left. Apparently, flatness of the distribution of thickness of oxide depends on the wafer roughness. It indicates the fact that the surface roughness of wafer is the important factor in film formation.
In this case, for some samples, the assumptions of the parallelism between a film and a substrate or of the uniform incidence angle of beams towards a sample, which are the theoretic premises of ellipsometry are no longer realized locally. Moreover, the more one observes a sample microscopically, the more a singularity appears irregularly in a measurement result of refractive index or of film thickness. These singularities which apparently seem to represent unstableness of a measurement result actually represent irregularity (although qualitative) existing in a sample itself.2)
For a statistical analysis, we calculated the spectrum of a film thickness in the center area of 256 ~256 pixel. FIG 2 is a spectrum of the whole area, and FIG 3 is a spectrum of 1-3 quarters. (Optical representation in which the center of the graph indicates a direct current component). (The wafer roughness is 0.3, 0.5, 1.0nm RMS from the left in the all following figures). Standard deviations of the spectrums in Fig.2 are 17.22A19.18A20.10 from the left. The figure shows that the high-frequency component increases as the wafer roughness increases.
2) Conventional one-spot-typed ellipsometer has been incapable of observing irregularity shown in the above because a diameter of optical beam as a probe is too long (about 1mmΣ), and a number of its measuring spots is too small. Ultra Clean Society, UC Standardization Committee, Working Group of Materials: Ultra Clean Technology 5(1993) 68(254)
FIG 2:Spectrums of film thickness in the center area of 256 ~ 256 pixel.
FIG 3:Spectrums of 1-3 quarters of film thickness in the center area of 256 ~256 pixel.
FIG 4A:Film thickness restored by the inverse transform which removed low-frequency components of the spectrum in FIG 2
FIG 4B:Film thickness restored by the inverse transform which removed high-frequency components of the spectrum in FIG 2
Information lost by the coarse graining can be restored by collecting large quantities of statistical data. As shown in FIG 1, film thickness is influenced by shape factors (such as roughness, flatness, etc.) of substrate so that it is effective to measure a distribution in the frequency area instead of a simple distribution of film thickness. It is often an effective analyzing technique to have a film thickness restored by the inverse FFT which extracted the frequency range corresponding to the focused shape factor from a spectrum.FIG 4 A is the restored film thickness without low-frequency components. The relation between irregularity of film thickness and substrate roughness is observed more clearly. FIG 4B is the restored film thickness without high-frequency components. Appeared colors of each figure showing film thickness is almost the same. One can observe mean value of film thickness, which does not depend on roughness of the substrate. The irregularity which still remains after performing these procedures should be interpreted as the unusual measuring point at which the various premises, such as the uniformity of an incidence angle, cannot be realized.
@A direct current component corresponds to an average value of film thickness which has been set up for the process from the outside. A high-frequency component depends on a wafer roughness as the initial condition of the process. It is not the average value of film thickness, which has generally been focused and practically been measured, but the fluctuate components that have their own characteristics of process and sample.
Conversely to the above analysis, on what kind of factor the low-frequency component of spectrum depends? As an experiment, we deposited on a wafer of almost the same roughness (RMS 0.3nm) by grouping ranges so that each of them represents almost the same flatness, GF3R (Global Front 3Points Range) and GBIR (Global Back-side Ideal Range)DFIG 5 is a representative result of measurement value which has been deposited oxide of 25nm thickness, and is the three-dimensional representation of film thickness. Representative values of wafer flatness is 1.0, 1.5, and 2.0Κm on TTV from the left. FIG 6 is the display of spectrum of film thickness by FFT. In this case, it is preferred to focus on the shape of spectrum near the direct currency component. The amplitude of spectrum near the direct currency component appears to be broader, i.e. lower Q factor, as sample has worse flatness. FIG 7 is the result of operating inverse FFT reserving the area near the direct currency component.
FIG 5:Oxide of 25nm thickness. Wafer roughness is RMS 0.3nm and the flatness is 1.0, 1.5, 2.0Κm on TTV from the left
FIG 6:Spectrum of measurement result in FIG 5
FIG 7:Film thickness restored by the inverse FFT which reserves the area near the direct currency components
As a conclusion, the mathematical analysis of measurement of film thickness by two-dimensional ellipsometer provides interesting procedures for the analysis of wafer roughness (and its influence in the deposition process). In this process, to which range of spectrum a film should be restored is up to an analyzerfs decision. Measurement results would be represented in a various appearance according to the decision. Through this step, the analyzer can obtain valuable information relating to the process and sample.
The quantitative conclusions of this analysis depend mainly on the surface resolution of the apparatus. As we, heureka. Co., is devoting ourselves in developing an apparatus that has more minute surface resolution, we are determined to further pursue this theme.