Deterministic Correction of Thickness Distribution by Direct Dry Etching

Thickness correction by numerically controlled plasma chemical vaporization machining (NC-PCVM) is performed in accordance with the following procedures: (1) The thickness distribution of the specimen is measured by an optical or electrical method. (2) The thickness error distribution is calculated by subtracting the target thickness from the measured thickness. (3) Since the removal or oxidation volume is proportional to the dwelling time of the plasma, the distribution of the scanning speed of the X-Y table is determined by the deconvolution of the thickness error distribution and the removal function that is a removal spot obtained in unit time. (4) Numerically controlled thickness correction is performed by raster scanning, as shown in Fig. 1, to deterministically obtain a wafer of uniform thickness (Mori et al. 2000a, b; Yamamura et al. 2008). In this correction process, the temporal stability and reproducibility of the removal function are superior to those of the mechanical machining process. This is because there is no wear of the electrode and the process gases are uniformly supplied to the plasma region, whereas in the mechanical removal process, the degradation of the tool head, which may be a grinding wheel or polishing pad, and the unevenness of the polishing pressure deteriorate the surface integrity. Furthermore, the removal function in NC-PCVM is insensitive to external disturbances, such as the vibration and thermal deformation of the machine and specimen owing to the noncontact removal or oxidation mechanism. Therefore, the PCVM equipment does not require high stiffness, in contrast to conventional mechanical machining equipment, and consequently, these processes realize cost-effective ultraprecision thickness correction.

NC Thinning and Correction of SOI Thickness

The NC-PCVM equipment, which includes a spherical rotary electrode, is used for thinning the silicon layer of SOI substrates (Mori et al. 2004). An atmospheric pressure gas mixture of He:CF4:O2 = 99.98:0.01:0.01 is filled in the chamber and a localized plasma is generated by supplying very high-frequency (VHF) power ( f = 150 MHz) between the electrode and the wafer. Commercially available 6-in. and 8-in. SOI wafers were used in our experiments. The thickness of the top silicon layer was measured by a spectroscopic ellipsometer.
A commercially available 6-in. SOI wafer with a thickness of 201.6 nm and a thickness variation of ± 4.1 nm was thinned and uniformized to 13.0 nm and ± 2.0 nm, respectively (Mori et al. 2004). After improving the stability of the parasitic capacitance of the apparatus, a commercially available 8-in. SOI wafer with a thickness of 97.5 nm and thickness variation (standard deviation) of 2.4 nm was thinned and improved to 7.5 and 0.38 nm, respectively, as shown in Fig. 2 (Sano et al. 2007).
Since RF power is applied directly between the electrode and the wafer in PCVM, the degradation of the processed surface by ion bombardment was of concern. Thus, we attempted to fabricate MOSFETs on SOI wafers thinned by both PCVM and conventional sacrificial oxidation and compared their performance. A commercial 8-in. SOI wafer was thinned by PCVM to a thickness of 63.8 nm. Another SOI wafer as a reference was thinned by a combination of sacrificial oxidation and wet etching of the oxide layer. MOSFETs were fabricated on the entire area of these wafers using 0.35-μm-process technology (Adan et al. 1996; Azuma et al. 1995). Figure 3 shows the Ids (source–drain current)–Vg (gate voltage) curves for the SOI n-MOSFETs. The curves for the MOSFET on the wafer fabricated by PCVM and the reference MOSFET are shown by filled squares and open squares, respectively. The leakage currents of the MOSFETs on both wafers were equally small. The subthreshold slopes were steep and almost equal. These results were the same for all other transistors on both wafers. Thus, it was shown that MOSFETs on an SOI wafer processed by PCVM operate normally. This means that PCVM induces not only no ion bombardment damage because of the small mean free path of the gas molecules in the atmospheric-pressure plasma but also no trace metal contamination, which degrades MOSFET performance.

Thickness Correction of Quartz Crystal Wafer

Open-air-type NC-PCVM equipment was used to correct the thickness distribution of a quartz crystal wafer (Yamamura et al. 2008; Ueda et al. 2010). A plasma generating unit is constructed from a coaxially arranged electrode and dielectric cover, and helium-based process gas is supplied to the electrode tip through the space between the electrode and dielectric cover. The replacement of the air in the vicinity of the electrode tip, which is surrounded by the dielectric cover and the specimen, with a helium-based process gas enables the generation of a stable glow discharge plasma at atmospheric pressure without any vacuum operation. The diameter of the electrode, which was made of aluminum alloy, is 3 mm. The composition and flow rate of the process gas are controlled by mass flow controllers. The plasma is generated between the electrode tip and the quartz crystal wafer by applying a radio-frequency (RF) electric field ( f = 13.56 MHz). An increase in the electric power to the localized plasma to increase the etching rate tends to cause a breakage or the formation of twins in the quartz crystal wafer by thermal stress because quartz crystal is brittle and has low thermal conductivity. Therefore, a function generator is built into the RF power supply to decrease the surface temperature of the quartz crystal wafer by generating pulse-modulated plasma (Ueda et al. 2010; Yamamura et al. 2009). The quartz crystal wafer is held by a vacuum chuck, which is installed on the X-Y table along with a heater. The relative position and scanning speed between the electrode and the quartz crystal wafer are controlled by the X-Y table, and motion in the Z-direction is driven by AC servomotors. The thickness distribution of the wafer is measured by a resonance frequency measurement system constructed from a noncontact electrode unit and a network analyzer. The frequency measurement point of the wafer is placed between a pair of probe electrodes with a gap distance of 30 μm. The resonance frequency of a small localized area of the wafer, which corresponds to the area of the probe electrode with a diameter of 3 mm, is measured by determining the capacitive coupling between the wafer and the electrodes. The localized thickness of the wafer t between the probe electrodes is converted from the resonance frequency f by using the relationship t (μm) = 1670/f (MHz). The removal volume distribution on the wafer, which represents the distribution of the volume to be removed, is calculated by subtracting the target thickness from the measured thickness distribution.
A double-sided polished AT-cut quartz crystal wafer with an average thickness of 100 μm was used as a specimen to evaluate our developed NC-PCVMtechnique. The flow rates of the reactive gases and the machining gap were He:CF4:O2 = 250:20:4 (cc/min) and 250 μm, respectively. Figure 4a shows the thickness distribution of the as-received wafer. The thickness of the quartz crystal wafer was converted from the resonance frequency, which was measured with a 4 mm pitch. Figure 4b shows the thickness distribution after correction by NC-PCVM. The thickness error of the wafer decreased from 122.6 nm peak-to-valley (p-v) to 14.9 nm p-v over an area of 24 x 24 mm2. The total correction time was 107 s. This result shows that the thickness uniformity required for final ion-beam trimming was successfully achieved. Figure 5a, b show histograms of the thickness deviation on the wafer from the average thickness before and after NC-PCVM, respectively. The standard deviation of the thickness deviation decreased from 33.2 to 3.2 nm.

The thickness correction improved resonant characteristic as shown in Fig. 6. Before thickness correction, many unwanted spurious peaks were observed near the main peak of the resonance curve. In contrast, there were no spurious peaks around the main peak for the corrected wafer. Figure 7 shows the thickness deviations of the wafer before and after thickness correction, where filled symbols indicate points where the resonance curve was measured. The thickness variations at the measurement points of the wafer before and after correction were 34.9 and 4.6 nm/mm, respectively. It is assumed that the improvement of the parallelism in the area facing the measurement probe reduced the number of spurious peaks.

The Q factor of a crystal oscillator manufactured using the wafer processed by NC-PCVM was approximately 1  x 105, which is equivalent to that of a conventional commercial oscillator; thus, there was no characteristic degradation of the oscillator due to plasma irradiation. In the case of the wafer processed by a reactive ion etching (RIE), large spurious peaks can be observed near the main peak (Nagaura and Yokomizo 1999). It is considered that these spurious peaks, which result in a decrease of the Q factor and a change in the resonance frequency of the oscillator, are caused by subsurface damage formed by the collision of high-energy ions. In contrast, the kinetic energy of ions in PCVM is very low because of the small mean free path under the atmospheric-pressure condition. In our previous work, the measurement of surface photovoltage (SPV) revealed that the surface defect density of a single-crystal silicon wafer processed by PCVM is equivalent to that of a surface processed by chemical etching using a mixture of hydrofluoric acid and nitric acid. On the other hand, a surface processed by mechanical polishing and argon ion sputtering had a large defect density of more than two orders of magnitude greater than that of the surface processed by PCVM (Mori et al. 2000b).
These results show that numerically controlled open-air-type PCVM is a promising process for improving the thickness uniformity of the AT-cut quartz crystal wafers without degrading the resonance properties.