Using Air Bearings in Vacuum to Control Stage Vibration

It is widely observed in the precision world that the ultimate limit on the ability to place a mechanism precisely is the ability to measure its position. As interferometric measurement techniques have improved, we are now faced with a situation where properties of the motion device itself limit the accuracy of the measurement. Typically, an interferometer measures the position of a mirror to which the substrate of interest (wafer, mask, etc.) is attached. While modern commercial interferometers can measure the position of the mirror to a small fraction of a nanometer, the location of the substrate with respect to the mirror can vary by many nanometers due to vibration in the motion mechanism.

In precision mechanics, the dictum from special relativity that there are no rigid bodies has ceased to be a theoretical curiosity, and become the central reality limiting the performance of precision mechanical systems. The combination of the mass m of the substrate and its compliance k create a resonant frequency

Vibration of the motion stage produces an acceleration a, which results in a displacement between the mirror and substrate

for vibrational frequencies well below the resonant frequency. Figure 1 shows the dependence of measurement error δ as a function of acceleration and structural resonance frequency

1. Vibrations induced by the stage mechanism cause relative motion between the interferometer and the substrate, resulting in inaccurate knowledge of the substrate location.

2. Air bearings typically operate with clearance between the stationary and moving parts on the order of 10 µm. To operate in vacuum, the small clearance is continued beyond the end of the bearing.

of the substrate-to-mirror connection. Even for relatively ambiguous substrate supports with resonant frequencies in the range of 500 Hz, vibrational accelerations must be limited to 1 mG to keep the metrology error below 1 nm. For a more common resonant frequency of 200 Hz, the vibration due to acceleration must be <40 µG to keep the error <1 nm. This simple analysis holds for vibration frequencies well below the resonance frequency. The situation can be substantially worse for vibrations near the resonant frequency where the motion is amplified.

For stages operating in air, difficulties associated with traditional rolling elements consisting of ball or roller bearings were overcome long ago through the widespread use of air bearings in the semiconductor industry. Air bearings have been used in 1× full-field scanners and 1× steppers since the early 1980s. While rolling elements have been tried in step and scan, all successful step-and-scan systems to date have relied on air bearings. The success of air bearings is due to their superior vibrational properties. Air bearings have been demonstrated with vibration levels at the microgravity level and below, while running at constant speed. In addition, they maintain the same low vibration while operating in the stationary condition and at very low speeds, as they do at normal scanning speeds.

3. Through the use of vacuum-scavenged air bearings, a relatively conventional gantry-style linear air-bearing stage can  be made to operate inside a vacuum chamber. Driving force is provided by linear motors. The plumbing is for the supply of high-pressure air to the bearing and the scavenging stem.

The new air-bearing-in-vacuum technology (Fig. 3) uses conventional journal-style air bearings. The exhaust of the air bearings is scavenged through a series of differential pumping ports. This limits the gas load into the main vacuum chamber to a level readily handled by a conventional vacuum pumping system. The benefits of this approach can be seen in Figure 4 . Earlier stage designs using ball screws or rolling-element linear ways have vibration levels in the 10-50 mG range. The stage using air bearings in vacuum and linear motors demonstrates 50 µG vibration levels. This quantum improvement in technology enables improved placement of features in pattern generators.

Stage-induced errors are only one of many sources of pattern placement errors on the mask. To separate stage-induced errors from electron optical and other sources, it is useful to study the repeatable and non-repeatable components of placement errors among masks written on the same pattern generator. By minimizing stage vibration, the attempt was to minimize the non-repeatable component of the placement error. The repeatable component of the placement error can then be cancelled by proper calibration of the machine.

4. Newly developed air-bearing-in-vacuum technology has demonstrated vibration levels of 50 µG. Typical high-performance rolling-element stages to date have achieved vibration levels of 10 mG for crossed-roller and ball-bearing linear ways, and 25 mG for ball screw-driven stages.

5. Three plates are written on the same machine. Shown here is the difference in position of the patterns on one of the plates measured against the three-plate average. This procedure suppresses systematic errors and accentuates random errors.

6. Average Y error is plotted as a function of the X coordinate for each of three plates. Each data point represents the average X error of the 11 points having the X coordinate on the abscissa and all 11 Y values. This procedure suppresses random errors and accentuates systematic errors. Variation between plates is consistent with measurement error. A highly repeatable, hence correctable, stage-error signature is observed.

where x_ij is the measurement and X_ij is the nominal coordinate. The quantity (x_ij-X_ij) is measured on an inspection tool with specified accuracy of 5 nm 3s . A similar procedure can be carried out for the Y axis systematic errors.

The results of this measurement procedure are shown for the X axis of a typical three-mask set in Figure 6 . Each curve represents the Y error determined for one of the three masks. The three curves overlay with a standard deviation of <1 nm. Several conclusions can be drawn from this result:

• The system has a highly repeatable (correctable) error of ~17 nm peak to peak. This corresponds well to an expected figure error in the interferometer of ~λ/40. Other repeatable sources such as stage pitch and roll can contribute to this error.
• Non-repeatable errors are of the same order as measurement error, having 3s values of a few nanometers. These errors are from all random sources and believed to be dominated by microscopic random noise in the electron beam deflection system.

The ability to place a pattern accurately on a mask is ultimately limited by the ability to measure the position of the mask relative to the writing beam. The use of air bearings in vacuum is motivated by the need to reduce the deleterious effect of stage vibration on that measurement. By limiting the stage vibration to 50 µG with this technology, it was shown that masks can be produced with highly repeatable and correctable error signatures. An overlay accuracy of 12 nm in X and Y has been demonstrated against a three-plate average.

With ever-tighter placement requirements, and the continued evolution toward lithography and inspection technology in vacuum, air-bearing-in-vacuum technology will become more widespread.