A new calibration standard for process pressure gauges
Luke D. Hinkle, MKS Instruments Inc., Andover, Massachusetts
Ever more stringent process requirements are driving the development of higher-performance gauging and control instrumentation for next-generation equipment. Total pressure will continue to be among the key physical parameters in advanced PVD, CVD, and etch processes. The 1-10 mtorr region has been problematic for traditional primary standards. Calibration of process instruments in this range has relied on transfer standard gauges that have themselves been calibrated at higher pressures against a primary standard. While this method has worked well in the past, a new primary standard for the mtorr range gives greater confidence in calibration.
Many new processes, including high-density plasma etch, advanced sputter deposition, plasma CVD, and plasma immersion ion implantation, operate in the range from 0.5-50 mtorr. Capacitance manometers or capacitance diaphragm gauges (CDGs) have been the mainstay of pressure measurement in vacuum semiconductor process control for the past 25 years. The specifications and low pressure utility of the general purpose CDG have steadily progressed, as shown by the lowest full scale ranges and "measurement cost" (the % of reading accuracy multiplied by the price in US$) (Fig. 1).
The trend toward measuring lower pressures with higher confidence raises the question: is there a suitable primary standard for a pressure of 1 mtorr? As with many such questions, the answer is "yes and no." Several national standards labs have built primary standards covering the millitorr range. A few of the labs have reported estimated uncertainties as low as 0.2 % of reading. This is, by definition, the state-of-the-art capability, but it is not easily transferred to process measurements.
For pressures above 100 mtorr, several methods for calibration with primary standards are readily available: mercury column manometers, oil column manometers, and dead weight testers . For lower pressures, a transfer standard CDG is traditionally employed. It is first calibrated against one of these primary standards at higher pressure and then its inherent linearity and stable zero allow interpolation to millitorr readings. Our goal is to establish a practical primary standard for calibration at each pressure of interest.
Figure 1. Plot of measurement cost vs. time for process instruments.
Overview of the method
Our technique is based on the gravitational force applied to a diaphragm when it is tilted from the horizontal position (port-horizontal) [2-5]. When a CDG is tilted from port-horizontal to port-down, the pressure exerted on the thin foil diaphragm by gravity is given by:
P = ??? g sin?, (1)
s = surface mass density of the diaphragm foil
g = acceleration due to gravity
q = angle between the axis of the diaphragm and horizontal.
Equation 1 has been used to describe attitude-related offsets in a CDG that was initially zeroed while in the horizontal port position.
For a pressure standard using this effect, a reference capacitance diaphragm sensor with a permanent vacuum reference is constructed using a well-characterized metal foil for the diaphragm (Fig. 2). The reference capacitance diaphragm sensor is essentially the same as a sensor in a typical CDG. With the sensor mounted rigidly to a rotary table, the attitude can be changed in a controlled manner, inducing a gravity pressure and subsequent "sag" in the diaphragm. A gas pressure on the diaphragm will balance the known gravity pressure at a given q. When the net pressure returns to zero, the gas pressure is equal to the gravity pressure, which is, in turn, determined by Eqn. 1. The pressure measurement uncertainty of the system is thus not dependent on the pressure calibration of the reference capacitance diaphragm sensor itself-the reference sensor indicates deviation of the diaphragm foil from a null point. The reference sensor and the related electronics must have zero stability and high signal-to-noise ratio, however.
The sensor is housed in a cast-aluminum enclosure at ambient temperature with the signal conditioning electronics mounted in a separate enclosure. This design minimizes thermal transpiration while providing a thermally stable environment over the period of a typical calibration process. The instrument is plumbed, via bellows, to a manifold that provides for stable pressure control from 1-100 mtorr and a base pressure of ~10-7 torr (Fig. 3). For calibration purposes, a port for the device under test (DUT) vacuum gauge is located on the manifold in a position where it will experience the same pressure as the reference CDG sensor. The latter is mounted on a precision rotary table with a direct reading optical encoder so that the angle q can be varied throughout the range from 0-908 (port horizontal to port down).
The system first reads the indicated zero while horizontal, then tilts to a specified q and controls the pressure in the manifold to maintain the reference signal at the null reading. This procedure ensures that the gas pressure precisely offsets the gravitational pressure on the diaphragm. Since the gravitational pressure is calculated from s, g, and q, each of which can be measured independently with traceability, the system presents the DUT with a known, traceable gas pressure. For the particular system described here, the reference sensor was fabricated with a sg of slightly more than 10 mtorr so that a 0 to 10-mtorr calibration can be performed with a 0-908 sweep. The output of the signal conditioning electronics was set to approximately 100 mtorr full scale.
Calibration of a DUT can be performed by generating a series of pressures, i.e., rotating the table to the appropriate angles in sequence (Fig. 4). The technique also allows bootstrapping to higher pressures (above sg) by briefly maintaining pressure control using an alternate gauge (not shown in Fig. 3) while rotating back to horizontal, resetting the null signal, and proceeding as before. Even at pressures up to 100 mtorr, the diaphragm of the reference sensor experiences such a small deflection relative to its diameter (<1 part in 104) that Eqn. 1 remains valid for subsequent calibration points (Fig. 4). Since the electrical output of the reference capacitance diaphragm sensor extends to 100 mtorr, the bootstrapping operation can be performed 10 times, for pressures up to 110 mtorr.
People normally use the term "accuracy" to describe how close a measuring instrument`s output is to the true value. For a primary standard (which, by definition, is not calibrated directly for the measured quantity), metrologists have agreed to express the measurement capability as the "combined uncertainty" of all the significant factors affecting the ability to determine the measured value.
The factors that affect the uncertainty of the pressure in this system can be divided into several categories. First, there are systematic, first-order factors such as the measurement of s, g, and sinq. There are also various other factors such as signal noise, pressure control stability, temperature gradient-induced phenomena, and drift of the reference capacitance diaphragm sensor. In each case, the estimated uncertainty takes into consideration the current capability of the system and technique. Future improvements in design and technique should give a corresponding reduction in estimated uncertainty. The table shows an overview of the component and combined estimated uncertainties for this standard. The analysis follows methods and guidelines from NIST  and ISO .
Figure 2..A reference capacitance diaphragm sensor with a permanent vacuum reference is constructed using a well-characterized metal foil as its diaphragm.
Figure 3..Primary pressure system overview.
Foil surface mass density s. The surface mass density s of the diaphragm is measured before assembly of the reference capacitance diaphragm sensor. A sample of foil is cut in an approximately square shape and flattened. Then, a coordinate measuring machine and/or optical scanner measures the sample area, and a precision mass balance determines the mass. These operations result in uncertainties of 0.05% for surface area and 0.005% for mass.
When using the coordinate measuring machine, the uncertainty in the area measurement results primarily from nonstraight edges, bowing or puckering of the sample, and the accuracy and operation of the coordinate measuring machine. The uncertainty of the optical scanner is primarily due to the resolution of the digital scanning, the ability to identify foil vs. background regions, and the length calibration of the scanning optics. With the foil samples, the optical scanning method is preferred, since it essentially integrates the actual area regardless of irregularities in shape.
Figure 4.Calibration sequence for a series of n angular positions and m bootstrapping steps.
During construction of the reference capacitance diaphragm sensor, the foil sample of known surface mass density is tensioned to form the diaphragm element. The tensioning process reduces the surface mass density by a slight amount (on the order of 0.01%), which can be corrected to better than 0.002% after construction.
Other practical issues considered in the surface mass density uncertainty are foil uniformity and extraneous deposits on the foil. We estimate the pressure uncertainty introduced by foil uniformity to be less than 0.02%. A change in the effective surface mass density can occur if oil, dust, or other contamination coats or adheres to the diaphragm surface after construction. Safeguards have been put in place to prevent pump oil vapor or particles from reaching the reference capacitance diaphragm sensor, but we can consider a worst-case situation for the purpose of this analysis. If 0.1 ?m of oil were to be deposited on the diaphragm, the resulting change in surface mass density would be approximately 0.02%.
Combining the above considerations (RSS), the surface mass density is determined with an estimated uncertainty of 0.058% and remains a first-order effect on pressure throughout the intended range.
Gravitational acceleration g. The local gravitational acceleration at our lab is known sufficiently well to make its uncertainty negligible. The nominal value has been corrected for altitude; the uncertainty is estimated to be less than 0.001% and is a first-order effect on pressure.
Attitude angle q. The uncertainties in the attitude angle are not first-order and are analyzed in three parts: uncertainty of rotational axis level, uncertainty of zero position level, and uncertainty of the swept angle qs = q-qo.
The rotational angle of the table, f, relative to the horizontal axis is set to be zero so that the angle to horizontal, q, is strictly a function of the table rotation. Considering the resolution of the level, the mechanical transfer, and the mounting structure of the reference capacitance diaphragm sensor, the uncertainty in f is 0.028. Since the dependence of pressure is proportional to cosf, the pressure uncertainty is negligible.
The uncertainty of qo, d(=qo-08), estimated to be less than 0.0178, introduces a pressure uncertainty that varies depending on the final swept angle qs. Consequently, the pressure uncertainty is different at different pressures. The dependence of the relative pressure uncertainty DP/P on d is
?P/P = cos? + (1-cos?s)sin?/sin?s-1 (2)
The value of d affects the uncertainty of higher pressures, where qs is large, more than lower pressures.
The uncertainty of the swept angle measurement, y, is primarily the result of the optical encoder resolution, specified at 0.018 unidirectional. The accuracy between any two line positions is better than ?0.0018. The positional uncertainty for unidirectional motion is therefore 0.0068 when expressed as a maximum deviation from the mean.
The associated pressure uncertainty is a function of angle and thus pressure according to
?P/P = cos? + cot?ssin?-1 (3)
Here, the pressure uncertainty is more pronounced at the lower pressures. The combined pressure uncertainty due to do and y is shown for specific pressures in the table.
Reference capacitance diaphragm sensor null signal. In practice, the null signal from the reference capacitance diaphragm sensor is subject to several modes of variability that can be classified as voltage resolution, sample noise, and instability over a calibration process. These contribute to the pressure uncertainty as an absolute pressure and hence have a greater effect at lower pressures.
The digital resolution of the voltage signal is set by the A/D converter in the instrumentation at 18 bits over 100 mtorr, or 4 ? 10-7 torr. The sample noise has been determined by analyzing the standard deviation of measurements for 100 consecutive samples that are taken by averaging over distinct 1-sec intervals. When analyzed in this way at base pressure and qo, the measured standard deviation for this apparatus is 5 ? 10-7 torr. The long term stability of the null signal over the period of a calibration process has been considered separately by measuring the typical drift of the signal over intervals of 5 min. The result, 6 ? 10-7 torr, is consistent with routine observations of the signal before and after actual calibration sequence trials.
While it may be over-conservative to combine the contributions as mutually exclusive events, doing so results in only a 9.3 ? 10-7 torr estimated uncertainty.
System induced.The potential contributions to the pressure uncertainty in the vacuum system include control stability, outgassing-related gradients, thermal transpiration, and parasitic tilting effects.
The pressure control method nulls the signal, from the reference CDG sensor, consistently within 0.05% of the total pressure for pressures between 1 and 5 mtorr and better than 3 ? 10-6 torr for pressures between 6 and 10 mtorr. The control software is designed to reject a calibration point that does not achieve this control band limit.
Pressure gradients due to the flow of controlled calibration gas have been avoided by proper layout of the system. Still, if an extraneous gas source (leak or outgassing) generates a local pressure gradient in the connecting conductance between the reference capacitance diaphragm sensor and the DUT, then a pressure difference will be unknowingly imposed. A pressure rate-of-rise test was performed to estimate the total extraneous gas load and evaluate the magnitude of such an effect (approximately 1.5 ? 10-8 torr l/sec). Even in the worst case, where the entire gas load is being generated at one end of the connecting tubing, the induced pressure difference is <10-7 torr.
Though thermal transpiration is a potential contributor to uncertainty in primary vacuum standards operating in this range, it is essentially a square root absolute temperature effect . The worst-case scenario of 0.38C temperature difference along the connecting tubing will cause <0.05% uncertainty in the pressure.
When the reference capacitance diaphragm sensor is tilted, any influences on the signal that are not the result of gravity acting on the diaphragm foil are defined as parasitic tilting effects. Possible causes are: electronic shifts due to convection cooling of the circuit, electronic shifts due to gravity-induced strains on circuit components, strains induced by the bending of the connecting vacuum bellows, and strains induced by gravity acting on the body of the sensor. These phenomena were not analyzed independently; the magnitude of the combined parasitic effects was experimentally assessed. A special test sensor with a very stiff (thick) diaphragm was installed in the system such that the electronics and mechanical arrangements remained the same. Operating the system by tilting to various angles and monitoring the signal (without the restoring pressure) showed that the parasitic effects were less than 0.05% of the equivalent pressure when operated as a pressure standard.
The practice of carefully calibrating a transfer standard CDG at higher pressures, then using its inherent linearity to extend to the mtorr range, has proved to be an effective and convenient method. In anticipation of future requirements for process pressure measurement, we have developed a primary pressure standard for this range.
The primary standard described here is designed to provide an automated calibration system for gas pressure in the range from 1 to 100 mtorr. The uncertainty analysis of this standard compares favorably with other primary standards in this range. The operation and maintenance of this system is simpler than that of a liquid column standard of similar performance. Unlike dynamic expansion or conductance-based systems, this standard is independent of gas properties and flow regimes and does not rely on a separate gas flow measurement. Its narrow range of optimal performance-two decades-is a limitation relative to some of the other primary standards. In principle, the operating range could be extended in either direction by at least one decade with appropriate modifications to the capacitance diaphragm sensor and system operation. n
The research discussed in this article was presented at the 43rd National Symposium of the American Vacuum Society, 1996. A paper on the presentation will be published in the proceedings of the meeting later in 1997.
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4. U.S. Patent No. 5,515,711.
5. L.D. Hinkle, J. Provost, D.J. Surette, "A Novel Primary Pressure Standard for Calibration in the mtorr Range," J. Vac. Sci. Technol. A, (to be published).
6. Natl. Inst. Stand. Technol., Technical Note 1297, 1994 Edition.
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LUKE HINKLE received his PhD degree in physics from Pennsylvania State University in 1989. He now serves as core technology team manager at MKS, concentrating on R&D for mass flow measurement and control technology, pressure measurement technology, and vacuum gauging. He has 11 years of experience in the vacuum technology field, and is one of the organizers of the SEMATECH mass flow controller training course. He is also an instructor for AVS short courses on mass flow controllers. MKS Instruments, 6 Shattuck Rd., Andover, MA 01810; ph 508/975-2350, fax 508/975-0093.