Two primary standards for low flows of gases

Journal of Research of the National Institute of Standards and Technology, July-August, 2004 by Robert F. Berg, Stuart A. Tison

We describe two primary standards for gas flow in the range from 0.1 to 1000 [micro]mol/s. (1 [micro]mol/s [congruent to] 1.3 c[m.sup.3]/min at 0[degrees]C and 1 atmosphere.) The first standard is a volumetric technique in which measurements of pressure, volume, temperature, and time are recorded while gas flows in or out of a stainless steel bellows at constant pressure. The second standard is a gravimetric technique. A small aluminum pressure cylinder supplies gas to a laminar flow meter, and the integrated throughput of the laminar flow meter is compared to the weight decrease of the cylinder. The two standards, which have standard uncertainties of 0.019%, agree to within combined uncertainties with each other and with a third primary standard at NIST based on pressure measurements at constant volume.

Key words: constant pressure; gas flow meter; gravimetric; laminar flow meter; nitrogen; primary standard; volumetric.

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1. Introduction

Integrated circuits are made in reaction chambers, or process "tools", each of which receives gases from several mass flow controllers at rates from 1 to 10 000 [micro]mol/s. (1 [micro]mol/s [congruent to] 1.3 c[m.sup.3]/min at 0[degrees]C and 1 atmosphere.) Flow uncertainties are typically 1% at present, but improvements to 0.5% are desired [1,2]. The role of the National Institute of Standards and Technology in achieving such improvements is to provide accurate primary standards for gas flow for the semiconductor industry, especially manufacturers of mass flow controllers. This paper describes two such standards whose uncertainty achieves the industry goal of 0.025% [1,2].

The first primary standard, which is based on measurements of pressure, volume, temperature, and time, is a constant-pressure flow meter (CPFM). Operation at constant pressure eliminates problems due to adiabatic heating or cooling that can appear in a constant-volume (pressure-rate-of-rise) technique. The CPFM is similar to a vacuum standard used at NIST [3] in that it inserts a piston into an oil-filled chamber; however, the piston is much larger and its drive train can handle pressures up to 900 kPa.

The second primary standard, the gravimetric flow meter (GFM), is an adaptation of techniques used in industry to calibrate commercial laminar flow meters [4] and in the NIST Gas Metrology Group to create accurately known gas mixtures. The GFM uses an electronic mass comparator to weigh a gas cylinder before and after a gas flow. The change of weight effectively calibrates a laminar flow meter (LFM) [5] whose measurements can be integrated to high accuracy. This technique is "static"; a "dynamic" gravimetric technique measures the cylinder's mass while the gas is flowing.

Both flow standards have standard uncertainties of 0.019%. (All uncertainties are reported as standard relative uncertainties corresponding to a coverage factor k = 1). We verified their trustworthiness by comparing them to each other and to a third primary flow standard based on pressure measurements at constant volume [6]. Sections 2 and 3 describe the construction, operation, and uncertainty of the CPFM and GFM respectively. Section 4 describes the comparisons of the CPFM and GFM with each other and with the third primary flow standard.

2. Constant-Pressure Flow Meter (CPFM)

2.1 Principle of Operation

Figure 1 is a schematic diagram of the CPFM. Its largest moving part is a piston that moves into or out of an oil-filled chamber. Consequently, gas flows out of or into a metal bellows contained in the oil chamber. A displacement [DELTA]x of the piston out of the oil chamber increases the bellows volume by ([pi][D.sup.2]/4)[DELTA]x, where D is the piston diameter. If the gas pressure P in the bellows remains constant, the number of moles of gas in the bellows increases by [DELTA]n, and the average flow rate during the interval [DELTA]t is

[dot.n.sub.CPFM] = [[DELTA]n]/[[DELTA]t] = [P/[[R.sub.gas]T(1 [B.sub.P]P)]][[[pi][D.sup.2][DELTA]x]/[4[DELTA]t]], (1)

[FIGURE 1 OMITTED]

where [R.sub.gas], T, and [B.sub.P] are the universal gas constant, the gas temperature, and the gas's second pressure virial coefficient, respectively.

During the flow measurement depicted in Fig. 1 the CPFM acts as a flow sink, and gas flows at a constant rate through the flow meter to be calibrated (transfer standard) and into the CPFM. (Moving the transfer standard from the input to the exhaust changes the CPFM from a flow sink to a flow source.) Eq. (1) is used periodically calculate the amount of gas accumulated in the CPFM bellows, which is compared to the integrated molar flow rate through the transfer standard.

2.2 Mechanical Components

The piston (102 mm diameter and 406 mm length) was ground from A-6 tool steel with a root-mean-square surface finish of 0.2 [micro]m. A coordinate measuring machine determined its diameter variations. The bellows is a commercially available, edge-welded, stainless-steel, vacuum bellows, with a spring constant of 1.2 kN/m. The maximum volume defined by its effective diameter (124 mm) and stroke (86 mm) is 1.04 L. Most of the bellows stroke can be used for flow measurements because the piston's diameter and allowed stroke (110 mm) define a swept volume of 0.90 L. ([DELTA]n = 0.036 mol at 100 kPa.)