A Non-Intrusive Analytic Temperature Model for Rate-of-Rise-Based Gas Flow Standards

Published

May 20, 2026

Author(s)

Aaron Johnson, Jodie Pope, Keith Gillis, John Wright, Christopher Crowley

Abstract

Accurate measurement of low gas flows is essential in semiconductor manufacturing, where mass flow controllers (MFCs) regulate gas stoichiometry during etching and deposition. The Rate-of-Rise (RoR) method, widely used for MFC calibration, determines mass flow rate by introducing steady gas flow into a vessel of known volume and calculating the rate of change in gas density. However, compression heating during filling generates a transient, non-uniform temperature field, causing errors in temperature measurement that propagate to density and, consequently, mass flow rate. We propose a novel RoR collection-vessel geometry with a long, slender, thermostatted tube that simplifies heat transfer, enabling an analytical solution for gas temperature. Our model, which was validated for five gases (Xe, SF6, CO2, N2, Ar), predicts the steady-state average gas temperature with a standard uncertainty of 37.5 mK, relying only on wall temperature and gas pressure measurements. The proposed long, slender collection vessel design and accompanying thermal model enhance RoR flow standards and support reliable, SI-traceable MFC calibration.

Proceedings Title

The 20th International Flow Measurement Conference FLOMEKO 2026

Conference Dates

May 17-20, 2026

Conference Location

Nara, JP

Conference Title

FLOMEKO 2026

Pub Type

Conferences

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Citation

Johnson, A. , Pope, J. , Gillis, K. , Wright, J. and Crowley, C. (2026), A Non-Intrusive Analytic Temperature Model for Rate-of-Rise-Based Gas Flow Standards, The 20th International Flow Measurement Conference FLOMEKO 2026, Nara, JP, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=961667 (Accessed June 10, 2026)

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