Wavelength-Modulation Laser Hygrometer for Ultrasensitive Detection of Water Vapor in Semiconductor Gases

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Wavelength-modulation laser hygrometer forultrasensitive detection of water vapor insemiconductor gases

David Christian Hovde, Joseph T. Hodges, Gregory E. Scace, and Joel A. Silver

Water vapor is measured by use of a near-infrared diode laser and wavelength-modulation absorptionspectroscopy. Humidity levels as low as 5 nmolymol @1 nmolymol 5 1 ppb ~1 ppb equals 1 part in 109!#of water vapor in air are measured with a sensitivity of better than 0.2 nmolymol ~3s!. The sensitivity,linearity, and stability of the technique are determined in experiments conducted at the NationalInstitute of Standards and Technology, Gaithersburg, Maryland, by use of the low frost-point humiditygenerator over the range from 5 nmolymol to 2.5 mmolymol of water vapor in air. The pressure-broadening coefficients for water broadened by helium @0.0199~6! cm21 atm21 HWHM# and by hydrogenchloride @0.268~6! cm21 atm21 HWHM# are reported for the water line at 1392.5 nm. © 2001 OpticalSociety of America

OCIS codes: 120.0120, 120.6200, 300.0300, 300.1030, 300.6260, 300.6380.

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1. Introduction

Measuring local concentrations of water vapor atmole fractions near nanomole-per-mole levels is im-portant in many industrial applications,1–3 especiallyhe fabrication of semiconductors. Sensitive meth-ds and instruments for measuring water vapornclude atmospheric-pressure ionization mass spec-rometry,4 chilled-mirror hygrometers, electrolytic

sensors,2 mechanical microbalances, and capacitanceensors. Shortcomings of these existing approachesnclude high costs, slow response times, poorly char-cterized surface interactions, indirect calibration, ornability to measure moisture in hydrogen, oxygen,nd condensible or corrosive gases.Of the optical methods that have been applied tooisture measurement Fourier transform infrared

FTIR! spectroscopy5 has the smallest dynamic rangend the poorest sensitivity ~;10 nmolymol!. Be-ause water vapor is a component of room air, the

D. C. Hovde [email protected]! and J. A. Silver are withSouthwest Sciences, Inc., 1570 Pacheco Street, Suite E-11, SantaFe, New Mexico 87505. J. T. Hodges and G. E. Scace are with theChemical Science and Technology Laboratory, National Instituteof Standards and Technology, Gaithersburg, Maryland 20899.

Received 1 June 2000; revised manuscript received 17 August2000.

0003-6935y01y060829-11$15.00y0© 2001 Optical Society of America

ntire FTIR spectroscopy optical path must be kept inn extremely dry enclosure, which adds significantlyo its cost and complexity. Intracavity laser absorp-ion spectroscopy is an extremely sensitive methodor humidity sensing.6 Unfortunately, it is difficult

to calibrate, has a limited dynamic range, and re-quires additional work to make it rugged enough forroutine industrial use. Cavity ring-down spectros-copy7,8 has the potential for high precision and accu-racy, but pulsed-laser sources remain costly andcomplex in the spectral regions of strongest waterabsorption. Sensitive single-mode cavity ring-downtechniques based on locking cw lasers to high-finessecavities may be able to approach the 0.01-nmolymolensitivity level.7 Water vapor has been measured

at nanomole-per-mole levels by use of lead-salt la-sers,9,10 but with their need for cryogenic cooling andfrequent beam diagnostics lead-salt laser systems aremore suited to laboratory experimentation than tocommercial instrumentation.

We report a wavelength-modulation laser hygrom-eter ~WMLH! for the ultrasensitive detection of watervapor.11 For detecting H2O this instrument com-bines wavelength-modulation absorption spectros-copy ~WMS!12–16 that uses near-infrared InGaAsPdiode lasers near 1392.5 nm with a multipass absorp-tion cell that is designed to minimize outgassing.Near-infrared lasers, originally developed for thecommunications industry, operate at room tempera-ture to produce light with excellent spatial and spec-

20 February 2001 y Vol. 40, No. 6 y APPLIED OPTICS 829

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tral properties. The WMLH is applicable tocorrosive as well as inert feed gases and has thedesired combination of linearity, response speed, sen-sitivity, and accuracy. The water-vapor level de-rived from a detailed numerical model of thespectroscopic signal is compared with humidity levelsin the range of 5 nmolymol to 2.5 mmolymol of watervapor in air and delivered by a stable thermodynamicsource. The stability of the laser system is deter-mined from the Allan variance of time series that isobtained during measurements of air containing 15and 100 nmolymol of water vapor. Pressure-broadening coefficients are reported for the1392.5-nm water line17 when broadened by He andHCl.

Other researchers have used near-infrared lasersto measure trace moisture levels in the nanomole-per-mole range. A near-infrared wavelength-modulation spectrometer for measuring water vaporin ammonia was recently reported by Wu et al.18,19

Their setup utilizes a single-pass, dual-beam ap-proach in which the signal from a dry reference cell issubtracted from a separate sample cell. A minimumdetectable absorbance of ;1.8 3 1027 was achieved,although the use of a single optical pass limited thesensitivity to 12 nmolymol. A two-beam approachalso was reported by Girard and Mauvais20 with thereference beam used to cancel the moisture signalthat arose from the purged beam path outside theirmultipass cell. A detection limit of 5 nmolymol wasreported in N2 and other gases on the basis of mea-surements made over the range of 0–10,000 nmolymol. In contrast to the previous research, theresults reported in this study were achieved withoutthe need for a reference detector and without contin-uously purging the external path.

Fig. 1. Schematic of the WMLH ~top! an

30 APPLIED OPTICS y Vol. 40, No. 6 y 20 February 2001

2. Experimental Apparatus

The diode laser absolute moisture sensor measuresthe amount of water vapor by the quantification ofthe absorbance of a single rotational line within avibrational-overtone band of water vapor. The lineat 1392.5 nm is chosen for its combination of linestrength, lack of known interfering absorbances, andavailability of single-frequency, InGaAsP diode la-sers that are based on distributed-feedback technol-ogy. Wavelength modulation is used to enhance thesignal-to-noise ratio ~SNR! in the absorption mea-surement by the reduction of the contribution of ex-cess ~laser! noise to the total noise current.12–16 Thelaser wavelength or frequency n is slowly rampedover the absorption line and simultaneously modu-lated at a frequency f with some modulation wave-orm nm~t! ~e.g., sine, triangle, or square wave!. The

absorption signal is quantified by lock-in detection, inthis case at twice the modulation frequency, 2f. Thistechnique improves the SNR by approximately 3 or-ders of magnitude12 compared with direct absorptionspectroscopy and results in an observed line shapethat is roughly the second derivative of the transmis-sion curve.13–16 Under computer control a spectralscan of this 2f line shape is recorded. The water-vapor concentration is determined by linear least-squares fitting21,22 of the resulting spectrum by use ofa theoretical model described below. After everyspectrum is measured ~approximately once per

inute! the water concentration is updated and dis-layed.The sensor design is based on a sealed laser head

hat is connected to a Herriott23,24 multipass cell ~Fig.1!, both built from 11.75-cm-diameter ~4.43-in.-

iameter! ultrahigh-vacuum stainless-steel flanges

tail of the laser-head assembly ~bottom!.
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sealed with copper gaskets. The laser ~Sensors Un-limited,25 Model SU1392 DFB-CD! and the 1-mm-diameter InGaAs detector are housed in the laserhead, and an antireflection-coated sapphire windowpermits the beam to enter and exit the Herriott cell.An electromagnet vibrates the diode-laser–aspheric-lens assembly ~see details in Fig. 1! to reduce the

etection of etalon fringes by approximately 2 ordersf magnitude.25,26 The Herriott cell consists of two-m-focal-length stainless-steel mirrors coated withiamond-machined nickel and separated by approxi-ately 94 cm. The beam enters the cell through a

lot cut in the mirror next to the laser head. Theptical path length depends on the ratio of the focalength of the mirrors to the mirror separation.23,24

For accommodating manufacturing tolerances in thefocal length and the cell length the mirrors aremounted by use of three screws to permit translationalong the optical axis as well as tip and tilt adjust-ment. The grooves necessary for constrained kine-matic motion are machined directly into the back faceof the stainless-steel mirror substrate, minimizingthe number of parts wetted by the measurement gas.An off-axis parabolic mirror focuses the beam exitingthe Herriott cell onto the detector.

The electronics include a computer for instrumentcontrol and data analysis, laser current and temper-ature controllers, laser modulation, detection, ampli-fication, and demodulation electronics, mechanicalmodulation, and pressure measurement. The laseris controlled by an ILX Model LDC 3722 current con-troller with a general-purpose interface bus controlfor temperature-tuning the laser. The laser-frequency temperature-tuning rate as measured witha traveling-mirror wavemeter is 212 GHzyK, and thedc-current tuning rate is 21.04 GHzymA. A typicalspectrum scans across 21 GHz.

The magnitude of the current-tuning rate for theapplied modulation is smaller than that of the dcfigure given above because of the finite heat capacityof the laser and its mount.26 Calibration of the mod-ulation depth is accomplished by the overmodulationof a narrow spectral line and then the fitting of theresultant line shape by the adjustment of themodulation-depth parameters. When a spectral lineis overmodulated the relative positions of the lobesare determined largely by the modulation depth; inthis limit the line shape only weakly influences theseparation of the lobes. The lobe separations aremeasured in terms of the frequency ramp ~deter-

ined in terms of the known dc-current-tuning rate!,hich means that the modulation calibration isighly correlated with the scan calibration. The in-ernal reproducibility of this method is estimated toe 3%. The modulation level used in this study wasypically 902 MHz ~baseline to peak!.

Spectra are obtained by the step scanning of theaser current—hence the laser center frequency—ver the absorption transition. The transmitted la-er power is measured by a photodiode. A customreamplifier separately amplifies the ac and the dchotocurrents. The 2f component of the ac pho-

tocurrent is measured by a true sine-wave lock-inamplifier, whereas the low-pass-filtered dc compo-nent is digitized by an auxiliary analog-to-digital con-verter on the lock-in amplifier. The ratio of thesetwo quantities at each frequency step ni ~for i 5 1,2, . . . ! constitutes the measured WMS spectrum.The main data-acquisition and data-fitting programcontinually scans the laser current and fits the re-sultant spectra. Typically, a spectrum is measuredwith approximately 90 equal laser-frequency steps in;70 s, giving an effective update rate on the water-vapor concentration of ;0.015 Hz. A general-purpose interface bus provides the interfacesbetween the computer and both the lock-in amplifier~which includes the digital-to-analog converters! andto the laser temperature–current controller. Agraphical user interface displays the measured spec-trum superimposed on the best-fit spectrum and alsodisplays a strip-chart-style graph of the measuredwater-vapor concentration. The results of the fit,including parameter values and uncertainties, arestored to a log file for later review.

The Herriott cell is evacuated by a corrosion-proofdirect-drive mechanical pump, and the sample pres-sure is monitored with a capacitance diaphragmgage. Pressures are regulated manually and aretypically maintained near 13.3 kPa ~100 Torr!. Thispressure provides the optimum in balancing the sig-nal strength, while keeping the line shape sufficientlynarrow so that the full shape can be recorded withinthe somewhat limited wavelength-scan range of thelaser.

Initial experiments conducted at Southwest Sci-ences, Inc., focused on the optimization of the SNR bymeasurement of the residual moisture in the boil-offfrom liquid nitrogen. The main source of noisearises from etalon fringes that are formed acciden-tally in the optical path. In the system describedhere there are two significant etalons: One has asmall free spectral range ~;69 MHz!, correspondingto a path difference of 4 times the Herriott cell length.This etalon is suppressed by the application to thelaser of an additional jitter modulation of approxi-mately 90 MHz with the method of Cassidy andReid.27 ~The 90-MHz jitter modulation slightly in-creases the effective linewidth of the laser; it is notapplied for the pressure-broadening measurementsand is neglected in the numerical model.! The sec-ond etalon has a larger free spectral range of 940MHz, corresponding to an optical path difference of32 cm. This difference is close to the round-trip dis-tance from the laser to either the sapphire window orHerriott cell entrance mirror. This etalon is sup-pressed by a combination of vibrating the laser,28,29

choosing a modulation depth for which this etalon isminimized ~a 902-MHz baseline-to-peak modulationdepth!,27 and blackening the back surface of the mir-ror and the metal parts near the window with agraphite slurry.

Quantitative measurements of water vapor in airare made by use of the new low frost-point humiditygenerator30 ~LFPG! at the National Institute of Stan-


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dards and Technology ~NIST! in Gaithersburg, Mary-land. The LFPG saturates a CO2-free stream of airwith water vapor by means of flowing the air throughan ice-coated channel that is maintained at constanttemperature and pressure. Its output can be pre-dicted from thermodynamic principles and underideal conditions is independent of the gas flow rate.The mole fraction of water vapor in the gas streamexiting the LFPG is computed in terms of thetemperature-dependent vapor pressure of hexagonalice31 and the measured total gas pressure. A smallcorrection, the so-called enhancement factor, for non-ideal mixing and nonideal gas effects is also ap-plied.32

At the lowest humidity levels the fractional uncer-tainty ~the 2-standard-deviation value! of the water-vapor mole fraction delivered by the LFPG isestimated to be &2%, a value that is dominated byuncertainty in the vapor pressure of the ice. Despitethis systematic uncertainty, the LFPG-generated hu-midity level can be maintained at a constant value forweeks by active control of the LFPG-saturator tem-perature. In practice, long-term variations of lessthan 2 mK in the saturator temperature are realized,corresponding to a fractional change of 0.04% in thewater-vapor mole-fraction levels produced for thesetests. On the basis of the saturator’s temperaturerange and stability the LFPG is expected to generatewater-vapor mole fractions ranging from 4 mmolymolto 3 nmolymol with differential changes in its outputas small as 10 pmolymol. The high precision and thewide dynamic range of this generator facilitate thetesting of the stability of the laser hygrometer over itsfull operational range. Also, the LFPG provides anindependent method for calibrating the response ofthe laser hygrometer. This result can be comparedwith the first-principles calibration, which is basedon spectroscopic and electronic gain factors.

A portion of the sample gas from the LFPG is me-tered into the laser-absorption cell by use of a critical-flow orifice. With this arrangement the flow ratesthrough the two systems can be controlled indepen-dently. Approximately 2 m of 0.25-in. ~0.63-cm!electropolished stainless-steel tubing is used to con-nect the output of the LFPG to the laser-absorptioncell.

Separately, pressure-broadening measurementsare made in ultrahigh-purity He ~Mattheson,99.999% pure! or in semiconductor-grade HCl gasMattheson, 99.995% pure!. The moisture in these

latter experiments arises from outgassing from theapparatus, resulting in water-vapor mole fractionsthat are estimated to be &10 mmolymol, which issufficiently low that the effects of self-broadening canbe neglected in the analysis. The sample tempera-ture for all measurements reported below is ;21 °C.

3. Analysis

Although diode-laser instruments have been cali-brated based on determining the signal strength froma known quantity of gas or based on the method ofstandard additions,9,20 it is also possible to calibrate


the instrument on the basis of only the known opticalpath length and the spectroscopic and the electronicgain factors.33 The spectroscopic parameters in-clude the line strength of water, pressure-broadening~Lorentzian! and Doppler-broadening ~Gaussian! linewidths, the frequency at the line center, and the mod-ulation depth of the laser.

The technique of WMS is well understood both the-oretically and experimentally.13–16 Because thediode-laser linewidth, which is usually less than ;50MHz HWHM, is much narrower than the spectrallinewidth, *500 MHz, the laser is assumed to probethe absorption line at a single frequency. The ratioof the modulation depth to the modulation frequencyis much greater than unity, ensuring that the instan-taneous laser frequency can be decomposed into thesum of a constant term ~the optical frequency! plus aslowly varying term ~corresponding to the low-frequency wavelength modulation!. The instanta-neous laser frequency is given by ni 1 nm~t!, where niis the center frequency and nm~t! is the wavelength-modulation waveform ~e.g., sine, triangle! of a char-cteristic frequency f.For a Lorentzian line shape and sinusoidal modu-

ation a closed-form solution for the WMS line shapexists.34 However, at the reduced pressure that op-

timizes the signals in the WMLH g~n! is modeledaccurately by a Voigt function for which a closed-formsolution to gWMS~n! is not available. Additionally, itis desirable to evaluate the signals from arbitrarynon-sinusoidal-modulation waveforms. Both casesrequire a numerical determination of the WMS lineshape. The WMS line shape gWMS~n! is found fromthe Voigt line shape35 g~n! by the computation of theinstantaneous absorption line shape g@ni 1 nm~t!# ateach value of ni. One full cycle of the modulationwaveform nm~t! is represented by 128 discrete steps.~If the modulation amplitude is large compared withthe linewidth, more steps are required.! The result-ng 128-point array is Fourier transformed; only thef component at the detection phase is retained asWMS~ni!.16 Computing the line shape for a complete

90-point spectrum thus requires 90 3 128 evalua-tions of the Voigt function and 90 fast Fourier trans-forms.

The measured spectrum is related to the theoreti-cal ratio of 2f to the dc photocurrent by

V2f

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where V is the measured voltage, G is the frequency-dependent electronic gain ~in volts per amperes!, R ishe detector responsivity ~in amperes per watts!, andis the transmitted laser power ~in watts!. We as-

umed that R2f 5 Rdc for the fast photodiode used todetect the transmitted laser power, as is expectedfrom its high bandwidth ~35 MHz! and low straycapacitance ~150 pF!. Lock-in demodulation recov-rs the ac photocurrent signal at the demodulationrequency 2f. Dividing this ac quantity by the dc

photocurrent converts the 2f signal into a fractional

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Table 1. Parameters Used to Compute Moisture Concentrations

change in transmitted laser intensity and thus ac-counts for changes in transmitted intensity that aredue to misalignment, broadband absorption by impu-rities, or thermal changes in detector responsivity.

The Beer–Lambert law relates the concentration ofwater molecules nH2O in the sample volume to theobserved intensity change passing through thesample. When the peak absorbance is sufficientlysmall that the linear form of the Beer law can be usedthe signal given by Eq. ~1! is linearly proportional tothe product of the line strength, the path length, andthe water concentration ~all of which are constantover the 20-ms modulation time scale! times the WMSspectral line shape gWMS~ni!. This linear relationbetween small changes in transmission and gas con-centration permits the use of a linear least-squaresanalysis to determine the best estimate of the waterconcentration.

Two extensions are made to this simple model ofthe Beer law absorption. First, the fit includes aquadratic baseline to account for electronic or opticalartifacts or both ~including nonlinear laser or elec-tronic responses, broad etalons, and distortions asso-ciated with the wings of adjacent lines!. Second, thederivative of the WMS line shape, taken with respectto frequency, is included. This derivative modelsany small frequency mismatch between the theoret-ical and the experimental spectra. Thus the water-vapor concentration is found by an unweighted least-squares fitting of each measured spectrum to a modelthat comprises five vectors: the WMS demodulatedVoigt line shape gWMS~n!, the derivative of this de-modulated line shape dgWMS~n!dn, and the quadraticaseline B:

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Vdc5 wH2OgWMS~n! 1 wDndgWMS~n!ydn 1 wB B. (2)

The results of the unweighted least-squares fit in-clude the five amplitude factors w, an estimate of thestatistical uncertainty in each factor, and the corre-lations among factors. When the center frequenciesof the observed and the theoretical spectral peaksoverlap the water concentration is related to the fit-ting coefficient by

nH2 O 5 wH2 O

Gdc

SlG2f, (3)

where S is the line strength and l is the optical pathength. The Voigt computation35 requires as input

the Lorentzian broadening width, the Doppler width,

Parameter Formula

Lorentz broadeninga P 3 0.03050 MHDoppler broadening 3.581 3 1027~TyMLine strengtha Not applicabPath length 50 passes 3 93.3 c

aValues were taken from the HITRAN database37 as computed

the scan voltage-to-frequency conversion factor, andthe baseline-to-peak modulation amplitude. Thespectroscopic parameters for the fit are listed in Table1. Measuring the Herriott cell pressure and temper-ature allows the mole fraction of the water vapor to becomputed by use of Eq. ~3! and the ideal-gas law.

The coefficient that multiplies the derivative of theline shape, wDn, is a measure of the frequency differ-ence between the observed spectral peak and the the-oretical peak and also is proportional to the amountof water vapor being measured. An integratingfeedback loop is operated to drive the ratio wDnywH2Oby the adjustment of the average laser current.In this manner the experimental peak is kept cen-tered on the theoretical peak. Peak misalignmentwould otherwise result in a systematic underestima-tion of the water concentration. By keeping the loopgain low, one can achieve a good performance even forwater-vapor mole-fraction levels near 5 nmolymol for

hich the SNR is modest. Peak-shift errors aremall after the instrument has warmed up. Theserrors are not expected to contribute significantly tohe total measurement error. However, it is alsoossible to use wDn to correct the estimated water-

vapor concentration by use of a Taylor approxima-tion.

The four principal assumptions in this implemen-tation of the least-squares analysis are ~1! the centerfrequency of the peak is properly identified, ~2! thespectrum contains no extraneous structure that isnot modeled by the quadratic background and theWMS line shape, ~3! the absorbance is small enoughhat the linear form of the Beer–Lambert law can besed, and ~4! the laser-frequency tuning varies lin-arly with the laser-diode current. Extensions ofhe computational treatment could include the ex-licit calculation of optically thick signals ~for 1molymol and 13.3 kPa only approximately 5 3 1026

of the laser power is absorbed at line center!, correc-ions for deviations of the modulation waveform fromn ideal sine wave and for the laser’s dc tuning frominear, and corrections for the finite laser linewidthresulting in a somewhat greater calibration accuracyt low pressure!.

4. Results and Discussion

A. Measurements by Use of National Institute ofStandards and Technology Traceable Standards

In the series of experiments performed at NIST theWMLH measured the water-vapor content of a sam-ple gas produced by NIST’s new LFPG30 over the

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range from 5 nmolymol to 2.5 mmolymol of watervapor in air. The WMS Voigt line shape is an excel-lent match to the observed signal, capturing 95% ofthe signal under high-SNR conditions. ~The re-maining mismatch may be due to the effects of am-plitude modulation,16 to nonlinear distortion of themodulation,36 or to weak effects from additional linesin the spectrum.! At low moisture concentrationshe deviation from the model is due to noise. A

MLH spectrum recorded at an expected LFPGater-vapor mole fraction of 5 nmolymol is shown inig. 2 together with the curve representing the sumf the spectral-line and the background terms. Theomputed fractional absorbance at the line centerhat is due to water vapor is 2.9 3 1025. The ratio of

the fitted signal to its standard deviation is 8.5. Therms sum of the residuals from a fit to this spectrum is3.8 3 1026 absorbance units. This low noise floor ischieved without the need to realign the laser afterransporting it to NIST for these measurements.

Figure 3 shows a linear regression of all the inter-

Fig. 2. Measured WMLH spectrum at 5 nmolymol of water vaporin air ~filled circles! converted from the raw lock-in amplifierydcratio to absorbance units and the fitted spectral data ~curve!.

Fig. 3. Measured versus the generated water-vapor mole frac-tion: The open circles represent the spectroscopic determinationof the water-vapor mole fraction by WMLH ~xw,WMS, left-handoordinate! plotted versus the LFPG-generated mole fractionxw,LFPG! as predicted from the saturator temperature and pres-

sure. The solid curve represents the linear fit to the WMLH data.The filled triangles ~residual, right-hand coordinate! correspond tothe WMLH measured value minus the predicted value of thewater-vapor mole fraction for which the predicted values werebased on the linear fit to the WMS data ~curve!.


omparison measurements, weighted by their ob-erved variances, and the associated residuals. Thisntercomparison of the two instruments shows excel-ent agreement over the entire range studied with theifference between the two systems being consistentith the estimated uncertainties in the spectroscopicarameters as well as the vapor pressure of the ice.he fitting residuals are scattered about zero with aaximum value of less than 15 nmolymol at the 2.5-molymol point. These data exhibit good linearitynd require only a 5% correction on the line-strengtharameter, yet they indicate a small backgroundevel of ;3 nmolymol. As is discussed below, thisffset is attributed primarily to water-vapor outgas-ing effects that originate in the laser-absorption cell.hese data were obtained over a span of several daysuring which time the system continued to dry outnd background levels continued to decrease. Heat-ng the Herriott cell to speed equilibration caused annacceptable loss of optical alignment. It is inter-sting to note that, after exposure of the instrumento the atmospheric humidity, a period of only 1 day isequired to reach a concentration of 10 nmolymol.

Two time series that were obtained by stepwisehanges in the LFPG set-point water-vapor mole frac-ion are illustrated in Fig. 4. The open circlesorrespond to the calibrated laser-hygrometer mea-urement, and the solid curve represents the ex-ected LFPG output. These data illustrate thetability of both systems and reveal that the WMLHs capable of tracking relatively fast transients in theumidity level ~e.g., factors of 2 in concentration on0-min time scales!. In Fig. 4~b! inspection of theMLH data reveals a relatively slow reduction

;0.14 ~nmolymol!yhr# in the background level, and

Fig. 4. Two time series of the LFPG expected output ~solid curve!and the water-vapor mole fraction as measured by the WMS sensor~open circles!.

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for LFPG set points of approximately 100 nmolymolor below this suggests that equilibration of theWMLH response is rate limited by the outgassing ofthe water vapor. Outgassing effects in the laser hy-grometer are investigated by variation of the volu-metric flow rate Q through the cell in the range of 2to 4 lymin. These tests were conducted at a fixedLFPG set-point water-vapor mole fraction. Thebackground water-vapor level scales with Q21, a re-ult that suggests that the background level is dom-nated by outgassing effects that occur within theerriott cell and not in the laser-head assembly or

he LFPG.In a test of possible outgassing from the LFPG the

as flow rate through the LFPG was varied at a fixedFPG saturator pressure and temperature, whileeeping the flow rate through the WMLH constant.nder ideal conditions, the LFPG output is indepen-ent of the flow rate, and any observed change can bettributed to small changes in outgassing effectsownstream of the generator or nonideal behavior ofhe LFPG saturator. Shown in Fig. 5 is the timeesponse of the WMLH and the expected LFPG out-ut. Prior to the changing of the flow rate theMLH response exhibits a noise level of ;0.4 nmolyol, a value that is consistent with calculated uncer-

ainties in the spectral fits. After an increase in theow rate in the LFPG from 3 to 4.5 lymin, the WMSesponse decreased by ;1 nmolymol, and within 25

min it restabilized to an average value that was ap-proximately 0.25 nmolymol lower than the originalvalue. After we reset the LFPG flow rate back to theoriginal level the laser-diode device detected another;1 nmolymol transient ~in the opposite direction! andeventually relaxed to the original mean value.These results show that the WMS device is capable of

Fig. 5. Time series of the LFPG expected water-vapor mode frac-tion ~dashed curve! and the WMS-measured water-vapor molefraction ~open and filled circles and solid curves!. The flow ratehrough the LFPG was abruptly changed from 3.0 lymin to 4.5

lymin at t ; 70 min and then set back to 3.0 lymin at t ; 120 min.or this test the flow rate through the WMS sample volume wasonstant. The mole fractions are expressed as a difference from aepresentative mean value.

resolving subnanomole-per-mole changes in thewater-vapor mole fraction on time scales of the orderof 10 min. Further, the measurements suggest thatthe water-vapor concentration delivered by the LFPGexhibits a residual amount of flow-rate dependence.This weak effect is ascribed to outgassing in the flowsystem downstream of the LFPG.

The Allan variance37,38 characterizes the WMLHnoise as a function of the signal-averaging time. Foreach measurement ensemble, the LFPG set-point hu-midity level is allowed to equilibrate at a fixed value,and the WMLH-measured water-vapor mole fractionis recorded over an extended time interval. The re-sults for two representative ensembles given byLFPG set-point water-vapor mole fractions of 15 and100 nmolymol @Figs. 6~a! and 6~b!, respectively# areummarized in Fig. 6. Here the square root of thellan variance is given as a function of the averaging

ime, and the corresponding distributions and Gauss-an fits to these data are shown as insets. Both dataets exhibit nearly Gaussian distributions with stan-ard deviations of ;0.4 nmolymol. For both sets ofata the Allan variance initially varies inversely withhe averaging time, as is expected for Gaussian sta-istics. However, in Fig. 6~a! the square root of thellan variance reaches a minimum value of ;65molymol for an averaging time of ;20 min, althoughtill longer averaging times might have been possiblead the system been fully equilibrated because itppears that the Allan variance at long averagingimes is dominated by a slow trend toward drier con-itions. In Fig. 6~b!, outgassing effects are less im-ortant because of the relatively high water-vaporoncentration in the sample gas, and no clear mini-um in the WMLH Allan variance is observed for

veraging times as long as 1 h. The standard devi-tion of the LFPG output mole-fraction data ~calcu-ated from the ensemble of the saturator’semperature and pressure measurements! is lesshan one tenth that of the WMS distribution, sug-esting that the observed variations in the WMSeasurement are not driven by temperature or pres-

ure fluctuations occurring within the LFPG satura-or.

From the Allan variance, one can evaluate the min-mum detectable concentration and the resolution ofhe diode-laser absolute moisture sensor. The Allanariance also shows that the resolution and the min-mum detectable concentration can be improved, butot without limit, by an increase in the averagingime. The minimum detectable concentration cane defined as the smallest signal that will produce aesult that is statistically different from zero. Sim-larly, the instrument resolution can be defined as themallest difference in sample concentration that istatistically significant. Inherent in these defini-ions is an assumption about statistical significancend about random noise in the measurements.dopting a 3-standard-deviation criterion for statis-

ical significance ~99.7% confidence level! reveals theinimum detectable change in the mole fraction of

he water vapor to be ;0.2 nmolymol for averaging


ts*r

mntstds6

aetrebpssvFMM

d

8

times of ;20 min. This result is consistent withhose discussed for Fig. 5 from which a statisticallyignificant change in the water-vapor mole fraction of0.25 nmolymol ~induced by the changing of the flow

ate through the LFPG! can be observed.A useful figure of merit for comparing the perfor-ance of absorption-measuring instruments is the

oise-equivalent absorption ~NEA!, defined here ashe minimum detectable absorption coefficient perquare root of the data-acquisition rate. As such,he NEA is a species-independent quantity because itoes not depend explicitly on the absorption crossection. On the basis of the results presented in Fig.the NEA of the WMLH is '3.5 3 1029 cm21yHz1y2.

Fig. 6. Square root of the Allan variance ~filled circles! plotted asa function of the averaging time for two time series that correspondto the WMS-measured mean water-vapor mole fractions of ~a! 18.9nmolymol and ~b! 100 nmolymol. The dashed curves representthe expected decay in the Allan variance for fluctuations that obeystationary Gaussian statistics. Shown in the inset of each graphis the corresponding distribution and Gaussian fit of the observedmole fractions. Note that, in ~a!, the optimum averaging is ap-proximately 1200 s and the square root of the Allan variance isapproximately 65 pmol of water vapor per mole of air.


Also, using a Herriott cell path length of l 5 4665 cmand an integration time of 70 s ~corresponding to onemeasurement of the water-vapor concentration!shows that this NEA figure is equivalent to an absor-bance level of 2 3 1026. Figures 5 and 6, which arebased on actual time-series measurements and therates at which entire spectra are recorded and fittedto yield updated values of the water-vapor concentra-tion, compare favorably with those obtained withother sensitive absorption methods.7,8

B. Sensitivity of the Fittings

Although the numerical fitting statistics provide es-timates of the random uncertainties in the fit param-eters ~concentration, frequency shift, and baselinevectors!, these uncertainties do not include system-tic errors in the fixed parameters, such as the broad-ning coefficient of water or the modulation depth ofhe laser. To evaluate the sensitivity of the data-ecovery algorithm to variations in the fixed param-ters requires that the computed water concentratione determined for a range of pressure-broadeningarameters, modulation amplitudes, scan rates, andecond-order nonlinear wavelength tuning by use of aingle spectral scan. Only the fit parameters arearied—the experimental data are held constant.or a nominal pressure-broadened half-width of 450Hz, a Doppler width of 315 MHz, a scan rate of 214HzymA, and a modulation amplitude of 903 MHz,

the sensitivities are as follows:

• Increasing the pressure-broadened contribu-tion to the line width by 4% increases the recoveredconcentration by 5%.

• Increasing the assumed scan rate by 4% in-creases the recovered water concentration by 2%.

• Increasing the modulation depth by 2% de-creases the recovered water concentration by 2%.

• Adding a nonlinear modulation term to mini-mize the fitting error changes the best pressure-broadening coefficient but has little effect ~0.2%! onthe recovered water concentration at a constantpressure-broadening coefficient.

The result of these tests is to clarify that thepressure-broadening and the laser-tuning parame-ters need to be well characterized. The publishedvalue for broadening of the 1392.53-nm water line byair, b 5 0.03050 MHzyPa ~0.1031 cm21 atm21!HWHM, fits our spectral data to within 5%.39 Theremaining variance appears as an asymmetry of theline and may be explained by residual amplitudemodulation of the diode laser.16

C. Broadening of the Water Line by Helium

To assess the performance of the WMLH in otherprocess gases, one must know the pressure-broadening coefficient. When He is used as the car-rier gas substantially narrower lines result. We usetwo methods to measure the linewidth in He at am-bient temperature ~21 °C!. In the first method the

irect-absorption spectrum of the water line is re-

b

@

0

a7tpb

tu

DV

corded as a function of the total pressure withoutmodulating the laser. Using static samples of Hecauses outgassing to raise the water-vapor mole frac-tion to the 10-mmolymol range, resulting in opticallythick ~.10% absorbance! signals. However, thewater-vapor mole fraction is sufficiently small thatself-broadening can be neglected when interpretingthe data. The data analysis consists of manuallyoptimizing the Lorentzian part of the linewidth andthe line amplitude of the spectrum modeled as theratio of a direct-absorption feature on a linear base-line function by use of a full-exponential Beer–Lambert law treatment. In the second method thewater concentration is reduced by the flowing of Hethrough the sample cell. Wavelength-modulationspectroscopy is used to record the resultant weakerabsorption signals. The linear approximation to theBeer–Lambert law with the wavelength-modulationtheory then is used to analyze the signals to deter-mine the Lorentzian part of the linewidth.

The results of the above-described test are shownin Fig. 7~a!. Good agreement is obtained betweenthe two methods. Over the range from 1 to 120 kPa~0.01 to 1.2 atm! of He pressure the pressure-

Fig. 7. Pressure-broadening measurement in He and HCl: ~a!ependence on He pressure of the Lorentzian component of theoigt linewidth of the water transition17 at 1392.53 nm as deter-

mined by WMS ~squares! and by direct absorption ~triangles!.The solid curve represents a fit of all the data constrained to a zerointercept whose slope @5.8~2! kHzyPa# is the He pressure-broadening coefficient. ~b! Lorentzian component of the watertransition plotted versus the HCl pressure as measured by directabsorption ~squares!. The solid curve is the same as for ~a! butwith a slope of 79~2! kHzyPa. The dashed, horizontal lines in eachgraph indicate the Doppler HWHM.

roadening coefficient of the ~1,0,1!20,2 4 ~0,0,0!30,3transition at 1392.53 nm ~Ref. 17! is 5.8~2!-kHzyPa0.0199~6!-cm21 atm21# HWHM, obtained by the fit-

ting of the combined data set constrained to a zerointercept. Gamache et al.40 summarized earlier mi-crowave investigations of the 31,3 4 22,0 rotationaltransition for which the room-temperature pressure-broadening measurements range from 0.0217~2! to.0220~22! cm21 atm21. Lazarev et al.41 reported a

slightly higher value of 0.024~6! cm21 atm21 for thepressure-broadening coefficient of the ~0,0,0!51,5 4~1,0,3!41,4 line of water by He. Those authors alsodiscuss the theoretical computation of pressurebroadening by rare gases and its dependence on therotational states of the water molecule.

D. Broadening of the Water Line by Hydrogen Chloride

HCl was studied as a broadener of the 1392.53-nmwater line because of its commercial importance insemiconductor manufacturing. These tests wereconstrained to measurements on static samples ofHCl by the limitations of the laboratory system forhandling hazardous gases. As a result, the mea-sured moisture level was in the 10-mmolymol range,nd only direct-absorption scans are reported in Fig.~b!. From a fitting of the Lorentzian contributiono the Voigt width, constrained to a zero intercept, theressure-broadening parameter was determined toe 79~2!-kHzyPa @0.268~6!-cm21 atm21# HWHM,

more than an order of magnitude greater than that ofHe. We are aware of only one other measurement ofthe HCl broadening coefficient. Inman and McAn-drew10 report a value of 0.15-cm21 atm21 HWHM forbroadening by HCl of the ~0,0,0!33,0 3 ~0,1,0!22,1midinfrared water line at 6863.95 nm.

Although a direct measurement by wavelengthmodulation of trace moisture in HCl is not reported inthis study, a reasonable estimation of the sensitivityfor its measurement can be deduced as follows: Thebroadening coefficient is 2.6 times greater for HClthan for air, so the system pressure must be droppedby a factor of 2.6 to achieve the same line shape. Thenoise expressed as an absolute water concentration isthen unchanged because the same modulation levelscan be used and the same etalon fringes will limitsensitivity. However, as a mixing ratio ~in nano-moles per mole!, the noise will be 2.6 times higher.Such measurements of moisture in dry HCl thereforewould be expected to show a Gaussian spread of 1.0nmolymol, provided the presence of HCl does not sig-nificantly alter the outgassing properties of the celland does not introduce spectral interferences. In asimilar fashion the sensitivity for detecting tracemoisture in He can be estimated.

E. Reducing Interference from Water Vapor

The absorption line is so strong that residual mois-ture inside commercially sealed lasers ~either 9-mmransistorlike cans with a window or fiber-pigtailednits! and detectors can overwhelm the trace signals

from the Herriott cell. This residual moisture signalcan be reduced by the removal of the laser, the de-


tct

c

wticidwr

8

tector window, or both and the filling of the laser headwith a pressurized ultradry inert gas, such as N2 orCO2.11 The spectral features of the residual mois-ure are pressure broadened and present a broadurved background that is easily distinguished fromhe sharper, low-pressure lines in the Herriott cell.42

This discrimination permits the achievement of ananomole-per-mole or better sensitivity even if theresidual humidity level in the head in the dry fill gasis a few micromoles per mole.

However, at nanomole-per-mole levels of moistureeven this degree of care may not be sufficient. Inaddition to the above efforts the laser head is treatedwith D2O vapor43 to convert the adsorbed and thegas-phase water to a mixture of D2O and HDO. Theisotopic change shifts the absorption frequency awayfrom the water line, although new spectral lines canbe observed in the same region. In a separate 1-yeartest this method was found to be more effective atreducing the H2O water-vapor signal than was theuse of calcium sulfate desiccant. The efficacy of thispassivation technique is also supported by the finding~reported above! that outgassing within the Herriottell dominated the observed background levels.

F. Use of Different Modulation Waveforms

The numerical model is capable of accepting non-sinusoidal-modulation waveforms. The best signal–etalon ratio is obtained by use of a triangle-modulationwaveform.44 However, when the triangle-current

aveform is applied to the laser the actual modulationhat results is distorted because the wavelength tun-ng of the laser arises largely from temperaturehanges in the laser junction. The finite heat capac-ty and the thermal conductivity cause frequency-ependent phase and amplitude distortion of theavelength modulation relative to the driving cur-

ent.26 Analysis of data that were collected by use ofa triangle-modulation waveform indicated that themodulation was filtered by a combination of these ther-mal effects and the finite bandwidth of the laser-current driver. Because accurate calculation of WMSsignals is possible only when the modulation is accu-rately known, either sinusoidal modulation should beused for quantitative work, a predistorted waveformmust be used, or the triangle waveform must be care-fully calibrated.

5. Conclusions

Measurements of the water-vapor concentration byuse of the wavelength-modulation laser hygrometerhave proved to be sensitive, precise, and accurate.Using a combination of methods to suppress etalonsand achieve high SNR’s achieved the best noise levelachieved, which was equivalent to 65 pmolymol in a20-min averaging window. The three-sigma detec-tion level, 195 pmolymol, corresponds to a frost pointof 2120 °C. The linearity of the instrument is ex-cellent, exhibiting an error of only 1% at water-vaporconcentrations in the micromole-per-mole range~frost points near 265 °C!. The most significant lim-


itation on the accuracy appears to be from outgassingwithin the sample region.

In contrast to an atmospheric-pressure ionizationmass spectrometer, the WMLH can be calibrated apriori on the basis of the measured spectral proper-ties of water vapor, the laser-tuning characteristics,and the electronic gains. Good agreement is ob-tained with a precision moisture source over therange from 5 nmolymol to 2.5 mmymol. This methodof calibration requires an accurate knowledge of themodulation waveform. A sine-wave–modulationwaveform is expected to yield the highest fidelity andshould give the most accurate results. Comparedwith a chilled-mirror hygrometer, the diode-lasersensor offers the advantages of a rapid time responseand a direct gas-phase measurement with no ambi-guity arising from the phase of the ice and its vaporpressure.

The sensitivity reported in this study is comparableto the near-infrared laser moisture measurementsreported by Girard and Mauvais20 and exceeds thoseobtained by Wu et al.18,19 These comparisons havebeen achieved without a second reference path andwithout the need for continuous purging of the pathexternal to the sample region. The data analysis isautomated: moisture readings are updated after ev-ery spectrum. A simple line-locking method hasbeen described.

Continued testing of the WMLH is planned. Pos-sible experiments include the study of differentialcomparisons of the LFPG with other sources of hu-midity, the measurement of material outgassingrates following controlled moisture challenges, andother experiments for improved standards or mate-rials science. This laser sensor can also serve as aprototype for an on-line diagnostic of feed gases usedin semiconductor manufacturing.

We are grateful to James Whetstone at NIST forhis role in enabling the WMS–LFPG intercomparisonexperiments. This study was funded by the U.S.Department of Commerce under contract 50-DKNB-5-00189.

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5. B. R. Stallard, L. H. Espinoza, R. K. Rowe, M. J. Garcia, andT. M. Niemczyk, “Trace water vapor detection in nitrogen andcorrosive gases by FTIR spectroscopy,” J. Electrochem. Soc.142, 2777–2782 ~1995!.

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Wavelength-Modulation Laser Hygrometer for Ultrasensitive Detection of Water Vapor in Semiconductor Gases