Vol. 2, No. 6/June 1985/J. Opt. Soc. Am. B 877

Absolute two-photon ionization yields for selected organicmolecules at 248 nm

William K. Bischel, Leonard J. Jusinski, Mark N. Spencer, and Donald J. Eckstrom

Chemical Physics Laboratory, SRI International, Menlo Park, California 94025

Received October 30, 1984; accepted January 24, 1985

Absolute two-photon ionization yields for benzene, fluorobenzene, diethylaniline, and trimethylamine have been

measured at 248 nm as a function of KrF laser fluence for two pulse lengths of approximately 8 and 20 nsec. We

have also investigated NO ionization yields at 226 and 193 nm. The ionization is a resonant process that can be

modeled as a four-level system. From the data, we derive ground-state absorption cross sections, intermediate-

state ionization cross sections, and effective intermediate-state lifetimes. In some cases, a small contribution to

the ionization yield from a direct nonresonant two-photon process can be inferred from the model.

1. INTRODUCTION

The multiphoton ionization (MPI) of atoms and moleculeshas been a topic of much research over the past decade.' Inparticular, two-photon ionization cross sections for some or-ganic molecules at excimer-laser wavelengths have been foundto be large.2 There are several current applications for whichlaser photoionization may prove useful. One example is the

development of high-power discharge switches, for whichphotoionization of a small admixture of an organic specieswould provide a uniform volume preionization. A relatedapplication uses laser-preionized channels to guide particlebeams to the target in fusion reactors. 3 4 A third applicationis in the field of mass spectrometry, in which in some cases

photoionization could replace electron bombardment as thepreferred ionization technique. There have been a numberof studies in the last-named field, particularly using ben-zene.5 7

For these applications, it is important to determine theoptimum species to serve as the photoionization medium andto establish accurate parameters that allow the degree ofionization to be calculated for arbitrary laser properties. Acomplete description of the photoionization process requiresdetermination of the ground-state absorption cross section(crlo), the intermediate-state ionization cross section (°21), theintermediate-state loss rate (Q) for resonant two-photonprocesses (sequential transitions involving a real intermediatestate), the nonresonant two-photon ionization cross section(anr) for other cases, and the relative contributions of bothtypes of processes.

Several studies have identified organic molecules with largemultiphoton ionization cross sections at excimer-laser wave-lengths.2 4 However, no systematic study has been made thatpermits direct comparison of the results from different labo-ratories. Furthermore, the previous results have not beenanalyzed in enough detail to permit confident extrapolationto arbitrary laser parameters. The goal of this study was toperform the required experiments and analyses for severalmolecules that gave high photoionization yields in variousprevious experiments.

The four organic molecules studied were benzene (C6H6),

fluorobenzene (C6H5F), diethylaniline [DEA, C6H5N(C2H5)2],

and trimethylamine [TMA, N(CH 3 )3]. Benzene was chosenbecause of its wide use in previous MPI studies, fluorobenzenewas of interest because it has a higher absorption cross sectionthan benzene at 248 nm,8 TMA was selected because it hadthe largest MPI cross section in previous studies in our labo-ratory,2 and DEA was found to have the largest MPI yield inexperiments at Sandia National Laboratory. In addition, weinvestigated NO at 248, 193, and 225 nm to compare the yieldsfor the most readily photoionized of the rare-gas atoms andsmall molecules. 9

2. EXPERIMENT

The experimental apparatus is ilustrated in Fig. 1. A LambdaPhysik EMG 101E excimer laser was operated primarily at248 nm (KrF) in a collimated beam geometry using a com-mercial unstable resonator cavity. The beam size was ap-proximately 9 mm X 22 mm, and the intensity was relativelyuniform over that dimension. The beam divergence was lessthan 1 mrad and hence traveled 2 m to the experimental cellwithout a significant change in the beam profile. Two 3.2-mm-diameter apertures in series limited the laser-beam crosssection in the experimental cell. The last aperture was placedas close to the ionization detector as possible (less than 3 cm)to minimize intensity variations that were due to diffraction.Because only a small part of the incident laser cross sectionwas used, the laser intensity was assumed to be spatiallyuniform in the sample region.

The laser energy per pulse through the aperture was mea-sured after the exit window of the cell using a Laser Precisionpyroelectric energy meter that had been recently factory-calibrated relative to National Bureau of Standards standards.The measurement was corrected for window transmission,which varied because of carbonaceous deposits from decom-posed organic molecules. The energy measurement waschecked using a Scientech calorimeter, and the two mea-surements agreed to better than 5%. The laser intensitythrough the cell was varied from 0.05 to 5 mJ by inserting upto 10 quartz plates in the beam before the defining aper-tures.

Experiments were performed using different laser pulselengths to determine the relative resonant and nonresonant

0740-3224/85/060877-09$02.00 © 1985 Optical Society of America

Bischel et al.

878 J. Opt. Soc. Am. B./Vol. 2, No. 6/June 1985

0.32-cm-DiameterAperture

High Vac:Pump Out(< 10-6 torr)

Meter

Gas In

Fig. 1. Experimental apparatus for the measurement of two-photonionization yields at 248 nm.

E 1250

7 100

g 75

0

i50CD,

wu 25z

no0 10 20 30 40 50

PULSE LENGTH (nsec)Fig. 2. Typical laser temporal pulse shapes used in the experiment.The dotted line is the 20-nsec-long pulse obtained using the standardlaser-gas mixture. The solid line is the shorter pulse obtained usingthe modified gas mixture (see text). The dashed line is the Gaussianpulse shape with a FWHM of 10 nsec used to model Eq. (2) (see text).The vertical scale is given in kilowatts per square centimeter for a laserpulse fluence of 1 mJ/cm 2 .

ionization yields. The pulse length was changed by varyingthe laser-gas mixture. The standard laser mix consisted of120 mbars of Kr, 120 mbars of a 5% F2 -in-He mixture, and thebalance He buffer gas to a total pressure of 2.5 bars. Thismixture gave the maximum laser energy (approximately 250mJ at 248 nm) and created a laser pulse that was approxi-mately 20 nsec long and had several humps in the temporalprofile. A typical intensity history taken with a Tektronix7844 oscilloscope and an EG&G FND 100 photodiode is shownas the dotted line in Fig. 2. This pulse width became shorteras the laser mixture aged, and thus the laser pulse shape andenergy had to be recorded simultaneously with the ionizationdata.

It was found that a shorter laser pulse could be obtained byusing 30 mbars of the 5% F2 -in-He mixture, 30 mbars of Kr,and the balance He to 2.5 bars. Then the pulse was smoothand approximately 8 nsec in duration, as illustrated by thesolid line in Fig. 2. This pulse shape did not vary significantlyas the laser mixture aged, but the laser energy decreased byup to a factor of 4.

The experimental cell was constructed from 20.3-cm-di-ameter stainless-steel pipe and was connected to a high-vac-uum system capable of evacuating the cell to approximately10-6 Torr. The gas under study was allowed to flow slowlythrough the cell to minimize systematic errors resulting fromoutgassing and photodissociation of the parent molecule.Most of the molecules used in this experiment were in liquidform with vapor pressures varying from 0.2 to 75 torr. Theair impurity was removed from the liquid sample by per-forming several freeze-pump-thaw cycles before the vaporwas used in the experiment. Typical pressures used in theexperiment varied from 1 to 20 mTorr. The pressure in thecell was measured using an MKS Baratron 1-Torr capacitivemanometer that had a last-digit resolution of 10-4 Torr.

The photoionization yield was determined by measuringthe positive-ion current from a known laser volume collectedon biased electrodes. The detector was constructed from twoparallel plates (3.5 cm X 7.5 cm), initially separated by 19 mm.The bottom plate had three sections that were electricallyisolated from one another. The central section of the platewas 2.5 cm long and was grounded through a Keithley Model602 electrometer; the two outside sections were directlygrounded. The top plate was biased with a positive voltagethat was varied from 45 to 180 V.

The collection efficiency of this ion detector was investi-gated by varying the plate voltage, the gas density, and thephotoion density. At certain values of E/N we observed anincrease in the positive ion yield because of multiplication.This multiplication factor is illustrated in Fig. 3 as a functionof E/N and the ion density initially produced in 3.8 mTorr ofbenzene. Note that the multiplication factor increases as theinitial ion density increases for a fixed E/N. This effect iscurrently not understood. Following the peak in the ionmultiphoton factor, the detection efficiency decreases as totalion density increases. This effect was previously interpretedas losses due to ion-ion recombination.2

The plate spacing was then varied to determine if the effectof ion multiplication could be minimized. When the spacingwas reduced to 5 mm or less, the ion current was constant forplate voltages from 45 to 180 V. Ion multiplication was not

Z3.00 0 EN= 7.5 x 10 1 3 V cm2

0 10 E/N = 3.9 x10 1 3 V cm2

U. A E/N 1.9x1 Vc 2

LU 180 V'

0cl: 2.00U

0u9

0 < 1.00NZ Benzene Pressure 3.8 mTorr IN. . dd .o - Plate Spacing 19 mm *, ,.-}ac.

107 108 109

POSITIVE ION DENSITY [NI cm-3

Fig. 3. Observed ion-detection efficiency as a function of EIN andinitial ion density N+ for a plate spacing of 19 mm and a benzenepressure of 3.8 mTorr. Note that the ion multiplication observed isa nonlinear function of N+. This multiplication was not observedwhen the plate spacing was reduced to less than 5 mm.

Bischel et al.

Vol. 2, No. 6/June 1985/J. Opt. Soc. Am. B 879

observed for any value of the initial ion density over the range

of gas densities used in the experiment (1-20 mTorr).Therefore the ion-collection efficiency was assumed to beunity.

Ionization-yield data were than obtained at plate spacingsof 5 and 2 mm for each of the molecules investigated. The topplate was biased at +90 V for both sets of measurements.When the spacing was reduced to 2 mm the spatial profile ofthe laser beam was slightly apertured, and a different laserexcitation volume had to be used to calculate the fractionalionization. The ionization yields measured using these twoplate spacings agreed to better than 10%, thus indicating thatsystematic errors resulting from ion multiplication had beenminimized.

When the cell was pumped out to less than 10-5 Torr andthe laser was operated at 10 Hz with a fluence of approxi-mately 1 mJ/cm2 through the 3.2-mm aperture, the back-ground current was approximately 10-12 A. This background,which increased linearly with laser fluence, is attributed to

electron production owing to surface photoionization byscattered laser photons. This background was subtractedfrom the measured ion currents, which varied from 10-12 to10-8 A, to determine the two-photon ionization yields.

3. RESULTS

Typical data from the experiment are illustrated in Fig. 4.Here the fractional ionization (ion density N+/gas density No)is plotted as a function of laser fluence for both benzene andDEA for the long and short laser pulse lengths given in Fig.2. For these data, the benzene pressure was 3.8 mTorr andthe DEA pressure was 2.2 mTorr. All ionization yields werelinearly dependent on density in these experiments. It wasfound that the yields depended quadratically on the laserfluence for both laser pulse lengths as long as the ion currentwas less than 3 nA (total number of 2 X 109 ions). For cur-rents larger than this, a dependence that was less than qua-dratic was observed as a result of the decrease in the ion-col-lection efficiency resulting from ion-ion recombination. 2 Wehave extracted absolute ionization-yield coefficients C byleast-squares fitting the data with ion currents less than 3 nAto the form N+/No = CF2 , where F is the laser fluence (mJ/cm2). This fit is illustrated in Fig. 4 for benzene by the dottedlines and for DEA by the dashed lines.

There is a substantial difference in the pulse-length de-pendence for the two molecules. The data for DEA show anenhancement of approximately 2.2 when the short laser pulseis used (high-intensity case), whereas the data for benzeneshow an enhancement of only about 1.08. This difference ismodeled in Section 4 as being due to the difference in the ef-

fective lifetimes of the resonant intermediate states for thetwo molecules.

Data of this type have been obtained for fluorobenzene andTMA in addition to DEA and benzene. For each molecule,four sets of data were taken on different days and using dif-ferent pulse lengths. The two-photon ionization-yield coef-ficient C was determined for all data sets, along with an ef-fective pulse length -r (defined in Section 4) of the laser pulseused to make the measurements. These coefficients are givenin Table 1 for the four molecules. The uncertainties listedin the table are the standard deviation in the fit parameter andgive a good representation of the relative error among the

z 1 0o4 DEA Fit

0

Z 9PO~~~~~~E

d o

10-6 /8

40

2 I

07 I IA1 I

2 4 6 80.1 1.0 10

LASER FLUENCE (mJ/cm2)

Fig. 4. Fractional ionization data at 248 nm as a function of laserfluence for benzene and DEA using the long (0) and short (a) lasertemporal pulse shapes illustrated in Fig. 2. The dotted and dashedlines are the fit to the data for benzene and DEA, respectively. Notethat the fractional ionization has a strong dependence on laser pulselength for DEA but not for benzene. The benzene pressure was variedbetween 4.2 and 8.6 mTorr and the DEA pressure was 2.2 mTorr forthese data.

measurements. These uncertainties do not include system-atic errors that may be present in the experiment. However,we believe that these systematic errors are less than ±10% ofthe given values since the data were cross checked by usingdifferent experimental configurations. In particular, the datataken for TMA agreed with our data obtained in a previousstudy to better than 10%, giving us confidence that the sys-tematic errors have been minimized.

NO was also investigated in this study for pump wave-lengths of 226 and 193 nm (no ionization yield could be mea-sured at 248 nm) to serve as a benchmark for the yields ob-tainable using small molecules. 9 Because of time limitations,the data obtained for NO listed in Table 1 are less extensivethan those acquired for the four organic molecules.

Photoabsorption cross sections (f 10) were also measuredfor these molecules and are listed in Table 1. They were de-termined by a direct measurement of the attenuation of thelaser intensity, i.e., alo = ln(Io/I)/NoL, where L is the celllength. The laser absorption was found to be independentof the intensity and linearly dependent on the gas density.The uncertainties in these absorption cross sections are esti-mated to be less than +5%, since several measurements weretaken under varying conditions.

The ionization yields reported here are effective yields forthe given laser parameters. The KrF laser is a broadbandlight source with a linewidth of approximately 100 cm'. Ifthe molecule has structure in the single-photon absorption

Bischel et al.

880 J. Opt. Soc. Am. B./Vol. 2, No. 6/June 1985

Table 1. Two-Photon Ionization Yields

FractionalIonization Ionization C

Molecule Potential (eV)a X (nm) r (nsec) 0lo (10-18 cm2 ) (10-6 cm4/mJ 2 )

Benzene 9.4 248 12.5 0.37 1.04 0.0312.0 1.08 + 0.026.45 1.10 + 0.036.10 1.18 + 0.02

Fluorobenzene 9.20 248 13.5 1.20 1.16 + 0.0212.7 1.14 ± 0.045.50 1.96 + 0.034.3 2.07 + 0.04

DEA 7.51 248 13.0 36.0 37.0 + 0.0912.8 37.3 + 0.055.30 83.5 + 0.35.30 82.4 + 0.3

TMA 7.80 248 13.2 0.75 1.52 + 0.0512.3 1.57 ± 0.037.40 1.77 + 0.015.65 1.83 + 0.04

NO 9.250 225 9.25 0.012 0.115.8 0.115

193 6.0 0.014 0.0004

a Ref. 33.

spectrum (as benzene, fluorobenzene, and NO have), theyields might be substantially increased if a narrow-bandsource were tuned to the peak of an absorption transition.However, the yields and parameters derived in Section 4 givean accurate picture of what can be accomplished with astandard KrF laser, and they serve as a lower limit on theyields obtainable by using a narrow-band, tunable lasersource.

4. DISCUSSION

A. Model of the Ionization ProcessA generalized schematic of the levels involved in the two-photon ionization process is given in Fig. 5. We model thisprocess using two ionization channels: a stepwise-resonantionization channel and a direct nonresonant ionizationchannel. We assume here that the rates associated with thetwo channel are completely independent of each other.

The stepwise-resonant ionization channel can be modeledby using a rate-equation approach as discussed by Zakheimand Johnson' 0 and by Reilly and Kompa,7 who analyzed thecase of benzene ionized at 248 and 193 nm. As in their case,the rate-equation approach used here is entirely adequate todescribe the population transfer because the experimentalconditions are such that coherent population-transfer effectsdo not occur. The legitimacy of the rate-equation approachfor multiphoton transitions in general is discussed by Acker-halt and Eberly." As illustrated in Fig. 5, our model treatsthe molecule as a four-level system with a ground state labeledby 0, a resonant intermediate state labeled by 1, an ionizationcontinuum labeled by 2, and an additional populationtrapping state, labeled by 3, to which the intermediate statehas an effective disappearance rate Q that has two contribu-tions, a radiative rate A and a nonradiative rate Knr, so thatQ = Ar + Knr. For the collision-free conditions investigated

in this experiment, K, is the intersystem transfer rate to level3.

The rate equations for the populations in the four-levelsystem under resonant excitation are as follows:

dt = h [oolN,- cr0No] + ArNi,

dN, = t) [2of~oNo - (o0 + cT21) N,] -QN1,

dN2 I(t)= - o -2 ,N ,dt hv

dN 3 = NiKnr,dt

(la)

(lb)

(Ic)

(ld)

with No(t) = No(0) - N, - N2 - N3 . Note that N2 is thesame as the experimental N+. Here o1, and °r21 are theground-state absorption cross section and the intermediate-state ionization cross section, respectively, (t) is the laserintensity in watts per square centimeter, v is the laser fre-quency, and No(0) is the initial ground-state population. Allthe other parameters have been defined above. The objectiveof this analysis is to derive the parameters 0lo, 21, and Q fromthe data given in Section 3, such that the ionization yields canbe predicted at arbitrary laser intensities and pulse shapes.

These equations can be solved analytically if the laser in-tensity has a rectangular temporal profile and a uniformspatial profile; the solution was given previously.7"10 However,they must be solved numerically for an arbitrary temporalprofile. Because the laser intensities in our experiment wererelatively small, we can make two approximations to obtainan integral solution to these equations. First, we assume thatthe ground state is not depleted, i.e., N(t) No. Second,we assume that none of the transitions is saturated. Then thefractional photoionization of the gas is given by the expres-sion

Bischel et al.

Bischel et al.

N= (A-2o)ioa2i C O(t)e-Qt X tk(t')eQt'dt'dt, (2)No '~A) (hi')2 -_ .J-t

where E is the laser pulse energy, A is the laser's cross-sec-tional area (assuming a uniform spatial distribution), and ¢(t)

is the normalized laser intensity defined by ¢(t) = I(t)/(E/A).

We define here the normalized fractional ionization (NFI) to

be the integral in Eq. (2). All other parameters have previ-ously been defined. We experimentally obtain 0(t) by digi-tizing each oscilloscope trace of the laser temporal profile(such as those given in Fig. 2) and normalizing it such that

O (t)dt 1. (3)

We can derive two limiting cases from Eq. (2). In the firstcase, the product of Q times the laser pulse length r is muchsmaller than 1 (Qr << 1), and we can approximate the integralin Eq. (2) to be

tNFI 3 0(t) X (t)dt'dt -0.5. (4)

t.

Note that this integral is exactly equal to 1/2 for all lasertemporal pulse shapes that have been properly normalized.Therefore, in this limiting case, the (unnormalized) fractionalionization scales as the square of the laser fluence, and thereis no dependence on the laser pulse length for constant laserfluence. We shall see below that the ionization yields for

benzene can be approximately modeled in this limit.For the second limiting case, Qr >> 1. In this case the in-

tegral in Eq. (2) reduces to

1 eONFI -X 02(t)dt, (5)

Q __

and the fractional ionization in Eq. (2) is now proportional to

Non-ResonantIonizationChannel

-_ 2 -

021

Two-Step ResonantIonization Channel

Ionization Limit

Ar

- 0 1 Ground State

Fig. 5. Generalized energy-level diagram for the two-photorization of molecules.

Vol. 2, No. 6/June 1985/J. Opt. Soc. Am. B 881

1.0 Tzo 0.8

W 0.6N.

0 0.4-j

zo 0.2

LL 0.1 _

2 0.08. _ 0 BenzeneN0.06 0 Fluorobenzene

0.04 A TMA0z I . I , I I , I I , I , I , I ,

0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10Qr

Fig. 6. NFI plotted as a function of QT. The solid line is an exact

calculation of the integral in Eq. (2) using the Gaussian pulse shapegiven in Fig. 2. The dotted line is a plot of the empirical formula given

in relation (7). The maximum difference between the two curves isless than 5%. The points on the graph are derived from the experi-mental ionization yields using Eqs. (2) and (8) and demonstrate theinternal consistency of the data set.

the integral of the laser intensity squared. Hence a changein the laser pulse length at constant fluence will have a largeeffect on the fractional ionization. We find that the ionization

yields for DEA are most closely modeled by this limit for ourlaser pulse lengths. These two limiting cases are essentiallythe same as have been derived by Olson et al.12

The integral in Eq. (2) can be represented by a simple ex-

pression if we define the laser p lse length r by

T= (t) X 0(t')dt'dt/ 02(t)dt

- 12 f - 2(t)dt1 (6)

Note that r is proportional to the ratio of the two limits dis-cussed above for the fractional ionization yields and can bethought of as an effective laser pulse length for two-photonionization. We can relate r to the full width at half-maximum

TP of the laser pulse if we assume a smooth analytical pulseshape. If we choose a Gaussian pulse shape, we find that -r= (7r/8 ln 2)1/ 2TP or -r = 0.753 TP. It is reasonable that r is

shorter than TP because only the most intense part of thepulse is effective in producing ions in a two-photon process.

r can be easily calculated for an arbitrary pulse shape and, as

we shall now show, is an extremely useful parameter in de-

scribing two-photon processes.The NFI calculated from Eq. (2) using the Gaussian pulse

3 shape illustrated in Fig. 2 is plotted in Fig. 6 as a function of

QT as the solid line. We have also calculated the NFI using

the two other pulse shapes in Fig. 3, and the results essentially

lie on the same solid line. This illustrates the fact that arbi-trary laser temporal pulse shapes with the same T will all giveapproximately the same fractional ionization.

We have found empirically that the NFI [the integral in Eq.

(2)] can be represented by the simple expression

NFI - 1/2 [1 + (QT) 4 /3]-3/ 4 .

n ion-

(7)

The dotted line in Fig. 6 is calculated from this formula. Ascan be seen, it is a good approximation to the actual integral

anr

1

882 J. Opt. Soc. Am. B./Vol. 2, No. 6/June 1985 Bischel et al.

Table 2. Derived Parameters for Modeling Two-Photon Ionization Yields

Intermediate StateFluorescence

aOlo (10-18 a2l (10-18 anr (10-27 Lifetime QuantumMolecule XO (nm) cm2 ) cm2 ) Q (nsec-') cm4 /W) State (nsec) Yield

Benzene 248 0.37 4.4 0.022a <0.5 IB2. 42-49a 0.08-0.07

Fluorobenzene 248 1.2 2.4 0.12b 3.6 'B, 8 .16 b 0 .0 9 6 b3.5 0.17c 0 (assumed)

DEA 248 36.0 11.6 0.66c 0 (assumed) -

TMA 248 0.75 2.8 0.022de 3.4 - 4 5 d,e 0-9 7 d4.0 0.057c 0 (assumed)

NO 248 0.0 - - 0.0001 - -225 0.012 14.0 0.0047e -0.1 A 2 (' = 0) 215f193 0.014 - - 0.005g

a Ref. 19.b Ref. 23.c Derived under the assumption that Ynr = 0.d Ref. 26.

Ref. 28.'Ref. 31.g Assumed to be only a nonresonant process.

(solid line), with a maximum deviation of less than 5%. Thusrelations (6) and (7) offer a simple way to calculate the frac-tional ionization for an arbitrary laser pulse shape. They also,provide us with a convenient method for extracting the pa-rameters necessary to calculate the fractional ionization atarbitrary laser intensity and pulse shapes.

The second ionization channel is a direct two-photon ion-ization process. A similar rate-equation analysis of a coupledthree-level system has also included a direct two-photonprocess.13 The inclusion of this second channel is justifiedby the many nearby nonresonant intermediate states that cancontribute to the direct two-photon ionization amplitude. Inaddition, since the excimer-laser bandwidth is so broad, asubstantial amount of the laser energy will be nonresonant ifthe absorption spectrum of the molecule is not completelyfilled with overlapping transitions (as is the case for NO). Wetherefore include this second channel in the analysis, althoughwe expect its contribution to the ionization yields to be a smallfraction of the resonant channel. We shall see below that thisadditional channel is necessary in some cases to explain theexperimental observations adequately.

The fractional ionization produced by a nonresonant two-photon process is

IN21 =a°er5W J2(t)dt, (8)\Nonr hv -J

where nr is the two-photon absorption coefficient in units ofcentimeters to the fourth power per watt. From the defini-tions of 0(t) and Eq. (6), this can be written as

(N2) = E2 nr

INo nr A 2hvT(

Combining the contributions from both ionization channelsand using the empirical formula for the integral given inrelation (7), we can model the fractional ionization in thelow-intensity limit as

N 2 1 E12 1 | 10 1f21 + hvanrlNo 2 A| (hi) 2 i[1 + (Qr) 4/3]3/4 r f (10)

Note that there are four unknown parameters in this formula:610, a2 1 , Q and anr. Since we measure the single-photonabsorption and the ionization yield for two different pulselengths, we can determine oa10 and any two of the three re-maining parameters. Therefore we must either assume thatthe direct nonresonant ionization channel is negligible or wemust determine one of the other parameters from anothersource. Fortunately, there are data in the literature on thelifetime of the resonant intermediate state for many organicmolecules. We discuss below the determination of theseparameters for each of the molecules investigated here. Asummary of the results is given in Table 2.

B. Benzene (C6H6 )Benzene has been one of the most thoroughly studied organicmolecules because of its importance in quantum chemistry.Recent research has focused on determining the multiphotonionization spectrum using mass analysis of the ion fragmentsfor visible5 14 and UV pump lasers.7"15"6 Interest has beendirected at probing the fragmentation pattern produced bythe high-intensity laser field, and there have been no previousabsolute ionization yields.

The resonant intermediate states for pump radiation at 248nm are vibronic levels of the B2U electronic state. This ab-sorption transition (B 2 , - 1Aig), which has its origin atapproximately 260 nm, has been studied by a number of re-searchers.17"18 The lifetimes and fluorescence quantum yieldsfor 22 vibronic states covering the wavelength range 290-247nm have been studied by Spears and Rice.19 Some of theselifetimes and quantum yields have been reexamined,2 0 withsome differences in results.

The KrF laser bandwidth overlaps several vibronic tran-sitions, the strongest of which are the A transition at 248.11nm and the B transition at 248.44 nm.19 The measuredlifetimes and quantum yields'9 for these two transition statesare given in Table 2. Since the fluorescence quantum yieldis not unity, the lifetime must have both a radiative and anonradiative contribution. It is generally argued19 that thenonradiative process (approximately 90% branching ratio) is

Vol. 2, No. 6/June 1985/J. Opt. Soc. Am. B 883Bischel et al.

the intersystem crossing to the 3B1, state. This state has an

electronic energy low enough that it would probably not bephotoionized by radiation at 248 nm.21

From the lifetime given in Ref. 19, we estimate an averagevalue for Q in our model of 0.022 nsec-1. Using Eq. (10), we

have determined the relevant cross sections from the ioniza-tion-yield measurements given in Table 1 to be a1 0 = 3.7 X

10-19 cm2 and a21 = 4.4 X 10-18 cm2. These parameters aregiven in Table 2. Since the absorption spectrum has struc-turel7 over the 100-cm1 bandwidth of the excimer laser, theabsorption cross section alo could be increased (possibly by

a factor of 2) if a narrow-band tunable dye laser were used as

the pump laser. This would enhance the ionization yield by

the ratio of the cross sections. The excited-state ionizationcross section U21, on the other hand, would not significantlychange with a reduction in laser bandwidth since this is abound-free transition with little structure.

We have used Eq. (2) to determine the NFI from the ion-ization yields given in Table 1, and these points are plotted

by the squares in Fig. 6. Since the product of Q-r is much less

than 1 for both pulse lengths used in this experiment, we can

see from Fig. 6 that we expect only an 8% difference in ion-

ization yields for the two pulse lengths. Any deviation from

this ratio would indicate that the nonresonant photoionizationchannel is making a significant contribution to the ionization:lyields. The relative ionization-yield data are reproducibleto approximately +5% and hence are not precise enough toallow us to make a determination of anr.

C. Fluorobenzene (C6 H5 F)

The UV absorption spectrum of fluorobenzene has been

studied by Wollman22 and by Abramson et al.23 The ab-

sorption transition in the region of 275-238 nm has been as-

signed to the 'B, - 'Al electronic transition, and the lifetimesand fluorescence quantum yields of 59 vibronic transitionshave been reported. 23 The 0, 2 X 1228 vibronic band occurs

at 248.27 nm (Ref. 23) and is probably the primary transitionpumped in this experiment. The effective disappearance ratefor this vibronic level has been determined to be Q = 0.123nsec'1,2 3 and we have measured the effective absorption cross

section for this transition of ago = 1.2 X 10-18 cm2.

Since the product of Qr ranges between 0.53 and 1.7 nsec-1

in our experiments, there is a substantial difference in thefractional ionization as a function of pulse length (see Fig. 6).

If we use the value of Q obtained from the literature, we derive

values for anr = 3.6 X 10-27 cm 4 /W and a2 1 = 2.4 X 10-18 cm2 .

If we assume that anr = 0, we then derive values of Q = 0.17

nsecC' and a2 1 = 3.5 X 10-18 cm2 . Since the literature value 2 3

of Q has error bars of +0.7%, it is unlikely that Q for our ex-

periment could be 42% larger than the previously publishedvalue. All processes that could cause a difference in Q in the

two experiments tend to make Q smaller (not larger) for theionization experiment than for the fluorescence experi-ment.

We therefore conclude that the literature value of Q is theproper one to use to model the fractional ionization and thatthe nonresonant ionization (NRI) channel must be includedto account properly for the ionization yield at high intensities.

If we subtract the NRI contribution to the ionization yieldsgiven in Table 1, we can plot the NF1 for the data in Fig. 6.

These points are represented by the circles in the figure andillustrates the consistency of the data.

As in the case of benzene, the use of a narrow-band laser

could yield a larger effective absorption cross section (aio), and

hence the ionization yields would be increased by the ratio of

the cross sections. We do not expect this effect to be largerthan a factor of 2.

D. Diethylaniline [C6H5N(CzH5)2]We have not been able to find a literature value for the lifetime

of the resonant intermediate state of DEA excited at 248 nm.Because fluorescence has been visually observed from DEA

when it is excited at 248 nm,8 the lifetime can be measured.Unfortunately, these data are not currently available; there-fore we analyzed our data by assuming that anr = 0. From the

data given in Table 1, we have derived the parameters alo =3.6 X 10-17 cm

2, °r2l = 1.2 X 10-17 cm2, and Q = 0.66 nsec-1.

Since in DEA the UV absorption spectrum appears to bestructureless,2 4 we anticipate that the absorption cross section,

and hence the ionization yields, will remain unchanged if thelaser bandwidth is narrowed.

DEA shows the fastest disappearance rate (Q) of all themolecules studied here; hence the values of QT range from 3.5

to 8.5. It is interesting that this value of Q is approximatelythe same as that determined for the first excited electronicstate of aniline vapor.25 We derive the NFI by using Eq. (2)

and the data in Table 1, and these points are plotted by thediamonds in Fig. 6. Note that DEA shows the largest de-pendence of the ionization yield on pulse length and that itsyield would be maximized for pulse lengths r < 1.6 nsec.Even for the longer excimer-laser pulses, the ionization yieldis a factor of 34 larger than benzene; hence DEA may be a

useful alternative to benzene for applications in which thelaser energy is limited. However, this molecule is fairly sticky,

giving a long pump-out time. In addition, its low vaporpressure, measured in our laboratory to be approximately 120mTorr at 250C, might limit its use in some situations.

E. Trimethylamine [N(CH3)31TMA has been considered as a possible medium for tunableUV laser radiation2 6 27 based on optical pumping at 248 nm.Hence there are measurements of the excited-state life-time2 6 28 that give Q = 0.022 nsec-1 and a quantum yield of

97%.28 The absorption spectrum has also been studied2 9 30

over the range 260-160 nm. It is a smooth, structurelessspectrum with three broad maxima. The absorption coeffi-cient T-1o has been measured in these studies to be 7-8 X 10-19

cm2 , which agrees well with our determination of 7.5 X 10-19

cm2 . Using Eq. (10) and the above value for Q, we derivevalues of a 21 = 2.8 X 10-18 cm2 and anr = 3.4 X 10-27 cm4 /W.

Again, if we assume that anr = 0, we derive values of Q = 0.057

nsec-' and 021 = 4.0 X 10-18 cm2.

This value for Q is a factor of 2 larger than the literature

value and hence cannot be correct, particularly when thefluorescence quantum yield is almost unity (thus accountingfor all the population that reaches the intermediate state).We therefore conclude that there must be a contribution tothe ionization yields from the nonresonant ionization channel

that is due to the continuum of nearby energy levels.In our previous study of TMA,2 we scanned a narrow-band

dye laser through the spectral region centered at 248 nm todetermine if there was any structure to the absorption coef-ficient and ionization yield. We observed no structure in this

experiment, and hence we conclude that the effective cross

884 J. Opt. Soc. Am. B./Vol. 2, No. 6/June 1985

sections reported here describe the ionization yields thatwould be obtained if a narrow-band laser were used in theexperiment.

We can compare these results with those given by our pre-vious study2 by noting that a in that study is related to thepresent parameters by

hv [1 + (Qr)4/3]3/4 + nr- (11)

Using the parameters of Table 2, we calculate that a = 3.2 X10-26 cm4/W, which is in good agreement with our previousdetermination of 3.6 x 10-26 cm4/W.

One other study of TMA derived excited-state absorptioncoefficients.2 5 In that study, Weyssenhoff and Kraus gavealo = 8.0 X 10-19 cm2, in agreement with our value, and a2l= 1.7 X 10-1 ci2, a factor of 1.6 smaller than our value, butthey give no value for Q. This is good agreement consideringthe potential systematic errors possible in these nonlinearexperiments. Using the data in Table 1 and subtracting thecontribution from the nonresonant channel, we calculatevalues for the normalized fractional ionization. These areplotted by the triangles in Fig. 6 and again demonstrate theconsistency of our data.

F. Nitric Oxide [NO]NO has no measurable absorption at 248 nm; hence the pre-viously observed ionization at 248 nm (Ref. 9) was a directtwo-photon process. We were not able to measure an absoluteyield at 248 nm and can give only an upper limit of nr < 5 X10-32 cm4/W. Resonant two-photon ionization processes cantake place at wavelengths that excite the A 2+ state throughthe gamma bands. The spectroscopy of this state has beenwell studied, 3' and lifetimes have been measured as a functionof rotational and vibrational level.3 2

We have Raman shifted our KrF excimer laser to the vi-cinity of the v' = 0 v" = 0 band at 226 nm by focusing it intoa cell containing approximately 6 bars of H2 and using theresulting first anti-Stokes line at 225.1 nm. Comparing thiswavelength with the absorption transitions in the gammabands, we find that it is resonant with rotational levels withK quantum numbers between 14 and 30 of the (0, 0) vibra-tional band. The measured lifetime for these levels is ap-proximately 215 nsec (Q = 0.0047).32 Because the fre-quency-conversion process is nonlinear, we were able to varythe pulse length only by a factor of 1.6, giving a Q productvarying from 0.027 to 0.043. Therefore we expect a pulse-length difference in the ionization yields only if there is asignificant contribution from the nonresonant two-photonionization channel. Although the statistics on the data arenot so good as those obtained for the organic molecules, wenevertheless observed a slight enhancement in the ionizationyields as the pulse length was decreased. This difference willhave to be quantified in future experiments.

Using the data given in Table 1, we derive the parametersal = 1.2 X 10-20 Cm 2 , (a2 1 = 1.4 X 10-17, and nr 1028

cm 4/W. We should stress that these coefficients are effectivevalues for the broadband excimer pump laser. If a narrow-band laser were used, the effective absorption cross sectionalo would certainly increase by several orders of magnitude,thus making the ionization yields for this molecule competi-tive with the organics.

Bischel et al.

The ionization yields for NO at 193 nm, obtained by usingan ArF gas mixture in the excimer laser, were approximately300 times smaller than those obtained at 225 nm. We werenot able to change the ArF pulse length by changing the gasmixture and, therefore, were not able to determine Q in thisexperiment. We analyzed the data by assuming that theprocess was completely nonresonant and determined the ef-fective two-photon absorption coefficient anr = 5 X 10-30 cm 4

as given in Table 2.

G. Extension to High Laser Fluences or High PressureThe integral solution expressed in Eq. (2) is valid only whenthe laser pulse does not cause ground-state depletion or sat-uration of a transition. When those limitations are not met,the kinetic equations (la)-(ld) must be solved numerically.However, the parameters determined in these experimentsand summarized in Table 2 are the appropriate values to usein the more complete solutions.

In the case of DEA, there is no direct measurement of theintermediate-state lifetime or its fluorescence quantum yield.In the absence of that information, it is not possible to isolatethe NRI cross section, nor is it possible to separate the de-duced value of Q into the Ar and Knr terms. In view of thesimilarity between the deduced value of Q and the measuredradiative decay rate for the first electronic state of aniline, itis probably a reasonable assumption to set Knr = 0 and Q =Ar, but experimental verification of those assumptions isdesirable.

For NO, the fluorescence quantum yield is again not spec-ified, but intersystem crossings are not possible, at least forthe lower vibrational levels, and the quantum yield must beunity. Then Knr = 0 and Q = An

All the Q values given in Table 2 are for low-pressure, col-lision-free conditions. At high pressures, the disappearancerate will be larger as a result of collisional quenching and/orcollision-induced intersystem crossing. If we assume a gas-kinetic rate of -10-10 cm3/sec, these collisional processes willbe comparable with the radiative and intersystem crossingrates when kN = 107 - 109/sec or N = 1017 - 10'9/cm 3.Thus, at pressures above a few Torr, the possibility of colli-sional effects must be considered.

5. SUMMARY AND CONCLUSION

In summary, we have measured absolute two-photon ioniza-tion yields for benzene, fluorobenzene, TMA, and DEA at 248nm and for NO at 225 and 193 nm. From these data and fromdata in the literature, we have derived four parameters thatallow the ionization yields to be modeled for an arbitrary laserfluence and pulse length. These parameters are summarizedin Table 2. In addition, we have derived an expression for theionization yields at low intensity that greatly simplifies thedata analysis for an arbitrary laser temporal pulse shape. Wehave also demonstrated that the method of varying the laserpulse length can be an extremely useful technique for deter-mining the lifetime of the resonant intermediate state, par-ticularly when the quantum yield for fluorescence is eithersmall or nonexistent.

If the experiments could be made using UV laser pulselengths varying by over an order of magnitude, a plot of theionization yields verse pulse length would uniquely determine

Vol. 2, No. 6/June 1985/J. Opt. Soc. Am. B 885

all four parameters without reference to independent ex-cited-state lifetime measurements.

ACKNOWLEDGMENTS

We thank D. L. Huestis for discussions on the modeling of thetwo-photon process. This work was supported by the DefenseAdvanced Research Project Agency through U.S. Office ofNaval Research contract no. N00014-81-C-0208.

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