Citation
The optogalvanic effect in a hollow cathode discharge

Material Information

Title:
The optogalvanic effect in a hollow cathode discharge a resonance detector for very weak light levels
Creator:
Petrucci, Giuseppe Antonio, 1963-
Publication Date:
Language:
English
Physical Description:
xiv, 202 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Atoms ( jstor )
Cathodes ( jstor )
Electric potential ( jstor )
Electrons ( jstor )
Ionization ( jstor )
Lamps ( jstor )
Lasers ( jstor )
Photons ( jstor )
Signals ( jstor )
Wavelengths ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Fluorescence spectroscopy ( lcsh )
Lead ( lcsh )
Neon ( lcsh )
Sodium ( lcsh )
Uranium ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1990.
Bibliography:
Includes bibliographical references (leaves 196-201).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Giuseppe Antonio Petrucci.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
025577433 ( ALEPH )
24529570 ( OCLC )
AHX0890 ( NOTIS )
AA00004769_00001 ( sobekcm )

Downloads

This item has the following downloads:


Full Text









THE OPTOGALVANIC EFFECT IN A HOLLOW CATHODE DISCHARGE:
A RESONANCE DETECTOR FOR VERY WEAK LIGHT LEVELS















By

GIUSEPPE ANTONIO PETRUCCI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1990





























Copyright 1990

by

Giuseppe Antonio Petrucci































Per i miei geniton













ACKNOWLEDGEMENTS


I would like to thank many group members, past and present, who helped

bring about the completion of this work and who made my stay here an enjoyable

and often-times interesting and confusing one. There are, of course, some who had

a more pronounced influence on me, during the course of this work. Josef

Simensson, my "circus friend", who jumped through all the hoops with me; Chris

Stevenson, for his much appreciated help in the lab; and, Norma Ayala, for policing

my wardrobe. They all helped very much to make some very frustrating times

tolerable. Their friendship outside of the lab was priceless.

I would like to thank Jim Winefordner for his guidance throughout this work.

His example of perseverance and hard work will always be with me.

I would also like to thank Ben Smith. His contributions to my work, both

practically and emotionally, are incalculable. His advice often kept me going when

my spirits were down. I think that I can safely say that without his help, the

completion of this dissertation would have been a monstrous task.

On a more practical nature, I would like to thank Steve Miles who made

invaluable contributions in the electronics part of this work. His willingness to help,

discuss with (and teach) me some of the "black magic" of electronics is greatly








appreciated. I should give a special thanks to the secretaries, Jeanne Karably and

Susan Ciccarone, for putting up with me and my "unique" questions.

Finally, I would like to thank my (soon to be) wife, Nancy. Whether she

realizes it or not, her support of and confidence in me has always strengthened my

heart. At times when I strongly doubted myself and my abilities, she brought back

into my life a perspective and respect for myself that I often lost.















TABLE OF CONTENTS


ACKNOWLEDGEMENTS ..........

LIST OF TABLES .................

LIST OF FIGURES ................

ABSTRACT .....................

CHAPTER 1

INTRODUCTION ...........

Need for a High Sensitivity Photon
Photon Detectors .............
Intent of Dissertation ..........


........................... iv


ix


............................. x


Detector ........

.. ..... .. ... ... .


CHAPTER 2

CONCEPT OF RESONANCE MONOCHROMATOR

Historical Background .........................
Resonance Spectrometers ......................
Fluorescence Resonance Spectrometer ..
Resonance Ionization Detector ........
Line Broadening Mechanisms ...................
Natural Broadening .................
Collisional Broadening ..............
Doppler Broadening ............

CHAPTER 3

OPTOGALVANIC EFFECT ....................

Introduction ................ ...............
Anatomy of a Glow Discharge ...................








Electrical Maintenance of the Discharge ............


CHAPTER 4

CONCEPT OF RESONANCE MONOCHROMATOR .......... 38

Introduction ............................................ 38
Theory ............................................... 39
Phenomenological Description of Ionization Mechanisms .......... 39
Evolution of OG Signals .................................. 40
Negative Voltage Changes ....................... 41
Positive Voltage Changes ....................... 44
Mathematical Treatment of OG Signals ....................... 49
Double-resonance Optogalvanic (DROG) Effect ................ 54

CHAPTER 5

CONSIDERATIONS ON THE INTERACTION OF ATOMS
WITH LIGHT ................................... .... 58

Absorption of Radiation .................................. 58
Laser Excitation of Atomic Transitions ........................ 60
Single-Step Excitation ......................... 60
Optical Saturation of an Atomic Transition .......... 63
Two-step Excitation ............................ 65

CHAPTER 6

EXPERIMENTAL ................................... 69

General Experimental Configuration ......................... 69
Pick-off Circuitry for OG Signal ............................. 74
One-step Excitation Experiments ............................ 74
Two-step Excitation Experiments ............................ 81
Timing of Laser Beams in Two-step Excitation Experiments ........ 81
Absorption Experiments ................................... 86
Saturation Curves ....................................... 91
Measurement for Enhancement of Two-step Excitation of Na
and Pb ............................................... 91


vii








CHAPTER 7


RESULTS AND DISCUSSION ...........................

Sodium OG Effect ......................................
Determination of Lamp Impedance .........................
Evaluation of Collisional Ionization Rate Constants by the


OG Effect


Two-step OG effect of Na .....
Lead OG Effect in the HCL ...
Neon OG Effect in the HCL ...
Electronic Configuration of Ne .
One-step Neon and Uranium OG
Case 1...............
Case2 ...............
Case3 ...............


Effect


Case 4 ..........................................
Neon OG Signal Dependence on Lamp Current ................
Double-resonance OG Effect of Ne .........................
Optimization of Boxcar Gate Position .......................
Alignment of Laser Beam(s) in the Hollow Cathode .............
Ionization Within the Negative Glow ...................
Ionization Within the Dark Space .....................
Two-step Enhancement of Ne OG Effect .....................
Evaluation of Ne OG in the HCL as a Sensitive Photon Detector ...


CHAPTER 8

FINAL COMMENTS ........

Summary ..................
Future Work ...............

REFERENCE LIST .........

BIOGRAPHICAL SKETCH ...


viii


92

92
100

103
104
110
117
117
122
125
131
136
146
151
154
157
161
162
167
167
175


192


202


.................


...........................
...........................









LIST OF TABLES

Table 1. Values used for calculating ni/nt in equations (26) and (27) ..... 68

Table 2. Listing of experimental components ...................... 73

Table 3. Experimental values for determining ni in equation (32) ....... 105

Table 4. Values used to calculate vi and v. in equation (44) ........... 163









LIST OF FIGURES

Figure 1. Resonance monochromator proposed by Sullivan and Walsh [23] 9

Figure 2. Resonance ionization detector .......................... 15

Figure 3. Normalized Lorentzian line profile ....................... 23

Figure 4. Normalized Gaussian line profile ........................ 25

Figure 5. Electrical regions of a dc discharge [53] ................... 30

Figure 6. Voltage distribution across a dc glow discharge .............. 32

Figure 7. Electron energy distribution across a dc glow discharge ........ 34

Figure 8. Oscilloscope trace of the negative OG signal for the
3s1 2S1/2 --> 3p 2P3/2 transition of Na ..................... 43

Figure 9. Oscilloscope trace of the positive OG signal for the
3P2 (Is5) --> 3D3 (2p9) transition of Ne .................... 46

Figure 10. Partial energy level diagram of Ne ....................... 48

Figure 11. Electric field distribution across the dc glow discharge ......... 52

Figure 12. Partial energy level diagram of Na ....................... 56

Figure 13. Possible excitation/deexcitation process in an atom ........... 62

Figure 14. General experimental configuration ........ .............. 71

Figure 15. Diagram of a common HCL (lamp 1) ..................... 76

Figure 16. Diagram of a Galvatron (see-through HCL) (lamp 2) ......... 78

Figure 17. a) Pick-off circuit for measuring OG signals
b) Diagram of housing for pick-off electronics and lamp holder .. 80

Figure 18. Alignment of laser(s) through lamp 1 ..................... 83

Figure 19. Alignment of laser(s) through lamp 2 ..................... 85









Figure 20.


Figure 21.

Figure 22.

Figure 23.

Figure 24.

Figure 25.


Figure 26. Two-step enhancement of Na OG signal


Oscilloscope trace of temporal coincidence of the two
laser beams at the hollow cathode ......................

Experimental configuration for absorption experiments .......

OG signals for ground state transitions of Na ..............

Example of signal-to-noise attainable using the OG effect ......

OG signal for excited state transition of Na ................

Plot of (Vout)1 vs R, for determination of lamp impedance ....


Collisional coupling of Na energy levels in the HCL ......... 109

Partial energy level diagram for Pb ...................... 112

Two-step enhancement for Pb OG signal ................. 114

Pb two-step OG signal vs lamp current ................... 116

OG spectrum of U/Ne lamp from 580 601 nm ............ 119

Expanded U OG spectrum from 580 601 nm ............. 121

OG spectrum of U/Ne lamp from 594 607 nm ............ 124

Saturation curve for 597.55 nm absorption of Ne ............ 128

Log-log plot of Figure 34 ............................. 130

Saturation curve for 598.80 nm absorption of Ne ............ 133

Log-log plot of Figure 36 ............................. 135

Proposed excitation/ionization scheme for 598.80 nm
absorption of Ne ................................... 138

Excitation scheme through a virtual level ................. 140


Figure 40. Saturation curve for 599.56 nm absorption of Ne ....


88

90

94

96

99

102

107


Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

Figure 33.

Figure 34.

Figure 35.

Figure 36.

Figure 37.

Figure 38.


Figure 39.








Figure 41.

Figure 42.

Figure 43.

Figure 44.


Figure 45.


Figure 46.

Figure 47.

Figure 48.


Figure 49.







Figure 50.


xii


Log-log plot of Figure 40 .............................

Saturation curve for 599.24 nm absorption of U ............

Log-log plot of Figure 42 .............................

Proposed excitation/ionization scheme for 599.24 nm
absorption of U ....................................

Plot of relative laser induced impedance change vs.
lamp current.......................................

Boxcar gate position considerations ......................

One-step ionization signal observed in cathode dark space ....

Convolution of ionization signals from cathode dark space
and negative glow region .............................

Two-step enhancement of Ne OG signal in HCL
a) Oscilloscope trace of one-step excitation OG signal of
Ne (ground state) ...................................
b) Oscilloscope trace of one-step excitation OG signal of
Ne (excited state) ...................................
c) Oscilloscope trace of two-step excitation enhancement of
OG signal of Ne ....................................

Scan showing simultaneous recording of absorption of X 12
and OG signal for determination of a ....................

Calibration curve for Ne RID in the HCL .................

Log-log plot of Figure 51 .............................

Plot of V(rms) vs lamp current ............. .........

Plot of signal-to-noise of Ne RID vs. lamp current ..........

Summary figure of results .............................


Figure

Figure

Figure

Figure

Figure


145

148

150


153


156

160

166


169



171

172

173


179

182

184

186

189

191













Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

OPTOGALVANIC EFFECT IN A HOLLOW CATHODE LAMP:
A SENSITIVE DETECTOR FOR VERY WEAK LIGHT LEVELS

By

GIUSEPPE ANTONIO PETRUCCI

DECEMBER 1990


Chairperson: James D. Winefordner
Major Department: Chemistry

Both one- and two-step excitation optogalvanic (OG) effects in two

commercially available hollow cathode lamps are studied. Elements studied are

sodium, lead, uranium and neon. Four different excitation/ionization mechanisms

were observed by the OG effect and are discussed. These include: 1) one-step

excitation followed by collisional ionization; 2) one-step excitation followed by

photoionization; 3) two-step excitation through a virtual level, followed by collisional

ionization; and, 4) two-step excitation through a virtual level, followed by

photoionization. The two-step excitation to a real level followed by collision and

photoionization were also observed for Ne. Two-step excitation enhancements in the

OG effect of Na, Pb and Ne, relative to the one-step excitation cases were

determined.


xiii








The use of a coupled, step-wise, two-step excitation of Ne in the hollow

cathode lamp was evaluated as a sensitive detector for very low light levels. The first

transition studied was the 3P2(ls5) --> 3D3(2p,), at a wavelength of 640.225 nm. The

excited state transition, coupled to the first transition, was the 3D3(2p9) --> 4d4'

transition, at 576.442 nm. The limiting experimental noise was determined to be the

shot noise of the hollow cathode lamp. Under optimized conditions, the

experimentally attained minimum detectable energy and number of photons were 6

x 1015 J and 2 x 104 photons, respectively. The limits of detection corresponding to

the theoretical shot noise limit in the experimental system were 1 x 1016 J and 4 x

102 photons.


xiv













CHAPTER 1
INTRODUCTION



Need for a high sensitivity photon detector


The search for and development of methods for determining traces of

elements is one of the most important trends in analytical chemistry [1].

Development of these methods is determined to a large extent by the needs of

various branches of science, technology and industry relating to the production and

use of ultrapure materials. Two examples of the need for ultra-trace analysis include

the study of the effect of impurities during the production of silicon solar-cells [2]

and the production of optical glass [3]. In meeting these needs, the problem of

measuring light intensities and their spectral distribution at very low levels is

becoming considerably important.

In contemporary optical spectroscopy, complex and expensive monochromators

and photon detectors are used for discriminating and detecting an extremely narrow

wavelength range in a light train with an arbitrary spectral composition. Such

instruments must possess high sensitivity to the photons to be detected and high

spectral resolution for reducing background noises. At present, two kinds of

photoelectric measurements are being used to accomplish the measurement of very

low light levels. These are referred to as analog [4,5] and digital [6,7] schemes.








2

With the digital method, contributions from photoelectrons are resolved in time so

that the signals in the form of electron pulses are detected by means of a pulse

counting system. This technique is the one of choice when concerned with the

measurement of ultra-low light levels.


Photon detectors


A detector of optical radiation is defined by the Commission Internationale

de l'Eclairage [8] as a device in which incident optical radiation produces a

measurable physical effect. Two classes of detectors of optical radiation produce a

measurable signal by one of two primary detection mechanisms: the photoelectric

effect (photon detectors) and the thermal effect (thermal detectors). Photon

detectors are the most common in optical spectroscopy for the measurement of low

light levels. Photomultipliers (PMTs) are the standard photon detector in

commercial spectroscopic instruments. Their basis of operation is the generation or

change of an electric signal by an external photoelectric effect in which a

photoelectron is emitted by a cathode and captured by a second electrode (or

dynode). The important feature of the PMT is the dynode system, which consists of

electrodes covered with special materials which emit various "secondary electrons"

per incident primary electron. The number of dynodes in PMTs ranges from 3-6,

resulting in a total gain or amplification of the cathodic photo-induced current of up

to 107 or more.








3

The detection of light has undergone a great metamorphosis since 1800 when

Sir William Herschel [9] used an ordinary thermometer to measure the intensity of

light passing through different filters. In 1831, Nobili and Melloni [10] developed

a thermocouple for the quantitation of light intensity. Samuel Pierpont Langley

[11], in 1881, developed the bolometer which was 30 times more sensitive than

Melloni's thermocouple. The bolometer is based on the change in resistance of a

wire as it is heated. By incorporating the wire into a Wheatstone bridge, high

sensitivities were possible. In 1884, W.N. Hartley [12] applied photographic

detection of light intensity to quantitative chemical analysis. The key development

in the use of photography as a means of detection for quantitative chemical analysis

was the concept of using an internal standard. The next step in the development of

detection systems for spectroscopy was the development of photoelectric detection.

The origins of photoelectric detection date back to Hertz [13,14,15]

who observed that a spark produced by one circuit was somehow transmitted through

space so as to induce a spark in a secondary circuit even though the two circuits were

not connected directly. By placing a slit and a quartz prism between the primary

spark and the induced spark gap, he was able to show that the effect occurred only

when the prism was arranged to transmit light in the ultraviolet region of the

spectrum. The next year, A. Righi [16] demonstrated that a small current could

be made to flow between a mesh grid and a polished metal plate when the plate was

irradiated. The study of the photoemissiveness of different materials, mostly

amalgams of alkali metals, was undertaken by Elster and Geitel [17] and the first








4

modern photoemissive surface was described by LR. Koller [18,19]. Even with

the great strides made in improving the sensitivity of photocathode materials, the

most sensitive surface could not pass a large amount of current without destroying

the photoemissive layer. In 1940, Rajchman and Snyder developed a nine-stage

electrostatically focused multiplier phototube that has served as a model for

"modern" photomultiplier tubes [20].

In general, the spectral responsiveness of photon detectors is selective, being

determined largely by the chemical-physical composition of the materials used to

absorb photons. This spectral responsivity of individual photocathode materials is

normally "limited" to a wavelength range of approximately 600-700 nm in width

[21]. This dictates that for higher spectral resolution of the detected line, a primary

disperser must be used to separate the incident light into its component wavelengths,

before it is made incident on the photocathode of the PMT. Monochromators are

the method of choice for wavelength dispersion of the incident light.

Monochromators with several dispersing stages in series are used for very high

resolution of the wavelength of interest and reduction of stray light.

Two main criteria used to evaluate monochromators are optical throughput

and resolution. The optical throughput of a monochromator is defined as the

amount of radiation reaching the detector for a given amount leaving the source.

The effective throughput of the entire monochromator is limited by the portion of

the instrument with the smallest throughput. In conventional monochromators, the

limiting throughput is either the entrance or exit slit of the monochromator.








5

The resolution, on the other hand, is a measure of the ability of the

monochromator to disperse incident light composed of many different wavelengths

into its component wavelengths. It is given by the product of the width of the

entrance or exit slit (assumed to be equal in this case) and the reciprocal linear

dispersion of the dispersing element in the monochromator. The product of the

throughput and resolution is constant for a given monochromator. However, since

resolution improves with narrower slit widths and throughput increases with wider

slit widths, the spectroscopist is constantly faced with a choice of compromise

conditions involving resolution and throughput.

For a single-stage monochromator the throughput is on the order of 10-103.

For multiple-stage monochromators, the overall throughput is a product of the

throughput of each stage. So, for a triple-stage monochromator, the fraction of

incident light that reaches the PMT is only 107-109. This inverse relation between

throughput and resolution is one of the major limitations of using conventional

detectors. The other major limitation is a result of the low quantum efficiency of the

photocathodes of PMTs.

The quantum efficiency is defined [8] as the ratio of the number of elementary

events (e.g., photoelectrons) contributing to the detector output to the number of

incident photons. For most cathode materials, the quantum efficiency is very low;

on the best sensitized commercial photosurfaces, the maximum yield reported is as

high as one electron for three light quanta incident on the photocathode. An ideal

photodetector has a quantum efficiency of 1; i.e. every incident photon produces one








6

photoelectron. All practical photocathode materials have quantum efficiencies of less

than 1. Therefore, a PMT could never detect a single photon from the source.

As described below, resonance spectrometers offer the advantages over

monochromator/PMT detection systems, of high spectral resolution (103 nm) in

conjunction with a high optical throughput (>0.5).


Intent of dissertation


The present work was intended to evaluate and characterize a photon detector

based on the optogalvanic effect in a commercial hollow cathode lamp. Optical

transitions of sodium, lead and neon, the inert filler gas were considered for the

detector. Both single- and double-resonance excitation schemes were used. Also,

several single-step transitions of Ne and U were studied in terms of excitation-

ionization mechanisms.













CHAPTER 2
CONCEPT OF RESONANCE MONOCHROMATOR



Historical Background


The requirements of high sensitivity and wavelength selectivity were already

met in 1905 through the simple and effective techniques for discriminating resonance

radiation of specific elements which were based on the resonance absorption of

photons and their subsequent re-emission in atomic vapors of the element [22].

Such a device is termed a resonance monochromator (RM) and was first proposed

in 1968 as an accessory for modern spectroscopy by Sullivan and Walsh [23]. The

basic concept of the RM, as a detector for atomic absorption spectroscopy, is shown

in Figure 1.

The light from several spectral lamps is collimated and passed through the

flame. The radiation transmitted is then passed into several RMs. Each spectral

lamp (or element of interest) has a corresponding RM. In Sullivan and Walsh's case,

the RMs were simply high current hollow cathode lamps to provide the requisite

atomic vapor density with minimal emission. Upon absorption of resonance radiation

by the RM, ground state analyte atoms would be excited and subsequently reemit the

radiation, which was observed at right angles to the incoming radiation. Each RM
















0

o


0
to


0

a















o







0
cd

0
53















I-
0
E















0
I-











0
o











-4
I-
0d
^3
0~
'u















-4
























LLI I








10

would then respond selectively to the transmitted intensity of the corresponding

analysis lamp.

Since 1968, resonance spectrometers based on several optical and electrical

principles have been studied, including fluorescence, ionization and optoacoustic

techniques. A variety of atom cells have also been studied for resonance detection.

Among these are flames [24] (laser enhanced ionization, LEI), hollow cathode

lamps [25,26] (Optogalvanic effect, OGE), high-frequency spectral lamps [27]

and furnaces [28]. Resonance monochromators, however, have been used mainly

for absorption experiments.


Resonance Spectrometers


Resonance spectrometers offer several important advantages over

conventional spectrometers. They possess an inherently high spectral resolution (10-3

nm), a large solid angle of collection of the incoming light (up to 2n sr), low intrinsic

noise, and high quantum efficiency, namely, the capability of single photon detection.

This is in contrast to photomultiplier tubes, which have maximum cathode efficiencies

of about 30%, meaning that at best, 3 photons are required on the average for the

detector to record an event. Also, as stated above, several different spectroscopic

techniques may be used as the basis for a RM. Two of the most studied are

fluorescence (fluorescence resonance spectrometer, FRS) and atomic ionization

(resonance ionization detector, RID). Atomic ionization is used here as a generic








11

term for all spectroscopies which are based upon the galvanic measurement of

ionization rate enhancements induced by the absorption of resonance radiation.

Fluorescence Resonance Spectrometer

The fluorescence-based resonance spectrometer has been the most widely used

by far. The resonance spectrometer proposed by Sullivan and Walsh [23] was of the

fluorescence type. The principle of operation is based on the absorption of the

resonance radiation of interest by atoms in the optical cell and the recording of the

emitted (resonance or non-resonance fluorescence) light. Such a resonance

spectrometer was used by Bolger [29] for the recording of weak Raman scattering.

In this experiment, a 10 ns, 1 kW pulsed tunable dye laser, with a bandwidth of 0.1

cm71 (S6 =0.002 nm) was used to illuminate the sample. The wavelength of the laser

was chosen so that the Raman scattered light was around 455 nm. This light was

used to excite Cs atoms. The fluorescence of the Cs atoms at 850 nm was then

measured as the analytical signal. The detector sensitivity was found to be

approximately 3 orders of magnitude higher than a dispersion system with a

conventional detector.

The first fluorescence resonance spectrometer (FRS) working with transitions

from excited states was proposed and studied by Gelbwachs et aL [30]. They

excited Na atoms in the FRS to the 4P3/2 state (1 =330.3 nm) with a dye laser.

Radiation from a xenon arc lamp, 3.42, 2.34, and 1.48 P m, was then absorbed by the

excited Na, promoting it to the 5S1/2, 4D5/2, and 5D5/2 levels, respectively. They then

observed fluorescence of the Na in the visible region at wavelengths of 616, 569, and








12

548 nm, respectively, for the three transitions. The same workers also proposed and

studied the only tunable FRS. This RM, based on potassium, was made tunable over

a narrow spectral range by shifting of the highly excited energy levels of K by the

quadratic Stark effect [31]. One of the problems of fluorescence-based resonance

spectrometers is the need still for a separate monochromator and photon detector.

With an FRS some means of isolating the fluorescent light from the FRS from other

wavelengths and a photoelectric detector are still required to measure the intensity

of fluorescent photons from the FRS. Therefore, the throughput and resolution

limitations of a monochromator/PMT detector are still applicable, albeit to a lesser

extent than in the simple case of detection with a monochromator and PMT. Also,

the less than unity quantum efficiency of the photocathode material of the PMT

places a fundamental limit on the minimum detectable number of photons.

Resonance Ionization Detector

Atomic ionization (AI) methods have been proven to be very sensitive

spectroscopic techniques [32,33]. They are based on the recording of charged

particles which are formed in the atom cell upon absorption of resonance radiation

followed by subsequent ionization of the excited atoms by various processes. In the

extreme case of detecting single charges, proportional gas counters are used. For

bulk measurement of a large number of charges formed, the impedance or current

change across the atom cell is measured. Limits of detection in normal atmospheric

pressure atomizers are in the low ng/mL to pg/mL (or pg to fg absolute detection

limits) [34]. V.S. Letokhov [35] was the first to draw attention to the fact that








13

it is possible to detect even single atoms by the AI method. This limit of single atom

detection, or SAD, was experimentally attained by Hurst et at, [36,37] for Cs and

by Bekov et at [38] for Na and Y. Detection of single atoms is possible by AI

because of the ability to detect charges with unity efficiency.

Matveev et at [39] first proposed the use of laser-enhanced ionization in a

flame as a photon detector. Work to date has been mainly on the theoretical

feasibility of such a detector [40,41,42]. Okada et at [43] were the first to

report quantitative results of a selective laser ionization photodetector. They

reported a minimum detectable energy, in the first wavelength, of 10" J, while Smith

et at [44] are the only workers to record a Raman spectrum with a RID. Their

minimum detectable energy can be estimated as approximately 1016 J at 285 nm.

The case of the RID (Figure 2) is very similar to that of the FRS. Radiation

(hv )emitted from the sample (SA) is conveyed by an optical system into the RID,

which contains a high concentration of atomic vapor. In the simple case of detecting

atomic emission or resonance fluorescence, the atomic vapor in the RID is the same

as the analyte of interest in the sample. Absorption of the radiation upon passing

into the RID causes a measurable change in the electrical properties of the RID.

For detection of scattered radiation (eg. Raman scatter), the RD becomes

much more favorable and versatile to use than conventional dispersive instruments

with photomultiplier detection. In Raman spectroscopy, for example, one is

interested in measuring the intensity of scattered radiation shifted in energy by a

characteristic amount from the central frequency of the exciting light. The












N

0






'I.



4-1


4,)
ob







4( 0
4)
5 o













0 03
0






eo









-S
co0
UN


0.-



04)
0



e,







*-







E4
















1<


-I r


tr


C~2


0,


2
~ P










frequency shift is characteristic for a particular scatterer and is given by


Av (1)



where Av-R is the characteristic Raman scatter energy, and 1/1a. and 1/.stok are

the wavelengths of the exciting light and Raman shifted light, respectively.

It is important to emphasize the inverted nature of the RID approach of

Raman scatter compared to conventional detection. In conventional Raman

spectroscopy, the spectrum of the Raman scattered light is obtained by imaging the

scattered light onto the entrance slit of a double monochromator. The

monochromator is then scanned from wavelengths longer than the exciting

wavelength to the central exciting wavelength, thereby observing the different A"'s

for the scatterer. In "RID" Raman spectroscopy, the detector operates at a fixed

wavelength, dictated by the energy level scheme of the "detector element." The

exciting light must therefore be scanned to shorter wavelengths than the expected

Raman scattered wavelengths. Any element can be chosen for the RID which gives

the best sensitivity and selectivity, and then the frequency of excitation for the

Raman scatter is chosen such that the scattered radiation will be at a frequency

detectable by the RID.

One of the major advantages of such a detector is that it will respond only to

wavelengths of radiation that are within the absorption bandwidths of the various








17

transitions of the RID element. Anything outside of the absorption bandwidth of the

RID element will not be absorbed and will therefore not produce a signal.


Line-Broadening Mechanisms


The absorption (response) bandwidth of the RID element will depend on the

operative broadening mechanism of the atomic line in the RID. This makes the RID

inherently insensitive to problematic scattered light. Atomic lines are not truly

monochromatic and do possess a finite frequency (or wavelength) distribution. The

finite widths obtained are a result of a variety of line-broadening phenomena. The

width of the line is normally characterized by the width at one-half the maximum

height, or full-width at half maximum, FWHM. All of the different line-broadening

phenomena result in a frequency distribution of the atomic transition which can be

described by either a Lorentzian or Gaussian expression. However, since more than

one line-broadening process can be operative at any one time, the overall profile is

neither purely Lorentzian or Gaussian, but a combination of the two, known as a

Voigt profile. The predominance of one or more of the line-broadening mechanisms

is a function of the chemical and physical environment of the absorbing or radiating

atom. The three most commonly discussed broadening mechanisms are natural

broadening, collisional or pressure broadening and Doppler broadening. Each will

be discussed briefly below.

Natural Broadening

Because of interaction of atoms with radiation fields and collisional processes,








18
the lower, i, and upper, j, energy states participating in the atomic excitation have a

finite lifetime, and this gives rise to uncertainties in the energy of both states

according to the Heisenberg uncertainty relation. Usually, the extent of the line-

broadening is determined by the much shorter lifetime of the upper state of the

transition. This is called lifetime or natural broadening. The FWHM due to natural

broadening is smaller than that due to other broadening mechanisms except in

extreme cases (eg. transitions to autoionizing levels of the atom). The spectral

profile of a naturally broadened line is described by a Lorentzian. The normalized

spectral profile due to natural broadening, SN, is given by


S 2/( Av, )
S 2( v ) (2)
AvN



where

AvN = FWHM of the naturally broadened line (Hz)

vm = frequency at the line center (Hz)

The width of a naturally broadened line, between two real energy states of the

atom (see below), is on the order of 107 Hz. In wavelength units, the FWHM, A~N

(m), is expressed as


AlN Av, (3)
C










where

s8 wavelength at the line center (m)

c speed of light (m s1)



For example for Na, at 589.0 nm, ALrP2x1014 m or 0.02 pm.

Collisional Broadening

The line profile is also influenced by collisions of the atom of interest with

other atoms of the same kind (Holtzmark broadening) or with foreign species

(Lorentz broadening). The amount of broadening caused by collisions increases with

the concentration of collision partners and hence, collisional broadening is sometimes

called pressure broadening. Collisions which leave the atom in the same energy state

(adiabatic collisions) have a more pronounced broadening effect than collisions that

leave the atom in a different energy state diabeticc collisions). The FWHM of the

spectral distribution resulting from adiabatic collisions, Av, (Hz), is given by


Aa oan (4)




where

a, optical cross section for adiabatic collisional broadening (cm2)

n. = density of collision partners (cm"3)

A = reduced mass of collision partners (g)








20
The total, normalized spectral profile, S,, for collisional broadening is also

Lorentzian and is given by equation (2) by replacing the natural FWHM, Av N, with

the collisional FWHM, A v. The typical FWHM of a collisionally broadened line is

on the order of 3 x 10"12 m or 3 pm.

If natural and collisional broadening are assumed to be mutually independent,

the resulting FWHM of the Lorentzian profile is




Av, Avc + AvN (5)



where Av is the FWHM from both adiabatic and diabetic collisions.

Doppler Broadening

A third major source of line-broadening is a result of the statistical

distribution of the velocities of the atoms absorbing radiation along the observation

path, called Doppler broadening. Because atoms are in motion with respect to the

observer, the Doppler effect causes a statistical distribution of frequencies absorbed

that is directly related to the velocity distribution. Briefly, the FWHM for Doppler

broadening, AvD (Hz), is given by



Av 2- 2(n 2)kT c (6)
m I c (6)









where

k = Boltzmann constant (J K-1)

m = atomic weight (g)

vm = central frequency (Hz)



The normalized spectral distribution, SvD, is described in this case by a

Gaussian relation and is given by



SVD J exp (n2)(v )2 (7)
AV/ L Av2



Typical Doppler broadened linewidths are on the order of 4 x 10T12 m or 4 pm. The

overall profiles for most atomic spectral lines are neither purely Gaussian nor purely

Lorentzian, but rather a combination of the two known as a Voigt profile.

The predominance of one type of line over another is largely dependent on

the environment of the atoms. For example, in an atmospheric pressure flame, one

might expect that collisional broadening would dominate over Doppler broadening,

whereas in a low pressure environment the opposite is expected to be true. The

importance of which broadening mechanism predominates is clear from Figures 3

and 4 which show the line profiles for purely collisionally and Doppler broadened

lines, respectively. These line profiles were plotted using equations (2) and (7) and

assuming a FWHM of each line of 1011 m. The selectivity of the RID under each

















0



















o
*1
I-1




cb.





0
C



.)








3













N
ct







g-





'5


























I
O t


T"
o.






0






0 0 0 0 0 0 0




uo dilosqB a!7ruIaa












0
0
O
0
0


0
0
o
d
O
O





o
d


0
0
0
c0

0
C C
0


O
0
0O


Sd T 0 q0 0 0 0 0 0
'-" -"- T -r 0" T


uo!ldjosqB 9A!ji'6gI









26

of these conditions can be readily obtained from these plots. For example in the

case of a Doppler broadened line, the fraction of the incident light falling within the

absorption linewidth of the detector element falls to 10'12, comparable to the stray

light rejection of a good doublemonochromator, at a wavelength only 3 x 1011 m or

30 pm from the central line (evaluated at 640.2 nm). The collisionally broadened

line on the other hand, has long tails, giving a fractional absorption of 107 as far out

as 6 nm away from the central line (evaluated at 640.2 nm). Therefore, a low

pressure cell, in which collisional broadening is not the dominant broadening

mechanism, is essential for highest wavelength selectivity.

One other advantage of the RID is that there are no limiting apertures,

limiting the optical throughput of the detector. This allows for a greater fraction of

the sample light to be collected and imaged into the RID, up to 50%. A good two-

stage monochromator will have an optical throughput of 105-106%. The product of

throughput and selectivity is constant for any one system. Clearly, the higher the

value of this product, the more selective and sensitive is the detector. The RM is the

only photon detector for which the detection efficiency need not be compromised for

better resolution or selectivity.














CHAPTER 3
OPTOGALVANIC EFFECT



Introduction


The optogalvanic (OG) effect is a change in the properties of an electrical

discharge caused by illuminating the discharge with radiation having a wavelength

corresponding to an atomic or molecular transition of a species in that discharge.

The effect was first observed by Foote and Mohler [45] in cesium-vapor filled hot

cathode diodes and Meissner et al. [46] and Penning [47] in rare gas glow

discharges. It was Penning who first discovered that an increase in breakdown

voltage occurred in a mixture of neon and argon when discharge tubes were

irradiated by emission from an identical tube.

Although the OG effect was first observed over 60 years ago, little work has

been done exploring its analytical capabilities. It was not until the development of

tunable lasers that the analytical potential of the OG effect began to emerge. Since

that time, the OG effect has found applications in optical spectroscopy [48],

analytical chemistry [49,50], laser stabilization [51] and wavelength

measurements and calibration [52], to name a few.











Anatomy of a Glow Discharge


The typical schematic representation of a dc glow discharge is shown in Figure

5 (taken from Nasser [53]). The normal glow discharge consists of 5 distinct

regions: 1) cathode dark space; 2) negative glow; 3) Faraday dark space; 4) positive

column; and 5) anode dark space. The corresponding diagnostic plots are given

below the figure. The positive column has by far, been the most probed and

modelled region. As the electrode separation is decreased, the negative glow and

cathode dark space remain unaffected, while the positive column shrinks, alluding to

the importance of these two regions in the maintenance of the discharge. When the

electrode separation is just a few times the cathode dark space length, only the dark

space and negative glow regions remain [54]. This is the normal operating mode of

hollow cathode lamps and is the experimental mode of operation in this work.

Note that almost the entire applied voltage is dropped across the cathode dark

space, while the negative glow remains essentially field-free. As such, its boundary

acts as a diffuse anode.

To maintain electrical balance in the system, the currents at the two

electrodes must be equal. Experimentally, however, it was observed [54] that the

current density at the anode was smaller than the random current density and so

there must be a decelerating field for the electrons at the anode. Figure 6 shows the

voltage distribution in a de glow discharge. The values given are for typical

experimental parameters used in this work. Figure 7, redrawn from Figure 6, is an































Figure 5. Electrical regions of a dc discharge [53].



























1st, 2nd ...
CATHODE LAYERS.


R SUPPLY
-- .-0


POSITIVE COLUMN
NEGATIVE GLOW\ ANODE GLOW


I FARADAY DARK SPACE
CATHODE
DARK SPACE (CROOKES. H




K!=


I
ITT
-A(




-I


> I i









t I I




4 ----


ANODE DARK SPACE
ORF)

LIGHT INTENSITh'




LLCTW.,IC E i i,


POTENTIAL




POSITIVE L3 A,
I:HARGE DE';SI T

NEGATIVE SPACf
CHARGE DNSI T Y
- IOTAL





I ,.S TELMP(f[ A I U F i!


ASTON
DARK
SPACE


i\


























































O
I-










v,
rU


I-

0




-o













CL























AC
5, M


S o



















5 0




















+ aB


- -I















































-d




0
U

-o

0


0



' i







0

U
c4





































a)a









35

electron energy diagram for the discharge and shows the potential barriers to

electron movement. The negative glow does not take a potential intermediate to

those of the electrodes, as might be intuitively expected, resulting in a potential well

between the cathode and anode. The electric fields in the system are restricted to

sheaths at each of the electrodes and are such as to repel electrons trying to reach

either electrode.


Electrical Maintenance of the Discharge


In the text by Chapman [54], ion pair contributions from possible ionization

mechanisms in the three regions of interest are calculated. He concludes that the

two most probable discharge maintenance mechanisms, both occurring in the

negative glow region, are ionization by impact with thermal electrons [54, p.117]


A* + e- A' + 2e- (8)



and associative ionization of metastables [54, p.122].


A' + A' A + A + e- (9)



Collisional ionization of ground state atoms of the inert gas by electron impact is not

very probable due to the high energy ( >21.6 eV for Ne) required.

Ionization of sputtered cathode atoms can occur by any of the above

mechanisms, as well as Penning ionization (10)












X* +M-X + M + e- (10)



where X represents a buffer gas atom, and direct ionization of ground state sputtered

atoms, since much lower electron energies are required ( < 12 eV).

It is interesting to examine how photo-induced transitions can affect these

ionization processes if A is Ne, for example. Under normal glow discharge

conditions, the electron energy distribution approximates a Maxwell-Boltzmann

distribution and falls rapidly above 16 eV [55], where inelastic collisions dominate

(excitation of excited electronic states and ionization of Ne). Several points should

be noted. First, the neon metastable states, Ne'm, will be efficiently populated by

electron-neon ground state collisions, since singlet-triplet excitation functions peak

near the threshold voltage for discharge maintenance [56]. The subscript m is used

to denote neon in the metastable state. Second, collisional ionization of metastable

neon by electrons [process (8) above], whose cross-section peaks at about 15 eV

[57] can be expected to become increasingly important at high discharge currents.

Finally, the electron-neon collision frequency (- 1010 s-1) exceeds both the neon-neon

collision frequency (107-108 s"1) at normal HCL pressures (typically 1-5 torr) and the

reciprocal of the shortest radiative lifetimes for the excited Ne atoms

[58,59,60]. One can conclude from the above that, regardless of the precise

mechanism of ionization, metastable Ne atoms play a central role in the maintenance

of the discharge, as discussed by Chapman [54]. This was also supported

experimentally by the work of Smyth et aL [61] and Hess and Harrison [62]. In









37

these experiments, the Ne' concentration was monitored with a mass spectrometer.

Substantial changes in the Ne+ density were detected and were found to correlate

qualitatively with the photon-induced voltage changes. One can therefore expect that

the dynamics, voltage and current characteristics of the discharge would be sensitive

to even small perturbations of the Ne'm population.

An immediate realization gained from contemporary literature on glow

discharges in general and more specifically hollow cathode discharges is that such

discharges are dynamic environments which do not readily lend themselves to precise,

detailed modeling. In fact, a unified and generally agreed upon (quantitative) theory

of the mechanisms which are operative in the glow discharge has yet to be

presented.














CHAPTER 4
OPTOGALVANIC EFFECT IN THE HOLLOW CATHODE DISCHARGE



Introduction


A great deal of experimental work has been performed in a variety of

discharges, many of which were "home-made" [63,64,65] and contained an

assortment of vapors, such as 12 [66,67], rare gases, such as Kr [68], He [69],

Ar [70] and Ne [71] and numerous mixtures thereof. Of most practical interest

to the analytical chemist, however, is the use of commercially available hollow

cathode discharges (HCDs) or lamps (HCLs) in OG experiments. Unfortunately,

knowledge of the operating characteristics and parameters of HCDs is largely

empirical. General conclusions, however, can been drawn from previous work about

the OG effects in glow discharges. Firstly, the impedance changes normally induced

by the introduction of a collimated beam of light that is resonant with an absorption

transition of a discharge species into a discharge are large (as high as 10% of the

quiescent voltage) and are easily measured. Secondly, it is well known that these

impedance changes can be positive or negative.














Theory


Numerous theories and mathematical expressions have been postulated to

quantify and more fully understand the OG effect in HCDs. These range from the

relatively simplistic theories of Erez et aL [72] and Smyth and Schenck [61] to the

more arduous and pedantic theories of Ben-Amar et aL [73] and Broglia et aL

[74]. As stated above however, no agreement has been made on any one, complete,

unified theory to describe the processes in an HCD.

A complete description of proposed theories and mathematical treatments of

this dynamic system are beyond the scope of this dissertation: a phenomenological

description of the HCD characteristics and mechanisms and a simplified

mathematical treatment of the OG process shall be presented herein as pertinent to

this work.


Phenomenological Description of Ionization Mechanisms


There are two principal mechanisms suggested to explain the impedance

change of a hollow cathode discharge upon illumination by resonant photons. The

first mechanism, analogous to the OG effect in flames [34] is based on the increase

in cross-sections for electron-collision induced ionization as the final state energy

approaches the ionization limit. This mechanism is believed to be the dominant one

in the cathode dark space due to the high concentration of energetic electrons. The









40

second mechanism, which is proposed to be dominant in the negative glow region,

is an increase in the electron temperature of the discharge [75] upon irradiation

with resonant photons. The basis for this mechanism, proposed by Keller et aL

[71,76], is the establishment of an equilibrium in a hollow cathode discharge

between thermal electrons and the atomic excitation through inelastic and

superelastic collisions between excited atoms and thermal electrons, such that, to a

first approximation, the electron temperature and the atomic excitation temperature

are equal. This results in an increase in the electron temperature and a

corresponding shift of the electron energy distribution toward higher energies,

producing more electrons with sufficient energy for ionization of discharge species.

These two ionization mechanisms are not exclusive to the particular regions of the

glow discharge. The overall formation of charges is certainly a convolution of the

two processes.


Evolution of OG Signals


Upon irradiation of a HCD, the voltage change across the discharge may be

positive or negative. The polarity of these voltage changes is a complex function of

the originating level of the transition, the lamp voltage or current, the region of the

discharge illuminated, the electrode geometries and the pressure of the discharge.

Most observed OG signals are negative in polarity. This includes some signals due

to the buffer gas and all signals due to sputtered cathode atoms.













Negative Voltage Changes

Signals which are due to transitions originating in non-metastable levels

generally lead to negative voltage changes across the discharge. The only case where

this might not be true is that of excitation from a non-metastable level which is

important in maintaining the discharge, to a level from which the probability of

ionization decreases. This is not very common, however. Upon absorption of

resonant photons, atoms are promoted to higher lying energy levels, thereby directly

or indirectly increasing the ionization rate in the discharge. Depending on the region

of the discharge irradiated, the mechanism leading to an increased ionization rate is

different as discussed above. In the negative glow, excitation of atoms in the

discharge leads to an increase of the electron temperature (energy) through inelastic

collisions between slow electrons and the excited atoms74. This shifts the electron

energy distribution to higher energies. In either the cathode dark space or negative

glow region, the end result is that is that as a result of atomic excitation there will

be more electrons with sufficient energy to ionize discharge species, resulting in an

increase in the conductivity of the discharge. Since the lamp is made to operate at

constant current, assuming simple Ohmic behavior, an increase of the conductivity,

or correspondingly a decrease in the resistance of the lamp, will result in a lower

voltage required to maintain the constant current. An example of such a negative

voltage change can be seen in Figure 8. This is an oscilloscope trace, obtained in

this case for the 3s1 2S, --> 3p1 2P3/2 transition of Na upon laser irradiation of the























z


































0
OD
c0











4-
cl
^



4-1
0





















0m
o












IS
o
1














o
r:-










60














43
































I-









A!P/AL 03









44
hollow cathode at 588.995 nm with a laser beam of 10 0pJ. This signal corresponds

to an approximate -2% change in the voltage between the lamp anode and cathode

while the laser is on.

Positive Voltage Changes

The case of positive voltage changes is much more involved and less

understood. All transitions originating from metastable states lead to positive voltage

changes upon irradiation by resonant photonsif those metastable states are important

in the maintenance of the discharge. An example of such a positive signal is given

in Figure 9 for the 3(P2(s) --> 3D3(2p9) transition of Ne. A partial energy level

diagram for Ne is given in Figure 10. Neither of these two states is radiatively

coupled to the Ne ground state. The upper level however, is coupled to other 2p,

levels through electron collisions. These other 2p levels are radiatively coupled to

the ground state indirectly through the non-metastable levels of the Is quartet, 3P1

(ls4) and 1P, (ls2). This was confirmed by monitoring an increase in the emission

from the 2p, and 2po levels when the exciting light was tuned to populate the 2p,

level. Since the maintenance of the discharge is closely tied to the Ne metastable

density, by depleting the metastable population, one effectively reduces the main

mechanisms for ionization, thereby decreasing the ionization rate. This leads to an

increase in the lamp impedance and a corresponding increase in the lamp voltage.

The positive signals evolve over a much larger time period, probably as a result of

indirect depletion of the metastable density because of the parity forbidden direct de-

excitation from the excited 2p, levels to the 'So ground state of neon. The fast


























O

O








I-
o





f0
Cl




A
-4










5.4
Q



I-


0




0
C








C.
I-











4)





0
0


o
4)






L.
ur
ff














1_






























"-0




CD
l)
Ln




E

F-


A!P/Aw 002
































Figure 10. Partial energy level diagram of Ne.











cm-1


173 932





160 000







150 000









130 000



0


Ne'

//////////////////////////////////^^^/////////


4s


-4p


iSo


Ne









49
negative signal is most probably a result of increased ionization by electron collisions

at the beginning of the laser pulse.


Mathematical Treatment of OG Signals


Only a limited mathematical treatment of the collection of charges formed

under the influence of an electric field will be considered here. Complete

mathematical treatments of the various charge formation and collection phenomena

in the glow discharge as a whole, consistent with the present level of understanding

of glow discharges can be found in references [73-77].

Analogous to the case of double resonance laser enhanced ionization in

flames [78], the simplest rate equation model for the OG process involves

saturation of one transition and a linear dependence of the other transition (and

ionization rate) on laser intensity. The production rate of charge density is given by


an-i K I(xt) (11)
at



where I(xt) is the space-time distribution of the laser intensity, K is a constant which

encompasses the various excitation, ionization and deactivation constants and n. and

n, are the electron and ion number densities, respectively. From Poisson's equation

and the applied potential, the effective field, E(x), between the negative glow and the

cathode is given by [74]












E(x) 2-- 1-I (12)

where V0 is the absolute value of the applied potential, and d is the distance between

the cathode and effective anode (see Figure 11). An electric charge created under

the influence of this field is driven to an electrode according to the equation


dv(x, E(x)-j 0v,(xt) (13)
dt m



where

ve electron velocity (m s')

e = electron charge (C)

m = electron mass (kg)

Be = electron collision frequency (s1)

An analogous equation can be written for ions formed. From the principle

of conservation of energy [79], we can obtain an expression for the induced current

signal:


iVo e f Eo(nv neve) d(A6) (14)
A8

where

E = electric field due to the voltage difference V0 (V/m)

vj, = electron and ion velocities, respectively

(m s-1)








































C.)
U2








U,




I...






-cl





C.)










I-i








52












ea)
o





0

a1
rcl









53
A6 volume between the cathode and effective anode where charges

are moving (m3)

i current signal (A).



E0 is constant and is given by


Eo (15)



where d is the width of the dark space. Neglecting the time-dependent behavior of

the current, and accounting for charges with different velocities being present in a

given position x, at the same time t, the integral in equation (14) can be replaced by

a sum over all charged particles;


i E( nv, n v ) (16)
d Re



Simplistically, we can conclude from equation (16) that the total current is

dependent on several factors, including:

1) population of the originating level of the optical transition and the

rates of ionization processes from all primary energy levels involved,

through ni and ne, and

2) the collision frequencies of the charges, through vi and v,.











Double-resonance Optogalvanic (DROG) Effect


Little work has been done until recently on the double-resonance OG effect.

It was first proposed by Vidal [80] in 1980. The DROG scheme serves to increase

the absolute magnitude of the OG signal by approximately one order of magnitude,

in the case of sputtered atoms. At the time of preparation of this dissertation, only

two papers had appeared in the literature on the double-resonance OG effect

[81,82]. Engleman and Keller [81] reported a 10- and 70- times double-resonance

enhancement of sodium and uranium, respectively, in the HCL, while Behrens et aL

[82] reported on the DROG signals of In and Ga.

For optical double-resonance OG spectroscopy, two lasers are chosen with

wavelengths corresponding to two successive transitions in the atom. In the case of

Na (Figure 12), the first laser, A 12, can be chosen at 588.995 nm and the second, 23,

is set at 568.822 nm. If the intensity of A 3 is chosen such that the transition is

saturated then every atom excited into level 2 will be further excited into level 3 with

unity probability. As a result, level one is coupled directly to level three. In a low-

energy environment and an atom with a high first excited level 2, the effective

population of level 3 is orders of magnitude greater when both 12 and A 3 are tuned

to resonance and applied to the atom reservoir, than if only A 12 (or 23) is applied.

This is a very well known effect and has been used extensively in flame laser

enhanced ionization (LEI) [83]. Double-resonance LEI has proven to be one of

the most sensitive spectroscopic techniques available. As discussed in the previous
































Figure 12. Partial energy level diagram of Na.























.86 eV






Tc'z
aj aj











I aI
C i


cm-1


41 450

34 549













16 973

16 956


2 3/2












2p
1/2


S3/2








2 /2
1/2









57
section, this extremely high sensitivity is due mainly to the high energy levels to which

an atom can be promoted by the successive absorption of two resonant photons.

If one of the more important mechanisms in maintaining the discharge is

energy transfer from the excited species to electrons through inelastic collisions, then

by exciting atoms to much higher energy states, a larger energy increase is imparted

to the electron population. This in turn increases the number of electrons with

sufficient energy to cause ionization of the buffer gas. Since the ionization rate

increases with the exponential of the electron energy, it is a significant effect on the

ionization enhancement in the negative glow region of the discharge.














CHAPTER 5
CONSIDERATIONS ON THE INTERACTION OF ATOMS WITH LIGHT



Absorption of Radiation


Upon passing polychromatic light through an assembly of atoms, it is observed

that distinct wavelength components of the light are absorbed by the atoms. The

wavelengths that are absorbed give a qualitative determination of the atoms present

in the assembly and, in certain cases, the amount of light absorbed is directly

proportional to the number of atoms of that kind present in the assembly. In the

case of atomic absorption analysis, and under an explicit set of assumptions, the most

used relation between the density of atoms and the amount of light absorbed is

Beer's Law (17)


# Goe-4 (17)



where o is the flux of the incident photons (photons s-'), t is the transmitted flux

(photons s'), k(A) is the absorption coefficient (cm-') and I is the thickness (cm) of

the absorber. The magnitude of k(A) is dependent on the wavelength of the incident

radiation, and the nature and concentration of the absorber. It is often more

convenient to express the absorption coefficient, k(A), as the product of the atomic









59
number density of absorbers, na (cm3), and the absorption cross section, a (A) (cm2),

of the particular absorption transition. The measured parameter in an atomic

absorption measurement is the absorption factor, a, defined as


S- (18)
00



or the fraction of the incident light that is absorbed. Integrating over the entire

spectral range of the incident radiation, yields


S- (19)




For a narrow spectral line source, the spectral profile of the source is much narrower

than that of the absorption coefficient, and equation (19) reduces to


aL 1 e-(?') (20)



In the limit where the factor a (A)nal << 1, aL is directly proportional to the

absorber number density. If the factor a(A)nl > 1, then aL = 1, and virtually all

resonant photons incident on the atom assembly are absorbed.













Laser Excitation of Atomic Transitions


The interpretation of the interaction of a laser beam with an assembly of

atoms is adequately and most simply described by a rate equations approach.

Referring to Figure 13, one sees that there are many process which the atom can

undergo upon interaction with radiation whose energy exactly corresponds to an

energy difference between energy states of the atom. The rate equations approach

will be described here only for the simplest case of single-resonance excitation by

absorption of one photon with deactivation from the excited level possible by

collisional ionization, stimulated emission, spontaneous emission and collisional

deactivation back to the originating level of the transition (taken to be the ground

electronic state of the atom). Also, as the quantity measured in this work was the

number of ions created during interaction of the laser beam with the atom assembly,

the rate equations will be solved for the change in number of ions with time.

Single-step excitation

The rate equations for excitation of an atom from level 1 to level 2 are:


dn,
nz2n2 (21)

d n(B12Pnp(X12) + k12)- n2(k,~ + A21 + ik + Bp.On))





















03
(U


,1



















C
(l
I














0
4>
*-*












I-
(d
C
4-









co





4C















I-
.0




























(cVfac


I' l











where

A21 rate of spontaneous emission (s-1)

B12 = Einstein coefficient for stimulated absorption (J-' Hz m3)

k21 = rate of collisional deactivation (s-1)

k2i s rate of collisional ionization (s-1)

PA (112) spectral energy density of the laser

(J Hzi1 m3)at wavelength 1 12



Using standard methods to solve these equations and assuming the transition

is not saturated (B12p (X12) < < A21 + k2) yields [84]


n, nr 1 e B12PA (22)
h21 + k + k .


It is clear from this equation that the ratio between the number of ions formed

during the laser pulse and the total atomic number density is dependent on the rate

of collisional ionization, the duration of the laser pulse the Einstein coefficient for

induced absorption and the rates of relaxation from level 2. Also, the ratio is

dependent on the spectral energy density of the laser.

Optical Saturation of an Atomic Transition

The excited state population of an atom can be greatly enhanced relative to

the thermal population of that state by resonant absorption of photons from a laser

beam. In fact, if the spectral irradiance of the laser beam is sufficiently high, the








64
populations of the two levels will be locked together in the ratio of their respective

degeneracies [85]. This spectral energy density is termed the saturation spectral

energy density (J m"3 Hz-1) and is given by [84]




h [A:'+k21+K I +(g2V +klI" -"
p (12)-/8- 7- t (23)




where

h Planck's constant (J s)

ki = rate of recombination (s"1)

gu degeneracy of upper level (dimens.)

gi degeneracy of lower level (dimens.)


If we achieve optical saturation, B12P(X12) > > (A21 + k21 + k2i), then the

rate of induced absorption is much greater than the sum of the deexcitation rates,

and


n,-nT 1 exp -g+g2 r (24)
I' 82









65
Although ni/nT is now independent of the spectral energy density, the ratio is still

directly proportional to the product of k2i& t,. The value of k2i depends on how close

level 2 is to the ionization continuum. Therefore, we can expect that the closer level

2 is to the ionization continuum, the greater the production of ions. However, for

nanosecond pulsed lasers, even saturation of the transition is not expected to be

significant because of the large energy deficit between level 2 and the ionization

continuum resulting from only single-step excitation. If there is a metastable

electronic state present in the atom which can act as a radiation trap, such as in the

case of Pb, then equation (24) becomes




n- n7k. 1 e -g2 (k.+A+ky) At,l (25)
k2A2+k g[g 1+ 2



In this case, even if the laser does saturate the transition, the ionization rate must

now be fast enough to overcome the loss rate from level 2 to the metastable trap.

Two-step Excitation

When two laser beams, tuned to different absorption transitions, are made

spatially and temporally coincident in the discharge, high lying atomic levels can be

efficiently populated. Under such double-resonance conditions, four distinct cases

are readily apparent:

1) linear dependence of ni on the spectral irradiance of both laser beams,









66
2) saturation of the first step, 1-->2 (p(;A12z)>>p),(,.12), and linear

dependence of ni on p,(A.2),

3) linear dependence of ni on pX (12) and saturation of the second step

{(P 23) >> P.23)}, and

4) Saturation of both steps.

Since we are primarily concerned with detection of low levels of photons

corresponding to i x, cases (2) and (4) are not applicable in our system. Either case

(1) or case (3) can be operative, case (3) being preferred.

Assuming that the rate equations approach is valid in our experiments,

Omenetto et aL [84] derived the expressions for the fraction of atoms ionized for

these two cases. Assuming collisional ionization to proceed instantaneously from

level 3, in case (1), where saturation conditions for neither step have been met,


n-ny 1-exp (- Bx()B,3(X3) At (26)
"21 k* l I
the number of ions created during the laser pulse, ni, is dependent on the spectral

energy densities of both laser beams and on all de-excitation processes which deplete

the first excited level, 2.

In the case of resonance ionization detection, the second step will always be

saturated, while the first step will be linear (since the photons being measured are

at A 12). For this case, assuming no collisional or radiative losses from level 2, the

number of ions produced is given by











n,-n [ 1 exp ( -B12PA(X12)At,)] (27)

In equation (27) it is also assumed that the atoms reach a level whose energy defect

with the ionization potential is so low that collisional ionization proceeds

instantaneously. This is a valid assumption in most double resonance excitation cases

of atoms in an energetic environment (e.g. flame, plasma, electrical discharge).

Therefore, in such a case, the number of ions created is directly proportional to the

laser pulse length and the spectral energy density (B12p, ( 12)) of the photon flux of

A12 Also, we see no dependence of ni on the spectral energy density of Az, or on any

de-excitation pathways from level 2, since Bzp, ( 3) > > A21 + k21.

Two conclusions that can be drawn from the above discussion are that, for

significant ionization from the uppermost laser excited level, a two-step excitation

scheme must be used and that, for unity ionization of all atoms excited to level 2 by

absorption of a photon (, 12), the spectral energy density of the second laser, p, (.23),

must be sufficient to saturate the transition.

Assuming some typical values (Table 1) for the variables in equations (26) and

(27) we find that in case of a linear interaction of both steps,


i- 10-2 (28)
nT

while for saturation of the second step


1 (29)
nT






















Values used for calculating ni/nt in eauqtions (26) and (27).


Variable Value Units

B12 1018 J' m3 s-'Hz

B3 1018 -1 m3 s-'Hz

A21 109 s-1

k21 109 s-1

At, 10 s


PA ( 12) 10-5 J m-2 Hz


Table 1.














CHAPTER 6
EXPERIMENTAL



General Experimental Configuration


The general experimental system used for all experiments is shown in Figure

14. A detailed listing of experimental components is given in Table 2. A frequency

doubled Nd:YAG laser (532 nm) operated at 30 Hz was used as the pumping source

for the dual dye laser system. The pump beam was split equally to pump each dye

laser. Typical output energy from the frequency doubled Nd:YAG laser was 240 mJ

per pulse with a pulse duration of 12 ns. The dye laser output was either used

directly for transitions in the visible region of the spectrum or frequency doubled for

UV transitions. In the case of UV transitions, the visible laser light was passed

through a KDP frequency doubling crystal; an autotracking system with angle

matching of the frequency doubled light ensured maximum output intensity while

scanning. The fundamental and second harmonic waves were separated by a

dispersive Pellin-Broca prism. If the laser wavelength was to be scanned, then the

Pellin-Broca prism was replaced with a right angle prism to prevent "walking" of the

beam during scanning. The two harmonics were then separated with a low bandpass

colored filter, which absorbed the visible wavelengths.

























































0
4-







1-
co
E




'-




a




F4
























































.4














Listing of experimental components.


Component Model No. Manufacturer
Nd:YAG laser YG 581-30 Quantel International, Santa
Clara, CA'
Dual Dye Laser TDL 50 Quantel International, Santa
Clara, CA'
Frequency Doublers HD 50 Quantel International, Santa
Clara, CA1
900 Quartz Prisms and Esco Products, Inc., Oak
Quartz Lenses Ridge, NJ
Neutral Density Filters -- Corion Corp., Hollistong, MA
High Power Laser Neutral FN-10,30,10,80 Optics for Research, Caldwell,
Density Filters NJ
Amplifier 113 EG&G PARC, Princeton, NJ
Boxcar Averager Gated SR250 Stanfor Research Systems, Palo
Integrator Alto, CA
Computer Interface SR245 Stanford Research Systems,
Palo Alto, CA
Computer PC-AT Northgate Computer Systems
Digital Oscilloscope 2430A Tektronix, Inc., Beaverton, OR
Chart Recorder D-5000 Houston Instruments, Austin,
TX


1 Now Continuum, Santa Clara, CA.


Table 2.
























Table 2.


--- continued


Component Model Manufacturer
Hollow Cathode Lamp L233 series Hamamatsu Corp.,
(Lamp 1) (Na, Pb and U) Bridgewater, NJ
Galvatron (Mg) L2783-12NE- Hamamatsu Corp.,
Mg Bridgewater, NJ
Hollow Cathode Lamp PMT-20A/N Bertan Associates, Hicksville,
Power Supply NY
Fast Photodiode ET 2000 Electro-Optics Technology,
Fremont, CA
Photodiode for Absorption PIN 10DP-SB United Detector Technologies,
Measurements Hawthorne, CA








74

Two commercially available hollow cathode lamps were used with different

hollow cathode designs. One (lamp 1) was a common HCL used for atomic

absorption analysis (Figure 15). In this lamp only one end of the hollow cathode was

open. The other lamp (lamp 2) (Figure 16) was a "Galvatron" used in wavelength

stabilization of dye lasers by the optogalvanic effect. This lamp is a "T" design in

which both ends of the hollow cathode are open.


Pick-off Circuitry for OG Signal


The circuit used to power the hollow cathode lamps and measure the AC

voltage across the discharge is shown in Figure 17a. It was entirely housed in a

shielded Pomona box (Figure 17b) to reduce pick-up of radio frequency noise. The

high voltage was supplied from a dc-dc high voltage power supply through a current

limiting resistor, RB. This resistor could be made external with the use of an isolated

BNC connector. A variable resistor within a decade resistor box was used for initial

studies. For final experiments, the optimum RB (20 kn) was hard-wired inside the

shielded box. The voltage across the discharge was AC coupled to the detection

electronics by a high voltage coupling capacitor.


One-step Excitation Experiments


For one-step excitation, laser 1 was steered via right angle prisms into the

discharge. The laser beam could be focused, depending on the experiment to be

performed. When the laser was not focused, it was apertured to just fill the hollow


















































E





0
1-1





ol
a














wi
QL
















ji-T-P ^
Eu U



o "7
LI' b

/ 3
I a
































Figure 16. Diagran of a Galvatron (lamp 2).









Cathode Anodes


Optical /
axis




Insulated ^y Insulated
support I support














Negative Dark
glow space


LasezL



Detail of
hollow cathode






























































o
05
So.



fo

S 0



Q-0


Q)*'


t~-











*8


p
on 6








81
cathode volume. Optogalvanic spectra were obtained by scanning the dye laser

wavelength while monitoring the AC voltage across the discharge.


Two-step Excitation Experiments


Lamp 1

The alignment of the lasers when using the single-open ended hollow

cathode is shown schematically in Figure 18. The two laser beams were made to

enter the hollow cathode at a slight angle to the cathode axis. Different focussing

configurations of the two beams were used. Placement of a lens at position 1

allowed only laser 1 to be focused, while placement of the lens in position 2

focused both beams into the hollow cathode. In either case, the position of the lens

was such that the beam(s) was (were) focused at the back surface of the cathode.

Lamp 2

The alignment of the lasers when using the double-open ended hollow

cathode is shown in Figure 19. In this case alignment is much easier since the beams

can be made counter-propagating, entering the cathode from opposite ends. Again,

different focussing configurations were used.


Timing of Laser Beams in Two-step Excitation Experiments


For either lamp, temporal coincidence of the two laser beams in the hollow

cathode was ensured with a fast photodiode (risetime <200 ps). The output of the

photodiode was connected to a fast digitizing oscilloscope. For timing optimization,






























































0

C(



c


0




1-1
o
















od













0.
.O
4a 0

2


<0-
u.


f^
-2 I


0
0 s
0 3
44
cis
pw


MIMI,-


0


u o


Ile






























































0

'-i





0
E













o,
Y.-
I-








c;
Q\























ta)
z


a)
T3
0


C-
u



























cu
ro
0
-4J














oj

cd
u
\d














()
C.)
04
Q,

o
5-4
'a








86

the fast photodiode was placed at the position to be occupied by the HCL Then

laser 1 and laser 2 were alternately made incident on the photodiode. The arrival

time of the two lasers at the photodiode was then noted. The laser pulse arriving

earlier at the photodiode was delayed by way of a prism delay line until temporal

coincidence with the other laser pulse at the photodiode was observed. To avoid

skewing of the measurements toward longer times, care was be taken to ensure

operation of the photodiode was within its linear operating range. Figure 20 is an

oscilloscope trace of the photodiode output. The two traces were obtained

consecutively for laser 1 and laser 2. Temporal coincidence of the two laser beams

was within 1 ns.


Absorption experiments


The experimental setup used to make absorption measurements (with lamp

2 only) is shown in Figure 21. The transmitted laser light was incident on a

photodiode while the laser was scanned through the transition of interest. Linearity

of the photodiode response was insured with a 0.3 neutral density filter. The output

of the photodiode was fed into the input of a boxcar. Output from the boxcar was

then sent to a personal computer and strip chart recorder for subsequent data

analysis.




Full Text

PAGE 1

7+( 2372*$/9$1,& ())(&7 ,1 $ +2//2: &$7+2'( ',6&+$5*( $ 5(621$1&( '(7(&725 )25 9(5< :($. /,*+7 /(9(/6 %\ *,86(33( $1721,2 3(758&&, $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

&RS\ULJKW E\ *LXVHSSH $QWRQLR 3HWUXFFL

PAGE 3

3HU L PLHL JHQLWRUL

PAGE 4

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f PH VRPH RI WKH EODFN PDJLF RI HOHFWURQLFV LV JUHDWO\ LY

PAGE 5

DSSUHFLDWHG VKRXOG JLYH D VSHFLDO WKDQNV WR WKH VHFUHWDULHV -HDQQH .DUDEO\ DQG 6XVDQ &LFFDURQH IRU SXWWLQJ XS ZLWK PH DQG P\ XQLTXH TXHVWLRQV )LQDOO\ ZRXOG OLNH WR WKDQN P\ VRRQ WR EHf ZLIH 1DQF\ :KHWKHU VKH UHDOL]HV LW RU QRW KHU VXSSRUW RI DQG FRQILGHQFH LQ PH KDV DOZD\V VWUHQJWKHQHG P\ KHDUW $W WLPHV ZKHQ VWURQJO\ GRXEWHG P\VHOI DQG P\ DELOLWLHV VKH EURXJKW EDFN LQWR P\ OLIH D SHUVSHFWLYH DQG UHVSHFW IRU P\VHOI WKDW RIWHQ ORVW Y

PAGE 6

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

PAGE 7

(OHFWULFDO 0DLQWHQDQFH RI WKH 'LVFKDUJH &+$37(5 &21&(37 2) 5(621$1&( 0212&+520$725 ,QWURGXFWLRQ 7KHRU\ 3KHQRPHQRORJLFDO 'HVFULSWLRQ RI ,RQL]DWLRQ 0HFKDQLVPV (YROXWLRQ RI 2* 6LJQDOV 1HJDWLYH 9ROWDJH &KDQJHV 3RVLWLYH 9ROWDJH &KDQJHV 0DWKHPDWLFDO 7UHDWPHQW RI 2* 6LJQDOV 'RXEOHUHVRQDQFH 2SWRJDOYDQLF '52*f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

PAGE 8

&+$37(5 5(68/76 $1' ',6&866,21 6RGLXP 2* (IIHFW 'HWHUPLQDWLRQ RI /DPS ,PSHGDQFH (YDOXDWLRQ RI &ROOLVLRQDO ,RQL]DWLRQ 5DWH &RQVWDQWV E\ WKH 2* (IIHFW 7ZRVWHS 2* HIIHFW RI 1D /HDG 2* (IIHFW LQ WKH +&/ 1HRQ 2* (IIHFW LQ WKH +&/ (OHFWURQLF &RQILJXUDWLRQ RI 1H 2QHVWHS 1HRQ DQG 8UDQLXP 2* (IIHFW &DVH &DVH &DVH &DVH 1HRQ 2* 6LJQDO 'HSHQGHQFH RQ /DPS &XUUHQW 'RXEOHUHVRQDQFH 2* (IIHFW RI 1H 2SWLPL]DWLRQ RI %R[FDU *DWH 3RVLWLRQ $OLJQPHQW RI /DVHU %HDPVf LQ WKH +ROORZ &DWKRGH ,RQL]DWLRQ :LWKLQ WKH 1HJDWLYH *ORZ ,RQL]DWLRQ :LWKLQ WKH 'DUN 6SDFH 7ZRVWHS (QKDQFHPHQW RI 1H 2* (IIHFW (YDOXDWLRQ RI 1H 2* LQ WKH +&/ DV D 6HQVLWLYH 3KRWRQ 'HWHFWRU &+$37(5 ),1$/ &200(176 6XPPDU\ )XWXUH :RUN 5()(5(1&( /,67 %,2*5$3+,&$/ 6.(7&+ YLLL

PAGE 9

/,67 2) 7$%/(6 7DEOH 9DOXHV XVHG IRU FDOFXODWLQJ Q MQ[ LQ HTXDWLRQV f DQG f 7DEOH /LVWLQJ RI H[SHULPHQWDO FRPSRQHQWV 7DEOH ([SHULPHQWDO YDOXHV IRU GHWHUPLQLQJ QW LQ HTXDWLRQ f 7DEOH 9DOXHV XVHG WR FDOFXODWH Yc DQG YH LQ HTXDWLRQ f L[

PAGE 10

/,67 2) ),*85(6 )LJXUH 5HVRQDQFH PRQRFKURPDWRU SURSRVHG E\ 6XOOLYDQ DQG :DOVK >@ )LJXUH 5HVRQDQFH LRQL]DWLRQ GHWHFWRU )LJXUH 1RUPDOL]HG /RUHQW]LDQ OLQH SURILOH )LJXUH 1RUPDOL]HG *DXVVLDQ OLQH SURILOH )LJXUH (OHFWULFDO UHJLRQV RI D GF GLVFKDUJH >@ )LJXUH 9ROWDJH GLVWULEXWLRQ DFURVV D GF JORZ GLVFKDUJH )LJXUH (OHFWURQ HQHUJ\ GLVWULEXWLRQ DFURVV D GF JORZ GLVFKDUJH )LJXUH 2VFLOORVFRSH WUDFH RI WKH QHJDWLYH 2* VLJQDO IRU WKH V6 Sr 3 WUDQVLWLRQ RI 1D )LJXUH 2VFLOORVFRSH WUDFH RI WKH SRVLWLYH 2* VLJQDO IRU WKH 3 Vf Sf WUDQVLWLRQ RI 1H )LJXUH 3DUWLDO HQHUJ\ OHYHO GLDJUDP RI 1H )LJXUH (OHFWULF ILHOG GLVWULEXWLRQ DFURVV WKH GF JORZ GLVFKDUJH )LJXUH 3DUWLDO HQHUJ\ OHYHO GLDJUDP RI 1D )LJXUH 3RVVLEOH H[FLWDWLRQGHH[FLWDWLRQ SURFHVV LQ DQ DWRP )LJXUH *HQHUDO H[SHULPHQWDO FRQILJXUDWLRQ )LJXUH 'LDJUDP RI D FRPPRQ +&/ ODPS f )LJXUH 'LDJUDP RI D *DOYDWURQ VHHWKURXJK +&/f ODPS f )LJXUH Df 3LFNRII FLUFXLW IRU PHDVXULQJ 2* VLJQDOV Ef 'LDJUDP RI KRXVLQJ IRU SLFNRII HOHFWURQLFV DQG ODPS KROGHU )LJXUH $OLJQPHQW RI ODVHUVf WKURXJK ODPS )LJXUH $OLJQPHQW RI ODVHUVf WKURXJK ODPS [

PAGE 11

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

PAGE 12

)LJXUH /RJORJ SORW RI )LJXUH )LJXUH 6DWXUDWLRQ FXUYH IRU QP DEVRUSWLRQ RI 8 )LJXUH /RJORJ SORW RI )LJXUH )LJXUH 3URSRVHG H[FLWDWLRQLRQL]DWLRQ VFKHPH IRU QP DEVRUSWLRQ RI 8 )LJXUH 3ORW RI UHODWLYH ODVHU LQGXFHG LPSHGDQFH FKDQJH YV ODPS FXUUHQW )LJXUH %R[FDU JDWH SRVLWLRQ FRQVLGHUDWLRQV )LJXUH 2QHVWHS LRQL]DWLRQ VLJQDO REVHUYHG LQ FDWKRGH GDUN VSDFH )LJXUH &RQYROXWLRQ RI LRQL]DWLRQ VLJQDOV IURP FDWKRGH GDUN VSDFH DQG QHJDWLYH JORZ UHJLRQ )LJXUH 7ZRVWHS HQKDQFHPHQW RI 1H 2* VLJQDO LQ +&/ Df 2VFLOORVFRSH WUDFH RI RQHVWHS H[FLWDWLRQ 2* VLJQDO RI 1H JURXQG VWDWHf Ef 2VFLOORVFRSH WUDFH RI RQHVWHS H[FLWDWLRQ 2* VLJQDO RI 1H H[FLWHG VWDWHf Ff 2VFLOORVFRSH WUDFH RI WZRVWHS H[FLWDWLRQ HQKDQFHPHQW RI 2* VLJQDO RI 1H )LJXUH 6FDQ VKRZLQJ VLPXOWDQHRXV UHFRUGLQJ RI DEVRUSWLRQ RI $ DQG 2* VLJQDO IRU GHWHUPLQDWLRQ RI D )LJXUH &DOLEUDWLRQ FXUYH IRU 1H 5,' LQ WKH +&/ )LJXUH /RJORJ SORW RI )LJXUH )LJXUH 3ORW RI 9UPVf YV ODPS FXUUHQW n )LJXUH 3ORW RI VLJQDOWRQRLVH RI 1H 5,' YV ODPS FXUUHQW )LJXUH 6XPPDU\ ILJXUH RI UHVXOWV [LL

PAGE 13

$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ 2372*$/9$1,& ())(&7 ,1 $ +2//2: &$7+2'( /$03 $ 6(16,7,9( '(7(&725 )25 9(5< :($. /,*+7 /(9(/6 %\ *,86(33( $1721,2 3(758&&, '(&(0%(5 &KDLUSHUVRQ -DPHV :LQHIRUGQHU 0DMRU 'HSDUWPHQW &KHPLVWU\ %RWK RQH DQG WZRVWHS H[FLWDWLRQ RSWRJDOYDQLF 2*f HIIHFWV LQ WZR FRPPHUFLDOO\ DYDLODEOH KROORZ FDWKRGH ODPSV DUH VWXGLHG (OHPHQWV VWXGLHG DUH VRGLXP OHDG XUDQLXP DQG QHRQ )RXU GLIIHUHQW H[FLWDWLRQLRQL]DWLRQ PHFKDQLVPV ZHUH REVHUYHG E\ WKH 2* HIIHFW DQG DUH GLVFXVVHG 7KHVH LQFOXGH f RQHVWHS H[FLWDWLRQ IROORZHG E\ FROOLVLRQDO LRQL]DWLRQ f RQHVWHS H[FLWDWLRQ IROORZHG E\ SKRWRLRQL]DWLRQ f WZRVWHS H[FLWDWLRQ WKURXJK D YLUWXDO OHYHO IROORZHG E\ FROOLVLRQDO LRQL]DWLRQ DQG f WZRVWHS H[FLWDWLRQ WKURXJK D YLUWXDO OHYHO IROORZHG E\ SKRWRLRQL]DWLRQ 7KH WZRVWHS H[FLWDWLRQ WR D UHDO OHYHO IROORZHG E\ FROOLVLRQ DQG SKRWRLRQL]DWLRQ ZHUH DOVR REVHUYHG IRU 1H 7ZRVWHS H[FLWDWLRQ HQKDQFHPHQWV LQ WKH 2* HIIHFW RI 1D 3E DQG 1H UHODWLYH WR WKH RQHVWHS H[FLWDWLRQ FDVHV ZHUH GHWHUPLQHG [LLL

PAGE 14

7KH XVH RI D FRXSOHG VWHSZLVH WZRVWHS H[FLWDWLRQ RI 1H LQ WKH KROORZ FDWKRGH ODPS ZDV HYDOXDWHG DV D VHQVLWLYH GHWHFWRU IRU YHU\ ORZ OLJKW OHYHOV 7KH ILUVW WUDQVLWLRQ VWXGLHG ZDV WKH 3OVf 'Sf DW D ZDYHOHQJWK RI QP 7KH H[FLWHG VWDWH WUDQVLWLRQ FRXSOHG WR WKH ILUVW WUDQVLWLRQ ZDV WKH 'Sf Gf WUDQVLWLRQ DW QP 7KH OLPLWLQJ H[SHULPHQWDO QRLVH ZDV GHWHUPLQHG WR EH WKH VKRW QRLVH RI WKH KROORZ FDWKRGH ODPS 8QGHU RSWLPL]HG FRQGLWLRQV WKH H[SHULPHQWDOO\ DWWDLQHG PLQLPXP GHWHFWDEOH HQHUJ\ DQG QXPEHU RI SKRWRQV ZHUH [ n DQG [ SKRWRQV UHVSHFWLYHO\ 7KH OLPLWV RI GHWHFWLRQ FRUUHVSRQGLQJ WR WKH WKHRUHWLFDO VKRW QRLVH OLPLW LQ WKH H[SHULPHQWDO V\VWHP ZHUH [ n DQG [ SKRWRQV [LY

PAGE 15

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

PAGE 16

:LWK WKH GLJLWDO PHWKRG FRQWULEXWLRQV IURP SKRWRHOHFWURQV DUH UHVROYHG LQ WLPH VR WKDW WKH VLJQDOV LQ WKH IRUP RI HOHFWURQ SXOVHV DUH GHWHFWHG E\ PHDQV RI D SXOVH FRXQWLQJ V\VWHP 7KLV WHFKQLTXH LV WKH RQH RI FKRLFH ZKHQ FRQFHUQHG ZLWK WKH PHDVXUHPHQW RI XOWUDORZ OLJKW OHYHOV 3KRWRQ GHWHFWRUV $ GHWHFWRU RI RSWLFDO UDGLDWLRQ LV GHILQHG E\ WKH &RPPLVVLRQ ,QWHUQDWLRQDOH GH Of(FODLUDJH >@ DV D GHYLFH LQ ZKLFK LQFLGHQW RSWLFDO UDGLDWLRQ SURGXFHV D PHDVXUDEOH SK\VLFDO HIIHFW 7ZR FODVVHV RI GHWHFWRUV RI RSWLFDO UDGLDWLRQ SURGXFH D PHDVXUDEOH VLJQDO E\ RQH RI WZR SULPDU\ GHWHFWLRQ PHFKDQLVPV WKH SKRWRHOHFWULF HIIHFW SKRWRQ GHWHFWRUVf DQG WKH WKHUPDO HIIHFW WKHUPDO GHWHFWRUVf 3KRWRQ GHWHFWRUV DUH WKH PRVW FRPPRQ LQ RSWLFDO VSHFWURVFRS\ IRU WKH PHDVXUHPHQW RI ORZ OLJKW OHYHOV 3KRWRPXOWLSOLHUV 307Vf DUH WKH VWDQGDUG SKRWRQ GHWHFWRU LQ FRPPHUFLDO VSHFWURVFRSLF LQVWUXPHQWV 7KHLU EDVLV RI RSHUDWLRQ LV WKH JHQHUDWLRQ RU FKDQJH RI DQ HOHFWULF VLJQDO E\ DQ H[WHUQDO SKRWRHOHFWULF HIIHFW LQ ZKLFK D SKRWRHOHFWURQ LV HPLWWHG E\ D FDWKRGH DQG FDSWXUHG E\ D VHFRQG HOHFWURGH RU G\QRGHf 7KH LPSRUWDQW IHDWXUH RI WKH 307 LV WKH G\QRGH V\VWHP ZKLFK FRQVLVWV RI HOHFWURGHV FRYHUHG ZLWK VSHFLDO PDWHULDOV ZKLFK HPLW YDULRXV VHFRQGDU\ HOHFWURQV SHU LQFLGHQW SULPDU\ HOHFWURQ 7KH QXPEHU RI G\QRGHV LQ 307V UDQJHV IURP UHVXOWLQJ LQ D WRWDO JDLQ RU DPSOLILFDWLRQ RI WKH FDWKRGLF SKRWRLQGXFHG FXUUHQW RI XS WR RU PRUH

PAGE 17

7KH GHWHFWLRQ RI OLJKW KDV XQGHUJRQH D JUHDW PHWDPRUSKRVLV VLQFH ZKHQ 6LU :LOOLDP +HUVFKHO >@ XVHG DQ RUGLQDU\ WKHUPRPHWHU WR PHDVXUH WKH LQWHQVLW\ RI OLJKW SDVVLQJ WKURXJK GLIIHUHQW ILOWHUV ,Q 1RELOL DQG 0HOORQL >@ GHYHORSHG D WKHUPRFRXSOH IRU WKH TXDQWLWDWLRQ RI OLJKW LQWHQVLW\ 6DPXHO 3LHUSRQW /DQJOH\ >@ LQ GHYHORSHG WKH ERORPHWHU ZKLFK ZDV WLPHV PRUH VHQVLWLYH WKDQ 0HOORQLf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

PAGE 18

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

PAGE 19

7KH UHVROXWLRQ RQ WKH RWKHU KDQG LV D PHDVXUH RI WKH DELOLW\ RI WKH PRQRFKURPDWRU WR GLVSHUVH LQFLGHQW OLJKW FRPSRVHG RI PDQ\ GLIIHUHQW ZDYHOHQJWKV LQWR LWV FRPSRQHQW ZDYHOHQJWKV ,W LV JLYHQ E\ WKH SURGXFW RI WKH ZLGWK RI WKH HQWUDQFH RU H[LW VOLW DVVXPHG WR EH HTXDO LQ WKLV FDVHf DQG WKH UHFLSURFDO OLQHDU GLVSHUVLRQ RI WKH GLVSHUVLQJ HOHPHQW LQ WKH PRQRFKURPDWRU 7KH SURGXFW RI WKH WKURXJKSXW DQG UHVROXWLRQ LV FRQVWDQW IRU D JLYHQ PRQRFKURPDWRU +RZHYHU VLQFH UHVROXWLRQ LPSURYHV ZLWK QDUURZHU VOLW ZLGWKV DQG WKURXJKSXW LQFUHDVHV ZLWK ZLGHU VOLW ZLGWKV WKH VSHFWURVFRSLVW LV FRQVWDQWO\ IDFHG ZLWK D FKRLFH RI FRPSURPLVH FRQGLWLRQV LQYROYLQJ UHVROXWLRQ DQG WKURXJKSXW )RU D VLQJOHVWDJH PRQRFKURPDWRU WKH WKURXJKSXW LV RQ WKH RUGHU RI ff )RU PXOWLSOHVWDJH PRQRFKURPDWRUV WKH RYHUDOO WKURXJKSXW LV D SURGXFW RI WKH WKURXJKSXW RI HDFK VWDJH 6R IRU D WULSOHVWDJH PRQRFKURPDWRU WKH IUDFWLRQ RI LQFLGHQW OLJKW WKDW UHDFKHV WKH 307 LV RQO\ nn 7KLV LQYHUVH UHODWLRQ EHWZHHQ WKURXJKSXW DQG UHVROXWLRQ LV RQH RI WKH PDMRU OLPLWDWLRQV RI XVLQJ FRQYHQWLRQDO GHWHFWRUV 7KH RWKHU PDMRU OLPLWDWLRQ LV D UHVXOW RI WKH ORZ TXDQWXP HIILFLHQF\ RI WKH SKRWRFDWKRGHV RI 307V 7KH TXDQWXP HIILFLHQF\ LV GHILQHG >@ DV WKH UDWLR RI WKH QXPEHU RI HOHPHQWDU\ HYHQWV HJ SKRWRHOHFWURQVf FRQWULEXWLQJ WR WKH GHWHFWRU RXWSXW WR WKH QXPEHU RI LQFLGHQW SKRWRQV )RU PRVW FDWKRGH PDWHULDOV WKH TXDQWXP HIILFLHQF\ LV YHU\ ORZ RQ WKH EHVW VHQVLWL]HG FRPPHUFLDO SKRWRVXUIDFHV WKH PD[LPXP \LHOG UHSRUWHG LV DV KLJK DV RQH HOHFWURQ IRU WKUHH OLJKW TXDQWD LQFLGHQW RQ WKH SKRWRFDWKRGH $Q LGHDO SKRWRGHWHFWRU KDV D TXDQWXP HIILFLHQF\ RI LH HYHU\ LQFLGHQW SKRWRQ SURGXFHV RQH

PAGE 20

SKRWRHOHFWURQ $OO SUDFWLFDO SKRWRFDWKRGH PDWHULDOV KDYH TXDQWXP HIILFLHQFLHV RI OHVV WKDQ 7KHUHIRUH D 307 FRXOG QHYHU GHWHFW D VLQJOH SKRWRQ IURP WKH VRXUFH $V GHVFULEHG EHORZ UHVRQDQFH VSHFWURPHWHUV RIIHU WKH DGYDQWDJHV RYHU PRQRFKURPDWRU307 GHWHFWLRQ V\VWHPV RI KLJK VSHFWUDO UHVROXWLRQ n QPf LQ FRQMXQFWLRQ ZLWK D KLJK RSWLFDO WKURXJKSXW !f ,QWHQW RI GLVVHUWDWLRQ 7KH SUHVHQW ZRUN ZDV LQWHQGHG WR HYDOXDWH DQG FKDUDFWHUL]H D SKRWRQ GHWHFWRU EDVHG RQ WKH RSWRJDOYDQLF HIIHFW LQ D FRPPHUFLDO KROORZ FDWKRGH ODPS 2SWLFDO WUDQVLWLRQV RI VRGLXP OHDG DQG QHRQ WKH LQHUW ILOOHU JDV ZHUH FRQVLGHUHG IRU WKH GHWHFWRU %RWK VLQJOH DQG GRXEOHUHVRQDQFH H[FLWDWLRQ VFKHPHV ZHUH XVHG $OVR VHYHUDO VLQJOHVWHS WUDQVLWLRQV RI 1H DQG 8 ZHUH VWXGLHG LQ WHUPV RI H[FLWDWLRQ LRQL]DWLRQ PHFKDQLVPV

PAGE 21

&+$37(5 &21&(37 2) 5(621$1&( 0212&+520$725 +LVWRULFDO %DFNJURXQG 7KH UHTXLUHPHQWV RI KLJK VHQVLWLYLW\ DQG ZDYHOHQJWK VHOHFWLYLW\ ZHUH DOUHDG\ PHW LQ WKURXJK WKH VLPSOH DQG HIIHFWLYH WHFKQLTXHV IRU GLVFULPLQDWLQJ UHVRQDQFH UDGLDWLRQ RI VSHFLILF HOHPHQWV ZKLFK ZHUH EDVHG RQ WKH UHVRQDQFH DEVRUSWLRQ RI SKRWRQV DQG WKHLU VXEVHTXHQW UHHPLVVLRQ LQ DWRPLF YDSRUV RI WKH HOHPHQW >@ 6XFK D GHYLFH LV WHUPHG D UHVRQDQFH PRQRFKURPDWRU 50f DQG ZDV ILUVW SURSRVHG LQ DV DQ DFFHVVRU\ IRU PRGHUQ VSHFWURVFRS\ E\ 6XOOLYDQ DQG :DOVK >@ 7KH EDVLF FRQFHSW RI WKH 50 DV D GHWHFWRU IRU DWRPLF DEVRUSWLRQ VSHFWURVFRS\ LV VKRZQ LQ )LJXUH 7KH OLJKW IURP VHYHUDO VSHFWUDO ODPSV LV FROOLPDWHG DQG SDVVHG WKURXJK WKH IODPH 7KH UDGLDWLRQ WUDQVPLWWHG LV WKHQ SDVVHG LQWR VHYHUDO 50V (DFK VSHFWUDO ODPS RU HOHPHQW RI LQWHUHVWf KDV D FRUUHVSRQGLQJ 50 ,Q 6XOOLYDQ DQG :DOVKfV FDVH WKH 50V ZHUH VLPSO\ KLJK FXUUHQW KROORZ FDWKRGH ODPSV WR SURYLGH WKH UHTXLVLWH DWRPLF YDSRU GHQVLW\ ZLWK PLQLPDO HPLVVLRQ 8SRQ DEVRUSWLRQ RI UHVRQDQFH UDGLDWLRQ E\ WKH 50 JURXQG VWDWH DQDO\WH DWRPV ZRXOG EH H[FLWHG DQG VXEVHTXHQWO\ UHHPLW WKH UDGLDWLRQ ZKLFK ZDV REVHUYHG DW ULJKW DQJOHV WR WKH LQFRPLQJ UDGLDWLRQ (DFK 50

PAGE 22

)LJXUH 5HVRQDQFH PRQRFKURPDWRU SURSRVHG E\ 6XOOLYDQ DQG :DOVK >@ IRU DWRPLF DEVRUSWLRQ VSHFWURVFRS\

PAGE 23

$720,& 63(&75$/ /$036 &21&$9( *5$7,1* $ $ )/$0( U 3+272&(//6 R? /= ),/7(56 &====@ ),/7(56 U79A\L 92

PAGE 24

ZRXOG WKHQ UHVSRQG VHOHFWLYHO\ WR WKH WUDQVPLWWHG LQWHQVLW\ RI WKH FRUUHVSRQGLQJ DQDO\VLV ODPS 6LQFH UHVRQDQFH VSHFWURPHWHUV EDVHG RQ VHYHUDO RSWLFDO DQG HOHFWULFDO SULQFLSOHV KDYH EHHQ VWXGLHG LQFOXGLQJ IOXRUHVFHQFH LRQL]DWLRQ DQG RSWRDFRXVWLF WHFKQLTXHV $ YDULHW\ RI DWRP FHOOV KDYH DOVR EHHQ VWXGLHG IRU UHVRQDQFH GHWHFWLRQ $PRQJ WKHVH DUH IODPHV >@ ODVHU HQKDQFHG LRQL]DWLRQ /(,f KROORZ FDWKRGH ODPSV >@ 2SWRJDOYDQLF HIIHFW 2*(f KLJKIUHTXHQF\ VSHFWUDO ODPSV >@ DQG IXUQDFHV >@ 5HVRQDQFH PRQRFKURPDWRUV KRZHYHU KDYH EHHQ XVHG PDLQO\ IRU DEVRUSWLRQ H[SHULPHQWV 5HVRQDQFH 6SHFWURPHWHUV 5HVRQDQFH VSHFWURPHWHUV RIIHU VHYHUDO LPSRUWDQW DGYDQWDJHV RYHU FRQYHQWLRQDO VSHFWURPHWHUV 7KH\ SRVVHVV DQ LQKHUHQWO\ KLJK VSHFWUDO UHVROXWLRQ n QPf D ODUJH VROLG DQJOH RI FROOHFWLRQ RI WKH LQFRPLQJ OLJKW XS WR Q VUf ORZ LQWULQVLF QRLVH DQG KLJK TXDQWXP HIILFLHQF\ QDPHO\ WKH FDSDELOLW\ RI VLQJOH SKRWRQ GHWHFWLRQ 7KLV LV LQ FRQWUDVW WR SKRWRPXOWLSOLHU WXEHV ZKLFK KDYH PD[LPXP FDWKRGH HIILFLHQFLHV RI DERXW b PHDQLQJ WKDW DW EHVW SKRWRQV DUH UHTXLUHG RQ WKH DYHUDJH IRU WKH GHWHFWRU WR UHFRUG DQ HYHQW $OVR DV VWDWHG DERYH VHYHUDO GLIIHUHQW VSHFWURVFRSLF WHFKQLTXHV PD\ EH XVHG DV WKH EDVLV IRU D 50 7ZR RI WKH PRVW VWXGLHG DUH IOXRUHVFHQFH IOXRUHVFHQFH UHVRQDQFH VSHFWURPHWHU )56f DQG DWRPLF LRQL]DWLRQ UHVRQDQFH LRQL]DWLRQ GHWHFWRU 5,'f $WRPLF LRQL]DWLRQ LV XVHG KHUH DV D JHQHULF

PAGE 25

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f OLJKW 6XFK D UHVRQDQFH VSHFWURPHWHU ZDV XVHG E\ %ROJHU >@ IRU WKH UHFRUGLQJ RI ZHDN 5DPDQ VFDWWHULQJ ,Q WKLV H[SHULPHQW D QV N: SXOVHG WXQDEOH G\H ODVHU ZLWK D EDQGZLGWK RI FPn 6; QPf ZDV XVHG WR LOOXPLQDWH WKH VDPSOH 7KH ZDYHOHQJWK RI WKH ODVHU ZDV FKRVHQ VR WKDW WKH 5DPDQ VFDWWHUHG OLJKW ZDV DURXQG QP 7KLV OLJKW ZDV XVHG WR H[FLWH &V DWRPV 7KH IOXRUHVFHQFH RI WKH &V DWRPV DW QP ZDV WKHQ PHDVXUHG DV WKH DQDO\WLFDO VLJQDO 7KH GHWHFWRU VHQVLWLYLW\ ZDV IRXQG WR EH DSSUR[LPDWHO\ RUGHUV RI PDJQLWXGH KLJKHU WKDQ D GLVSHUVLRQ V\VWHP ZLWK D FRQYHQWLRQDO GHWHFWRU 7KH ILUVW IOXRUHVFHQFH UHVRQDQFH VSHFWURPHWHU )56f ZRUNLQJ ZLWK WUDQVLWLRQV IURP H[FLWHG VWDWHV ZDV SURSRVHG DQG VWXGLHG E\ *HOEZDFKV HW DO >@ 7KH\ H[FLWHG 1D DWRPV LQ WKH )56 WR WKH 3 VWDWH $ QPf ZLWK D G\H ODVHU 5DGLDWLRQ IURP D [HQRQ DUF ODPS DQG 0P ZDV WKHQ DEVRUEHG E\ WKH H[FLWHG 1D SURPRWLQJ LW WR WKH 6 DQG OHYHOV UHVSHFWLYHO\ 7KH\ WKHQ REVHUYHG IOXRUHVFHQFH RI WKH 1D LQ WKH YLVLEOH UHJLRQ DW ZDYHOHQJWKV RI DQG

PAGE 26

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f PHWKRGV KDYH EHHQ SURYHQ WR EH YHU\ VHQVLWLYH VSHFWURVFRSLF WHFKQLTXHV >@ 7KH\ DUH EDVHG RQ WKH UHFRUGLQJ RI FKDUJHG SDUWLFOHV ZKLFK DUH IRUPHG LQ WKH DWRP FHOO XSRQ DEVRUSWLRQ RI UHVRQDQFH UDGLDWLRQ IROORZHG E\ VXEVHTXHQW LRQL]DWLRQ RI WKH H[FLWHG DWRPV E\ YDULRXV SURFHVVHV ,Q WKH H[WUHPH FDVH RI GHWHFWLQJ VLQJOH FKDUJHV SURSRUWLRQDO JDV FRXQWHUV DUH XVHG )RU EXON PHDVXUHPHQW RI D ODUJH QXPEHU RI FKDUJHV IRUPHG WKH LPSHGDQFH RU FXUUHQW FKDQJH DFURVV WKH DWRP FHOO LV PHDVXUHG /LPLWV RI GHWHFWLRQ LQ QRUPDO DWPRVSKHULF SUHVVXUH DWRPL]HUV DUH LQ WKH ORZ QJP/ WR SJP/ RU SJ WR IJ DEVROXWH GHWHFWLRQ OLPLWVf >@ 96 /HWRNKRY >@ ZDV WKH ILUVW WR GUDZ DWWHQWLRQ WR WKH IDFW WKDW

PAGE 27

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n ZKLOH 6PLWK HW DO >@ DUH WKH RQO\ ZRUNHUV WR UHFRUG D 5DPDQ VSHFWUXP ZLWK D 5,' 7KHLU PLQLPXP GHWHFWDEOH HQHUJ\ FDQ EH HVWLPDWHG DV DSSUR[LPDWHO\ n DW QP 7KH FDVH RI WKH 5,' )LJXUH f LV YHU\ VLPLODU WR WKDW RI WKH )56 5DGLDWLRQ KY 5HPLWWHG IURP WKH VDPSOH 6$f LV FRQYH\HG E\ DQ RSWLFDO V\VWHP LQWR WKH 5,' ZKLFK FRQWDLQV D KLJK FRQFHQWUDWLRQ RI DWRPLF YDSRU ,Q WKH VLPSOH FDVH RI GHWHFWLQJ DWRPLF HPLVVLRQ RU UHVRQDQFH IOXRUHVFHQFH WKH DWRPLF YDSRU LQ WKH 5,' LV WKH VDPH DV WKH DQDO\WH RI LQWHUHVW LQ WKH VDPSOH $EVRUSWLRQ RI WKH UDGLDWLRQ XSRQ SDVVLQJ LQWR WKH 5,' FDXVHV D PHDVXUDEOH FKDQJH LQ WKH HOHFWULFDO SURSHUWLHV RI WKH 5,' )RU GHWHFWLRQ RI VFDWWHUHG UDGLDWLRQ HJ 5DPDQ VFDWWHUf WKH 5' EHFRPHV PXFK PRUH IDYRUDEOH DQG YHUVDWLOH WR XVH WKDQ FRQYHQWLRQDO GLVSHUVLYH LQVWUXPHQWV ZLWK SKRWRPXOWLSOLHU GHWHFWLRQ ,Q 5DPDQ VSHFWURVFRS\ IRU H[DPSOH RQH LV LQWHUHVWHG LQ PHDVXULQJ WKH LQWHQVLW\ RI VFDWWHUHG UDGLDWLRQ VKLIWHG LQ HQHUJ\ E\ D FKDUDFWHULVWLF DPRXQW IURP WKH FHQWUDO IUHTXHQF\ RI WKH H[FLWLQJ OLJKW 7KH

PAGE 28

)LJXUH 6FKHPDWLF RI D UHVRQDQFH LRQL]DWLRQ GHWHFWRU 7KH RSWLFDO SURFHVVHV RFFXUULQJ LQ WKH VDPSOH DWRPL]HU 6$f DQG UHVRQDQFH LRQL]DWLRQ GHWHFWRU 5,'f DUH JLYHQ RQ WKH ULJKW VLGH RI WKH GUDZLQJ

PAGE 29

/$6(56 5,'

PAGE 30

IUHTXHQF\ VKLIW LV FKDUDFWHULVWLF IRU D SDUWLFXODU VFDWWHUHU DQG LV JLYHQ E\ $Yr 6WRNHV f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f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

PAGE 31

WUDQVLWLRQV RI WKH 5,' HOHPHQW $Q\WKLQJ RXWVLGH RI WKH DEVRUSWLRQ EDQGZLGWK RI WKH 5,' HOHPHQW ZLOO QRW EH DEVRUEHG DQG ZLOO WKHUHIRUH QRW SURGXFH D VLJQDO /LQH%URDGHQLQJ 0HFKDQLVPV 7KH DEVRUSWLRQ UHVSRQVHf EDQGZLGWK RI WKH 5,' HOHPHQW ZLOO GHSHQG RQ WKH RSHUDWLYH EURDGHQLQJ PHFKDQLVP RI WKH DWRPLF OLQH LQ WKH 5,' 7KLV PDNHV WKH 5,' LQKHUHQWO\ LQVHQVLWLYH WR SUREOHPDWLF VFDWWHUHG OLJKW $WRPLF OLQHV DUH QRW WUXO\ PRQRFKURPDWLF DQG GR SRVVHVV D ILQLWH IUHTXHQF\ RU ZDYHOHQJWKf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

PAGE 32

WKH ORZHU L DQG XSSHU M HQHUJ\ VWDWHV SDUWLFLSDWLQJ LQ WKH DWRPLF H[FLWDWLRQ KDYH D ILQLWH OLIHWLPH DQG WKLV JLYHV ULVH WR XQFHUWDLQWLHV LQ WKH HQHUJ\ RI ERWK VWDWHV DFFRUGLQJ WR WKH +HLVHQEHUJ XQFHUWDLQW\ UHODWLRQ 8VXDOO\ WKH H[WHQW RI WKH OLQHn EURDGHQLQJ LV GHWHUPLQHG E\ WKH PXFK VKRUWHU OLIHWLPH RI WKH XSSHU VWDWH RI WKH WUDQVLWLRQ 7KLV LV FDOOHG OLIHWLPH RU QDWXUDO EURDGHQLQJ 7KH ):+0 GXH WR QDWXUDO EURDGHQLQJ LV VPDOOHU WKDQ WKDW GXH WR RWKHU EURDGHQLQJ PHFKDQLVPV H[FHSW LQ H[WUHPH FDVHV HJ WUDQVLWLRQV WR DXWRLRQL]LQJ OHYHOV RI WKH DWRPf 7KH VSHFWUDO SURILOH RI D QDWXUDOO\ EURDGHQHG OLQH LV GHVFULEHG E\ D /RUHQW]LDQ 7KH QRUPDOL]HG VSHFWUDO SURILOH GXH WR QDWXUDO EURDGHQLQJ 6A LV JLYHQ E\ 6 f Y}f $Yf ZKHUH $YQ V ):+0 RI WKH QDWXUDOO\ EURDGHQHG OLQH +]f Y P IUHTXHQF\ DW WKH OLQH FHQWHU +]f 7KH ZLGWK RI D QDWXUDOO\ EURDGHQHG OLQH EHWZHHQ WZR UHDO HQHUJ\ VWDWHV RI WKH DWRP VHH EHORZf LV RQ WKH RUGHU RI +] ,Q ZDYHOHQJWK XQLWV WKH ):+0 $$1 Pf LV H[SUHVVHG DV $$f F 1 f

PAGE 33

ZKHUH ; F ZDYHOHQJWK DW WKH OLQH FHQWHU Pf VSHHG RI OLJKW P Vnf )RU H[DPSOH IRU 1D DW QP $$1m[O2n P RU SP &ROOLVLRQDO %URDGHQLQJ 7KH OLQH SURILOH LV DOVR LQIOXHQFHG E\ FROOLVLRQV RI WKH DWRP RI LQWHUHVW ZLWK RWKHU DWRPV RI WKH VDPH NLQG +ROW]PDUN EURDGHQLQJf RU ZLWK IRUHLJQ VSHFLHV /RUHQW] EURDGHQLQJf 7KH DPRXQW RI EURDGHQLQJ FDXVHG E\ FROOLVLRQV LQFUHDVHV ZLWK WKH FRQFHQWUDWLRQ RI FROOLVLRQ SDUWQHUV DQG KHQFH FROOLVLRQDO EURDGHQLQJ LV VRPHWLPHV FDOOHG SUHVVXUH EURDGHQLQJ &ROOLVLRQV ZKLFK OHDYH WKH DWRP LQ WKH VDPH HQHUJ\ VWDWH DGLDEDWLF FROOLVLRQVf KDYH D PRUH SURQRXQFHG EURDGHQLQJ HIIHFW WKDQ FROOLVLRQV WKDW OHDYH WKH DWRP LQ D GLIIHUHQW HQHUJ\ VWDWH GLDEDWLF FROOLVLRQVf 7KH ):+0 RI WKH VSHFWUDO GLVWULEXWLRQ UHVXOWLQJ IURP DGLDEDWLF FROOLVLRQV $YD +]f LV JLYHQ E\ f ZKHUH D Q ; D RSWLFDO FURVV VHFWLRQ IRU DGLDEDWLF FROOLVLRQDO EURDGHQLQJ FPf GHQVLW\ RI FROOLVLRQ SDUWQHUV FPnf UHGXFHG PDVV RI FROOLVLRQ SDUWQHUV Jf

PAGE 34

7KH WRWDO QRUPDOL]HG VSHFWUDO SURILOH 6f/ IRU FROOLVLRQDO EURDGHQLQJ LV DOVR /RUHQW]LDQ DQG LV JLYHQ E\ HTXDWLRQ f E\ UHSODFLQJ WKH QDWXUDO ):+0 $Y1 ZLWK WKH FROOLVLRQDO ):+0 $YD 7KH W\SLFDO ):+0 RI D FROOLVLRQDOO\ EURDGHQHG OLQH LV RQ WKH RUGHU RI [ n P RU SP ,I QDWXUDO DQG FROOLVLRQDO EURDGHQLQJ DUH DVVXPHG WR EH PXWXDOO\ LQGHSHQGHQW WKH UHVXOWLQJ ):+0 RI WKH /RUHQW]LDQ SURILOH LV $Y $YF $Yf f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f LV JLYHQ E\ $Y ,Q fN7 P Y & f

PAGE 35

ZKHUH N %ROW]PDQQ FRQVWDQW .nf P DWRPLF ZHLJKW Jf Y P FHQWUDO IUHTXHQF\ +]f 7KH QRUPDOL]HG VSHFWUDO GLVWULEXWLRQ 6f' LV GHVFULEHG LQ WKLV FDVH E\ D *DXVVLDQ UHODWLRQ DQG LV JLYHQ E\ ?' I2 MfY Y f§ H[S $ Y '?I $ Y f 7\SLFDO 'RSSOHU EURDGHQHG OLQHZLGWKV DUH RQ WKH RUGHU RI [ n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f DQG f DQG DVVXPLQJ D ):+0 RI HDFK OLQH RI n P 7KH VHOHFWLYLW\ RI WKH 5,' XQGHU HDFK

PAGE 36

)LJXUH 1RUPDOL]HG /RUHQW]LDQ OLQH SURILOH REWDLQHG XVLQJ HTXDWLRQ f DQG DVVXPLQJ D ):+0 RI SP

PAGE 37

5HODWLYH DEVRUSWLRQ 1! 2ZDYHOHQJWK VKLIW QPf

PAGE 39

:DYHOHQJWK VKLIW QPf 1!

PAGE 40

RI WKHVH FRQGLWLRQV FDQ EH UHDGLO\ REWDLQHG IURP WKHVH SORWV )RU H[DPSOH LQ WKH FDVH RI D 'RSSOHU EURDGHQHG OLQH WKH IUDFWLRQ RI WKH LQFLGHQW OLJKW IDOOLQJ ZLWKLQ WKH DEVRUSWLRQ OLQHZLGWK RI WKH GHWHFWRU HOHPHQW IDOOV WR f FRPSDUDEOH WR WKH VWUD\ OLJKW UHMHFWLRQ RI D JRRG GRXEOHPRQRFKURPDWRU DW D ZDYHOHQJWK RQO\ [ n P RU SP IURP WKH FHQWUDO OLQH HYDOXDWHG DW QPf 7KH FROOLVLRQDOO\ EURDGHQHG OLQH RQ WKH RWKHU KDQG KDV ORQJ WDLOV JLYLQJ D IUDFWLRQDO DEVRUSWLRQ RI f DV IDU RXW DV QP DZD\ IURP WKH FHQWUDO OLQH HYDOXDWHG DW QPf 7KHUHIRUH D ORZ SUHVVXUH FHOO LQ ZKLFK FROOLVLRQDO EURDGHQLQJ LV QRW WKH GRPLQDQW EURDGHQLQJ PHFKDQLVP LV HVVHQWLDO IRU KLJKHVW ZDYHOHQJWK VHOHFWLYLW\ 2QH RWKHU DGYDQWDJH RI WKH 5,' LV WKDW WKHUH DUH QR OLPLWLQJ DSHUWXUHV OLPLWLQJ WKH RSWLFDO WKURXJKSXW RI WKH GHWHFWRU 7KLV DOORZV IRU D JUHDWHU IUDFWLRQ RI WKH VDPSOH OLJKW WR EH FROOHFWHG DQG LPDJHG LQWR WKH 5,' XS WR b $ JRRG WZR VWDJH PRQRFKURPDWRU ZLOO KDYH DQ RSWLFDO WKURXJKSXW RI rnb 7KH SURGXFW RI WKURXJKSXW DQG VHOHFWLYLW\ LV FRQVWDQW IRU DQ\ RQH V\VWHP &OHDUO\ WKH KLJKHU WKH YDOXH RI WKLV SURGXFW WKH PRUH VHOHFWLYH DQG VHQVLWLYH LV WKH GHWHFWRU 7KH 50 LV WKH RQO\ SKRWRQ GHWHFWRU IRU ZKLFK WKH GHWHFWLRQ HIILFLHQF\ QHHG QRW EH FRPSURPLVHG IRU EHWWHU UHVROXWLRQ RU VHOHFWLYLW\

PAGE 41

&+$37(5 2372*$/9$1,& ())(&7 ,QWURGXFWLRQ 7KH RSWRJDOYDQLF 2*f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

PAGE 42

$QDWRP\ RI D *ORZ 'LVFKDUJH 7KH W\SLFDO VFKHPDWLF UHSUHVHQWDWLRQ RI D GF JORZ GLVFKDUJH LV VKRZQ LQ )LJXUH WDNHQ IURP 1DVVHU >@f 7KH QRUPDO JORZ GLVFKDUJH FRQVLVWV RI GLVWLQFW UHJLRQV f FDWKRGH GDUN VSDFH f QHJDWLYH JORZ f )DUDGD\ GDUN VSDFH f SRVLWLYH FROXPQ DQG f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

PAGE 43

)LJXUH (OHFWULFDO UHJLRQV RI D GF GLVFKDUJH >@

PAGE 44

VW &$7+2'(

PAGE 45

)LJXUH 9ROWDJH GLVWULEXWLRQ DFURVV D GF JORZ GLVFKDUJH

PAGE 46

&DWKRGH 6KHDWK 9ROWDJH $QRGH 6KHDWK 9ROWDJH X! WR

PAGE 47

)LJXUH (OHFWURQ HQHUJ\ GLVWULEXWLRQ DFURVV D GF JORZ GLVFKDUJH

PAGE 48

9Sf \ &DWKRGH $QRGH X! A

PAGE 49

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r Ha $r Ha f DQG DVVRFLDWLYH LRQL]DWLRQ RI PHWDVWDEOHV > S@ $r $r A $r $ Ha f &ROOLVLRQDO LRQL]DWLRQ RI JURXQG VWDWH DWRPV RI WKH LQHUW JDV E\ HOHFWURQ LPSDFW LV QRW YHU\ SUREDEOH GXH WR WKH KLJK HQHUJ\ H9 IRU 1Hf UHTXLUHG ,RQL]DWLRQ RI VSXWWHUHG FDWKRGH DWRPV FDQ RFFXU E\ DQ\ RI WKH DERYH PHFKDQLVPV DV ZHOO DV 3HQQLQJ LRQL]DWLRQ f

PAGE 50

;r 0 ; 0r Ha f ZKHUH ; UHSUHVHQWV D EXIIHU JDV DWRP DQG GLUHFW LRQL]DWLRQ RI JURXQG VWDWH VSXWWHUHG DWRPV VLQFH PXFK ORZHU HOHFWURQ HQHUJLHV DUH UHTXLUHG H9f ,W LV LQWHUHVWLQJ WR H[DPLQH KRZ SKRWRLQGXFHG WUDQVLWLRQV FDQ DIIHFW WKHVH LRQL]DWLRQ SURFHVVHV LI $ LV 1H IRU H[DPSOH 8QGHU QRUPDO JORZ GLVFKDUJH FRQGLWLRQV WKH HOHFWURQ HQHUJ\ GLVWULEXWLRQ DSSUR[LPDWHV D 0D[ZHOO%ROW]PDQQ GLVWULEXWLRQ DQG IDOOV UDSLGO\ DERYH H9 >@ ZKHUH LQHODVWLF FROOLVLRQV GRPLQDWH H[FLWDWLRQ RI H[FLWHG HOHFWURQLF VWDWHV DQG LRQL]DWLRQ RI 1Hf 6HYHUDO SRLQWV VKRXOG EH QRWHG )LUVW WKH QHRQ PHWDVWDEOH VWDWHV 1HfP ZLOO EH HIILFLHQWO\ SRSXODWHG E\ HOHFWURQQHRQ JURXQG VWDWH FROOLVLRQV VLQFH VLQJOHWWULSOHW H[FLWDWLRQ IXQFWLRQV SHDN QHDU WKH WKUHVKROG YROWDJH IRU GLVFKDUJH PDLQWHQDQFH >@ 7KH VXEVFULSW P LV XVHG WR GHQRWH QHRQ LQ WKH PHWDVWDEOH VWDWH 6HFRQG FROOLVLRQDO LRQL]DWLRQ RI PHWDVWDEOH QHRQ E\ HOHFWURQV >SURFHVV f DERYH@ ZKRVH FURVVVHFWLRQ SHDNV DW DERXW H9 >@ FDQ EH H[SHFWHG WR EHFRPH LQFUHDVLQJO\ LPSRUWDQW DW KLJK GLVFKDUJH FXUUHQWV )LQDOO\ WKH HOHFWURQQHRQ FROOLVLRQ IUHTXHQF\ a Vnf H[FHHGV ERWK WKH QHRQQHRQ FROOLVLRQ IUHTXHQF\ Vnf DW QRUPDO +&/ SUHVVXUHV W\SLFDOO\ WRUUf DQG WKH UHFLSURFDO RI WKH VKRUWHVW UDGLDWLYH OLIHWLPHV IRU WKH H[FLWHG 1H DWRPV >@ 2QH FDQ FRQFOXGH IURP WKH DERYH WKDW UHJDUGOHVV RI WKH SUHFLVH PHFKDQLVP RI LRQL]DWLRQ PHWDVWDEOH 1H DWRPV SOD\ D FHQWUDO UROH LQ WKH PDLQWHQDQFH RI WKH GLVFKDUJH DV GLVFXVVHG E\ &KDSPDQ >@ 7KLV ZDV DOVR VXSSRUWHG H[SHULPHQWDOO\ E\ WKH ZRUN RI 6P\WK HW DO >@ DQG +HVV DQG +DUULVRQ >@ ,Q

PAGE 51

WKHVH H[SHULPHQWV WKH 1H FRQFHQWUDWLRQ ZDV PRQLWRUHG ZLWK D PDVV VSHFWURPHWHU 6XEVWDQWLDO FKDQJHV LQ WKH 1H GHQVLW\ ZHUH GHWHFWHG DQG ZHUH IRXQG WR FRUUHODWH TXDOLWDWLYHO\ ZLWK WKH SKRWRQLQGXFHG YROWDJH FKDQJHV 2QH FDQ WKHUHIRUH H[SHFW WKDW WKH G\QDPLFV YROWDJH DQG FXUUHQW FKDUDFWHULVWLFV RI WKH GLVFKDUJH ZRXOG EH VHQVLWLYH WR HYHQ VPDOO SHUWXUEDWLRQV RI WKH 1HrP SRSXODWLRQ $Q LPPHGLDWH UHDOL]DWLRQ JDLQHG IURP FRQWHPSRUDU\ OLWHUDWXUH RQ JORZ GLVFKDUJHV LQ JHQHUDO DQG PRUH VSHFLILFDOO\ KROORZ FDWKRGH GLVFKDUJHV LV WKDW VXFK GLVFKDUJHV DUH G\QDPLF HQYLURQPHQWV ZKLFK GR QRW UHDGLO\ OHQG WKHPVHOYHV WR SUHFLVH GHWDLOHG PRGHOLQJ ,Q IDFW D XQLILHG DQG JHQHUDOO\ DJUHHG XSRQ TXDQWLWDWLYHf WKHRU\ RI WKH PHFKDQLVPV ZKLFK DUH RSHUDWLYH LQ WKH JORZ GLVFKDUJH KDV \HW WR EH SUHVHQWHG

PAGE 52

&+$37(5 2372*$/9$1,& ())(&7 ,1 7+( +2//2: &$7+2'( ',6&+$5*( ,QWURGXFWLRQ $ JUHDW GHDO RI H[SHULPHQWDO ZRUN KDV EHHQ SHUIRUPHG LQ D YDULHW\ RI GLVFKDUJHV PDQ\ RI ZKLFK ZHUH KRPHPDGH >@ DQG FRQWDLQHG DQ DVVRUWPHQW RI YDSRUV VXFK DV >@ UDUH JDVHV VXFK DV .U >@ +H >@ $U >@ DQG 1H >@ DQG QXPHURXV PL[WXUHV WKHUHRI 2I PRVW SUDFWLFDO LQWHUHVW WR WKH DQDO\WLFDO FKHPLVW KRZHYHU LV WKH XVH RI FRPPHUFLDOO\ DYDLODEOH KROORZ FDWKRGH GLVFKDUJHV +&'Vf RU ODPSV +&/Vf LQ 2* H[SHULPHQWV 8QIRUWXQDWHO\ NQRZOHGJH RI WKH RSHUDWLQJ FKDUDFWHULVWLFV DQG SDUDPHWHUV RI +&'V LV ODUJHO\ HPSLULFDO *HQHUDO FRQFOXVLRQV KRZHYHU FDQ EHHQ GUDZQ IURP SUHYLRXV ZRUN DERXW WKH 2* HIIHFWV LQ JORZ GLVFKDUJHV )LUVWO\ WKH LPSHGDQFH FKDQJHV QRUPDOO\ LQGXFHG E\ WKH LQWURGXFWLRQ RI D FROOLPDWHG EHDP RI OLJKW WKDW LV UHVRQDQW ZLWK DQ DEVRUSWLRQ WUDQVLWLRQ RI D GLVFKDUJH VSHFLHV LQWR D GLVFKDUJH DUH ODUJH DV KLJK DV b RI WKH TXLHVFHQW YROWDJHf DQG DUH HDVLO\ PHDVXUHG 6HFRQGO\ LW LV ZHOO NQRZQ WKDW WKHVH LPSHGDQFH FKDQJHV FDQ EH SRVLWLYH RU QHJDWLYH

PAGE 53

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

PAGE 54

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

PAGE 55

1HJDWLYH 9ROWDJH &KDQJHV 6LJQDOV ZKLFK DUH GXH WR WUDQVLWLRQV RULJLQDWLQJ LQ QRQPHWDVWDEOH OHYHOV JHQHUDOO\ OHDG WR QHJDWLYH YROWDJH FKDQJHV DFURVV WKH GLVFKDUJH 7KH RQO\ FDVH ZKHUH WKLV PLJKW QRW EH WUXH LV WKDW RI H[FLWDWLRQ IURP D QRQPHWDVWDEOH OHYHO ZKLFK LV LPSRUWDQW LQ PDLQWDLQLQJ WKH GLVFKDUJH WR D OHYHO IURP ZKLFK WKH SUREDELOLW\ RI LRQL]DWLRQ GHFUHDVHV 7KLV LV QRW YHU\ FRPPRQ KRZHYHU 8SRQ DEVRUSWLRQ RI UHVRQDQW SKRWRQV DWRPV DUH SURPRWHG WR KLJKHU O\LQJ HQHUJ\ OHYHOV WKHUHE\ GLUHFWO\ RU LQGLUHFWO\ LQFUHDVLQJ WKH LRQL]DWLRQ UDWH LQ WKH GLVFKDUJH 'HSHQGLQJ RQ WKH UHJLRQ RI WKH GLVFKDUJH LUUDGLDWHG WKH PHFKDQLVP OHDGLQJ WR DQ LQFUHDVHG LRQL]DWLRQ UDWH LV GLIIHUHQW DV GLVFXVVHG DERYH ,Q WKH QHJDWLYH JORZ H[FLWDWLRQ RI DWRPV LQ WKH GLVFKDUJH OHDGV WR DQ LQFUHDVH RI WKH HOHFWURQ WHPSHUDWXUH HQHUJ\f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r 3 WUDQVLWLRQ RI 1D XSRQ ODVHU LUUDGLDWLRQ RI WKH

PAGE 56

)LJXUH 2VFLOORVFRSH WUDFH RI WKH QHJDWLYH 2* VLJQDO IRU WKH V 6 Sr 3 WUDQVLWLRQ RI 1D

PAGE 57

P9G L 7LPH -86 G 9 f

PAGE 58

KROORZ FDWKRGH DW QP ZLWK D ODVHU EHDP RIm P7KLV VLJQDO FRUUHVSRQGV WR DQ DSSUR[LPDWH b FKDQJH LQ WKH YROWDJH EHWZHHQ WKH ODPS DQRGH DQG FDWKRGH ZKLOH WKH ODVHU LV RQ 3RVLWLYH 9ROWDJH &KDQJHV 7KH FDVH RI SRVLWLYH YROWDJH FKDQJHV LV PXFK PRUH LQYROYHG DQG OHVV XQGHUVWRRG $OO WUDQVLWLRQV RULJLQDWLQJ IURP PHWDVWDEOH VWDWHV OHDG WR SRVLWLYH YROWDJH FKDQJHV XSRQ LUUDGLDWLRQ E\ UHVRQDQW SKRWRQV LI WKRVH PHWDVWDEOH VWDWHV DUH LPSRUWDQW LQ WKH PDLQWHQDQFH RI WKH GLVFKDUJH $Q H[DPSOH RI VXFK D SRVLWLYH VLJQDO LV JLYHQ LQ )LJXUH IRU WKH 3OVf 'Sf WUDQVLWLRQ RI 1H $ SDUWLDO HQHUJ\ OHYHO GLDJUDP IRU 1H LV JLYHQ LQ )LJXUH 1HLWKHU RI WKHVH WZR VWDWHV LV UDGLDWLYHO\ FRXSOHG WR WKH 1H JURXQG VWDWH 7KH XSSHU OHYHO KRZHYHU LV FRXSOHG WR RWKHU Sc OHYHOV WKURXJK HOHFWURQ FROOLVLRQV 7KHVH RWKHU S OHYHOV DUH UDGLDWLYHO\ FRXSOHG WR WKH JURXQG VWDWH LQGLUHFWO\ WKURXJK WKH QRQPHWDVWDEOH OHYHOV RI WKH ,V TXDUWHW 3M OVf DQG 3M OVf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n H[FLWDWLRQ IURP WKH H[FLWHG Sc OHYHOV WR WKH b JURXQG VWDWH RI QHRQ 7KH IDVW

PAGE 59

)LJXUH 2VFLOORVFRSH WUDFH RI WKH SRVLWLYH 2* VLJQDO IRU WKH 3 OVf Sf WUDQVLWLRQ RI 1H

PAGE 60

$ 3$Z

PAGE 61

)LJXUH 3DUWLDO HQHUJ\ OHYHO GLDJUDP RI 1H

PAGE 62

FP 222 222 222 1H V S 2 1H

PAGE 63

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f RQ ODVHU LQWHQVLW\ 7KH SURGXFWLRQ UDWH RI FKDUJH GHQVLW\ LV JLYHQ E\ GQH[Wf GW ,[Wf f ZKHUH ,[Wf LV WKH VSDFHWLPH GLVWULEXWLRQ RI WKH ODVHU LQWHQVLW\ LV D FRQVWDQW ZKLFK HQFRPSDVVHV WKH YDULRXV H[FLWDWLRQ LRQL]DWLRQ DQG GHDFWLYDWLRQ FRQVWDQWV DQG QH DQG Qc DUH WKH HOHFWURQ DQG LRQ QXPEHU GHQVLWLHV UHVSHFWLYHO\ )URP 3RLVVRQfV HTXDWLRQ DQG WKH DSSOLHG SRWHQWLDO WKH HIIHFWLYH ILHOG ([f EHWZHHQ WKH QHJDWLYH JORZ DQG WKH FDWKRGH LV JLYHQ E\ >@

PAGE 64

([f 9f Gf f ZKHUH 9 LV WKH DEVROXWH YDOXH RI WKH DSSOLHG SRWHQWLDO DQG G LV WKH GLVWDQFH EHWZHHQ WKH FDWKRGH DQG HIIHFWLYH DQRGH VHH )LJXUH f $Q HOHFWULF FKDUJH FUHDWHG XQGHU WKH LQIOXHQFH RI WKLV ILHOG LV GULYHQ WR DQ HOHFWURGH DFFRUGLQJ WR WKH HTXDWLRQ GYH[Wf GW ([f 3YIFUf P f ZKHUH 9H HOHFWURQ YHORFLW\ P Vnf H HOHFWURQ FKDUJH &f P HOHFWURQ PDVV NJf H HOHFWURQ FROOLVLRQ IUHTXHQF\ Vnf $Q DQDORJRXV HTXDWLRQ FDQ EH ZULWWHQ IRU LRQV IRUPHG )URP WKH SULQFLSOH RI FRQVHUYDWLRQ RI HQHUJ\ >@ ZH FDQ REWDLQ DQ H[SUHVVLRQ IRU WKH LQGXFHG FXUUHQW VLJQDO ZKHUH ( L9 H (RIOL9L a QH9H! Af f ƒ HOHFWULF ILHOG GXH WR WKH YROWDJH GLIIHUHQFH 9 9Pf HOHFWURQ DQG LRQ YHORFLWLHV UHVSHFWLYHO\ P Vnf

PAGE 65

)LJXUH (OHFWULF ILHOG GLVWULEXWLRQ DFURVV WKH GF JORZ GLVFKDUJH

PAGE 66

&DWKRGH (IIHFWLYH DQRGH /U? 1!

PAGE 67

$6 YROXPH EHWZHHQ WKH FDWKRGH DQG HIIHFWLYH DQRGH ZKHUH FKDUJHV DUH PRYLQJ Pf L FXUUHQW VLJQDO $f ( LV FRQVWDQW DQG LV JLYHQ E\ (f f ZKHUH G LV WKH ZLGWK RI WKH GDUN VSDFH 1HJOHFWLQJ WKH WLPHGHSHQGHQW EHKDYLRU RI WKH FXUUHQW DQG DFFRXQWLQJ IRU FKDUJHV ZLWK GLIIHUHQW YHORFLWLHV EHLQJ SUHVHQW LQ D JLYHQ SRVLWLRQ [ DW WKH VDPH WLPH W WKH LQWHJUDO LQ HTXDWLRQ f FDQ EH UHSODFHG E\ D VXP RYHU DOO FKDUJHG SDUWLFOHV rn ( QL9L a QH9H f f 8 QF 6LPSOLVWLFDOO\ ZH FDQ FRQFOXGH IURP HTXDWLRQ f WKDW WKH WRWDO FXUUHQW LV GHSHQGHQW RQ VHYHUDO IDFWRUV LQFOXGLQJ f SRSXODWLRQ RI WKH RULJLQDWLQJ OHYHO RI WKH RSWLFDO WUDQVLWLRQ DQG WKH UDWHV RI LRQL]DWLRQ SURFHVVHV IURP DOO SULPDU\ HQHUJ\ OHYHOV LQYROYHG WKURXJK Qc DQG QH DQG WKH FROOLVLRQ IUHTXHQFLHV RI WKH FKDUJHV WKURXJK Yc DQG YH f

PAGE 68

'RXEOHUHVRQDQFH 2SWRJDOYDQLF '52* (IIHFW /LWWOH ZRUN KDV EHHQ GRQH XQWLO UHFHQWO\ RQ WKH GRXEOHUHVRQDQFH 2* HIIHFW ,W ZDV ILUVW SURSRVHG E\ 9LGDO >@ LQ 7KH '52* VFKHPH VHUYHV WR LQFUHDVH WKH DEVROXWH PDJQLWXGH RI WKH 2* VLJQDO E\ DSSUR[LPDWHO\ RQH RUGHU RI PDJQLWXGH LQ WKH FDVH RI VSXWWHUHG DWRPV $W WKH WLPH RI SUHSDUDWLRQ RI WKLV GLVVHUWDWLRQ RQO\ WZR SDSHUV KDG DSSHDUHG LQ WKH OLWHUDWXUH RQ WKH GRXEOHUHVRQDQFH 2* HIIHFW >@ (QJOHPDQ DQG .HOOHU >@ UHSRUWHG D DQG WLPHV GRXEOHUHVRQDQFH HQKDQFHPHQW RI VRGLXP DQG XUDQLXP UHVSHFWLYHO\ LQ WKH +&/ ZKLOH %HKUHQV HW DO >@ UHSRUWHG RQ WKH '52* VLJQDOV RI ,Q DQG *D )RU RSWLFDO GRXEOHUHVRQDQFH 2* VSHFWURVFRS\ WZR ODVHUV DUH FKRVHQ ZLWK ZDYHOHQJWKV FRUUHVSRQGLQJ WR WZR VXFFHVVLYH WUDQVLWLRQV LQ WKH DWRP ,Q WKH FDVH RI 1D )LJXUH f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f >@ 'RXEOHUHVRQDQFH /(, KDV SURYHQ WR EH RQH RI WKH PRVW VHQVLWLYH VSHFWURVFRSLF WHFKQLTXHV DYDLODEOH $V GLVFXVVHG LQ WKH SUHYLRXV

PAGE 69

)LJXUH 3DUWLDO HQHUJ\ OHYHO GLDJUDP RI 1D

PAGE 71

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

PAGE 72

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fV /DZ f I!RHm: f ZKHUH LV WKH IOX[ RI WKH LQFLGHQW SKRWRQV SKRWRQV Vnf LV WKH WUDQVPLWWHG IOX[ SKRWRQV Vnf N;f LV WKH DEVRUSWLRQ FRHIILFLHQW FPnf DQG LV WKH WKLFNQHVV FPf RI WKH DEVRUEHU 7KH PDJQLWXGH RI N;f LV GHSHQGHQW RQ WKH ZDYHOHQJWK RI WKH LQFLGHQW UDGLDWLRQ DQG WKH QDWXUH DQG FRQFHQWUDWLRQ RI WKH DEVRUEHU ,W LV RIWHQ PRUH FRQYHQLHQW WR H[SUHVV WKH DEVRUSWLRQ FRHIILFLHQW N;f DV WKH SURGXFW RI WKH DWRPLF

PAGE 73

QXPEHU GHQVLW\ RI DEVRUEHUV Q FPnf DQG WKH DEVRUSWLRQ FURVV VHFWLRQ D $f FPf RI WKH SDUWLFXODU DEVRUSWLRQ WUDQVLWLRQ 7KH PHDVXUHG SDUDPHWHU LQ DQ DWRPLF DEVRUSWLRQ PHDVXUHPHQW LV WKH DEVRUSWLRQ IDFWRU D GHILQHG DV D f RU WKH IUDFWLRQ RI WKH LQFLGHQW OLJKW WKDW LV DEVRUEHG ,QWHJUDWLQJ RYHU WKH HQWLUH VSHFWUDO UDQJH RI WKH LQFLGHQW UDGLDWLRQ \LHOGV IL!8OHr:QfG; f )RU D QDUURZ VSHFWUDO OLQH VRXUFH WKH VSHFWUDO SURILOH RI WKH VRXUFH LV PXFK QDUURZHU WKDQ WKDW RI WKH DEVRUSWLRQ FRHIILFLHQW DQG HTXDWLRQ f UHGXFHV WR FOO f ,Q WKH OLPLW ZKHUH WKH IDFWRU D$fQD/ LV GLUHFWO\ SURSRUWLRQDO WR WKH DEVRUEHU QXPEHU GHQVLW\ ,I WKH IDFWRU R$fQ! WKHQ D/ DQG YLUWXDOO\ DOO UHVRQDQW SKRWRQV LQFLGHQW RQ WKH DWRP DVVHPEO\ DUH DEVRUEHG

PAGE 74

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f $OVR DV WKH TXDQWLW\ PHDVXUHG LQ WKLV ZRUN ZDV WKH QXPEHU RI LRQV FUHDWHG GXULQJ LQWHUDFWLRQ RI WKH ODVHU EHDP ZLWK WKH DWRP DVVHPEO\ WKH UDWH HTXDWLRQV ZLOO EH VROYHG IRU WKH FKDQJH LQ QXPEHU RI LRQV ZLWK WLPH 6LQJOHVWHS H[FLWDWLRQ 7KH UDWH HTXDWLRQV IRU H[FLWDWLRQ RI DQ DWRP IURP OHYHO WR OHYHO DUH GQL aGW f A f GQ :OA3[Af fAL A A A3 Aff GW

PAGE 75

)LJXUH 3RVVLEOH H[FLWDWLRQGHH[FLWDWLRQ SURFHVV LQ DQ DWRP UHVXOWLQJ IURP LOOXPLQDWLRQ ZLWK D ODVHU EHDP

PAGE 77

ZKHUH $ UDWH RI VSRQWDQHRXV HPLVVLRQ Vnf % V (LQVWHLQ FRHIILFLHQW IRU VWLPXODWHG DEVRUSWLRQ -n +] Pf NO UDWH RI FROOLVLRQDO GHDFWLYDWLRQ Vnf NL UDWH RI FROOLVLRQDO LRQL]DWLRQ Vnf S$ ;f VSHFWUDO HQHUJ\ GHQVLW\ RI WKH ODVHU +] PnfDW ZDYHOHQJWK ; 8VLQJ VWDQGDUG PHWKRGV WR VROYH WKHVH HTXDWLRQV DQG DVVXPLQJ WKH WUDQVLWLRQ LV QRW VDWXUDWHG %S$$f $ Nf \LHOGV >@ Q L H[S ? $U A A AL f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

PAGE 78

SRSXODWLRQV RI WKH WZR OHYHOV ZLOO EH ORFNHG WRJHWKHU LQ WKH UDWLR RI WKHLU UHVSHFWLYH GHJHQHUDFLHV >@ 7KLV VSHFWUDO HQHUJ\ GHQVLW\ LV WHUPHG WKH VDWXUDWLRQ VSHFWUDO HQHUJ\ GHQVLW\ Pn +]ff DQG LV JLYHQ E\ >@ S[ Df 0 $?NNL? ^ $O 8L$ Nc! -L f ZKHUH K V 3ODQFNfV FRQVWDQW Vf Nc UDWH RI UHFRPELQDWLRQ Vnf JX GHJHQHUDF\ RI XSSHU OHYHO GLPHQVf J GHJHQHUDF\ RI ORZHU OHYHO GLPHQVf ,I ZH DFKLHYH RSWLFDO VDWXUDWLRQ %S$;f ! $ N NLf WKHQ WKH UDWH RI LQGXFHG DEVRUSWLRQ LV PXFK JUHDWHU WKDQ WKH VXP RI WKH GHH[FLWDWLRQ UDWHV DQG QLaQ7 H[S J ? O -f

PAGE 79

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f EHFRPHV QLAL W\$ANA H[S AL$LNcf $Wc 6L 6 f ,Q WKLV FDVH HYHQ LI WKH ODVHU GRHV VDWXUDWH WKH WUDQVLWLRQ WKH LRQL]DWLRQ UDWH PXVW QRZ EH IDVW HQRXJK WR RYHUFRPH WKH ORVV UDWH IURP OHYHO WR WKH PHWDVWDEOH WUDS 7ZRVWHS ([FLWDWLRQ :KHQ WZR ODVHU EHDPV WXQHG WR GLIIHUHQW DEVRUSWLRQ WUDQVLWLRQV DUH PDGH VSDWLDOO\ DQG WHPSRUDOO\ FRLQFLGHQW LQ WKH GLVFKDUJH KLJK O\LQJ DWRPLF OHYHOV FDQ EH HIILFLHQWO\ SRSXODWHG 8QGHU VXFK GRXEOHUHVRQDQFH FRQGLWLRQV IRXU GLVWLQFW FDVHV DUH UHDGLO\ DSSDUHQW f OLQHDU GHSHQGHQFH RI QW RQ WKH VSHFWUDO LUUDGLDQFH RI ERWK ODVHU EHDPV

PAGE 80

f VDWXUDWLRQ RI WKH ILUVW VWHS a! S$$ f! !S$V$ f DQG OLQHDU GHSHQGHQFH RI QW RQ S$$f f OLQHDU GHSHQGHQFH RI Q[ RQ S$$f DQG VDWXUDWLRQ RI WKH VHFRQG VWHS ^3Df ! 3 D Af`f DQA f 6DWXUDWLRQ RI ERWK VWHSV 6LQFH ZH DUH SULPDULO\ FRQFHUQHG ZLWK GHWHFWLRQ RI ORZ OHYHOV RI SKRWRQV FRUUHVSRQGLQJ WR $ FDVHV f DQG f DUH QRW DSSOLFDEOH LQ RXU V\VWHP (LWKHU FDVH f RU FDVH f FDQ EH RSHUDWLYH FDVH f EHLQJ SUHIHUUHG $VVXPLQJ WKDW WKH UDWH HTXDWLRQV DSSURDFK LV YDOLG LQ RXU H[SHULPHQWV 2PHQHWWR HW DO >@ GHULYHG WKH H[SUHVVLRQV IRU WKH IUDFWLRQ RI DWRPV LRQL]HG IRU WKHVH WZR FDVHV $VVXPLQJ FROOLVLRQDO LRQL]DWLRQ WR SURFHHG LQVWDQWDQHRXVO\ IURP OHYHO LQ FDVH f ZKHUH VDWXUDWLRQ FRQGLWLRQV IRU QHLWKHU VWHS KDYH EHHQ PHW QLaQ7 H[S Ar3 fA 3 rAf $U f  WKH QXPEHU RI LRQV FUHDWHG GXULQJ WKH ODVHU SXOVH Q[ LV GHSHQGHQW RQ WKH VSHFWUDO HQHUJ\ GHQVLWLHV RI ERWK ODVHU EHDPV DQG RQ DOO GHH[FLWDWLRQ SURFHVVHV ZKLFK GHSOHWH WKH ILUVW H[FLWHG OHYHO ,Q WKH FDVH RI UHVRQDQFH LRQL]DWLRQ GHWHFWLRQ WKH VHFRQG VWHS ZLOO DOZD\V EH VDWXUDWHG ZKLOH WKH ILUVW VWHS ZLOO EH OLQHDU VLQFH WKH SKRWRQV EHLQJ PHDVXUHG DUH DW $ f )RU WKLV FDVH DVVXPLQJ QR FROOLVLRQDO RU UDGLDWLYH ORVVHV IURP OHYHO WKH QXPEHU RI LRQV SURGXFHG LV JLYHQ E\

PAGE 81

QQ W > H[3 A3[AOAAf@ f ,Q HTXDWLRQ f LW LV DOVR DVVXPHG WKDW WKH DWRPV UHDFK D OHYHO ZKRVH HQHUJ\ GHIHFW ZLWK WKH LRQL]DWLRQ SRWHQWLDO LV VR ORZ WKDW FROOLVLRQDO LRQL]DWLRQ SURFHHGV LQVWDQWDQHRXVO\ 7KLV LV D YDOLG DVVXPSWLRQ LQ PRVW GRXEOH UHVRQDQFH H[FLWDWLRQ FDVHV RI DWRPV LQ DQ HQHUJHWLF HQYLURQPHQW HJ IODPH SODVPD HOHFWULFDO GLVFKDUJHf 7KHUHIRUH LQ VXFK D FDVH WKH QXPEHU RI LRQV FUHDWHG LV GLUHFWO\ SURSRUWLRQDO WR WKH ODVHU SXOVH OHQJWK DQG WKH VSHFWUDO HQHUJ\ GHQVLW\ %S$$ff RI WKH SKRWRQ IOX[ RI $ $OVR ZH VHH QR GHSHQGHQFH RI QW RQ WKH VSHFWUDO HQHUJ\ GHQVLW\ RI $ RU RQ DQ\ GHH[FLWDWLRQ SDWKZD\V IURP OHYHO VLQFH %AA$Af ! $ N 7ZR FRQFOXVLRQV WKDW FDQ EH GUDZQ IURP WKH DERYH GLVFXVVLRQ DUH WKDW IRU VLJQLILFDQW LRQL]DWLRQ IURP WKH XSSHUPRVW ODVHU H[FLWHG OHYHO D WZRVWHS H[FLWDWLRQ VFKHPH PXVW EH XVHG DQG WKDW IRU XQLW\ LRQL]DWLRQ RI DOO DWRPV H[FLWHG WR OHYHO E\ DEVRUSWLRQ RI D SKRWRQ $f WKH VSHFWUDO HQHUJ\ GHQVLW\ RI WKH VHFRQG ODVHU SA$Af PXVW EH VXIILFLHQW WR VDWXUDWH WKH WUDQVLWLRQ $VVXPLQJ VRPH W\SLFDO YDOXHV 7DEOH f IRU WKH YDULDEOHV LQ HTXDWLRQV f DQG f ZH ILQG WKDW LQ FDVH RI D OLQHDU LQWHUDFWLRQ RI ERWK VWHSV f ZKLOH IRU VDWXUDWLRQ RI WKH VHFRQG VWHS Q Q 7 f

PAGE 82

7DEOH 9DOXHV XVHG IRU FDOFXODWLQJ Q MQW LQ HDXTWLRQV f DQG f 9DULDEOH 9DOXH 8QLWV %M P VA+] A -n P Vn +] D Vn NL Vn $W V 3DA f n Pn +]n

PAGE 83

&+$37(5 (;3(5,0(17$/ *HQHUDO ([SHULPHQWDO &RQILJXUDWLRQ 7KH JHQHUDO H[SHULPHQWDO V\VWHP XVHG IRU DOO H[SHULPHQWV LV VKRZQ LQ )LJXUH $ GHWDLOHG OLVWLQJ RI H[SHULPHQWDO FRPSRQHQWV LV JLYHQ LQ 7DEOH $ IUHTXHQF\ GRXEOHG 1G <$* ODVHU QPf RSHUDWHG DW +] ZDV XVHG DV WKH SXPSLQJ VRXUFH IRU WKH GXDO G\H ODVHU V\VWHP 7KH SXPS EHDP ZDV VSOLW HTXDOO\ WR SXPS HDFK G\H ODVHU 7\SLFDO RXWSXW HQHUJ\ IURP WKH IUHTXHQF\ GRXEOHG 1G<$* ODVHU ZDV PSHU SXOVH ZLWK D SXOVH GXUDWLRQ RI QV 7KH G\H ODVHU RXWSXW ZDV HLWKHU XVHG GLUHFWO\ IRU WUDQVLWLRQV LQ WKH YLVLEOH UHJLRQ RI WKH VSHFWUXP RU IUHTXHQF\ GRXEOHG IRU 89 WUDQVLWLRQV ,Q WKH FDVH RI 89 WUDQVLWLRQV WKH YLVLEOH ODVHU OLJKW ZDV SDVVHG WKURXJK D .'3 IUHTXHQF\ GRXEOLQJ FU\VWDO DQ DXWRWUDFNLQJ V\VWHP ZLWK DQJOH PDWFKLQJ RI WKH IUHTXHQF\ GRXEOHG OLJKW HQVXUHG PD[LPXP RXWSXW LQWHQVLW\ ZKLOH VFDQQLQJ 7KH IXQGDPHQWDO DQG VHFRQG KDUPRQLF ZDYHV ZHUH VHSDUDWHG E\ D GLVSHUVLYH 3HOOLQ%URFD SULVP ,I WKH ODVHU ZDYHOHQJWK ZDV WR EH VFDQQHG WKHQ WKH 3HOOLQ%URFD SULVP ZDV UHSODFHG ZLWK D ULJKW DQJOH SULVP WR SUHYHQW ZDONLQJ RI WKH EHDP GXULQJ VFDQQLQJ 7KH WZR KDUPRQLFV ZHUH WKHQ VHSDUDWHG ZLWK D ORZ EDQGSDVV FRORUHG ILOWHU ZKLFK DEVRUEHG WKH YLVLEOH ZDYHOHQJWKV

PAGE 84

)LJXUH *HQHUDO H[SHULPHQWDO FRQILJXUDWLRQ

PAGE 86

7DEOH /LVWLQJ RI H[SHULPHQWDO FRPSRQHQWV &RPSRQHQW 0RGHO 1R 0DQXIDFWXUHU 1G<$* ODVHU <* 4XDQWHO ,QWHUQDWLRQDO 6DQWD &ODUD &$ 'XDO '\H /DVHU 7'/ 4XDQWHO ,QWHUQDWLRQDO 6DQWD &ODUD &$ )UHTXHQF\ 'RXEOHUV +' 4XDQWHO ,QWHUQDWLRQDO 6DQWD &ODUD &$ r 4XDUW] 3ULVPV DQG 4XDUW] /HQVHV f§ (VFR 3URGXFWV ,QF 2DN 5LGJH 11HXWUDO 'HQVLW\ )LOWHUV f§ &RULRQ &RUS +ROOLVWRQJ 0$ +LJK 3RZHU /DVHU 1HXWUDO 'HQVLW\ )LOWHUV )1 2SWLFV IRU 5HVHDUFK &DOGZHOO 1$PSOLILHU (*t* 3$5& 3ULQFHWRQ 1%R[FDU $YHUDJHU *DWHG ,QWHJUDWRU 65 6WDQIRU 5HVHDUFK 6\VWHPV 3DOR $OWR &$ &RPSXWHU ,QWHUIDFH 65 6WDQIRUG 5HVHDUFK 6\VWHPV 3DOR $OWR &$ &RPSXWHU 3&$7 1RUWKJDWH &RPSXWHU 6\VWHPV 'LJLWDO 2VFLOORVFRSH $ 7HNWURQL[ ,QF %HDYHUWRQ 25 &KDUW 5HFRUGHU +RXVWRQ ,QVWUXPHQWV $XVWLQ 7; L 1RZ &RQWLQXXP 6DQWD &ODUD &$

PAGE 87

7DEOH f§ FRQWLQXHG &RPSRQHQW 0RGHO 0DQXIDFWXUHU +ROORZ &DWKRGH /DPS /DPS f 1D 3E DQG 8f / VHULHV +DPDPDWVX &RUS %ULGJHZDWHU 1*DOYDWURQ 0Jf /1( 0J +DPDPDWVX &RUS %ULGJHZDWHU 1+ROORZ &DWKRGH /DPS 3RZHU 6XSSO\ 307$1 %HUWDQ $VVRFLDWHV +LFNVYLOOH 1< )DVW 3KRWRGLRGH (7 (OHFWUR2SWLFV 7HFKQRORJ\ )UHPRQW &$ 3KRWRGLRGH IRU $EVRUSWLRQ 0HDVXUHPHQWV 3,1 '36% 8QLWHG 'HWHFWRU 7HFKQRORJLHV +DZWKRUQH &$

PAGE 88

7ZR FRPPHUFLDOO\ DYDLODEOH KROORZ FDWKRGH ODPSV ZHUH XVHG ZLWK GLIIHUHQW KROORZ FDWKRGH GHVLJQV 2QH ODPS f ZDV D FRPPRQ +&/ XVHG IRU DWRPLF DEVRUSWLRQ DQDO\VLV )LJXUH f ,Q WKLV ODPS RQO\ RQH HQG RI WKH KROORZ FDWKRGH ZDV RSHQ 7KH RWKHU ODPS ODPS f )LJXUH f ZDV D *DOYDWURQ XVHG LQ ZDYHOHQJWK VWDELOL]DWLRQ RI G\H ODVHUV E\ WKH RSWRJDOYDQLF HIIHFW 7KLV ODPS LV D 7 GHVLJQ LQ ZKLFK ERWK HQGV RI WKH KROORZ FDWKRGH DUH RSHQ 3LFNRII &LUFXLWU\ IRU 2* 6LJQDO 7KH FLUFXLW XVHG WR SRZHU WKH KROORZ FDWKRGH ODPSV DQG PHDVXUH WKH $& YROWDJH DFURVV WKH GLVFKDUJH LV VKRZQ LQ )LJXUH D ,W ZDV HQWLUHO\ KRXVHG LQ D VKLHOGHG 3RPRQD ER[ )LJXUH Ef WR UHGXFH SLFNXS RI UDGLR IUHTXHQF\ QRLVH 7KH KLJK YROWDJH ZDV VXSSOLHG IURP D GFGF KLJK YROWDJH SRZHU VXSSO\ WKURXJK D FXUUHQW OLPLWLQJ UHVLVWRU 5% 7KLV UHVLVWRU FRXOG EH PDGH H[WHUQDO ZLWK WKH XVH RI DQ LVRODWHG %1& FRQQHFWRU $ YDULDEOH UHVLVWRU ZLWKLQ D GHFDGH UHVLVWRU ER[ ZDV XVHG IRU LQLWLDO VWXGLHV )RU ILQDO H[SHULPHQWV WKH RSWLPXP 5% NQf ZDV KDUGZLUHG LQVLGH WKH VKLHOGHG ER[ 7KH YROWDJH DFURVV WKH GLVFKDUJH ZDV $& FRXSOHG WR WKH GHWHFWLRQ HOHFWURQLFV E\ D KLJK YROWDJH FRXSOLQJ FDSDFLWRU 2QHVWHS ([FLWDWLRQ ([SHULPHQWV )RU RQHVWHS H[FLWDWLRQ ODVHU ZDV VWHHUHG YLD ULJKW DQJOH SULVPV LQWR WKH GLVFKDUJH 7KH ODVHU EHDP FRXOG EH IRFXVVHG GHSHQGLQJ RQ WKH H[SHULPHQW WR EH SHUIRUPHG :KHQ WKH ODVHU ZDV QRW IRFXVVHG LW ZDV DSHUWXUHG WR MXVW ILOO WKH KROORZ

PAGE 89

)LJXUH 'LDJUDP RI D FRPPRQ +&/ ODPS f

PAGE 90

$QRGH 6KLHOG ,QVXODWHG VXSSRUW +ROORZ FDWKRGH ,QVXODWHG VXSSRUW 'HWDLO RI KROORZ FDWKRGH

PAGE 91

)LJXUH 'LDJUDQ RI D *DOYDWURQ ODPS f

PAGE 92

&DWKRGH $QRGHV 1HJDWLYH 'DUN 'HWDLO RI KROORZ FDWKRGH

PAGE 93

)LJXUH Df 3LFNRII FLUFXLW IRU PHDVXULQJ 2* VLJQDOV Ef 3RPRQD ER[ HQFDVLQJ SLFNRII FLUFXLWU\

PAGE 94

9DULDEOH UHVLVWRU 6,*1$/ 287 RR R

PAGE 95

FDWKRGH YROXPH 2SWRJDOYDQLF VSHFWUD ZHUH REWDLQHG E\ VFDQQLQJ WKH G\H ODVHU ZDYHOHQJWK ZKLOH PRQLWRULQJ WKH $& YROWDJH DFURVV WKH GLVFKDUJH 7ZRVWHS ([FLWDWLRQ ([SHULPHQWV /DPS 7KH DOLJQPHQW RI WKH ODVHUV ZKHQ XVLQJ WKH VLQJOHRSHQ HQGHG KROORZ FDWKRGH LV VKRZQ VFKHPDWLFDOO\ LQ )LJXUH 7KH WZR ODVHU EHDPV ZHUH PDGH WR HQWHU WKH KROORZ FDWKRGH DW D VOLJKW DQJOH WR WKH FDWKRGH D[LV 'LIIHUHQW IRFXVVLQJ FRQILJXUDWLRQV RI WKH WZR EHDPV ZHUH XVHG 3ODFHPHQW RI D OHQV DW SRVLWLRQ DOORZHG RQO\ ODVHU WR EH IRFXVVHG ZKLOH SODFHPHQW RI WKH OHQV LQ SRVLWLRQ IRFXVVHG ERWK EHDPV LQWR WKH KROORZ FDWKRGH ,Q HLWKHU FDVH WKH SRVLWLRQ RI WKH OHQV ZDV VXFK WKDW WKH EHDPVf ZDV ZHUHf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f 7KH RXWSXW RI WKH SKRWRGLRGH ZDV FRQQHFWHG WR D IDVW GLJLWL]LQJ RVFLOORVFRSH )RU WLPLQJ RSWLPL]DWLRQ

PAGE 96

)LJXUH $OLJQPHQW RI ODVHUVf WKURXJK ODPS

PAGE 97

/DVHU (IIHFWLYH DQRGH 1HJDWLYH JORZ n&DWKRGH GDUN VSDFH

PAGE 98

)LJXUH $OLJQPHQW RI ODVHUVf WKURXJK ODPS

PAGE 99

&DWKRGH GDUN VSDFH &DWKRGH /DVHU 1HJDWLYH JORZ /DVHU

PAGE 100

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f LV VKRZQ LQ )LJXUH 7KH WUDQVPLWWHG ODVHU OLJKW ZDV LQFLGHQW RQ D SKRWRGLRGH ZKLOH WKH ODVHU ZDV VFDQQHG WKURXJK WKH WUDQVLWLRQ RI LQWHUHVW /LQHDULW\ RI WKH SKRWRGLRGH UHVSRQVH ZDV LQVXUHG ZLWK D QHXWUDO GHQVLW\ ILOWHU 7KH RXWSXW RI WKH SKRWRGLRGH ZDV IHG LQWR WKH LQSXW RI D ER[FDU 2XWSXW IURP WKH ER[FDU ZDV WKHQ VHQW WR D SHUVRQDO FRPSXWHU DQG VWULS FKDUW UHFRUGHU IRU VXEVHTXHQW GDWD DQDO\VLV

PAGE 101

)LJXUH 2VFLOORVFRSH WUDFH RI WHPSRUDO FRLQFLGHQFH RI WKH WZR ODVHU EHDPV DW WKH KROORZ FDWKRGH

PAGE 102

P H 9R W D J H UX !r LG UX 6 ‘ 6 P9

PAGE 103

)LJXUH ([SHULPHQWDO FRQILJXUDWLRQ IRU DEVRUSWLRQ H[SHULPHQWV

PAGE 104

E YR R

PAGE 105

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f DQG WKH RWKHU ODVHU ZDV VFDQQHG WKURXJK WKH WUDQVLWLRQ

PAGE 106

&+$37(5 5(68/76 $1' ',6&866,21 6RGLXP 2* HIIHFW 6RGLXP ZDV FKRVHQ DV DQ HOHPHQW IRU SUHOLPLQDU\ VWXG\ IRU VHYHUDO UHDVRQV )LUVW LW SRVVHVVHV D UHODWLYHO\ VLPSOH OHYHO HQHUJ\ VFKHPH )LJXUH f $OVR VSHFWURVFRSLF GDWD FW U $f IRU DOO WUDQVLWLRQV FRQVLGHUHG LQ WKLV ZRUN DUH ZHOO NQRZQ 6HFRQG 1D LV VSXWWHUHG HIILFLHQWO\ E\ $U ILOO JDV RI 1D +&/f JLYLQJ KLJK QXPEHU GHQVLW\ RI WKH 1D DWRPV ZLWKLQ WKH GLVFKDUJH 7KLUG DQG PRUH SUDFWLFDOO\ WUDQVLWLRQV IRU ERWK WKH JURXQGVWDWH DQG H[FLWHGVWDWH WUDQVLWLRQV RI 1D DUH LQ WKH YLVLEOH UHJLRQ RI WKH VSHFWUXP 7KLV JUHDWO\ IDFLOLWDWHG ODVHU RSHUDWLRQ VLQFH QR IUHTXHQF\ GRXEOLQJ RI WKH G\H ODVHU IXQGDPHQWDO ZDYHOHQJWK ZDV UHTXLUHG DQG DOLJQPHQW HVSHFLDOO\ LQ WKH FDVH RI GRXEOH UHVRQDQFH 2* VSHFWURVFRS\f RI WKH ODVHU EHDPV LQ WKH +&/ ZDV PRUH HDVLO\ DFKLHYHG 7KH 2* VLJQDO REWDLQHG IRU ERWK JURXQG VWDWH WUDQVLWLRQV LV VKRZQ LQ )LJXUH 7KH HQHUJ\ RI WKH ODVHU ZDV DSSUR[LPDWHO\ P ZKLFK FRUUHVSRQGV WR D VSHFWUDO HQHUJ\ GHQVLW\ RI [ n P +] DVVXPLQJ D EHDP GLDPHWHU RI PP DQG ODVHU EDQGZLGWK $ $ [ P 7KH ODVHU EHDP ZDV SDVVHG XQIRFXVVHG LQWR WKH ODPS WR FRYHU WKH HQWLUH KROORZ FDWKRGH DQG VFDQQHG WKURXJK ERWK WUDQVLWLRQV 7KH H[FHOOHQW VLJQDOWRQRLVH 61f REWDLQDEOH FDQ EH VHHQ IURP )LJXUH IRU RSWLPL]HG

PAGE 107

)LJXUH 2* VLJQDOV IRU JURXQG VWDWH WUDQVLWLRQV RI 1D

PAGE 108

2* VLJQDO DX ZDYHOHQJWK QPf

PAGE 109

)LJXUH ([DPSOH RI VLJQDOWRQRLVH DWWDLQDEOH XVLQJ WKH 2* HIIHFW

PAGE 110

2* 6LJQDO DXf 92 2V

PAGE 111

H[SHULPHQWDO FRQGLWLRQV IRU 1D 7KH RULJLQ RI WKH VPDOO SHDN PDUNHG ZLWK DQ DVWHULVN LV DVVXPHG WR EH GXH WR DQ LPSXULW\ LQ WKH FDWKRGH DV LW ZDV QRW REVHUYHG LQ RWKHU 1D +&/V 1R DWWHPSW ZDV PDGH WR DVVLJQ WKLV SHDN WR DQ HOHPHQW )LJXUH VKRZV WKH VLJQDO REWDLQHG ZKLOH VFDQQLQJ RQO\ WKH VHFRQG ODVHU WKURXJK WKH QP H[FLWHG VWDWH WUDQVLWLRQ RI 1D 7KH 61 LV FOHDUO\ GHJUDGHG UHODWLYH WR WKH JURXQG VWDWH WUDQVLWLRQ FDVH 7KLV EHKDYLRU LV UHDGLO\ H[SODLQHG E\ WKH IDFW WKDW WKH QXPEHU GHQVLW\ RI DWRPV LQ WKH H[FLWHG VWDWH LV PXFK ORZHU WKDQ WKDW RI DWRPV LQ WKH JURXQG VWDWH 7KHUHIRUH DOWKRXJK D ODUJHU IUDFWLRQ RI WKH WRWDO QXPEHU GHQVLW\ ZLOO EH LRQL]HG IURP WKH H[FLWHG VWDWH WKH DEVROXWH QXPEHU RI LRQV FUHDWHG ZLOO EH OHVV 6LQFH ZH DVVXPH WKH SRSXODWLRQV RI WKH GLIIHUHQW VWDWHV WR IROORZ D 0D[ZHOO%ROW]PDQQ GLVWULEXWLRQ DQ HVWLPDWH RI WKH GLIIHUHQFH WR EH H[SHFWHG LQ WKH VLJQDO WR QRLVH FDQ EH FDOFXODWHG :H H[SHFW WKH SRSXODWLRQ RI OHYHO UHODWLYH WR WKDW RI OHYHO WR EH JLYHQ E\ Q Q O f§H[S $ ( N7 rf f ZKHUH $( JWI N 7H HQHUJ\ GLIIHUHQFH EHWZHHQ WKH WZR OHYHOV RI WKH WUDQVLWLRQ -f GHJHQHUDF\ RI WKH ORZHU DQG XSSHU OHYHO UHVSHFWLYHO\ GLPHQVf %ROW]PDQQ FRQVWDQW .nf HOHFWURQ WHPSHUDWXUH RI WKH V\VWHP .f

PAGE 112

)LJXUH 2* VLJQDO IRU H[FLWHG VWDWH WUDQVLWLRQ RI 1D

PAGE 113

2* 6LJQDO DX ZDYHOHQJWK QPf 92 92

PAGE 114

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r/ 5E 5O f ZKHUH 9V LV WKH VRXUFH YROWDJH %\ SORWWLQJ 9Af YV 5% D VWUDLJKW OLQH UHVXOWV ZLWK VORSH HTXDO WR 5OAf DQG LQWHUFHSW HTXDO WR 9VfB 6XFK D SORW REWDLQHG IRU WKH *DOYDWURQ LV VKRZQ LQ )LJXUH )URP WKLV SORW 9V DQG 5/ ZHUH IRXQG WR EH [ n 9 DQG [ RKPV UHVSHFWLYHO\

PAGE 115

)LJXUH 3ORW RI .Afn YV 5E XVHG IRU GHWHUPLQDWLRQ RI ODPS LPSHGDQFH

PAGE 116

9RXWff 5 EDOODVW RKPVf 6

PAGE 117

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f QL f $8 f W 5O f H f ZKHUH WZ WHPSRUDO ZLQGRZ RI GHWHFWLRQ HOHFWURQLFV WLPH WR LQWHJUDWH VLJQDO DUHDf Vf H HOHFWURQLF FKDUJH &f 8VLQJ WKH H[SHULPHQWDO YDOXHV JLYHQ LQ WDEOH Qc [O 5HDUUDQJLQJ HTXDWLRQ f \LHOGV rL r 9 V f

PAGE 118

)URP HTXDWLRQ f DQG DVVXPLQJ >@ Q7 } FP D ODVHU SXOVH OHQJWK RI p V JO J O DQG DQ LUUDGLDWHG GLVFKDUJH YROXPH RI FP NLm Vn 7KLV LV FRPSDUDEOH WR LWV FRXQWHUSDUW LQ IODPHV 7KHUHIRUH E\ XVLQJ VLPSOH 2* PHDVXUHPHQWV WR GHWHUPLQH WKH LRQ QXPEHU GHQVLW\ LQ FRPELQDWLRQ ZLWK DEVRUSWLRQ PHDVXUHPHQWV WR GHWHUPLQH WKH JURXQG VWDWH DWRP RU RULJLQDWLQJ OHYHOf QXPEHU GHQVLW\ D UHDVRQDEOH HVWLPDWH RI WKH FROOLVLRQDO UDWH FRQVWDQW NL FDQ EH GHWHUPLQHG 7ZRVWHS 2* (IIHFW RI 1D 2I PRUH GLUHFW EHDULQJ RQ WKH SXUSRVH RI WKLV ZRUN LV WKH 2* HIIHFW REVHUYHG ZKHQ WZR ODVHU EHDPV WXQHG WR WZR GLIIHUHQW DEVRUSWLRQ WUDQVLWLRQV RI DQ HOHPHQW LQ WKH GLVFKDUJH DUH PDGH WHPSRUDOO\ DQG VSDWLDOO\ FRLQFLGHQW LQ WKH GLVFKDUJH ,Q WKH FDVH RI 1D IURP )LJXUH f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fWUDQVLWLRQ DQG ; A ZDV VFDQQHG WKURXJK ERWK WKH FRQQHFWLQJ WUDQVLWLRQ 3 QPf DQG QRQFRQQHFWLQJ WUDQVLWLRQ

PAGE 119

7DEOH ([SHULPHQWDO YDOXHV IRU GHWHUPLQLQJ Q^ LQ HTXDWLRQ f 9DULDEOH 0DJQLWXGH 8QLW WZ V 5O [ 2KPV $9 9

PAGE 120

)LJXUH 7ZRVWHS HQKDQFHPHQW RI 1D 2* VLJQDO Df $ WXQHG WR WKH UHVRQDQFH WUDQVLWLRQ DQG $ GHWXQHG IURP UHVRQDQFH E\ ƒ Ef $ GHWXQHG IURP UHVRQDQFH E\ ƒ DQG $ WXQHG WR WKH H[FLWHGVWDWH UHVRQDQFH WUDQVLWLRQ Ff ERWK ODVHUV WXQHG WR WKH UHVSHFWLYH UHVRQDQFH WUDQVLWLRQV

PAGE 121

2 R 7LPH FRRUGLQDWH DXf R ‘-

PAGE 122

)LJXUH &ROOLVLRQDO FRXSOLQJ RI 1D HQHUJ\ OHYHOV LQ WKH +&/

PAGE 123

2* VLJQDO DXf

PAGE 124

3K QPf $Q HQKDQFHPHQW ZDV REVHUYHG IRU ERWK FDVHV 1R VXFK HQKDQFHPHQW ZDV REVHUYHG ZKHQ ;Q ZDV GHWXQHG IURP WKH UHVRQDQW ZDYHOHQJWK LQGLFDWLQJ VRPH FROOLVLRQDO FRXSOLQJ EHWZHHQ WKH 3 DQG 3: VWDWHV 7KH VDPH HIIHFW ZDV REVHUYHG ZKHQ ; ZDV WXQHG WR WKH 69 a! 3A QPf WUDQVLWLRQ /HDG 2* (IIHFW LQ WKH +&/ /HDG LV DQRWKHU FODVVLFDO HOHPHQW RIWHQ VWXGLHG E\ VSHFWURVFRSLVWV /LNH 1D LW DIIRUGV D QHDUO\ LGHDO ZHOO FKDUDFWHUL]HG HQHUJ\ OHYHO VFKHPH ZLWK WKH DGGLWLRQDO LQWHUHVW RI D PHWDVWDEOH OHYHO $ SDUWLDO HQHUJ\ OHYHO GLDJUDP IRU 3E LV JLYHQ LQ )LJXUH 7KH LRQL]DWLRQ HQKDQFHPHQW REWDLQHG LQ WKH WZRVWHS VFKHPH IRU 3E LQ WKH +&/ ZDV REWDLQHG LQ WKLV ZRUN IRU WKH ILUVW WLPH 7KH HQKDQFHPHQW LV DERXW WLPHV RYHU WKH VLQJOH VWHS FDVH VHH )LJXUH f 7KLV ORZ HQKDQFHPHQW LV PDLQO\ D UHVXOW RI WKH KLJK GHJUHH RI SKRWRLRQL]DWLRQ IURP WKH DEVRUSWLRQ RI WZR SKRWRQV DW QP [ FPnf ZKLFK LV PRUH WKDQ HQRXJK HQHUJ\ WR LRQL]H WKH OHDG DWRPV >LRQL]DWLRQ SRWHQWLDO ,3f FPn@ 7KH VDPH DUJXPHQWV DQG GHVFULSWLRQV JLYHQ IRU 1D ZLWK UHJDUG WR WKH VLQJOH DQG WZRVWHS UHVXOWV DUH UHDGLO\ H[WHQGHG WR WKH 3E FDVH 1R REYLRXV HIIHFWV UHVXOWLQJ IURP WKH SUHVHQFH RI D PHWDVWDEOH OHYHO RU WUDS ZHUH HYLGHQW )LJXUH VKRZV WKH GHSHQGHQFH RI WKH REVHUYHG WZRVWHS 2* VLJQDO IRU 3E RQ WKH ODPS FXUUHQW 7KH QXPEHU RI VSXWWHUHG DWRPV DOVR LQFUHDVHV ZLWK DQ LQFUHDVH LQ FXUUHQW DQG FRUUHVSRQGLQJO\ WKH QXPEHU GHQVLW\ RI DWRPV DYDLODEOH IRU DEVRUSWLRQ

PAGE 125

)LJXUH 3DUWLDO HQHUJ\ OHYHO GLDJUDP IRU 3E

PAGE 126

FP

PAGE 127

)LJXUH 7ZRVWHS HQKDQFHPHQW IRU 3E 2* VLJQDO %RWK ODVHUV ZHUH FRLQFLGHQW LQ WKH KROORZ FDWKRGH ZLWK Df N WXQHG WR WKH UHVRQDQFH WUDQVLWLRQ DQG $ GHWXQHG IURP UHVRQDQFH E\ ƒ Ef $ GHWXQHG IURP UHVRQDQFH E\ ƒ DQG $ WXQHG WR WKH H[FLWHG VWDWH UHVRQDQFH WUDQVLWLRQ DQG Ff ERWK ODVHUV WXQHG WR WKH UHVSHFWLYH UHVRQDQFH WUDQVLWLRQV

PAGE 128

2* VLJQDO DX 7LPH FRRUGLQDWH DXf

PAGE 129

)LJXUH 3E WZRVWHS 2* VLJQDO YV ODPS FXUUHQW

PAGE 130

/r , / L / M L L L L L 21 /DPS FXUUHQW P$f

PAGE 131

RI SKRWRQV IURP WKH ODVHU EHDP LQFUHDVHV 7KHUHIRUH DQ LQFUHDVH LQ WKH 2* VLJQDO RFFXUV ZLWK LQFUHDVLQJ ODPS FXUUHQW 1HRQ 2* (IIHFW LQ WKH +&/ &RPSDULVRQ RI WKH PDJQLWXGH RI WKH 1HfP 2* HIIHFW UHODWLYH WR WKDW RI VSXWWHUHG DWRPV FDQ EH PDGH IURP )LJXUH 7KLV LV DQ 2* VSHFWUXP RI 8 LQ DQ +&/ REWDLQHG E\ SDVVLQJ RQH ODVHU XQIRFXVVHG LQWR WKH +&/ DQG VFDQQLQJ RYHU WKH ODVLQJ UDQJH RI WKH G\H 0DQ\ 8 SHDNV PDUNHG ZLWK rf ZHUH UHFRUGHG DORQJ ZLWK WKH PXFK VWURQJHU 1HfP SHDNV 7KH PDJQLWXGHV RI WKH 1HfP VLJQDOV DUH RQ DYHUDJH [ JUHDWHU WKDQ WKH 8 VLJQDOV ,W VKRXOG DOVR EH NHSW LQ PLQG WKDW LQ REWDLQLQJ WKLV VSHFWUXP WKH H[SHULPHQW KDG QRW EHH RSWLPL]HG IRU 1H 7KLV 1HfP HQKDQFHPHQW LV LQ DFFRUGDQFH ZLWK WKH FHQWUDO UROH DWWULEXWHG WR 1Hf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f 3OVf 3rOVf DQG n3AO6Mf LQ WKH /6 FRXSOLQJ DQG 3DVFKHQ

PAGE 132

)LJXUH 2* VSHFWUXP RI 81H ODPS IURP QP

PAGE 133

2* 6LJQDO P9f

PAGE 134

)LJXUH ([SDQGHG 8 2* VSHFWUXP IURP QP

PAGE 135

2* 6LJQDO P9f 1! ZDYHOHQJWK QPf

PAGE 136

QRWDWLRQ UHVSHFWLYHO\ 7UDQVLWLRQV DUH REVHUYHG IURP HDFK RI WKHVH VWDWHV WR WKH S OHYHOV WHQ VWDWHVf DQG IURP WKH S OHYHOV WR KLJKHU HOHFWURQLF VWDWHV VXFK DV V DQG Gf 7KH S DQG KLJKHUO\LQJ VWDWHV KDYH VKRUW UDGLDWLYH OLIHWLPHV >@ LQ FRQWUDVW WR WKH FRQVLGHUDEO\ ORQJHU OLIHWLPHV RI WKH ,V VWDWHV 7KH 3OVf DQG 3OVf VWDWHV DUH PHWDVWDEOH OLIHWLPHV W!nVf ZKLOH WKH VKRUW UDGLDWLYH OLIHWLPHV RI WKH 3OVf DQG AO6Mf VWDWHV DUH OHQJWKHQHG E\ UDGLDWLYH WUDSSLQJ WmVf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f PHFKDQLVPV RI SKRWRQ DEVRUSWLRQ DQG LRQL]DWLRQ 7KUHH IURP DEVRUSWLRQ E\ 1H DQG RQH IURP 8 DEVRUSWLRQ (DFK ZLOO EH GHDOW ZLWK VHSDUDWHO\

PAGE 137

)LJXUH 2* VSHFWUXP RI 81H ODPS IURP QP

PAGE 138

$ DV Q 24 S Ur Krf D R }f§r Ur 3! 24 &2 R FU S 3 24 &2 ZDYHOHQJWK Q Pf KM

PAGE 139

&DVH 7KH DEVRUSWLRQ JLYLQJ ULVH WR WKH SHDN RFFXUULQJ DW QP )LJXUH f LV D ZHOO NQRZQ WUDQVLWLRQ IRU 1H 3OVf 3Sf 7KH VDWXUDWLRQ FXUYH YDULDWLRQ RI 2* VLJQDO ZLWK S$ $ f IRU WKLV SHDN LV VKRZQ LQ )LJXUH ,I ZH DVVXPH WKDW WKH PDJQLWXGH RI WKH 2* VLJQDO LV GLUHFWO\ SURSRUWLRQDO WR WKH QXPEHU RI LRQV FUHDWHG GXULQJ WKH ODVHU SXOVH QR DPSOLILFDWLRQ HIIHFWVf WKHQ WKH EHKDYLRU RI WKH 2* VLJQDO LV H[SHFWHG WR IROORZ WKH JHQHUDO HTXDWLRQ >@ 2*(9faADDUn >DO DOLr!nnf@ f ZKHUH ffnp3DAfAAAL3DAfrA >A3DAfA@r A 3$A f A AA 3 $A f A A D WA3$AfA@AL A 3 $ A f A r Ar3 $ A QfLr A f $W ORZ VSHFWUDO HQHUJ\ GHQVLWLHV HTXDWLRQ f UHGXFHV WR 2*( Q7: QWH5/ H[S A3DAA $ $ W N AAAL M f

PAGE 140

$ OLQHDU UHODWLRQVKLS H[LVWV EHWZHHQ WKH 2* VLJQDO DQG %S$;f $W KLJKHU VSHFWUDO HQHUJ\ GHQVLWLHV WKHUH PD\ EH VHYHUDO PHFKDQLVP E\ ZKLFK WKH VLJQDO EHFRPHV LQGHSHQGHQW RI WKH VSHFWUDO HQHUJ\ GHQVLW\ RI WKH ODVHU ,Q WKH OLPLW ZKHUH WKH UDWH RI LQGXFHG DEVRUSWLRQ LV PXFK JUHDWHU WKDQ WKH VXP RI UDGLDWLYH DQG FROOLVLRQDO GHDFWLYDWLRQ WKDW LV %S$$f !! $ N NLf HTXDWLRQ f UHGXFHV WR 2*( 9f Q7: QWH5/ H[S H 9 f§f§ L f? f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f YV ORJ SD$ff VKRXOG UHVXOW LQ D FXUYH ZLWK WZR GLVWLQFW VORSHV 7KLV LV VHHQ LQ )LJXUH 7KH ILUVW SDUW RI WKH FXUYH \LHOGV D VORSH RI s LQGLFDWLQJ D OLQHDU GHSHQGHQFH RI WKH

PAGE 141

)LJXUH 6DWXUDWLRQ FXUYH IRU QP DEVRUSWLRQ RI 1H

PAGE 142

2* 6LJQDO DXf S[;f : P QP f

PAGE 143

)LJXUH /RJORJ SORW RI )LJXUH

PAGE 144

S B/ 2 bO U 2L 1! 7 U R rf 4 RG A /2 r/ ,' &' UR R /M .f R /RJ 2* 6LJQDOf X! R

PAGE 145

2* VLJQDO RQ WKH ODVHU LQWHQVLW\ 7KH VHFRQG SDUW RI WKH FXUYH \LHOGV D VORSH RI s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f LV VWLOO REVHUYHG &DVJ 7KH VHFRQG FDVH JLYHV ULVH WR WKH SHDN DW QP 7R WKH EHVW RI WKH DXWKRUfV NQRZOHGJH LWV REVHUYDWLRQ KDV QRW \HW EHHQ SUHYLRXVO\ UHSRUWHG LQ WKH OLWHUDWXUH 7KH VDWXUDWLRQ FXUYH IRU WKLV SHDN LV VKRZQ LQ )LJXUH 7KH ORJORJ FXUYH LV VKRZQ LQ )LJXUH ,Q WKLV FDVH DW OHDVW WKUHH GLVWLQFW UHJLRQV RI WKH FXUYH DUH DSSDUHQW $JDLQ WKH LQLWLDO SDUW RI WKH FXUYH \LHOGV D VORSH RI s LQGLFDWLQJ D OLQHDU GHSHQGHQFH RI WKH 2* VLJQDO RQ WKH ODVHU LQWHQVLW\ 7KLV ZRXOG LQGLFDWH WKDW WKH WUDQVLWLRQ LV EHWZHHQ WZR UHDO ERXQG OHYHOV RI WKH DWRP 1HrPf IROORZHG E\ FROOLVLRQDO LRQL]DWLRQ RI WKH H[FLWHG DWRP )URP WDEXODWHG YDOXHV RI WKH HQHUJ\ OHYHOV RI 1H >@ D SRVVLEOH WUDQVLWLRQ IURP WKH 3 f OHYHO DW FPn RFFXUV WR WKH 3r f OHYHO DW FPn 7KH HQHUJ\ GLIIHUHQFH EHWZHHQ WKHVH WZR OHYHOV FP FRUUHVSRQGV YHU\ FORVHO\ WR WKH HQHUJ\ VXSSOLHG E\ WKH ODVHU SKRWRQV FP DIWHU WKH REVHUYHG ZDYHOHQJWK ZDV FRUUHFWHG IRU WKH UHIUDFWLYH LQGH[ RI DLU )XUWKHU VXSSRUW IRU RXU DVVLJQPHQW OLHV LQ WKH SRODULW\ RI WKH

PAGE 146

)LJXUH 6DWXUDWLRQ FXUYH IRU QP DEVRUSWLRQ RI 1H

PAGE 147

2* 6LJQDO DXf S[;Lf : P QP f

PAGE 148

)LJXUH /RJORJ SORW RI )LJXUH

PAGE 149

/RJ 2* 6LJQDOf /RJ S[ ;f f

PAGE 150

VLJQDO 7KH REVHUYHG YROWDJH FKDQJH ZDV RI QHJDWLYH SRODULW\ )LJXUH f LQGLFDWLQJ WKDW WKLV VLJQDO PRVW SUREDEO\ UHVXOWHG IURP D WUDQVLWLRQ LQYROYLQJ KLJK O\LQJ H[FLWHG VWDWHV RI 1H DQG QRW WKH PHWDVWDEOH VWDWHV DV GLVFXVVHG DERYH 7KH PLGGOH SRUWLRQ RI WKH FXUYH DJDLQ \LHOGV D VPDOO VORSH LQGLFDWLQJ YLUWXDO LQGHSHQGHQFH RI VLJQDO IURP WKH ODVHU LQWHQVLW\ DV H[SHFWHG LQ D VLPSOH WUDQVLWLRQ EHWZHHQ WZR ERXQG OHYHOV IROORZHG E\ FROOLVLRQDO LRQL]DWLRQ 7KH VORSH RI WKH ILQDO VHFWLRQ RI WKLV FXUYH LV s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-N $W Df f

PAGE 151

)LJXUH 3URSRVHG H[FLWDWLRQLRQL]DWLRQ VFKHPH IRU QP DEVRUSWLRQ RI 1H

PAGE 152

FP S 9

PAGE 153

)LJXUH 7ZRSKRWRQ H[FLWDWLRQ VFKHPH WKURXJK D YLUWXDO OHYHO

PAGE 154

FP r3

PAGE 155

ZKHUH L! IUHTXHQF\ RI WKH DEVRUEHG SKRWRQ +]f r?N V IUHTXHQF\ RI WKH WUDQVLWLRQ EHWZHHQ WKH RULJLQDWLQJ OHYHO DQG WKH FORVHVW UHDO OHYHO WR WKH YLUWXDO OHYHO +]f )RU H[DPSOH LQ WKLV FDVH $(LFPnf r F f f FPa[r6[O FPV [O2X V n 7KHUHIRUH $W [On V RU IHPWRVHFRQGV IVf )RU WKH WZRSKRWRQ WUDQVLWLRQ WR WDNH SODFH ERWK SKRWRQV PXVW EH DEVRUEHG E\ WKH DWRP GXULQJ WKLV IV LQWHUYDO 6LQFH WKH WUDQVLWLRQ LQYROYHV WKH VLPXOWDQHRXV DEVRUSWLRQ RI WZR SKRWRQV IURP WKH ODVHU EHDP D VTXDUH GHSHQGHQFH RI WKH 2* VLJQDO LV H[SHFWHG RQ WKH VSHFWUDO HQHUJ\ GHQVLW\ RI WKH ODVHU 7KH VDWXUDWLRQ FXUYH IRU VXFK D WUDQVLWLRQ LV VKRZQ LQ )LJXUH IRU WKH QP DEVRUSWLRQ RI 1H 7KH VORSH RI WKH ORJORJ SORW )LJXUH f LV sf 1R VDWXUDWLRQ RI WKH WUDQVLWLRQ FDQ EH VHHQ HYHQ DW WKH KLJKHU VSHFWUDO HQHUJ\ GHQVLWLHV 7KLV LV UHDVRQDEOH VLQFH WKH QRUPDO DEVRUSWLRQ FURVV VHFWLRQV IRU WZRSKRWRQ SURFHVVHV WKURXJK YLUWXDO OHYHOV f FPf DUH PDQ\ RUGHUV RI PDJQLWXGH VPDOOHU WKDQ WUDQVLWLRQV EHWZHHQ ERXQG OHYHOV n FPf

PAGE 156

)LJXUH 6DWXUDWLRQ FXUYH IRU QP DEVRUSWLRQ RI 1H

PAGE 157

2* 6LJQDO DXf S[;f : P QP f

PAGE 158

)LJXUH /RJORJ SORW RI )LJXUH

PAGE 159

/RJ 2* 6LJQDOf /RJ S[ ;f f

PAGE 160

&DVH 7KH ILQDO FDVH LV DQ H[WHQVLRQ RI FDVH DQG ZDV REVHUYHG IRU WKH QP DEVRUSWLRQ WUDQVLWLRQ RI 8 7KH VDWXUDWLRQ FXUYH IRU WKLV WUDQVLWLRQ LV JLYHQ LQ )LJXUH 7KH ORJORJ SORW )LJXUH f FRQVLVWV RI WKUHH GLVWLQFW UHJLRQV 7KH ILUVW KDV D VORSH RI sf LQGLFDWLQJ DV DERYH D WZRSKRWRQ SURFHVV WKURXJK D YLUWXDO OHYHO $ SODWHDX WKHQ RFFXUV LQGLFDWLQJ VDWXUDWLRQ RI WKLV SURFHVV QRW REVHUYHG LQ WKH SUHYLRXV FDVHf $ SRVVLEOH UHDVRQ IRU VDWXUDWLRQ RI WKLV WZRSKRWRQ WUDQVLWLRQ LV WKH ORQJHU OLIHWLPH RI WKH YLUWXDO OHYHO GXH WR LWV FORVHU SUR[LPLW\ WR D UHDO OHYHO WKDQ ZDV WKH YLUWXDO OHYHO LQ FDVH f 7KH HIIHFWLYH OLIHWLPH RI WKLV YLUWXDO OHYHO FDQ EH HVWLPDWHG DV DERYH WR EH [ n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f

PAGE 161

)LJXUH 6DWXUDWLRQ FXUYH IRU QP DEVRUSWLRQ RI 8

PAGE 162

2* 6LJQDO DXf S[;f : P QP f

PAGE 163

)LJXUH /RJORJ SORW RI )LJXUH

PAGE 164

2* 6LJQDO DXf S[;f : P QP f

PAGE 165

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f $V EHFRPHV VPDOOHU NcS LV H[SHFWHG WR SOD\ D PRUH LPSRUWDQW UROH LQ LRQL]DWLRQ RI WKH DWRPV UHODWLYH WR FROOLVLRQDO LRQL]DWLRQ 8UDQLXP KDV DQ LRQL]DWLRQ SRWHQWLDO RI FPn H9f $EVRUSWLRQ RI WKUHH SKRWRQV DW QP DIWHU FRUUHFWLRQ IRU WKH LQGH[ RI UHIUDFWLRQ RI DLU LPSDUWV DQ HQHUJ\ RI FPn H9f WR WKH 8 DWRP (0 LV WKHUHIRUH RQO\ FPn H9f 7KH VORSH RI WKH ILQDO SRUWLRQ RI WKH VDWXUDWLRQ FXUYH )LJXUH f LV s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

PAGE 166

)LJXUH 3URSRVHG H[FLWDWLRQLRQL]DWLRQ VFKHPH IRU QP DEVRUSWLRQ RI 8

PAGE 167

FP L D D &0 LQ D D mLL &0 P

PAGE 168

UHTXLUHG IRU VWDEOH RSHUDWLRQ RI WKH GLVFKDUJH WKH JUHDWHU ZRXOG EH WKH GHSHQGHQFH RI WKH HOHFWULFDO SURSHUWLHV RI WKH GLVFKDUJH RQ SHUWXUEDWLRQV RI WKH 1H PHWDVWDEOH SRSXODWLRQ 7KH UHODWLYH ODVHULQGXFHG LPSHGDQFH FKDQJH RI WKH GLVFKDUJH FDQ EH H[SUHVVHG DV $ 5O 5O ODVHU RQf 5W ODVHU RIIf 5O 5O ODVHU RIIf f )LJXUH LV D SORW RI WKH ODVHULQGXFHG LPSHGDQFH FKDQJH UHODWLYH WR WKH GF RSHUDWLQJ FXUUHQW RI WKH GLVFKDUJH $V FDQ EH VHHQ WKH UHODWLYH LPSHGDQFH FKDQJH LV PD[LPXP DW WKH ORZHU RSHUDWLQJ FXUUHQWV H[KLELWLQJ DQ H[SRQHQWLDO UHODWLRQ 'RXEOHUHVRQDQFH 2* (IIHFW RI 1H 0DQ\ GRXEOH UHVRQDQFH H[FLWDWLRQ VFKHPHV PD\ EH FKRVHQ IRU 1H )LJXUH f 2QH PLJKW WKHUHIRUH DVN ZKDW FULWHULRQ VKRXOG EH XVHG WR FKRRVH WKH EHVW VFKHPHVf IRU 2* VSHFWURVFRS\ LQ WKH +&/ 3K\VLFDO LQWXLWLRQ GLFWDWHV WKDW WKH JUHDWHU WKH SUREDELOLW\ RI DEVRUSWLRQ RI D SKRWRQ E\ WKH 1H WKH PRUH VHQVLWLYH WKH GHWHFWRU ZRXOG EH IRU ORZ OLJKW OHYHOV 7KHUHIRUH LW LV ORJLFDO WR DVVXPH WKDW WKH WUDQVLWLRQ SRVVHVVLQJ WKH KLJKHVW RVFLOODWRU VWUHQJWK >@ RU DEVRUSWLRQ FURVV VHFWLRQ D Af ZRXOG OHDG WR WKH JUHDWHVW VHQVLWLYLW\ >1RWH ,Q WKH OLWHUDWXUH WKH RVFLOODWRU VWUHQJWKV DUH RIWHQ UHSRUWHG DV JI YDOXHV ZKHUH J LV WKH GHJHQHUDF\ RI WKH HQHUJ\ OHYHO@ $OVR IURP HTXDWLRQ f D VFKHPH VKRXOG EH FKRVHQ VXFK WKDW WKH HQHUJ\ RI WKH RULJLQDWLQJ OHYHO RI WKH ILUVW WUDQVLWLRQ LV ORZ HQRXJK WR HQVXUH D KLJK SRSXODWLRQ

PAGE 169

)LJXUH 3ORW RI UHODWLYH ODVHULQGXFHG LPSHGDQFH FKDQJH YV ODPS FXUUHQW

PAGE 170

$5 5 /DPS FXUUHQW $f

PAGE 171

LQ WKH +&/ ,GHDOO\ RQH ZRXOG OLNH WR XVH WKH JURXQG VWDWH RI 1H GXH WR LWV H[WUHPHO\ VWURQJ RVFLOODWRU VWUHQJWK DQG KLJK QXPEHU GHQVLW\ LQ WKH GLVFKDUJH +RZHYHU WKH ZDYHOHQJWK RI DEVRUSWLRQ RI WKLV WUDQVLWLRQ OLHV LQ WKH IDU 89 a QPf DQG LV WKHUHIRUH XQVXLWDEOH IRU PDQ\ UHDVRQV WKH PRVW LPSRUWDQW RI ZKLFK DUH WKDW WKLV ZDYHOHQJWK LV HIIHFWLYHO\ DEVRUEHG E\ DLU DQG WKDW QR WXQDEOH ODVHU VRXUFHV DUH DYDLODEOH LQ WKLV UHJLRQ RI WKH HOHFWURPDJQHWLF VSHFWUXP 7KH WZR WUDQVLWLRQV XVHG LQ WKLV ZRUN ZHUH $ QP DQG $ QP 7KH ILUVW WUDQVLWLRQ FKRVHQ LV E\ IDU WKH VWURQJHVW RI DQ\ RI WKH WUDQVLWLRQV RULJLQDWLQJ IURP WKH ILUVW H[FLWHG HOHFWURQLF VWDWH RI 1H 1H PHWDVWDEOHV DUH H[FLWHG IURP WKH 3OVf WR WKH 'Sf VWDWH WKH JI YDOXH LV >@ FRPSDUHG WR WKH QH[W VWURQJHVW DEVRUSWLRQ ZLWK D JI YDOXH RI $OVR DV VWDWHG WKLV WUDQVLWLRQ RULJLQDWHV LQ D PHWDVWDEOH VWDWH RI 1H DQG LV WKHUHIRUH H[SHFWHG WR EH FULWLFDO LQ DIIHFWLQJ GLVFKDUJH FKDUDFWHULVWLFV 7KH VHFRQG WUDQVLWLRQ 'Sf a G SURPRWHV WKH DWRP WR ZLWKLQ H9 RI WKH LRQL]DWLRQ SRWHQWLDO RI 1H LQVXULQJ WKDW LRQL]DWLRQ IURP WKLV OHYHO RFFXUV LQVWDQWDQHRXVO\ E\ HOHFWURQ FROOLVLRQ LQ WKH HQHUJHWLF GLVFKDUJH 7KLV WUDQVLWLRQ LV DOVR WKH VWURQJHVW H[FLWHG VWDWH WUDQVLWLRQ RI 1H ZLWK D JI YDOXH RI 2SWLPL]DWLRQ RI %R[FDU *DWH 3RVLWLRQ 7KH JDWH RU REVHUYDWLRQ ZLQGRZ RI WKH GHWHFWLRQ HOHFWURQLFV PXVW EH RSWLPL]HG SULRU WR PDNLQJ DQ\ PHDVXUHPHQWV 7KH WZR FDVHV RI VLQJOH DQG GRXEOHn UHVRQDQFH 2* HIIHFW PXVW EH FRQVLGHUHG VHSDUDWHO\ $OVR WKH REVHUYDWLRQ RI WKH 1H 2* HIIHFW FDQ EH PDGH XVLQJ GLIIHUHQW VFKHPHV RI JDWH SRVLWLRQ DQG ZLGWK

PAGE 172

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

PAGE 173

)LJXUH %R[HDU JDWH SRVLWLRQ FRQVLGHUDWLRQV

PAGE 175

RI WKH ODVHU EHDPVf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f HOHFWURQV 7KH FKDUJHV IRUPHG KRZHYHU DUH QRW VXEMHFWHG WR DQ LQWHQVH HOHFWULF ILHOG 7KH HQHUJ\ RI WKHUPDO HOHFWURQV LQ WKH JORZ UHJLRQ UDQJH IURP H9 H9 ZKLFK LV QRW DGHTXDWH WR LRQL]H JURXQG VWDWH QHRQ DWRPV ,3 H9f ,I D 0D[ZHOOLDQ GLVWULEXWLRQ RI WKH HOHFWURQ HQHUJ\ LV DVVXPHG WKH IUDFWLRQ RI HOHFWURQV ZLWK HQRXJK HQHUJ\ WR LRQL]H PHWDVWDEOH QHRQ DWRPV $ (UHTm H9 LV DERXW [ n ,I QHRQ LV H[FLWHG WR ZLWKLQ H9 RI WKH LRQL]DWLRQ OLPLW WKHQ WKH IUDFWLRQ RI HOHFWURQV ZLWK HQRXJK HQHUJ\ WR LRQL]H WKH KLJKO\ H[FLWHG QHRQ LQFUHDVHV WR

PAGE 176

7DNLQJ WKLV LQWR FRQVLGHUDWLRQ DORQJ ZLWK WKH KLJK QXPEHU GHQVLW\ RI WKHUPDO HOHFWURQV LQ WKH JORZ UHJLRQ QA FPnf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m \ Yf N7H f ZKHUH 9S LV WKH SRWHQWLDO RI WKH SODVPD UHODWLYH WR WKH DEVROXWH YDOXH RI WKH DSSOLHG SRWHQWLDO DQG 7H LV WKH HOHFWURQ WHPSHUDWXUH 9S FDQ EH DSSUR[LPDWHG E\ N7 9S 9I f§ ,Q ?98 f ZKHUH 9I LV WKH SRWHQWLDO DSSOLHG DFURVV WKH HOHFWURGHV DQG YH DQG Sc DUH WKH PHDQ VTXDUH HOHFWURQ DQG LRQ YHORFLWLHV UHVSHFWLYHO\ 8VLQJ HTXDWLRQ f DQG WKH SDUDPHWHUV JLYHQ LQ 7DEOH

PAGE 177

7DEOH 9DOXHV XVHG WR FDOFXODWH Yc DQG YH LQ HTXDWLRQ f 9DULDEOH 0DJQLWXGH 8QLW 7H 7L PH [ n J PL [ ,4n J

PAGE 178

Y f WKH PHDQ VTXDUH YHORFLWLHV FDQ EH FDOFXODWHG \LHOGLQJ YH [O FP Vn DQG Yc [O FP Vn 6XEVWLWXWLQJ WKHVH YDOXHV EDFN LQWR HTXDWLRQ f DQG IRU DQ DSSOLHG YROWDJH RI 9 9S LV FDOFXODWHG WR EH 9 6XEVWLWXWLQJ WKLV YDOXH IRU WKH SODVPD SRWHQWLDO EDFN LQWR HTXDWLRQ f \LHOGV D SUREDELOLW\ RI [O&7r 7KH QHW UHVXOW LV WKDW WKH HOHFWURQV EHFRPH WUDSSHG LQ WKH JORZ UHJLRQ JHQHUDOO\ EHLQJ UHIOHFWHG DW WKH LQWHUIDFHV ZLWK WKH HOHFWURGH VKHDWKV LQFOXGLQJ WKH VKHDWK ZDOO EHIRUH HYHQWXDOO\ RYHUFRPLQJ WKH DQRGH EDUULHU 7KH HIIHFWLYH SDWK OHQJWK FROOHFWLRQ WLPHf LV WKHUHE\ LQFUHDVHG DV QHFHVVDU\ WR PDLQWDLQ WKH HOHFWURQ DQG LRQ GHQVLWLHV E\ HOHFWURQ LPSDFW LRQL]DWLRQ ,QWXLWLYHO\ RQH ZRXOG H[SHFW WKDW WKH DEVROXWH PDJQLWXGH RI WKH FXUUHQW GHQVLW\ DW WKH DQRGH ZRXOG EH DSSUR[LPDWHO\ WKH VDPH LQ ERWK FDVHV LRQL]DWLRQ LQ WKH GDUN VSDFH DQG LRQL]DWLRQ LQ WKH JORZ UHJLRQf %HFDXVH RI WKH WUDSSLQJ RI WKH ORZ HQHUJ\ HOHFWURQV ZLWKLQ WKH JORZ UHJLRQ WKH UDWH RI HOHFWURQ FROOHFWLRQ DW WKH DQRGH LQ WKH JORZ UHJLRQ LRQL]DWLRQ FDVH ZLOO EH PXFK PRUH H[WHQGHG DQG GHOD\HG LQ WLPH UHODWLYH WR WKH GDUN VSDFH LRQL]DWLRQ FDVH 7KLV LV LQGHHG ZKDW ZDV REVHUYHG H[SHULPHQWDOO\ :KHQ WKH ODVHU LV IRFXVVHG LQWR WKH GDUN VSDFH D IDVW UHODWLYHO\ VKDUS LRQL]DWLRQ VLJQDO LV REVHUYHG )LJXUH f ,I RQ WKH RWKHU KDQG WKH ODVHU LV IRFXVVHG LQWR WKH FHQWUDO SRUWLRQ RI WKH JORZ UHJLRQ WKH

PAGE 179

)LJXUH 2QHVWHS LRQL]DWLRQ VLJQDO REVHUYHG LQ FDWKRGH GDUN VSDFH

PAGE 180

P9G

PAGE 181

LRQL]DWLRQ VLJQDO LV ORQJHU E\ DSSUR[LPDWHO\ D IDFWRU RI f DQG GHOD\HG LQ WLPH E\ DSSUR[LPDWHO\ PV ,I WKH ODVHU LV QRW IRFXVVHG DQG FRYHUV WKH HQWLUH GLVFKDUJH WKHQ WKH REVHUYHG VLJQDO )LJXUH f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

PAGE 182

)LJXUH &RQYROXWLRQ RI LRQL]DWLRQ VLJQDOV IURP FDWKRGH GDUN VSDFH DQG QHJDWLYH JORZ UHJLRQ

PAGE 183

S VUL 6 f P9G c 9

PAGE 184

)LJXUH 7ZRVWHS H[FLWDWLRQ HQKDQFHPHQW RI 1H 2* HIIHFW LQ WKH +&/ Df 2VFLOORVFRSH WUDFH RI RQHVWHS H[FLWDWLRQ 2* VLJQDO RI 1H JURXQG VWDWHf Ef 2VFLOORVFRSH WUDFH RI RQHVWHS H[FLWDWLRQ 2* VLJQDO RI 1H H[FLWHG VWDWHf Ff 2VFLOORVFRSH WUDFH RI WZRVWHS H[FLWDWLRQ HQKDQFHPHQW RI 2* VLJQDO RI 1H

PAGE 185

P9G L P H c-V G L 9 f

PAGE 186

P9G L

PAGE 187

$ 3 VUL f D XX L P9G c

PAGE 188

QP 7KLV WUDQVLWLRQ RULJLQDWHV LQ WKH PHWDVWDEOH VWDWH RI 1H $V H[SHFWHG WKH VLJQDO VKRZV D IDVW QHJDWLYH JRLQJ SXOVH GXH WR LQLWLDO LRQL]DWLRQ HQKDQFHPHQW IROORZHG E\ D PXFK VORZHU SRVLWLYH JRLQJ SXOVH UHVXOWLQJ IURP GHSOHWLRQ RI WKH 1H PHWDVWDEOH SRSXODWLRQ 7KH VSHFWUDO HQHUJ\ GHQVLW\ RI WKH ODVHU ZDV [ n Pn +]n 7KLV FRUUHVSRQGV WR DSSUR[LPDWHO\ SKRWRQV 7KH PD[LPXP QHJDWLYH YROWDJH FKDQJH LV 9 )LJXUH E LV WKH 2* VLJQDO REWDLQHG E\ LUUDGLDWLQJ WKH GLVFKDUJH ZLWK $ ZLWK D VSHFWUDO HQHUJ\ GHQVLW\ RI [ n Pn +]n $V FDQ EH VHHQ WKH VLJQDOWRQRLVH LV PXFK ZRUVH WKDQ LQ WKH SUHYLRXV FDVH 7KLV GHFUHDVH LQ 61 LV WKH UHVXOW RI WZR PDLQ IDFWRUV )LUVW WKH WUDQVLWLRQ RULJLQDWHV LQ D PXFK KLJKHU HQHUJ\ VWDWH Sf RI 1H WKDQ WKH SUHYLRXV RQH 7KHUHIRUH RQH FDQ H[SHFW WKH SRSXODWLRQ GHQVLW\ RI WKLV OHYHO WR EH PXFK ORZHU WKDQ WKDW RI WKH PHWDVWDEOH OHYHO 6HFRQG WKLV H[FLWHG OHYHO GRHV QRW SOD\ D FHQWUDO UROH LQ WKH PDLQWHQDQFH RI WKH GLVFKDUJH DV GLVFXVVHG DERYH WKHUHIRUH RQH ZRXOG QRW H[SHFW WKH HOHFWULFDO FKDUDFWHULVWLFV RI WKH GLVFKDUJH WR EH DV VHQVLWLYH WR SRSXODWLRQ FKDQJHV LQ WKLV HQHUJ\ VWDWH )LJXUH F LV WKH 2* VLJQDO UHVXOWLQJ IURP WKH VLPXOWDQHRXV LOOXPLQDWLRQ RI WKH GLVFKDUJH E\ ERWK ODVHUVWXQHG WR WKH WZR WUDQVLWLRQV 7KH PD[LPXP YROWDJH FKDQJH DFURVV WKH GLVFKDUJH REVHUYHG LQ WKLV FDVH ZDV 9 WLPHV WKDW REVHUYHG LQ WKH FDVH RI LOOXPLQDWLRQ RI WKH GLVFKDUJH E\ WKH ILUVW ODVHU EHDP DORQH $OVR LQ WKH WZRVWHS FDVH ZKLOH WKH VSHFWUDO HQHUJ\ GHQVLW\ RI $ UHPDLQHG WKH VDPH WKH HQHUJ\ GHQVLW\ RI $ ZDV GHFUHDVHG E\ RUGHUV RI PDJQLWXGH UHODWLYH WR WKH LOOXPLQDWLRQ E\ $ DORQH 7KHUHIRUH D WZRVWHS HQKDQFHPHQW RI RYHU ZDV REVHUYHG IRU WKLV GRXEOH UHVRQDQFH VFKHPH RI 1H RYHU WKH VLQJOH UHVRQDQFH FDVH

PAGE 189

(YDOXDWLRQ RI 1H 2* LQ WKH +&/ DV D 6HQVLWLYH 3KRWRQ 'HWHFWRU &RPSDULVRQ RI D GHWHFWRU HYDOXDWHG IRU WUDQVLHQW VLJQDOV 5,'f WR D GHWHFWRU HYDOXDWHG IRU VWHDG\VWDWH VLJQDOV 307f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

PAGE 190

SHUIRUPDQFH FKDUDFWHULVWLFV RI WKH 1H +&/ 5,' ZDV WKH TXDQWXP HIILFLHQF\ RI WKH GHWHFWRU 7KLV TXDQWLW\ FDQ DOVR EH XVHG IRU FKDUDFWHUL]LQJ 307V DQG LV D FKDUDFWHULVWLF IXQFWLRQ RI WKH FDWKRGH PDWHULDO 7KH TXDQWXP HIILFLHQF\ 4( LV GHILQHG DV WKH UDWLR RI WKH QXPEHU RI HOHPHQWDU\ HYHQWV FRQWULEXWLQJ WR WKH GHWHFWRU RXWSXW WR WKH QXPEHU RI LQFLGHQW SKRWRQV 4( FKDUJHV FUHDWHG SKRWRQV LQFLGHQW f ,W JLYHV D GLUHFW PHDVXUH RI WKH FRQYHUVLRQ HIILFLHQF\ RI WKH GHWHFWRU LQ WHUPV RI QXPEHU RI HYHQWV PHDVXUHG SHU QXPEHU RI HYHQWV RFFXUULQJ ,Q PRUH FRPPRQO\ PHDVXUHG TXDQWLWLHV WKH TXDQWXP HIILFLHQF\ FDQ DOVR EH H[SUHVVHG DV WKH UDGLDQW FDWKRGLF VHQVLWLYLW\ V LQ P$ RXWSXW SHU : RI LQFLGHQW UDGLDWLRQ 7KH PD[LPXP UDGLDQW FDWKRGLF VHQVLWLYLW\ IRU D FRPPRQ 307 5 +DPDPDWVX &RUSf LV P$: 7KH SKRWRFDWKRGH TXDQWXP HIILFLHQF\ FDQ EH FDOFXODWHG IURP WKLV WR EH HnSK ,Q WKH 5,' WKH QXPEHU RI FKDUJHV LH HOHFWURQVf FUHDWHG GXULQJ WKH ODVHU SXOVH LV UHDGLO\ FDOFXODWHG IURP NQRZOHGJH RI WKH DUHD XQGHU WKH VLJQDO SURGXFHG E\ D VLQJOH ODVHU SXOVH 9 Vf DQG WKH ODPS LPSHGDQFH E\ XVLQJ HTXDWLRQ f ,I WKH SKRWRQ HQHUJ\ RI N LV GLVWULEXWHG RYHU D ODUJHU IUHTXHQF\ UDQJH WKDQ WKDW DFFHSWHG E\ WKH GHWHFWRU WKHQ D FRUUHFWLRQ PXVW EH PDGH IRU WKH QXPEHU RI LQFLGHQW SKRWRQV WKDW DUH QRW DEVRUEHG E\ WKH 1H ,Q RXU FDVH WKH OLQHZLGWK e$ RI WKH ODVHU ZKRVH HQHUJ\ LV EHLQJ PHDVXUHG LV EURDGHU WKDQ WKH DEVRUSWLRQ OLQHZLGWK

PAGE 191

RI WKH 1H LQ WKH +&/ 6$DEV 7KHUHIRUH D FRUUHFWLRQ PXVW EH PDGH IRU WKH SKRWRQV WKDW DUH WUDQVPLWWHG WKURXJK WKH +&/ :H GHILQH WKH HIIHFWLYH TXDQWXP HIILFLHQF\ KfL FKDUJHV FUHDWHG SKRWRQV DEVRUEHG FKDUJHV FUHDWHG SKRWRQV LQFLGHQW H[S R0QOA f@r f ZKHUH DV GLVFXVVHG DERYH WKH IDFWRU > H[SD $ fQOf@ LV VLPSO\ WKH IUDFWLRQ RI WKH LQFLGHQW SKRWRQV DEVRUEHG D KL 4( > H[S RLAf@f 4( f K D $ VLPSOH DEVRUSWLRQ H[SHULPHQW ZDV SHUIRUPHG WR GHWHUPLQH WKH PDJQLWXGH RI WKH FRUUHFWLRQ IDFWRU $ W\SLFDO WUDFH REWDLQHG LQ WKLV SDUW RI WKH H[SHULPHQW LQ VKRZQ LQ )LJXUH 7KH LQWHQVLW\ RI WKH ODVHU DW $ WUDQVPLWWHG WKURXJK WKH KROORZ FDWKRGH DQG WKH 2* VLJQDO LQWHQVLW\ ZHUH PRQLWRUHG VLPXOWDQHRXVO\ $V H[SHFWHG WKH WUDQVPLWWHG LQWHQVLW\ RI WKH ODVHU EHDP LV D PLQLPXP ZKHQ WKH RSWRJDOYDQLF DFWLYLW\ LV D PD[LPXP $YHUDJLQJ WKH UHVXOWV IURP VXFK VFDQV DQG NQRZLQJ WKH

PAGE 192

)LJXUH 6FDQ VKRZLQJ VLPXOWDQHRXV UHDGLQJ RI DEVRUSWLRQ RI $ DQG 2* VLJQDO IRU GHWHUPLQDWLRQ RI

PAGE 193

7UDQVPLWWDQFH :DYHOHQJWK QPf (f§f 2* VLJQDO 9f

PAGE 194

ODVHU OLQHZLGWK WR EH [ n P D ZDV IRXQG WR EH 6R b RI WKH LQFLGHQW SKRWRQV DW WKLV ZDYHOHQJWK ZHUH ZLWKLQ WKH $DEV RI 1H LQ WKH +&/ $ FDOLEUDWLRQ FXUYH REWDLQHG IRU WKH 1H WZRVWHS H[FLWDWLRQ XQGHU VWXG\ LV JLYHQ LQ )LJXUH 7KH VORSH RI WKLV FXUYH JLYHV WKH TXDQWXP HIILFLHQF\ RI WKH GHWHFWRU )URP )LJXUH D VORSH RI sf HSK LV REWDLQHG 7KHUHIRUH DW OHDVW XQGHU WKH RSHUDWLQJ DVVXPSWLRQV RI WKLV ZRUN XQLW\ SKRWRQ GHWHFWLRQ HIILFLHQF\ KDV EHHQ REWDLQHG $ ORJORJ SORW RI WKLV FXUYH LV JLYHQ LQ )LJXUH 7KH OLQHDU G\QDPLF UDQJH /'5f IRU WKH GHWHFWRU LV DSSUR[LPDWHO\ RUGHUV RI PDJQLWXGH )URP Q f WKH UDGLDQW VHQVLWLYLW\ DW QPf LV FDOFXODWHG WR EH P$: 7R VXPPDUL]H VR IDU WKH 1H 2* HIIHFW LQ WKH +&/ LV FDSDEOH RI VLQJOHn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f WKDW FDQ EH H[SHFWHG LQ WKLV

PAGE 195

)LJXUH &DOLEUDWLRQ FXUYH IRU 1H 5,' LQ WKH +&/

PAGE 196

f n 1f SKRWRQV DEVRUEHG

PAGE 197

)LJXUH /RJORJ SORW RI )LJXUH

PAGE 198

/RJ HOHFWURQV SURGXFHGf / /RJ SKRWRQV L L L L L L L L L L DEVRUEHGf

PAGE 199

)LJXUH 3ORW RI H[SHULPHQWDO DQG WKHRUHWLFDO 9UPVf YV ODPS FXUUHQW

PAGE 200

UPVf 9f WKHRU f ODVHU RII $ ODVHU RQ /DPS FXUUHQW P$f

PAGE 201

W\SH RI H[SHULPHQWDO DUUDQJHPHQW FDQ EH FDOFXODWHG IURP HTXDWLRQ PVf 5O f ZKHUH % GHWHFWLRQ IUHTXHQF\ EDQGZLGWK UHVSRQVH +]f 5O ODPS LPSHGDQFH Qf LWR GF RSHUDWLQJ FXUUHQW RI WKH ODPS $f $ SORW RI 9WKHRUPVf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n UHVSHFWLYHO\ DUH REWDLQHG 7KH WKHRUHWLFDO OLPLWV DUH FRUUHVSRQGLQJO\ [ SKRWRQV DQG [ -

PAGE 202

)LJXUH 3ORW RI VLJQDOWRQRLVH RI 1H 5,' YV ODPS FXUUHQW

PAGE 203

/DPS FXUUHQW $f RR 92

PAGE 204

)LJXUH 6XPPDU\ ILJXUH RI UHVXOWV VKRZLQJ WKH FDOLEUDWLRQ FXUYH DORQJ ZLWK WKH OLPLWLQJ H[SHULPHQWDO GDVKHG OLQHf DQG WKHRUHWLFDO GRWWHG OLQHf QRLVHV

PAGE 205

HOHFWURQV SURGXFHG WW /DVHU (QHUJ\ -f 4 4 +} SKRWRQV DEVRUEHG 2*6 P9f

PAGE 206

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

PAGE 207

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n UHVSHFWLYHO\ 7KH FRUUHVSRQGLQJ WKHRUHWLFDO OLPLWV ZHUH [ SKRWRQV DQG [ )XWXUH :RUN 7KH GLUHFWLRQ RI IXWXUH ZRUN VKRXOG EH WRZDUGV WKH HYDOXDWLRQ RI GLIIHUHQW NLQGV RI KROORZ FDWKRGH DQG ORZSUHVVXUH GLVFKDUJHV DV SRVVLEOH UHVRQDQFH LRQL]DWLRQ GHWHFWRUV $W SUHVHQW WKH PLQLPXP GHWHFWDEOH HQHUJ\ DQG QXPEHU RI SKRWRQV LV VHW E\ WKH VKRW QRLVH RI WKH ODPS 7KUHH SRVVLEOH DYHQXHV DUH RSHQ WR RYHUFRPH WKHVH SUREOHPV f LQFUHDVLQJ WKH YROXPH RI WKH GHWHFWRU LOOXPLQDWHG E\ WKH ODVHU EHDPV VKRXOG UHVXOW LQ DQ LQFUHDVHG SKRWRQ VHQVLWLYLW\ UHVXOWLQJ LQ D ORZHU PLQLPXP GHWHFWDEOH HQHUJ\ f XVH RI DQ REVWUXFWHG JORZ GLVFKDUJH KDV VKRZQ WR SURYLGH VLJQDOV VRPH WLPHV ODUJHU WKDQ D FRQYHQWLRQDO KROORZ FDWKRGH GLVFKDUJH DQG f KROORZ FDWKRGH GLVFKDUJHV FDQ EH GHVLJQHG ZKLFK FDQ RSHUDWH EHORZ HYHQ WKH WKHRUHWLFDO VKRW QRLVH OLPLW

PAGE 208

$OVR WKH XVH RI ORZSUHVVXUH FHOOV RI DWRPLF YDSRUV DV UHVHUYRLUV IRU WKH 5,' KROG SRWHQWLDO SURPLVH 7KH ORZ SUHVVXUH ZRXOG HQVXUH 'RSSOHU EURDGHQHG OLQHV ZLWK WKH FRUUHVSRQGLQJO\ KLJK ZDYHOHQJWK VHOHFWLYLW\ ,Q WKLV FDVH KRZHYHU WKH DWRPV ZRXOG KDYH WR EH SKRWRLRQL]HG RU ILHOG LRQL]HG VLQFH WKH QXPEHU GHQVLW\ RI FROOLVLRQ SDUWQHUV LV UHODWLYHO\ ORZ DQG WKH DWRP HQYLURQPHQW LV RI UHODWLYHO\ ORZ HQHUJ\ 3KRWRLRQL]DWLRQ PD\ SURFHHG HLWKHU E\ DEVRUSWLRQ RI D SKRWRQ ZKRVH HQHUJ\ LV JUHDWHU WKDQ WKH HQHUJ\ GHILFLW EHWZHHQ WKH KLJKHVW H[FLWHG OHYHO DQG WKH LRQL]DWLRQ FRQWLQXXP RU E\ SURPRWLRQ RI WKH DWRP LQWR DQ DXWRLRQL]LQJ OHYHO $Q DXWRLRQL]LQJ OHYHO LV D UHDO DWRPLF OHYHO LQ WKH LRQL]DWLRQ FRQWLQXXP $Q DWRP SURPRWHG LQWR DQ DXWRLRQL]LQJ OHYHO VSRQWDQHRXVO\ GHFD\V WR WKH LRQ 7KH DEVRUSWLRQ FURVVVHFWLRQV IRU DXWRLRQL]LQJ WUDQVLWLRQV DUH RI WKH VDPH RUGHU RI PDJQLWXGH DV WUDQVLWLRQV EHWZHHQ ERXQG DWRPLF OHYHOV DQG RUGHUV RI PDJQLWXGH JUHDWHU WKDQ SKRWRLRQL]DWLRQ FURVV VHFWLRQV 7KHUHIRUH LW LV PXFK HDVLHU WR HQVXUH VDWXUDWLRQ RI DQ DXWRLRQL]DWLRQ WUDQVLWLRQ WKDQ D SKRWRLRQL]LQJ WUDQVLWLRQ ,Q ILHOG LRQL]DWLRQ DWRPV H[FLWHG WR KLJKO\LQJ 5\GEHUJ OHYHOV RI WKH DWRP DUH LRQL]HG E\ DSSOLFDWLRQ RI D KLJK LQWHQVLW\ HOHFWULF ILHOG EHWZHHQ WZR SODWHV 7KH PDJQLWXGH RI WKLV ILHOG LV QRUPDOO\ RQ WKH RUGHU RI N9FP ,Q WKH FDVH RI DXWRLRQL]DWLRQ RI WKH DWRPV DX[LOLDU\ SODWHV PXVW EH LQWURGXFHG LQWR WKH FHOO WR FROOHFW WKH LRQV IRUPHG ZKHUHDV IRU ILHOG LRQL]DWLRQ WKH LRQL]LQJ SODWHV PD\ DOVR VHUYH DV WKH FROOHFWLRQ HOHFWURGHV 8QOLNH WKH HOHFWULF GLVFKDUJH D PDMRU DGYDQWDJH RI WKH ORZ YDSRU SUHVVXUH FHOO LV WKDW WKHUH LV HVVHQWLDOO\ QR EDFNJURXQG LRQL]DWLRQ 7KHUHIRUH WKH SRWHQWLDO IRU

PAGE 209

VLQJOHSKRWRQ GHWHFWLRQ LV PXFK KLJKHU 8QIRUWXQDWHO\ IRU VXFK D GHWHFWRU DQ LQHUW JDV FRXOG QRW EH XVHG DV D GHWHFWRU HOHPHQW VLQFH WKHUH ZRXOG QRW EH D VLJQLILFDQW SRSXODWLRQ RI WKH PHWDVWDEOH VWDWH 7KLV KRZHYHU PD\ SURYH WR EH D PLQRU GLVDGYDQWDJH ZKHQ FRPSDUHG WR WKH QHJOLJLEOH EDFNJURXQG RI WKH ORZSUHVVXUH FHOO

PAGE 210

5()(5(1&( /,67 7ROJ $QDO\VW f -5 'DYLV -U $ 5RKDWJL 5+ +RSNLQV 3' %ODLV 3 5DL&KRXGKXU\ -5 0F&RUPLFN DQG +& 0ROOHQNRSI ,((( 7UDP (OHFWURQ 'HYLFHV (' f 7< .RPHWDQL $QDO &KHP f <+ 3DR 51 =LWWHU DQG -( *ULIILWKV 2SW 6RF $P f <+ 3DR DQG -( *ULIILWKV &KHP 3K\V f &$ 0RUWRQ $SSO 2SW f 0/ )UDQNOLQ +RUOLFN DQG +9 0DOPVWDGW $QDO &KHP f &RPPLVVLRQ ,QWHUQDWLRQDOH GH Of(FODLUDJH ,QWHUQDWLRQDO /LJKWLQJ 9RFDEXODU\ 3XEO 1R &,( 3DULV : +HUVFKHO 3KLO 7UDP 5R\ 6RF f /1RELOL DQG 00HOORQL $QQ &KLP 3K\V f 63 /DQJOH\ 1DWXUH f :1 +DUWOH\ 3KLO 7UDP f + +HUW] $QQ 3K\V f + +HUW] $QQ 3K\V f + +HUW] $QQ 3K\V f $ 5LJKL 3KLO 0DJ f (OVWHU DQG + *HLWHO $QQ 3K\V f /5 5ROOHU 2SW 6RF $P f /5 5ROOHU 3K\V 5HY f -$ 5DMFKPDQ DQG 5/ 6Q\GHU (OHFWURQLFV f

PAGE 211

9. =ZRU\NLQ DQG (* 5DPEHUJ 3KRWRHOHFWULFLW\ DQG ,WV $SSOLFDWLRQV :LOH\ DQG 6RQV 1HZ
PAGE 212

0DWYHHY 1% =RURY DQG
PAGE 213

' 7RQ7KDW 05 )ODQQHU\ 9L\V 5HY $ f DQG UHIHUHQFHV WKHUHLQ (: 0F'DQLHO &ROOLVLRQ SKHQRPHQD LQ LRQL]HG JDVHV :LOH\ 1HZ
PAGE 214

.& 6P\WK 3. 6FKHQFN &KHP 3K\V /HWW f *6 +XUVW 0* 3D\QH 6' .UDPHU DQG -3
PAGE 215

( 9RLJWPDQ $SSO 6SHF )HE f LQ SUHVV ( 9RLJWPDQ DQG -' :LQHIRUGQHU 3URJ $QD/ $WRP 6SHFWURVF f -( /DZOHU $, )HUJXVRQ -(0 *ROGVPLWK '+ -DFNVRQ DQG $/ 6FKDZORZ 3K\V 5HY /HWW f

PAGE 216

%,2*5$3+,&$/ 6.(7&+ *LXVHSSH $QWRQLR 3HWUXFFL ZDV ERUQ LQ )DLFFKLR %1f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

PAGE 217

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
PAGE 218

7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ LQ WKH &ROOHJH RI /LEHUDO $UWV DQG 6FLHQFHV DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 'HFHPEHU 'HDQ *UDGXDWH 6FKRRO

PAGE 219

) IORULGD $ - / B fr}


THE OPTOGALVANIC EFFECT IN A HOLLOW CATHODE DISCHARGE:
A RESONANCE DETECTOR FOR VERY WEAK LIGHT LEVELS
By
GIUSEPPE ANTONIO PETRUCCI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1990

Copyright 1990
by
Giuseppe Antonio Petrucci

Per i miei genitori

ACKNOWLEDGEMENTS
I would like to thank many group members, past and present, who helped
bring about the completion of this work and who made my stay here an enjoyable
and often-times interesting and confusing one. There are, of course, some who had
a more pronounced influence on me, during the course of this work. Josef
Simensson, my "circus friend", who jumped through all the hoops with me; Chris
Stevenson, for his much appreciated help in the lab; and, Norma Ayala, for policing
my wardrobe. They all helped very much to make some very frustrating times
tolerable. Their friendship outside of the lab was priceless.
I would like to thank Jim Winefordner for his guidance throughout this work.
His example of perseverance and hard work will always be with me.
I would also like to thank Ben Smith. His contributions to my work, both
practically and emotionally, are incalculable. His advice often kept me going when
my spirits were down. I think that I can safely say that without his help, the
completion of this dissertation would have been a monstrous task.
On a more practical nature, I would like to thank Steve Miles who made
invaluable contributions in the electronics part of this work. His willingness to help,
discuss with (and teach) me some of the "black magic" of electronics is greatly
iv

appreciated. I should give a special thanks to the secretaries, Jeanne Karably and
Susan Ciccarone, for putting up with me and my "unique" questions.
Finally, I would like to thank my (soon to be) wife, Nancy. Whether she
realizes it or not, her support of and confidence in me has always strengthened my
heart. At times when I strongly doubted myself and my abilities, she brought back
into my life a perspective and respect for myself that I often lost.
v

TABLE OF CONTENTS
ACKNOWLEDGEMENTS iv
LIST OF TABLES ix
LIST OF FIGURES x
ABSTRACT xiii
CHAPTER 1
INTRODUCTION 1
Need for a High Sensitivity Photon Detector 1
Photon Detectors 2
Intent of Dissertation 6
CHAPTER 2
CONCEPT OF RESONANCE MONOCHROMATOR 7
Historical Background 7
Resonance Spectrometers 10
Fluorescence Resonance Spectrometer 11
Resonance Ionization Detector 12
Line Broadening Mechanisms 17
Natural Broadening 17
Collisional Broadening 19
Doppler Broadening 20
CHAPTER 3
OPTOGALVANIC EFFECT 27
Introduction 27
Anatomy of a Glow Discharge 28
vi

Electrical Maintenance of the Discharge
35
CHAPTER 4
CONCEPT OF RESONANCE MONOCHROMATOR 38
Introduction 38
Theory 39
Phenomenological Description of Ionization Mechanisms 39
Evolution of OG Signals 40
Negative Voltage Changes 41
Positive Voltage Changes 44
Mathematical Treatment of OG Signals 49
Double-resonance Optogalvanic (DROG) Effect 54
CHAPTER 5
CONSIDERATIONS ON THE INTERACTION OF ATOMS
WITH LIGHT 58
Absorption of Radiation 58
Laser Excitation of Atomic Transitions 60
Single-Step Excitation 60
Optical Saturation of an Atomic Transition 63
Two-step Excitation 65
CHAPTER 6
EXPERIMENTAL 69
General Experimental Configuration 69
Pick-off Circuitry for OG Signal 74
One-step Excitation Experiments 74
Two-step Excitation Experiments 81
Timing of Laser Beams in Two-step Excitation Experiments 81
Absorption Experiments 86
Saturation Curves 91
Measurement for Enhancement of Two-step Excitation of Na
and Pb 91
vii

CHAPTER 7
RESULTS AND DISCUSSION 92
Sodium OG Effect 92
Determination of Lamp Impedance 100
Evaluation of Collisional Ionization Rate Constants by the
OG Effect 103
Two-step OG effect of Na 104
Lead OG Effect in the HCL 110
Neon OG Effect in the HCL 117
Electronic Configuration of Ne 117
One-step Neon and Uranium OG Effect 122
Case 1 125
Case 2 131
Case 3 136
Case 4 146
Neon OG Signal Dependence on Lamp Current 151
Double-resonance OG Effect of Ne 154
Optimization of Boxcar Gate Position 157
Alignment of Laser Beam(s) in the Hollow Cathode 161
Ionization Within the Negative Glow 162
Ionization Within the Dark Space 167
Two-step Enhancement of Ne OG Effect 167
Evaluation of Ne OG in the HCL as a Sensitive Photon Detector . . . 175
CHAPTER 8
FINAL COMMENTS 192
Summary 192
Future Work 193
REFERENCE LIST 196
BIOGRAPHICAL SKETCH 202
viii

LIST OF TABLES
Table 1. Values used for calculating n jnx in equations (26) and (27) 68
Table 2. Listing of experimental components 73
Table 3. Experimental values for determining nt in equation (32) 105
Table 4. Values used to calculate v¡ and ve in equation (44) 163
ix

LIST OF FIGURES
Figure 1. Resonance monochromator proposed by Sullivan and Walsh [23] 9
Figure 2. Resonance ionization detector 15
Figure 3. Normalized Lorentzian line profile 23
Figure 4. Normalized Gaussian line profile 25
Figure 5. Electrical regions of a dc discharge [53] 30
Figure 6. Voltage distribution across a dc glow discharge 32
Figure 7. Electron energy distribution across a dc glow discharge 34
Figure 8. Oscilloscope trace of the negative OG signal for the
3s12S1/2 -- > 3p* 2P3/2 transition of Na 43
Figure 9. Oscilloscope trace of the positive OG signal for the
3P2 (1s5) --> 3D3 (2p9) transition of Ne 46
Figure 10. Partial energy level diagram of Ne 48
Figure 11. Electric field distribution across the dc glow discharge 52
Figure 12. Partial energy level diagram of Na 56
Figure 13. Possible excitation/deexcitation process in an atom 62
Figure 14. General experimental configuration 71
Figure 15. Diagram of a common HCL (lamp 1) 76
Figure 16. Diagram of a Galvatron (see-through HCL) (lamp 2) 78
Figure 17. a) Pick-off circuit for measuring OG signals
b) Diagram of housing for pick-off electronics and lamp holder . . 80
Figure 18. Alignment of laser(s) through lamp 1 83
Figure 19. Alignment of laser(s) through lamp 2 85
x

Figure 20. Oscilloscope trace of temporal coincidence of the two
laser beams at the hollow cathode 88
Figure 21. Experimental configuration for absorption experiments 90
Figure 22. OG signals for ground state transitions of Na 94
Figure 23. Example of signal-to-noise attainable using the OG effect 96
Figure 24. OG signal for excited state transition of Na 99
Figure 25. Plot of (Fout)_1 vs Rb for determination of lamp impedance .... 102
Figure 26. Two-step enhancement of Na OG signal 107
Figure 27. Collisional coupling of Na energy levels in the HCL 109
Figure 28. Partial energy level diagram for Pb 112
Figure 29. Two-step enhancement for Pb OG signal 114
Figure 30. Pb two-step OG signal vs lamp current 116
Figure 31. OG spectrum of U/Ne lamp from 580 - 601 nm 119
Figure 32. Expanded U OG spectrum from 580 - 601 nm 121
Figure 33. OG spectrum of U/Ne lamp from 594 - 607 nm 124
Figure 34. Saturation curve for 597.55 nm absorption of Ne 128
Figure 35. Log-log plot of Figure 34 130
Figure 36. Saturation curve for 598.80 nm absorption of Ne 133
Figure 37. Log-log plot of Figure 36 135
Figure 38. Proposed excitation/ionization scheme for 598.80 nm
absorption of Ne 138
Figure 39. Excitation scheme through a virtual level 140
Figure 40. Saturation curve for 599.56 nm absorption of Ne 143
xi

145
Figure 41. Log-log plot of Figure 40
Figure 42. Saturation curve for 599.24 nm absorption of U 148
Figure 43. Log-log plot of Figure 42 150
Figure 44. Proposed excitation/ionization scheme for 599.24 nm
absorption of U 153
Figure 45. Plot of relative laser induced impedance change vs.
lamp current 156
Figure 46. Boxcar gate position considerations 160
Figure 47. One-step ionization signal observed in cathode dark space .... 166
Figure 48. Convolution of ionization signals from cathode dark space
and negative glow region 169
Figure 49. Two-step enhancement of Ne OG signal in HCL
a) Oscilloscope trace of one-step excitation OG signal of
Ne (ground state) 171
b) Oscilloscope trace of one-step excitation OG signal of
Ne (excited state) 172
c) Oscilloscope trace of two-step excitation enhancement of
OG signal of Ne 173
Figure 50. Scan showing simultaneous recording of absorption of A.12
and OG signal for determination of a 179
Figure 51. Calibration curve for Ne RID in the HCL 182
Figure 52. Log-log plot of Figure 51 184
Figure 53. Plot of V(rms) vs lamp current .' 186
Figure 54. Plot of signal-to-noise of Ne RID vs. lamp current 189
Figure 55. Summary figure of results 191
xii

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
OPTOGALVANIC EFFECT IN A HOLLOW CATHODE LAMP:
A SENSITIVE DETECTOR FOR VERY WEAK LIGHT LEVELS
By
GIUSEPPE ANTONIO PETRUCCI
DECEMBER 1990
Chairperson: James D. Winefordner
Major Department: Chemistry
Both one- and two-step excitation optogalvanic (OG) effects in two
commercially available hollow cathode lamps are studied. Elements studied are
sodium, lead, uranium and neon. Four different excitation/ionization mechanisms
were observed by the OG effect and are discussed. These include: 1) one-step
excitation followed by collisional ionization; 2) one-step excitation followed by
photoionization; 3) two-step excitation through a virtual level, followed by collisional
ionization; and, 4) two-step excitation through a virtual level, followed by
photoionization. The two-step excitation to a real level followed by collision and
photoionization were also observed for Ne. Two-step excitation enhancements in the
OG effect of Na, Pb and Ne, relative to the one-step excitation cases were
determined.
xiii

The use of a coupled, step-wise, two-step excitation of Ne in the hollow
cathode lamp was evaluated as a sensitive detector for very low light levels. The first
transition studied was the 3P2(ls5) --> 3D3(2p9), at a wavelength of 640.225 nm. The
excited state transition, coupled to the first transition, was the 3D3(2p9) --> 4d4’
transition, at 576.442 nm. The limiting experimental noise was determined to be the
shot noise of the hollow cathode lamp. Under optimized conditions, the
experimentally attained minimum detectable energy and number of photons were 6
x 10'15 J and 2 x 104 photons, respectively. The limits of detection corresponding to
the theoretical shot noise limit in the experimental system were 1 x 10'16 J and 4 x
102 photons.
xiv

CHAPTER 1
INTRODUCTION
Need for a high sensitivity photon detector
The search for and development of methods for determining traces of
elements is one of the most important trends in analytical chemistry [1].
Development of these methods is determined to a large extent by the needs of
various branches of science, technology and industry relating to the production and
use of ultrapure materials. Two examples of the need for ultra-trace analysis include
the study of the effect of impurities during the production of silicon solar-cells [2]
and the production of optical glass [3]. In meeting these needs, the problem of
measuring light intensities and their spectral distribution at very low levels is
becoming considerably important.
In contemporary optical spectroscopy, complex and expensive monochromators
and photon detectors are used for discriminating and detecting an extremely narrow
wavelength range in a light train with an arbitrary spectral composition. Such
instruments must possess high sensitivity to the photons to be detected and high
spectral resolution for reducing background noises. At present, two kinds of
photoelectric measurements are being used to accomplish the measurement of very
low light levels. These are referred to as analog [4,5] and digital [6,7] schemes.
1

2
With the digital method, contributions from photoelectrons are resolved in time so
that the signals in the form of electron pulses are detected by means of a pulse
counting system. This technique is the one of choice when concerned with the
measurement of ultra-low light levels.
Photon detectors
A detector of optical radiation is defined by the Commission Internationale
de l’Eclairage [8] as a device in which incident optical radiation produces a
measurable physical effect. Two classes of detectors of optical radiation produce a
measurable signal by one of two primary detection mechanisms: the photoelectric
effect (photon detectors) and the thermal effect (thermal detectors). Photon
detectors are the most common in optical spectroscopy for the measurement of low
light levels. Photomultipliers (PMTs) are the standard photon detector in
commercial spectroscopic instruments. Their basis of operation is the generation or
change of an electric signal by an external photoelectric effect in which a
photoelectron is emitted by a cathode and captured by a second electrode (or
dynode). The important feature of the PMT is the dynode system, which consists of
electrodes covered with special materials which emit various "secondary electrons"
per incident primary electron. The number of dynodes in PMTs ranges from 3-6,
resulting in a total gain or amplification of the cathodic photo-induced current of up
to 107 or more.

3
The detection of light has undergone a great metamorphosis since 1800 when
Sir William Herschel [9] used an ordinary thermometer to measure the intensity of
light passing through different filters. In 1831, Nobili and Melloni [10] developed
a thermocouple for the quantitation of light intensity. Samuel Pierpont Langley
[11], in 1881, developed the bolometer which was 30 times more sensitive than
Melloni’s thermocouple. The bolometer is based on the change in resistance of a
wire as it is heated. By incorporating the wire into a Wheatstone bridge, high
sensitivities were possible. In 1884, W.N. Hartley [12] applied photographic
detection of light intensity to quantitative chemical analysis. The key development
in the use of photography as a means of detection for quantitative chemical analysis
was the concept of using an internal standard. The next step in the development of
detection systems for spectroscopy was the development of photoelectric detection.
The origins of photoelectric detection date back to Hertz [13,14,15]
who observed that a spark produced by one circuit was somehow transmitted through
space so as to induce a spark in a secondary circuit even though the two circuits were
not connected directly. By placing a slit and a quartz prism between the primary
spark and the induced spark gap, he was able to show that the effect occurred only
when the prism was arranged to transmit light in the ultraviolet region of the
spectrum. The next year, A. Righi [16] demonstrated that a small current could
be made to flow between a mesh grid and a polished metal plate when the plate was
irradiated. The study of the photoemissiveness of different materials, mostly
amalgams of alkali metals, was undertaken by Elster and Geitel [17] and the first

4
modern photoemissive surface was described by L.R. Koller [18,19]. Even with
the great strides made in improving the sensitivity of photocathode materials, the
most sensitive surface could not pass a large amount of current without destroying
the photoemissive layer. In 1940, Rajchman and Snyder developed a nine-stage
electrostatically focussed multiplier phototube that has served as a model for
"modern" photomultiplier tubes [20].
In general, the spectral responsiveness of photon detectors is selective, being
determined largely by the chemical-physical composition of the materials used to
absorb photons. This spectral responsivity of individual photocathode materials is
normally "limited" to a wavelength range of approximately 600-700 nm in width
[21]. This dictates that for higher spectral resolution of the detected line, a primary
disperser must be used to separate the incident light into its component wavelengths,
before it is made incident on the photocathode of the PMT. Monochromators are
the method of choice for wavelength dispersion of the incident light.
Monochromators with several dispersing stages in series are used for very high
resolution of the wavelength of interest and reduction of stray light.
Two main criteria used to evaluate monochromators are optical throughput
and resolution. The optical throughput of a monochromator is defined as the
amount of radiation reaching the detector for a given amount leaving the source.
The effective throughput of the entire monochromator is limited by the portion of
the instrument with the smallest throughput. In conventional monochromators, the
limiting throughput is either the entrance or exit slit of the monochromator.

5
The resolution, on the other hand, is a measure of the ability of the
monochromator to disperse incident light composed of many different wavelengths
into its component wavelengths. It is given by the product of the width of the
entrance or exit slit (assumed to be equal in this case) and the reciprocal linear
dispersion of the dispersing element in the monochromator. The product of the
throughput and resolution is constant for a given monochromator. However, since
resolution improves with narrower slit widths and throughput increases with wider
slit widths, the spectroscopist is constantly faced with a choice of compromise
conditions involving resolution and throughput.
For a single-stage monochromator the throughput is on the order of 10‘2-10‘3.
For multiple-stage monochromators, the overall throughput is a product of the
throughput of each stage. So, for a triple-stage monochromator, the fraction of
incident light that reaches the PMT is only 10'7-10'9. This inverse relation between
throughput and resolution is one of the major limitations of using conventional
detectors. The other major limitation is a result of the low quantum efficiency of the
photocathodes of PMTs.
The quantum efficiency is defined [8] as the ratio of the number of elementary
events (e.g., photoelectrons) contributing to the detector output to the number of
incident photons. For most cathode materials, the quantum efficiency is very low;
on the best sensitized commercial photosurfaces, the maximum yield reported is as
high as one electron for three light quanta incident on the photocathode. An ideal
photodetector has a quantum efficiency of 1; i.e. every incident photon produces one

6
photoelectron. All practical photocathode materials have quantum efficiencies of less
than 1. Therefore, a PMT could never detect a single photon from the source.
As described below, resonance spectrometers offer the advantages over
monochromator/PMT detection systems, of high spectral resolution (10'3 nm) in
conjunction with a high optical throughput (>0.5).
Intent of dissertation
The present work was intended to evaluate and characterize a photon detector
based on the optogalvanic effect in a commercial hollow cathode lamp. Optical
transitions of sodium, lead and neon, the inert filler gas were considered for the
detector. Both single- and double-resonance excitation schemes were used. Also,
several single-step transitions of Ne and U were studied in terms of excitation-
ionization mechanisms.

CHAPTER 2
CONCEPT OF RESONANCE MONOCHROMATOR
Historical Background
The requirements of high sensitivity and wavelength selectivity were already
met in 1905 through the simple and effective techniques for discriminating resonance
radiation of specific elements which were based on the resonance absorption of
photons and their subsequent re-emission in atomic vapors of the element [22].
Such a device is termed a resonance monochromator (RM) and was first proposed
in 1968 as an accessory for modern spectroscopy by Sullivan and Walsh [23]. The
basic concept of the RM, as a detector for atomic absorption spectroscopy, is shown
in Figure 1.
The light from several spectral lamps is collimated and passed through the
flame. The radiation transmitted is then passed into several RMs. Each spectral
lamp (or element of interest) has a corresponding RM. In Sullivan and Walsh’s case,
the RMs were simply high current hollow cathode lamps to provide the requisite
atomic vapor density with minimal emission. Upon absorption of resonance radiation
by the RM, ground state analyte atoms would be excited and subsequently reemit the
radiation, which was observed at right angles to the incoming radiation. Each RM
7

Figure 1. Resonance monochromator proposed by Sullivan and Walsh [23] for atomic absorption spectroscopy.

ATOMIC SPECTRAL
LAMPS
CONCAVE
GRATING
A
A
FLAME
r1 PHOTOCELLS
/o\
L7Z//1 FILTERS 1////1
r77//l FILTERS rTyyyi
VO

10
would then respond selectively to the transmitted intensity of the corresponding
analysis lamp.
Since 1968, resonance spectrometers based on several optical and electrical
principles have been studied, including fluorescence, ionization and optoacoustic
techniques. A variety of atom cells have also been studied for resonance detection.
Among these are flames [24] (laser enhanced ionization, LEI), hollow cathode
lamps [25,26] (Optogalvanic effect, OGE), high-frequency spectral lamps [27]
and furnaces [28]. Resonance monochromators, however, have been used mainly
for absorption experiments.
Resonance Spectrometers
Resonance spectrometers offer several important advantages over
conventional spectrometers. They possess an inherently high spectral resolution (10'3
nm), a large solid angle of collection of the incoming light (up to 2n sr), low intrinsic
noise, and high quantum efficiency, namely, the capability of single photon detection.
This is in contrast to photomultiplier tubes, which have maximum cathode efficiencies
of about 30%, meaning that at best, 3 photons are required on the average for the
detector to record an event. Also, as stated above, several different spectroscopic
techniques may be used as the basis for a RM. Two of the most studied are
fluorescence (fluorescence resonance spectrometer, FRS) and atomic ionization
(resonance ionization detector, RID). Atomic ionization is used here as a generic

11
term for all spectroscopies which are based upon the galvanic measurement of
ionization rate enhancements induced by the absorption of resonance radiation.
Fluorescence Resonance Spectrometer
The fluorescence-based resonance spectrometer has been the most widely used
by far. The resonance spectrometer proposed by Sullivan and Walsh [23] was of the
fluorescence type. The principle of operation is based on the absorption of the
resonance radiation of interest by atoms in the optical cell and the recording of the
emitted (resonance or non-resonance fluorescence) light. Such a resonance
spectrometer was used by Bolger [29] for the recording of weak Raman scattering.
In this experiment, a 10 ns, 1 kW pulsed tunable dye laser, with a bandwidth of 0.1
cm'1 (SX =0.002 nm) was used to illuminate the sample. The wavelength of the laser
was chosen so that the Raman scattered light was around 455 nm. This light was
used to excite Cs atoms. The fluorescence of the Cs atoms at 850 nm was then
measured as the analytical signal. The detector sensitivity was found to be
approximately 3 orders of magnitude higher than a dispersion system with a
conventional detector.
The first fluorescence resonance spectrometer (FRS) working with transitions
from excited states was proposed and studied by Gelbwachs et al [30]. They
excited Na atoms in the FRS to the 4P3/2 state (A. =330.3 nm) with a dye laser.
Radiation from a xenon arc lamp, 3.42, 2.34, and 1.48 |im, was then absorbed by the
excited Na, promoting it to the 5S1/2, 4D5/2, and 5D5/,2 levels, respectively. They then
observed fluorescence of the Na in the visible region at wavelengths of 616, 569, and

12
548 nm, respectively, for the three transitions. The same workers also proposed and
studied the only tunable FRS. This RM, based on potassium, was made tunable over
a narrow spectral range by shifting of the highly excited energy levels of K by the
quadratic Stark effect [31]. One of the problems of fluorescence-based resonance
spectrometers is the need still for a separate monochromator and photon detector.
With an FRS some means of isolating the fluorescent light from the FRS from other
wavelengths and a photoelectric detector are still required to measure the intensity
of fluorescent photons from the FRS. Therefore, the throughput and resolution
limitations of a monochromator/PMT detector are still applicable, albeit to a lesser
extent than in the simple case of detection with a monochromator and PMT. Also,
the less than unity quantum efficiency of the photocathode material of the PMT
places a fundamental limit on the minimum detectable number of photons.
Resonance Ionization Detector
Atomic ionization (AI) methods have been proven to be very sensitive
spectroscopic techniques [32,33]. They are based on the recording of charged
particles which are formed in the atom cell upon absorption of resonance radiation
followed by subsequent ionization of the excited atoms by various processes. In the
extreme case of detecting single charges, proportional gas counters are used. For
bulk measurement of a large number of charges formed, the impedance or current
change across the atom cell is measured. Limits of detection in normal atmospheric
pressure atomizers are in the low ng/mL to pg/mL (or pg to fg absolute detection
limits) [34]. V.S. Letokhov [35] was the first to draw attention to the fact that

13
it is possible to detect even single atoms by the AI method. This limit of single atom
detection, or SAD, was experimentally attained by Hurst et al, [36,37] for Cs and
by Bekov et al [38] for Na and Y. Detection of single atoms is possible by AI
because of the ability to detect charges with unity efficiency.
Matveev et al [39] first proposed the use of laser-enhanced ionization in a
flame as a photon detector. Work to date has been mainly on the theoretical
feasibility of such a detector [40,41,42]. Okada et aL [43] were the first to
report quantitative results of a selective laser ionization photodetector. They
reported a minimum detectable energy, in the first wavelength, of 10'11 J, while Smith
et al. [44] are the only workers to record a Raman spectrum with a RID. Their
minimum detectable energy can be estimated as approximately 10'16 J at 285 nm.
The case of the RID (Figure 2) is very similar to that of the FRS. Radiation
(hv Remitted from the sample (SA) is conveyed by an optical system into the RID,
which contains a high concentration of atomic vapor. In the simple case of detecting
atomic emission or resonance fluorescence, the atomic vapor in the RID is the same
as the analyte of interest in the sample. Absorption of the radiation upon passing
into the RID causes a measurable change in the electrical properties of the RID.
For detection of scattered radiation (eg. Raman scatter), the RD becomes
much more favorable and versatile to use than conventional dispersive instruments
with photomultiplier detection. In Raman spectroscopy, for example, one is
interested in measuring the intensity of scattered radiation shifted in energy by a
characteristic amount from the central frequency of the exciting light. The

Figure 2.
Schematic of a resonance ionization detector. The optical processes occurring in the sample atomizer
(SA) and resonance ionization detector (RID) are given on the right side of the drawing.

LASERS
RID

16
frequency shift is characteristic for a particular scatterer and is given by
Av* "
Stokes
(1)
where A\TR is the characteristic Raman scatter energy, and 1/A.exc and l/A.Stokes are
the wavelengths of the exciting light and Raman shifted light, respectively.
It is important to emphasize the inverted nature of the RID approach of
Raman scatter compared to conventional detection. In conventional Raman
spectroscopy, the spectrum of the Raman scattered light is obtained by imaging the
scattered light onto the entrance slit of a double monochromator. The
monochromator is then scanned from wavelengths longer than the exciting
wavelength to the central exciting wavelength, thereby observing the different Av’s
for the scatterer. In "RID" Raman spectroscopy, the detector operates at a fixed
wavelength, dictated by the energy level scheme of the "detector element." The
exciting light must therefore be scanned to shorter wavelengths than the expected
Raman scattered wavelengths. Any element can be chosen for the RID which gives
the best sensitivity and selectivity, and then the frequency of excitation for the
Raman scatter is chosen such that the scattered radiation will be at a frequency
detectable by the RID.
One of the major advantages of such a detector is that it will respond only to
wavelengths of radiation that are within the absorption bandwidths of the various

17
transitions of the RID element. Anything outside of the absorption bandwidth of the
RID element will not be absorbed and will therefore not produce a signal.
Line-Broadening Mechanisms
The absorption (response) bandwidth of the RID element will depend on the
operative broadening mechanism of the atomic line in the RID. This makes the RID
inherently insensitive to problematic scattered light. Atomic lines are not truly
monochromatic and do possess a finite frequency (or wavelength) distribution. The
finite widths obtained are a result of a variety of line-broadening phenomena. The
width of the line is normally characterized by the width at one-half the maximum
height, or full-width at half maximum, FWHM. All of the different line-broadening
phenomena result in a frequency distribution of the atomic transition which can be
described by either a Lorentzian or Gaussian expression. However, since more than
one line-broadening process can be operative at any one time, the overall profile is
neither purely Lorentzian or Gaussian, but a combination of the two, known as a
Voigt profile. The predominance of one or more of the line-broadening mechanisms
is a function of the chemical and physical environment of the absorbing or radiating
atom. The three most commonly discussed broadening mechanisms are natural
broadening, collisional or pressure broadening and Doppler broadening. Each will
be discussed briefly below.
Natural Broadening
Because of interaction of atoms with radiation fields and collisional processes,

18
the lower, i, and upper, j, energy states participating in the atomic excitation have a
finite lifetime, and this gives rise to uncertainties in the energy of both states
according to the Heisenberg uncertainty relation. Usually, the extent of the line¬
broadening is determined by the much shorter lifetime of the upper state of the
transition. This is called lifetime or natural broadening. The FWHM due to natural
broadening is smaller than that due to other broadening mechanisms except in
extreme cases (eg. transitions to autoionizing levels of the atom). The spectral
profile of a naturally broadened line is described by a Lorentzian. The normalized
spectral profile due to natural broadening, S^, is given by
S
2/( )
Av„
where
Avn = FWHM of the naturally broadened line (Hz)
v m = frequency at the line center (Hz)
The width of a naturally broadened line, between two real energy states of the
atom (see below), is on the order of 107 Hz. In wavelength units, the FWHM, AA.N
(m), is expressed as
AA„
c
N
(3)

where
X
19
c
wavelength at the line center (m)
speed of light (m s'1)
For example for Na, at 589.0 nm, AAN«2xlO'14 m or 0.02 pm.
Collisional Broadening
The line profile is also influenced by collisions of the atom of interest with
other atoms of the same kind (Holtzmark broadening) or with foreign species
(Lorentz broadening). The amount of broadening caused by collisions increases with
the concentration of collision partners and hence, collisional broadening is sometimes
called pressure broadening. Collisions which leave the atom in the same energy state
(adiabatic collisions) have a more pronounced broadening effect than collisions that
leave the atom in a different energy state (diabatic collisions). The FWHM of the
spectral distribution resulting from adiabatic collisions, Ava (Hz), is given by
(4)
where
a
n.
X
a
optical cross section for adiabatic collisional broadening (cm2)
density of collision partners (cm'3)
reduced mass of collision partners (g)

20
The total, normalized spectral profile, S„L, for collisional broadening is also
Lorentzian and is given by equation (2) by replacing the natural FWHM, AvN, with
the collisional FWHM, Ava. The typical FWHM of a collisionally broadened line is
on the order of 3 x 10'12 m or 3 pm.
If natural and collisional broadening are assumed to be mutually independent,
the resulting FWHM of the Lorentzian profile is
Av¿ - Avc + Av„ (5)
where Avc is the FWHM from both adiabatic and diabatic collisions.
Doppler Broadening
A third major source of line-broadening is a result of the statistical
distribution of the velocities of the atoms absorbing radiation along the observation
path, called Doppler broadening. Because atoms are in motion with respect to the
observer, the Doppler effect causes a statistical distribution of frequencies absorbed
that is directly related to the velocity distribution. Briefly, the FWHM for Doppler
broadening, AvD (Hz), is given by
Av
2 (In 2)kT
m
1/2 v
C
(6)

where
k
21
Boltzmann constant (J K'1)
m = atomic weight (g)
v m â–  central frequency (Hz)
The normalized spectral distribution, S„D, is described in this case by a
Gaussian relation and is given by
\D
2VHÜ2 (Zn2)(v - v J2
— exp
A v D\fñ A v D
(7)
Typical Doppler broadened linewidths are on the order of 4 x 10'12 m or 4 pm. The
overall profiles for most atomic spectral lines are neither purely Gaussian nor purely
Lorentzian, but rather a comination of the two known as a Voigt profile.
The predominance of one type of line over another is largely dependent on
the environment of the atoms. For example, in an atmospheric pressure flame, one
might expect that collisional broadening would dominate over Doppler broadening,
whereas in a low pressure environment the opposite is expected to be true. The
importance of which broadening mechanism predominates is clear from Figures 3
and 4 which show the line profiles for purely collisionally and Doppler broadened
lines, respectively. These line profiles were plotted using equations (2) and (7) and
assuming a FWHM of each line of 10'11 m. The selectivity of the RID under each

Figure 3. Normalized Lorentzian line profile obtained using equation (2) and assuming a FWHM of 10 pm.

Relative absorption
N>
OJ
wavelength shift (nm)


Wavelength
J I
0.0500
shift (nm)
N>
Ln

26
of these conditions can be readily obtained from these plots. For example in the
case of a Doppler broadened line, the fraction of the incident light falling within the
absorption linewidth of the detector element falls to 10‘12, comparable to the stray
light rejection of a good doublemonochromator, at a wavelength only 3 x 10'11 m or
30 pm from the central line (evaluated at 640.2 nm). The collisionally broadened
line on the other hand, has long tails, giving a fractional absorption of 10‘7 as far out
as 6 nm away from the central line (evaluated at 640.2 nm). Therefore, a low
pressure cell, in which collisional broadening is not the dominant broadening
mechanism, is essential for highest wavelength selectivity.
One other advantage of the RID is that there are no limiting apertures,
limiting the optical throughput of the detector. This allows for a greater fraction of
the sample light to be collected and imaged into the RID, up to 50% . A good two-
stage monochromator will have an optical throughput of 10*5-10'6%. The product of
throughput and selectivity is constant for any one system. Clearly, the higher the
value of this product, the more selective and sensitive is the detector. The RM is the
only photon detector for which the detection efficiency need not be compromised for
better resolution or selectivity.

CHAPTER 3
OPTOGALVANIC EFFECT
Introduction
The optogalvanic (OG) effect is a change in the properties of an electrical
discharge caused by illuminating the discharge with radiation having a wavelength
corresponding to an atomic or molecular transition of a species in that discharge.
The effect was first observed by Foote and Mohler [45] in cesium-vapor filled hot
cathode diodes and Meissner et al. [46] and Penning [47] in rare gas glow
discharges. It was Penning who first discovered that an increase in breakdown
voltage occurred in a mixture of neon and argon when discharge tubes were
irradiated by emission from an identical tube.
Although the OG effect was first observed over 60 years ago, little work has
been done exploring its analytical capabilities. It was not until the development of
tunable lasers that the analytical potential of the OG effect began to emerge. Since
that time, the OG effect has found applications in optical spectroscopy [48],
analytical chemistry [49,50], laser stabilization [51] and wavelength
measurements and calibration [52], to name a few.
27

28
Anatomy of a Glow Discharge
The typical schematic representation of a dc glow discharge is shown in Figure
5 (taken from Nasser [53]). The normal glow discharge consists of 5 distinct
regions: 1) cathode dark space; 2) negative glow; 3) Faraday dark space; 4) positive
column; and 5) anode dark space. The corresponding diagnostic plots are given
below the figure. The positive column has by far, been the most probed and
modelled region. As the electrode separation is decreased, the negative glow and
cathode dark space remain unaffected, while the positive column shrinks, alluding to
the importance of these two regions in the maintenance of the discharge. When the
electrode separation is just a few times the cathode dark space length, only the dark
space and negative glow regions remain [54]. This is the normal operating mode of
hollow cathode lamps and is the experimental mode of operation in this work.
Note that almost the entire applied voltage is dropped across the cathode dark
space, while the negative glow remains essentially field-free. As such, its boundary
acts as a diffuse anode.
To maintain electrical balance in the system, the currents at the two
electrodes must be equal. Experimentally, however, it was observed [54] that the
current density at the anode was smaller than the random current density and so
there must be a decelerating field for the electrons at the anode. Figure 6 shows the
voltage distribution in a dc glow discharge. The values given are for typical
experimental parameters used in this work. Figure 7, redrawn from Figure 6, is an

Figure 5. Electrical regions of a dc discharge [53].

30
1st.
CATHODE

Figure 6. Voltage distribution across a dc glow discharge.

Cathode
Sheath
Voltage
Anode
Sheath
Voltage
u>
to

Figure 7. Electron energy distribution across a dc glow discharge.

(100+Vp)
y.
Cathode
Anode
04
4^

35
electron energy diagram for the discharge and shows the potential barriers to
electron movement. The negative glow does not take a potential intermediate to
those of the electrodes, as might be intuitively expected, resulting in a potential well
between the cathode and anode. The electric fields in the system are restricted to
sheaths at each of the electrodes and are such as to repel electrons trying to reach
either electrode.
Electrical Maintenance of the Discharge
In the text by Chapman [54], ion pair contributions from possible ionization
mechanisms in the three regions of interest are calculated. He concludes that the
two most probable discharge maintenance mechanisms, both occurring in the
negative glow region, are ionization by impact with thermal electrons [54, p.117]
A* + e~ - A* + 2e~ (8)
and associative ionization of metastables [54, p.122].
A* + A* ^ A* + A + e~ (9)
Collisional ionization of ground state atoms of the inert gas by electron impact is not
very probable due to the high energy ( >21.6 eV for Ne) required.
Ionization of sputtered cathode atoms can occur by any of the above
mechanisms, as well as Penning ionization (10)

36
X* + M -+ X + M* + e~ (10)
where X represents a buffer gas atom, and direct ionization of ground state sputtered
atoms, since much lower electron energies are required ( < 12 eV).
It is interesting to examine how photo-induced transitions can affect these
ionization processes if A is Ne, for example. Under normal glow discharge
conditions, the electron energy distribution approximates a Maxwell-Boltzmann
distribution and falls rapidly above 16 eV [55], where inelastic collisions dominate
(excitation of excited electronic states and ionization of Ne). Several points should
be noted. First, the neon metastable states, Ne’m, will be efficiently populated by
electron-neon ground state collisions, since singlet-triplet excitation functions peak
near the threshold voltage for discharge maintenance [56]. The subscript m is used
to denote neon in the metastable state. Second, collisional ionization of metastable
neon by electrons [process (8) above], whose cross-section peaks at about 15 eV
[57] can be expected to become increasingly important at high discharge currents.
Finally, the electron-neon collision frequency (~ 1010 s'1) exceeds both the neon-neon
collision frequency (107-108 s'1) at normal HCL pressures (typically 1-5 torr) and the
reciprocal of the shortest radiative lifetimes for the excited Ne atoms
[58,59,60]. One can conclude from the above that, regardless of the precise
mechanism of ionization, metastable Ne atoms play a central role in the maintenance
of the discharge, as discussed by Chapman [54]. This was also supported
experimentally by the work of Smyth et al. [61] and Hess and Harrison [62]. In

37
these experiments, the Ne+ concentration was monitored with a mass spectrometer.
Substantial changes in the Ne+ density were detected and were found to correlate
qualitatively with the photon-induced voltage changes. One can therefore expect that
the dynamics, voltage and current characteristics of the discharge would be sensitive
to even small perturbations of the Ne*m population.
An immediate realization gained from contemporary literature on glow
discharges in general and more specifically hollow cathode discharges is that such
discharges are dynamic environments which do not readily lend themselves to precise,
detailed modeling. In fact, a unified and generally agreed upon (quantitative) theory
of the mechanisms which are operative in the glow discharge has yet to be
presented.

CHAPTER 4
OPTOGALVANIC EFFECT IN THE HOLLOW CATHODE DISCHARGE
Introduction
A great deal of experimental work has been performed in a variety of
discharges, many of which were "home-made" [63,64,65] and contained an
assortment of vapors, such as I2 [66,67], rare gases, such as Kr [68], He [69],
Ar [70] and Ne [71] and numerous mixtures thereof. Of most practical interest
to the analytical chemist, however, is the use of commercially available hollow
cathode discharges (HCDs) or lamps (HCLs) in OG experiments. Unfortunately,
knowledge of the operating characteristics and parameters of HCDs is largely
empirical. General conclusions, however, can been drawn from previous work about
the OG effects in glow discharges. Firstly, the impedance changes normally induced
by the introduction of a collimated beam of light that is resonant with an absorption
transition of a discharge species into a discharge are large (as high as 10% of the
quiescent voltage) and are easily measured. Secondly, it is well known that these
impedance changes can be positive or negative.
38

39
Theory
Numerous theories and mathematical expressions have been postulated to
quantify and more fully understand the OG effect in HCDs. These range from the
relatively simplistic theories of Erez et aL [72] and Smyth and Schenck [61] to the
more arduous and pedantic theories of Ben-Amar et al. [73] and Broglia et aL
[74]. As stated above however, no agreement has been made on any one, complete,
unified theory to describe the processes in an HCD.
A complete description of proposed theories and mathematical treatments of
this dynamic system are beyond the scope of this dissertation: a phenomenological
description of the HCD characteristics and mechanisms and a simplified
mathematical treatment of the OG process shall be presented herein as pertinent to
this work.
Phenomenological Description of Ionization Mechanisms
There are two principal mechanisms suggested to explain the impedance
change of a hollow cathode discharge upon illumination by resonant photons. The
first mechanism, analogous to the OG effect in flames [34] is based on the increase
in cross-sections for electron-collision induced ionization as the final state energy
approaches the ionization limit. This mechanism is believed to be the dominant one
in the cathode dark space due to the high concentration of energetic electrons. The

40
second mechanism, which is proposed to be dominant in the negative glow region,
is an increase in the electron temperature of the discharge [75] upon irradiation
with resonant photons. The basis for this mechanism, proposed by Keller et aL
[71,76], is the establishment of an equilibrium in a hollow cathode discharge
between thermal electrons and the atomic excitation through inelastic and
superelastic collisions between excited atoms and thermal electrons, such that, to a
first approximation, the electron temperature and the atomic excitation temperature
are equal. This results in an increase in the electron temperature and a
corresponding shift of the electron energy distribution toward higher energies,
producing more electrons with sufficient energy for ionization of discharge species.
These two ionization mechanisms are not exclusive to the particular regions of the
glow discharge. The overall formation of charges is certainly a convolution of the
two processes.
Evolution of OG Signals
Upon irradiation of a HCD, the voltage change across the discharge may be
positive or negative. The polarity of these voltage changes is a complex function of
the originating level of the transition, the lamp voltage or current, the region of the
discharge illuminated, the electrode geometries and the pressure of the discharge.
Most observed OG signals are negative in polarity. This includes some signals due
to the buffer gas and all signals due to sputtered cathode atoms.

41
Negative Voltage Changes
Signals which are due to transitions originating in non-metastable levels
generally lead to negative voltage changes across the discharge. The only case where
this might not be true is that of excitation from a non-metastable level which is
important in maintaining the discharge, to a level from which the probability of
ionization decreases. This is not very common, however. Upon absorption of
resonant photons, atoms are promoted to higher lying energy levels, thereby directly
or indirectly increasing the ionization rate in the discharge. Depending on the region
of the discharge irradiated, the mechanism leading to an increased ionization rate is
different as discussed above. In the negative glow, excitation of atoms in the
discharge leads to an increase of the electron temperature (energy) through inelastic
collisions between slow electrons and the excited atoms74. This shifts the electron
energy distribution to higher energies. In either the cathode dark space or negative
glow region, the end result is that is that as a result of atomic excitation there will
be more electrons with sufficient energy to ionize discharge species, resulting in an
increase in the conductivity of the discharge. Since the lamp is made to operate at
constant current, assuming simple Ohmic behavior, an increase of the conductivity,
or correspondingly a decrease in the resistance of the lamp, will result in a lower
voltage required to maintain the constant current. An example of such a negative
voltage change can be seen in Figure 8. This is an oscilloscope trace, obtained in
this case for the 3s1 2SH --> 3p* 2P3/2 transition of Na upon laser irradiation of the

Figure 8. Oscilloscope trace of the negative OG signal for the 3s1 2S1/2 --> 3p* 2P3/2 transition of Na.

20 mV/d i
Time ( 5 JUS / d I V )
4^
OJ

44
hollow cathode at 588.995 nm with a laser beam of« 10 mJ. This signal corresponds
to an approximate -2% change in the voltage between the lamp anode and cathode
while the laser is on.
Positive Voltage Changes
The case of positive voltage changes is much more involved and less
understood. All transitions originating from metastable states lead to positive voltage
changes upon irradiation by resonant photons if those metastable states are important
in the maintenance of the discharge. An example of such a positive signal is given
in Figure 9 for the 3P2(ls5) --> 3D3(2p9) transition of Ne. A partial energy level
diagram for Ne is given in Figure 10. Neither of these two states is radiatively
coupled to the Ne ground state. The upper level however, is coupled to other 2p¡
levels through electron collisions. These other 2p levels are radiatively coupled to
the ground state indirectly through the non-metastable levels of the Is quartet, 3Pj
(ls4) and !Pj (ls2). This was confirmed by monitoring an increase in the emission
from the 2pg and 2p10 levels when the exciting light was tuned to populate the 2p9
level. Since the maintenance of the discharge is closely tied to the Ne metastable
density, by depleting the metastable population, one effectively reduces the main
mechanisms for ionization, thereby decreasing the ionization rate. This leads to an
increase in the lamp impedance and a corresponding increase in the lamp voltage.
The positive signals evolve over a much larger time period, probably as a result of
indirect depletion of the metastable density because of the parity forbidden direct de¬
excitation from the excited 2p¡ levels to the % ground state of neon. The fast

Figure 9.
Oscilloscope trace of the positive OG signal for the 3P2 (ls5) --> 3D3 (2p9) transition of Ne.

46
A ! P/Aw 002

Figure 10. Partial energy level diagram of Ne.

48
cm
173 932
160 OOO
150 OOO
130 OOO
Ne+
4s 4p
O
Ne

49
negative signal is most probably a result of increased ionization by electron collisions
at the beginning of the laser pulse.
Mathematical Treatment of OG Signals
Only a limited mathematical treatment of the collection of charges formed
under the influence of an electric field will be considered here. Complete
mathematical treatments of the various charge formation and collection phenomena
in the glow discharge as a whole, consistent with the present level of understanding
of glow discharges can be found in references [73-77].
Analogous to the case of double resonance laser enhanced ionization in
flames [78], the simplest rate equation model for the OG process involves
saturation of one transition and a linear dependence of the other transition (and
ionization rate) on laser intensity. The production rate of charge density is given by
dnei(x,t)
dt
- K I(x,t)
(11)
where I(x,t) is the space-time distribution of the laser intensity, K is a constant which
encompasses the various excitation, ionization and deactivation constants and ne and
n¡ are the electron and ion number densities, respectively. From Poisson’s equation
and the applied potential, the effective field, E(x), between the negative glow and the
cathode is given by [74]

50
E(x) - -
2V„
1--
d)
(12)
where V0 is the absolute value of the applied potential, and d is the distance between
the cathode and effective anode (see Figure 11). An electric charge created under
the influence of this field is driven to an electrode according to the equation
dve(x,t)
dt
--E(x)- Veve(xj)
TtX
(13)
where
Vc
electron velocity (m s'1)
e =
electron charge (C)
m =
electron mass (kg)
6e -
electron collision frequency (s'1)
An analogous equation can be written for ions formed. From the principle
of conservation of energy [79], we can obtain an expression for the induced current
signal:
where
E0
iVo - e / E0(nivi - nve) d(A6) (14)
At>
electric field due to the voltage difference V0 (V/m)
electron and ion velocities, respectively
(m s'1)

Figure 11. Electric field distribution across the dc glow discharge.

Cathode
Effective
anode
Lr\
tO

53
AS = volume between the cathode and effective anode where charges
are moving (m3)
i = current signal (A).
E0 is constant and is given by
E„ - (15)
where d is the width of the dark space. Neglecting the time-dependent behavior of
the current, and accounting for charges with different velocities being present in a
given position x, at the same time t, the integral in equation (14) can be replaced by
a sum over all charged particles;
*' - 4 E( niVi ~ neVe ) (16)
a nc
Simplistically, we can conclude from equation (16) that the total current is
dependent on several factors, including:
1) population of the originating level of the optical transition and the
rates of ionization processes from all primary energy levels involved,
through n¡ and ne, and
the collision frequencies of the charges, through v¡ and ve.
2)

54
Double-resonance Optogalvanic (DROG1 Effect
Little work has been done until recently on the double-resonance OG effect.
It was first proposed by Vidal [80] in 1980. The DROG scheme serves to increase
the absolute magnitude of the OG signal by approximately one order of magnitude,
in the case of sputtered atoms. At the time of preparation of this dissertation, only
two papers had appeared in the literature on the double-resonance OG effect
[81,82]. Engleman and Keller [81] reported a 10- and 70- times double-resonance
enhancement of sodium and uranium, respectively, in the HCL, while Behrens et al
[82] reported on the DROG signals of In and Ga.
For optical double-resonance OG spectroscopy, two lasers are chosen with
wavelengths corresponding to two successive transitions in the atom. In the case of
Na (Figure 12), the first laser, A. 12, can be chosen at 588.995 nm and the second, A. 23,
is set at 568.822 nm. If the intensity of A.23 is chosen such that the transition is
saturated then every atom excited into level 2 will be further excited into level 3 with
unity probability. As a result, level one is coupled directly to level three. In a low-
energy environment and an atom with a high first excited level 2, the effective
population of level 3 is orders of magnitude greater when both A,12 and A. 23 are tuned
to resonance and applied to the atom reservoir, than if only A. 12 (or A. 33) is applied.
This is a very well known effect and has been used extensively in flame laser
enhanced ionization (LEI) [83]. Double-resonance LEI has proven to be one of
the most sensitive spectroscopic techniques available. As discussed in the previous

Figure 12. Partial energy level diagram of Na.

1/2

57
section, this extremely high sensitivity is due mainly to the high energy levels to which
an atom can be promoted by the successive absorption of two resonant photons.
If one of the more important mechanisms in maintaining the discharge is
energy transfer from the excited species to electrons through inelastic collisions, then
by exciting atoms to much higher energy states, a larger energy increase is imparted
to the electron population. This in turn increases the number of electrons with
sufficient energy to cause ionization of the buffer gas. Since the ionization rate
increases with the exponential of the electron energy, it is a significant effect on the
ionization enhancement in the negative glow region of the discharge.

CHAPTER 5
CONSIDERATIONS ON THE INTERACTION OF ATOMS WITH LIGHT
Absorption of Radiation
Upon passing polychromatic light through an assembly of atoms, it is observed
that distinct wavelength components of the light are absorbed by the atoms. The
wavelengths that are absorbed give a qualitative determination of the atoms present
in the assembly and, in certain cases, the amount of light absorbed is directly
proportional to the number of atoms of that kind present in the assembly. In the
case of atomic absorption analysis, and under an explicit set of assumptions, the most
used relation between the density of atoms and the amount of light absorbed is
Beer’s Law (17)
$ . (17)
where $0 is the flux of the incident photons (photons s'1), $ is the transmitted flux
(photons s'1), k(X) is the absorption coefficient (cm'1) and / is the thickness (cm) of
the absorber. The magnitude of k(X) is dependent on the wavelength of the incident
radiation, and the nature and concentration of the absorber. It is often more
convenient to express the absorption coefficient, k(X), as the product of the atomic
58

59
number density of absorbers, n3 (cm'3), and the absorption cross section, a (X) (cm2),
of the particular absorption transition. The measured parameter in an atomic
absorption measurement is the absorption factor, a, defined as
a
(18)
or the fraction of the incident light that is absorbed. Integrating over the entire
spectral range of the incident radiation, yields
/*Wo(l ~e~°Wn/)dX
(19)
For a narrow spectral line source, the spectral profile of the source is much narrower
than that of the absorption coefficient, and equation (19) reduces to
at - 1 - (20)
In the limit where the factor a(X)nJ << 1, aL is directly proportional to the
absorber number density. If the factor o(X)nJ > 1, then aL = 1, and virtually all
resonant photons incident on the atom assembly are absorbed.

60
Laser Excitation of Atomic Transitions
The interpretation of the interaction of a laser beam with an assembly of
atoms is adequately and most simply described by a rate equations approach.
Referring to Figure 13, one sees that there are many process which the atom can
undergo upon interaction with radiation whose energy exactly corresponds to an
energy difference between energy states of the atom. The rate equations approach
will be described here only for the simplest case of single-resonance excitation by
absorption of one photon with deactivation from the excited level possible by
collisional ionization, stimulated emission, spontaneous emission and collisional
deactivation back to the originating level of the transition (taken to be the ground
electronic state of the atom). Also, as the quantity measured in this work was the
number of ions created during interaction of the laser beam with the atom assembly,
the rate equations will be solved for the change in number of ions with time.
Single-step excitation
The rate equations for excitation of an atom from level 1 to level 2 are:
dni
~dx ‘ (21)
dn2
ni[B\2P+ ^\t)~ ”2(^2i + ^21 + ^21 + ^21P 1(^12^)
dt

Figure 13. Possible excitation/deexcitation process in an atom resulting from illumination with a laser beam.

62

63
where
A21 = rate of spontaneous emission (s'1)
B12 s Einstein coefficient for stimulated absorption (J'1 Hz m3)
k21 = rate of collisional deactivation (s'1)
k2i = rate of collisional ionization (s'1)
pA (X12) = spectral energy density of the laser
(J Hz"1 m'3)at wavelength X 12.
Using standard methods to solve these equations and assuming the transition
is not saturated (B12pA(A.12) << A21 + k21) yields [84]
n
i
/
1 - exp
\
Ar,
^21 + ^21 + ^2i J
(22)
It is clear from this equation that the ratio between the number of ions formed
during the laser pulse and the total atomic number density is dependent on the rate
of collisional ionization, the duration of the laser pulse the Einstein coefficient for
induced absorption and the rates of relaxation from level 2. Also, the ratio is
dependent on the spectral energy density of the laser.
Optical Saturation of an Atomic Transition
The excited state population of an atom can be greatly enhanced relative to
the thermal population of that state by resonant absorption of photons from a laser
beam. In fact, if the spectral irradiance of the laser beam is sufficiently high, the

64
populations of the two levels will be locked together in the ratio of their respective
degeneracies [85]. This spectral energy density is termed the saturation spectral
energy density (J m'3 Hz’1) and is given by [84]
Pi ttia>-
La)
(A2\+k21+k7i\
1 +
{ A2l ;
.
UJ ku JJ
-l
(23)
where
h s Planck’s constant (J s)
k¡, s rate of recombination (s'1)
gu = degeneracy of upper level (dimens.)
g, = degeneracy of lower level (dimens.)
If we achieve optical saturation, B12pA(X12) > > (A21 + k21 + k2i), then the
rate of induced absorption is much greater than the sum of the deexcitation rates,
and
ni-nT
1 - exp
( g \
l )\
(24)

65
Although nt/nT is now independent of the spectral energy density, the ratio is still
directly proportional to the product of k2lAtv The value of k2i depends on how close
level 2 is to the ionization continuum. Therefore, we can expect that the closer level
2 is to the ionization continuum, the greater the production of ions. However, for
nanosecond pulsed lasers, even saturation of the transition is not expected to be
significant because of the large energy deficit between level 2 and the ionization
continuum resulting from only single-step excitation. If there is a metastable
electronic state present in the atom which can act as a radiation trap, such as in the
case of Pb, then equation (24) becomes
k2i+A22/+k22/
(
1 - exp
82
(^21 +A22i+k22¡) At¡
8^82
(25)
In this case, even if the laser does saturate the transition, the ionization rate must
now be fast enough to overcome the loss rate from level 2 to the metastable trap.
Two-step Excitation
When two laser beams, tuned to different absorption transitions, are made
spatially and temporally coincident in the discharge, high lying atomic levels can be
efficiently populated. Under such double-resonance conditions, four distinct cases
are readily apparent:
1) linear dependence of nt on the spectral irradiance of both laser beams,

66
2) saturation of the first step, l-->2 (pA(A. 12)> >pAs(A. 12), and linear
dependence of nt on pA(A,23),
3) linear dependence of ni on pA(A.12) and saturation of the second step
{Pa23) > > P a (^23)}’ an^
4) Saturation of both steps.
Since we are primarily concerned with detection of low levels of photons
corresponding to A.12, cases (2) and (4) are not applicable in our system. Either case
(1) or case (3) can be operative, case (3) being preferred.
Assuming that the rate equations approach is valid in our experiments,
Omenetto et al. [84] derived the expressions for the fraction of atoms ionized for
these two cases. Assuming collisional ionization to proceed instantaneously from
level 3, in case (1), where saturation conditions for neither step have been met,
nrnT
1-exp
^*12P 12^23 P *(^23)
Ar,
/j
(26)
/421 + ¿21
the number of ions created during the laser pulse, nx, is dependent on the spectral
energy densities of both laser beams and on all de-excitation processes which deplete
the first excited level, 2.
In the case of resonance ionization detection, the second step will always be
saturated, while the first step will be linear (since the photons being measured are
at A. 12). For this case, assuming no collisional or radiative losses from level 2, the
number of ions produced is given by

67
n.-n
t [ 1 exP (
(27)
In equation (27) it is also assumed that the atoms reach a level whose energy defect
with the ionization potential is so low that collisional ionization proceeds
instantaneously. This is a valid assumption in most double resonance excitation cases
of atoms in an energetic environment (e.g. flame, plasma, electrical discharge).
Therefore, in such a case, the number of ions created is directly proportional to the
laser pulse length and the spectral energy density (B12pA(A.12)) of the photon flux of
A.12. Also, we see no dependence of nt on the spectral energy density of A. 23 or on any
de-excitation pathways from level 2, since B-^^A.^) > > A21 + k21.
Two conclusions that can be drawn from the above discussion are that, for
significant ionization from the uppermost laser excited level, a two-step excitation
scheme must be used and that, for unity ionization of all atoms excited to level 2 by
absorption of a photon (A.12), the spectral energy density of the second laser, p^A.^),
must be sufficient to saturate the transition.
Assuming some typical values (Table 1) for the variables in equations (26) and
(27) we find that in case of a linear interaction of both steps,
(28)
while for saturation of the second step
n
n
T
1
(29)

68
Table 1. Values used for calculating njnt in eauqtions (26) and (27).
Variable
Value
Units
Bj2
1018
J1 m3 s^Hz
^23
1018
J'1 m3 s'1 Hz
a21
109
s'1
k2i
109
s'1
At,
10-8
s
Pa(^ 12)
10'5
J m'2 Hz'1

CHAPTER 6
EXPERIMENTAL
General Experimental Configuration
The general experimental system used for all experiments is shown in Figure
14. A detailed listing of experimental components is given in Table 2. A frequency
doubled Nd: YAG laser (532 nm) operated at 30 Hz was used as the pumping source
for the dual dye laser system. The pump beam was split equally to pump each dye
laser. Typical output energy from the frequency doubled Nd:YAG laser was 240 mJ
per pulse with a pulse duration of 12 ns. The dye laser output was either used
directly for transitions in the visible region of the spectrum or frequency doubled for
UV transitions. In the case of UV transitions, the visible laser light was passed
through a KDP frequency doubling crystal; an autotracking system with angle
matching of the frequency doubled light ensured maximum output intensity while
scanning. The fundamental and second harmonic waves were separated by a
dispersive Pellin-Broca prism. If the laser wavelength was to be scanned, then the
Pellin-Broca prism was replaced with a right angle prism to prevent "walking" of the
beam during scanning. The two harmonics were then separated with a low bandpass
colored filter, which absorbed the visible wavelengths.
69

Figure 14. General experimental configuration.


72
Table 2. Listing of experimental components.
Component
Model No.
Manufacturer
Nd:YAG laser
YG 581-30
Quantel International, Santa
Clara, CA1
Dual Dye Laser
TDL 50
Quantel International, Santa
Clara, CA1
Frequency Doublers
HD 50
Quantel International, Santa
Clara, CA1
90° Quartz Prisms and
Quartz Lenses
—
Esco Products, Inc., Oak
Ridge, NJ
Neutral Density Filters
—
Corion Corp., Hollistong, MA
High Power Laser Neutral
Density Filters
FN-10,30,10,80
Optics for Research, Caldwell,
NJ
Amplifier
113
EG&G PARC, Princeton, NJ
Boxcar Averager Gated
Integrator
SR250
Stanfor Research Systems, Palo
Alto, CA
Computer Interface
SR245
Stanford Research Systems,
Palo Alto, CA
Computer
PC-AT
Northgate Computer Systems
Digital Oscilloscope
2430A
Tektronix, Inc., Beaverton, OR
Chart Recorder
D-5000
Houston Instruments, Austin,
TX
i
Now Continuum, Santa Clara, CA.

73
Table 2. — continued
Component
Model
Manufacturer
Hollow Cathode Lamp
(Lamp 1) (Na, Pb and U)
L233 series
Hamamatsu Corp.,
Bridgewater, NJ
Galvatron (Mg)
L2783-12NE-
Mg
Hamamatsu Corp.,
Bridgewater, NJ
Hollow Cathode Lamp
Power Supply
PMT-20A/N
Bertan Associates, Hicksville,
NY
Fast Photodiode
ET 2000
Electro-Optics Technology,
Fremont, CA
Photodiode for Absorption
Measurements
PIN 10DP-SB
United Detector Technologies,
Hawthorne, CA

74
Two commercially available hollow cathode lamps were used with different
hollow cathode designs. One (lamp 1) was a common HCL used for atomic
absorption analysis (Figure 15). In this lamp only one end of the hollow cathode was
open. The other lamp (lamp 2) (Figure 16) was a "Galvatron" used in wavelength
stabilization of dye lasers by the optogalvanic effect. This lamp is a "T" design in
which both ends of the hollow cathode are open.
Pick-off Circuitry for OG Signal
The circuit used to power the hollow cathode lamps and measure the AC
voltage across the discharge is shown in Figure 17a. It was entirely housed in a
shielded Pomona box (Figure 17b) to reduce pick-up of radio frequency noise. The
high voltage was supplied from a dc-dc high voltage power supply through a current
limiting resistor, RB. This resistor could be made external with the use of an isolated
BNC connector. A variable resistor within a decade resistor box was used for initial
studies. For final experiments, the optimum RB (20 kn) was hard-wired inside the
shielded box. The voltage across the discharge was AC coupled to the detection
electronics by a high voltage coupling capacitor.
One-step Excitation Experiments
For one-step excitation, laser 1 was steered via right angle prisms into the
discharge. The laser beam could be focussed, depending on the experiment to be
performed. When the laser was not focussed, it was apertured to just fill the hollow

Figure 15. Diagram of a common HCL (lamp 1).

Anode
Insulated
â– npport
Insulated
support
Detail of
hollow cathode

Figure 16. Diagran of a Galvatron (lamp 2).

Cathode Anodes
Negative Dark
Detail of
hollow cathode

Figure 17.
(a) Pick-off circuit for measuring OG signals
(b) Pomona box encasing pick-off circuitry.

Variable
resistor
SIGNAL
OUT
oo
o

81
cathode volume. Optogalvanic spectra were obtained by scanning the dye laser
wavelength while monitoring the AC voltage across the discharge.
Two-step Excitation Experiments
Lamp 1
The alignment of the lasers when using the single-open ended hollow
cathode is shown schematically in Figure 18. The two laser beams were made to
enter the hollow cathode at a slight angle to the cathode axis. Different focussing
configurations of the two beams were used. Placement of a lens at position 1
allowed only laser 1 to be focussed, while placement of the lens in position 2
focussed both beams into the hollow cathode. In either case, the position of the lens
was such that the beam(s) was (were) focussed at the back surface of the cathode.
Lamp 2
The alignment of the lasers when using the double-open ended hollow
cathode is shown in Figure 19. In this case alignment is much easier since the beams
can be made counter-propagating, entering the cathode from opposite ends. Again,
different focussing configurations were used.
Timing of Laser Beams in Two-step Excitation Experiments
For either lamp, temporal coincidence of the two laser beams in the hollow
cathode was ensured with a fast photodiode (risetime <200 ps). The output of the
photodiode was connected to a fast digitizing oscilloscope. For timing optimization,

Figure 18. Alignment of laser(s) through lamp 1.

Laser
- 1
Laser
Effective
anode
Negative
glow
'Cathode
dark space

Figure 19. Alignment of laser(s) through lamp 2.

Cathode
dark space
Cathode
Laser 1
Negative
glow
Laser 2
00

86
the fast photodiode was placed at the position to be occupied by the HCL. Then
laser 1 and laser 2 were alternately made incident on the photodiode. The arrival
time of the two lasers at the photodiode was then noted. The laser pulse arriving
earlier at the photodiode was delayed by way of a prism delay line until temporal
coincidence with the other laser pulse at the photodiode was observed. To avoid
skewing of the measurements toward longer times, care was be taken to ensure
operation of the photodiode was within its linear operating range. Figure 20 is an
oscilloscope trace of the photodiode output. The two traces were obtained
consecutively for laser 1 and laser 2. Temporal coincidence of the two laser beams
was within 1 ns.
Absorption experiments
The experimental setup used to make absorption measurements (with lamp
2 only) is shown in Figure 21. The transmitted laser light was incident on a
photodiode while the laser was scanned through the transition of interest. Linearity
of the photodiode response was insured with a 0.3 neutral density filter. The output
of the photodiode was fed into the input of a boxcar. Output from the boxcar was
then sent to a personal computer and strip chart recorder for subsequent data
analysis.

Figure 20. Oscilloscope trace of temporal coincidence of the two laser beams at the hollow cathode.

m e
Vo I t a g e
m •-*
co ru
â– 
3
<
88
20.0mV

Figure 21. Experimental configuration for absorption experiments.

-b.
vo
o

91
Saturation Curves
Saturation curves were obtained by systematically reducing the intensity of the
laser beam incident on the HCL with neutral density filters. The signal intensity was
then plotted as a function of the spectral energy density of the laser.
Measurement of Enhancement of Two-step Excitation of Na and Pb
The contributions to the OG signal from one-step excitation were obtained
by having both lasers incident in the hollow cathode. Keeping one laser beam off
the resonant wavelength of the corresponding transition, the other laser was scanned
through its resonant transition. For example, to determine the contribution to the
OG signal in the case of Na, from the 588.995 nm transition alone, the second
wavelength was set at about 0.1 nm off resonance and the first laser was scanned
from 588.800 nm to 589.200 nm. To determine the enhanced signal, one laser was
set on resonance (usually A. 23) and the other laser was scanned through the transition.

CHAPTER 7
RESULTS AND DISCUSSION
Sodium OG effect
Sodium was chosen as an element for preliminary study for several reasons.
First, it possesses a relatively simple 3 level energy scheme (Figure 12). Also,
spectroscopic data (ct12, r, A21) for all transitions considered in this work are well
known. Second, Na is sputtered efficiently by Ar (fill gas of Na HCL) giving high
number density of the Na atoms within the discharge. Third, and more practically,
transitions for both the ground-state and excited-state transitions of Na are in the
visible region of the spectrum. This greatly facilitated laser operation, since no
frequency doubling of the dye laser fundamental wavelength was required, and
alignment (especially in the case of double resonance OG spectroscopy) of the laser
beams in the HCL was more easily achieved.
The OG signal obtained for both ground state transitions is shown in Figure
22. The energy of the laser was approximately 1 m J, which corresponds to a spectral
energy density of 6.12 x 10'12 J m'3 Hz"1, assuming a beam diameter of 2 mm, and
laser bandwidth, A A. =2 x 10"11 m. The laser beam was passed, unfocussed, into the
lamp to cover the entire hollow cathode, and scanned through both transitions. The
excellent signal-to-noise (S/N) obtainable can be seen from Figure 23, for optimized
92

Figure 22. OG signals for ground state transitions of Na.

OG signal (a.u.
wavelength (nm)

Figure 23. Example of signal-to-noise attainable using the OG effect.

0 G Signal (a.u.)
VO
ov

97
experimental conditions for Na. The origin of the small peak marked with an
asterisk is assumed to be due to an impurity in the cathode, as it was not observed
in other Na HCLs. No attempt was made to assign this peak to an element.
Figure 24 shows the signal obtained while scanning only the second laser
through the 568.822 nm excited state transition of Na. The S/N is clearly degraded
relative to the ground state transition case. This behavior is readily explained by the
fact that the number density of atoms in the excited state is much lower than that of
atoms in the ground state. Therefore, although a larger fraction of the total number
density will be ionized from the excited state, the absolute number of ions created
will be less. Since we assume the populations of the different states to follow a
Maxwell-Boltzmann distribution, an estimate of the difference to be expected in the
signal to noise can be calculated. We expect the population of level 2, relative to
that of level 1 to be given by
n
n
2
1
8l (
—exp
81
A E
kT.
*)
(30)
where
AE
gu
k
Te
energy difference between the two levels of the transition (J)
degeneracy of the lower and upper level, respectively (dimens.)
Boltzmann constant (J K'1)
electron temperature of the system (K).

Figure 24. OG signal for excited state transition of Na.

OG Signal (a.u.
wavelength (nm)
VO
VO

100
Tt is used here since the assumption is made that there is a rapid equilibrium
established between the electron and atomic temperatures. Tc has been
approximated by other workers [75] to be on the order of 4000 K. Therefore, in the
case of Na, the ratio n2/nx calculates to 0.004. From this simplistic calculation, we
expect the S/N of the OG signal from this excited state transition to be
approximately 2 orders of magnitude smaller based on steady-state population
considerations alone.
Determination of Lamp Impedance
If we assume that the dc impedance of the discharge, RLdc, is approximately
equal to the ac impedance, RLac, then a simple Ohmic calculation can be used to
determine the lamp impedance. If we treat the lamp as a simple resistor, the laser-
induced voltage change as a function of the ballast resistor, at constant current, can
be fit to the equation
out
KRL
Rb + Rl
(31)
where Vs is the source voltage. By plotting (V^,)"1 vs RB a straight line results with
slope equal to (Rl^)"1 and intercept equal to (Vs)'\ Such a plot obtained for the
Galvatron is shown in Figure 25. From this plot Vs and RL were found to be 5.43
x 10‘3 V and 9.34 x 104 ohms, respectively.

Figure 25.
Plot of (K^,)'1 vs Rb used for determination of lamp impedance.

(V(out))-1
R ballast (ohms)
S

103
Evaluation of Collisional Ionization Rate Constants bv the OG Effect
The OG signal also provides us with a means of directly calculating the
collisional ionization rate constant for atomic transitions in the HCL, since the
mehtod provides us with a direct measure of the number of ions created within the
laser pulse. In the case of single-step excitation of Na, the absolute magnitude of the
OG signal, A V, obtained with saturation of the optical transition from level 1 to 2,
was approximately 0.04 V. The number of ions that this corresponds to can be
obtained from equation (32)
ni = ”,
AK • t
Rl • e
(32)
where
tw
temporal window of detection electronics (time to integrate
signal area) (s)
e =
electronic charge (C).
Using the experimental values given in table 3, n¡ = 6.2xl07. Rearranging equation
(24) yields
V -111
_ _ülY_h
«tJU +
g2-A','
Rl
-1
(33)

104
From equation (33), and assuming [86] nT »1012 cm"3, a laser pulse length of 10"®
s, gl=g2=l, and an irradiated discharge volume of 0.01 cm3, k2i« 106 s'1. This is
comparable to its counterpart in flames. Therefore, by using simple OG
measurements to determine the ion number density, in combination with absorption
measurements to determine the ground state atom (or originating level) number
density, a reasonable estimate of the collisional rate constant, k2i, can be determined.
Two-step OG Effect of Na
Of more direct bearing on the purpose of this work is the OG effect observed
when two laser beams, tuned to two different absorption transitions of an element
in the discharge, are made temporally and spatially coincident in the discharge. In
the case of Na (from Figure 26) an enhancement in the ionization rate of about 10
times occurs when the two laser beams are tuned to two successive transitions of Na
and made coincident in the discharge. In this case however, the second step was not
completely saturating. Photoelectric effects from the high intensity laser beam
striking the cathode prevented the use of laser intensities high enough to ensure
saturation.
It is interesting to note that in order for a two-step enhancement to be
observed, the two transitions need not necessarily share a common level. For
example, Figure 27 shows the two-step OG signal for Na. In this case, A. 12 was set
to the 2Syi --> 2P3/2 (588.995 nm)transition and A^ was scanned through both the
connecting transition, 2P3/2 --> 2D3/2 (568.822 nm), and non-connecting transition,

105
Table 3. Experimental values for determining n{ in equation (32).
Variable
Magnitude
Unit
tw
lO"6
s
Rl
4 x 104
Ohms
AV
0.04
V

Figure 26. Two-step enhancement of Na OG signal.
a) A.12 tuned to the resonance transition and A.23 detuned from resonance by 1 Á
b) A. 12 detuned from resonance by 1 Á and A.23 tuned to the excited-state resonance transition
c) both lasers tuned to the respective resonance transitions.

0
O
o
Time coordinate (a.u.)
o

Figure 27. Collisional coupling of Na energy levels in the HCL.

OG signal (a.u.)

110
2Ph -- > 2D3/2 (568.266 nm). An enhancement was observed for both cases. No such
enhancement was observed when kn was detuned from the resonant wavelength,
indicating some collisional coupling between the 2P3/2 and 2PW states. The same
effect was observed when X.12 was tuned to the 2SV5 ~> 2P^ (589.595 nm) transition.
Lead OG Effect in the HCL
Lead is another classical element often studied by spectroscopists. Like Na,
it affords a nearly ideal, well characterized energy level scheme, with the additional
interest of a metastable level. A partial energy level diagram for Pb is given in
Figure 28.
The ionization enhancement obtained in the two-step scheme for Pb in the
HCL was obtained in this work for the first time. The enhancement is about 3 times
over the single step case (see Figure 29). This low enhancement is mainly a result
of the high degree of photoionization from the absorption of two photons at 283.31
nm (2x35297 cm'1) which is more than enough energy to ionize the lead atoms
[ionization potential (IP) = 59821 cm'1].
The same arguments and descriptions given for Na with regard to the single-
and two-step results are readily extended to the Pb case. No obvious effects resulting
from the presence of a metastable level or trap were evident.
Figure 30 shows the dependence of the observed two-step OG signal for Pb
on the lamp current. The number of sputtered atoms also increases with an increase
in current and correspondingly, the number density of atoms available for absorption

Figure 28. Partial energy level diagram for Pb.

112
cm
59 821
51 944
35 287
10 650
0
1

Figure 29. Two-step enhancement for Pb OG signal. Both lasers were coincident in the hollow cathode, with
a) k 12 tuned to the resonance transition and A. 23 detuned from resonance by 1 Á,
b) A12 detuned from resonance by 1 Á and A.23 tuned to the excited state resonance transition, and
c) both lasers tuned to the respective resonance transitions.

OG signal (a.u.
Time coordinate (a.u.)

Figure 30. Pb two-step OG signal vs lamp current.

350
280
210
140
70
0 L*
2.0
J I I I L
4.8
i
7.6
J I L
10.4
j i i i i i
13.2 16.0
ON
Lamp current (mA)

117
of photons from the laser beam increases. Therefore an increase in the OG signal
occurs with increasing lamp current.
Neon OG Effect in the HCL
Comparison of the magnitude of the Ne’m OG effect relative to that of
sputtered atoms can be made from Figure 31. This is an OG spectrum of U in an
HCL obtained by passing one laser, unfocussed, into the HCL and scanning over the
lasing range of the dye. Many U peaks (marked with *) were recorded, along with
the much stronger Ne’m peaks. The magnitudes of the Ne’m signals are on average
5x greater than the U signals. It should also be kept in mind that in obtaining this
spectrum, the experiment had not bee optimized for Ne. This Ne’m "enhancement"
is in accordance with the central role attributed to Ne’m in maintenance of the
discharge [54,62,77]. One would intuitively expect that the greater the active role the
perturbed atom has on the electrical properties of the discharge, the greater would
be the magnitude of the OG effect. Figure 32 gives an expanded view of the U OG
signals, better showing the detail of the U spectrum.
Electronic Configuration of Ne
Neon has a much more complicated and intricately interconnected energy
scheme than Pb or Na. A partial energy level diagram for Ne is given in Figure 10.
The lowest excited electronic configuration of neon [2p53s] yields four Is states,
designated 3P2(ls5), 3P1(ls4), 3P°(ls3) and 'P^lSj) in the LS coupling and Paschen

Figure 31. OG spectrum of U/Ne lamp from 580 - 601 nm.

OG Signal (mV)

Figure 32. Expanded U OG spectrum from 580 - 601 nm.

OG Signal (mV)
K)
wavelength (nm)

122
notation, respectively. Transitions are observed from each of these states to the 2p
levels (ten states) and from the 2p levels to higher electronic states (such as 3s and
4d). The 2p and higher-lying states have short radiative lifetimes [87], in contrast
to the considerably longer lifetimes of the Is states. The 3P2(ls5) and 3P0(ls3) states
are metastable (lifetimes t>10'3s), while the short radiative lifetimes of the 3P1(ls4)
and ^(lSj) states are lengthened by radiative trapping (t«10"5s). By far, the
strongest photon-induced voltage changes occur for transitions which originate in the
Is levels, with transitions originating in the 2p levels typically giving signals 50-100
times smaller. These differences in signal magnitudes reflect the much larger
populations of the Is relative to the 2p states. In addition, the Is --> 2p transitions
always directly affect the concentration of metastables in the discharge, regardless of
the Is level involved [77].
One-step Neon and Uranium OG effect
Figure 33 is an OG spectrum obtained for Ne in a U hollow cathode lamp by
scanning the dye laser. This OG spectrum contains signals from four different
possible (single-wavelength) mechanisms of photon absorption and ionization: Three
from absorption by Ne and one from U absorption. Each will be dealt with
separately.

Figure 33. OG spectrum of U/Ne lamp from 594 - 607 nm.

A
as
n
OQ
P
«"♦"
â—„
co
<
o
>—*
P>
OQ
CO
o
cr
p
P
OQ
CO
wavelength (n m)
hj
-F^

125
Case 1
The absorption giving rise to the peak occurring at 597.55 nm (Figure 33) is
a well known transition for Ne, 3P2(ls5) --> 1P1(2p5). The saturation curve, variation
of OG signal with pA (A. 12), for this peak is shown in Figure 34.
If we assume that the magnitude of the OG signal is directly proportional to
the number of ions created during the laser pulse (no amplification effects), then the
behavior of the OG signal is expected to follow the general equation [84]
OGE(V)--^-(a,-a2y' [a,(l- a2(l-i*>4'')] (34)
where
“3“'®12Pa(^12)+^Í2+^24+^2iPa(^12)+/*21+^21
^12 P12) +^12 + ^2¿+^21 P 12) +^21 +^21
a t^!2PA^12)+^12]^2i
^12Pa^12)+^21+^í + ^2iPa^12)+^21+^21
(35)
At low spectral energy densities, equation (34) reduces to
OGE (10-
nTW
nteRL
- exp
^12p¿(^12^2i A /
Ar.
k ^21+^21+^2i j
(36)

126
A linear relationship exists between the OG signal and B12pA(X12). At higher
spectral energy densities, there may be several mechanism by which the signal
becomes independent of the spectral energy density of the laser. In the limit where
the rate of induced absorption is much greater than the sum of radiative and
collisional deactivation, that is B12pA(A.12) >> (A21 + k21 + k2i), equation (34)
reduces to
OGE (V)-
nTW
nteRL
1 - exp
( e V
— M»,
1
00
+
(37)
Therefore, at high spectral energy densities, the OG effect will become independent
of the laser energy.
The plateau at higher laser intensities may also be an electrical phenomenon
specific to the discharge. At higher laser intensities, a large number density of
charges is created in the discharge. Therefore, one could envision the case where the
large number of charges would limit the transport rate and collection efficiency of
those charges. This might be the case if the current supplied to the lamp became
insufficient to carry all the charges at the higher concentrations. In either case, the
sloping off of the calibration curve is limited to the range of light intensities over
which the detector response will be linear.
Converting all values to log10 and plotting log (OG signal) vs log (pa(A.12))
should result in a curve with two distinct slopes. This is seen in Figure 35. The first
part of the curve yields a slope of 1.08 ± 0.11, indicating a linear dependence of the

Figure 34. Saturation curve for 597.55 nm absorption of Ne.

OG Signal (a.u.)
128
px(X12) (W m 2 nm 1)

Figure 35. Log-log plot of Figure 34.

p
_L O
%l r
Oi -
03
N>
T
r
o -*•
(Q od
^ LO
•L.
ID
CD
ro
o
LJ
N)
o
0.32
0.74
Log (OG Signal)
u>
o

131
OG signal on the laser intensity. The second part of the curve yields a slope of 0.22
± 0.022, indicating virtual independence of the signal on the laser intensity. The
slope of this portion of the curve is not zero because of experimental artifacts, mainly
resulting from the spatial and temporal inhomogeneity of the laser beam [88].
Ifthe laser beam is of poor spatial and temporal quality, then the energy density
across the beam is not uniform. As a result, even though the transition may be
saturated at the beam center, the relationship at the outer edges of the beam is still
linear and an increasing OG signal with increasing px (A. 12) is still observed.
Casg.2
The second case gives rise to the peak at 598.80 nm. To the best of the
author’s knowledge, its observation has not yet been previously reported in the
literature. The saturation curve for this peak is shown in Figure 36. The log-log
curve is shown in Figure 37. In this case, at least three distinct regions of the curve
are apparent. Again, the initial part of the curve yields a slope of 1.09 ± 0.12,
indicating a linear dependence of the OG signal on the laser intensity. This would
indicate that the transition is between two real, bound levels of the atom (Ne*m),
followed by collisional ionization of the excited atom. From tabulated values of the
energy levels of Ne [89], a possible transition from the 2P3/2 (J=2) level at 150317.8
cm'1 occurs to the 2P°3/2 (J = 2) level at 167013.5 cm1. The energy difference between
these two levels, 16695.7 cm1, corresponds very closely to the energy supplied by the
laser photons, 16695.4 cm1, after the observed wavelength was corrected for the
refractive index of air. Further support for our assignment lies in the polarity of the

Figure 36. Saturation curve for 598.80 nm absorption of Ne.

OG Signal (a.u.)
133
px(X 12) (W m 2 nm 1)

Figure 37. Log-log plot of Figure 36.

Log (OG Signal)
135
Log (px (X12) )

136
signal. The observed voltage change was of negative polarity (Figure 33) indicating
that this signal most probably resulted from a transition involving high lying excited
states of Ne and not the metastable states, as discussed above. The middle portion
of the curve again yields a small slope, indicating virtual independence of signal from
the laser intensity, as expected in a simple transition between two bound levels,
followed by collisional ionization. The slope of the final section of this curve is 0.70
±.08 indicating again, a dependence of the OG signal on the laser intensity. A
possible absorption-ionization mechanism to describe such behavior is shown in
Figure 38. The first transition is saturated and therefore no longer dependent on the
laser intensity. Absorption of a second photon will transfer enough energy to the
atom to excite it into the ionization continuum. Although such processes have
smaller absorption cross-sections than transitions between two bound levels, because
of the increasing laser intensity photoionization becomes significant. Due to the
lower probability of such an event taking place however, this final absorption process
is not saturated at the laser intensities present at the cathode.
Case 3
A contrasting case is the one in which the first excitation is through a virtual,
or non-bound level of the atom. This is shown schematically in Figure 39. The
virtual level, v, exists for a very short lifetime dictated by the Heisenberg uncertainty
relation. This lifetime is approximated by [90]
o
¿Jk
At -
a)
1
(38)

Figure 38. Proposed excitation/ionization scheme for 598.80 nm absorption of Ne.

138
cm 1
173 932
167 013
150 317
!p<
3/2
V
3/2

Figure 39. Two-photon excitation scheme through a virtual level.

140
cm 1
173 932
167 810
151 040
3/2
134 461 *P
1

141
where
=
frequency of the absorbed photon (Hz)
“¡,1c S
frequency of the transition between the originating level and the
closest real level to the virtual level (Hz).
For example, in this case,
- AEicm'1) * c (39)
- (151040-134461) cm~x*2.999Sxl010 cm/s
- 4.970xlOu s1
Therefore, At=3.5xl0'13 s or 350 femtoseconds (fs). For the two-photon transition
to take place, both photons must be absorbed by the atom during this 350 fs interval.
Since the transition involves the simultaneous absorption of two photons from
the laser beam, a square dependence of the OG signal is expected on the spectral
energy density of the laser. The saturation curve for such a transition is shown in
Figure 40 for the 599.56 nm absorption of Ne. The slope of the log-log plot (Figure
41) is 2.00 (±0.11). No saturation of the transition can be seen, even at the higher
spectral energy densities. This is reasonable since the normal absorption cross-
sections for two-photon processes through virtual levels (10‘18 cm2) are many orders
of magnitude smaller than transitions between bound levels (10'12 cm2).

Figure 40. Saturation curve for 599.56 nm absorption of Ne.

OG Signal (a.u.)
143
px(X12) (W m2 nm 1)

Figure 41. Log-log plot of Figure 40.

Log (OG Signal)
145
Log (px (X12) )

146
Case 4
The final case is an extension of case 3 and was observed for the 599.24 nm
absorption transition of U. The saturation curve for this transition is given in Figure
42. The log-log plot (Figure 43) consists of three distinct regions. The first has a
slope of 2.07 (±0.25) indicating, as above, a two-photon process through a virtual
level. A plateau then occurs indicating saturation of this process (not observed in the
previous case). A possible reason for saturation of this two-photon transition is the
longer lifetime of the virtual level due to its closer proximity to a real level than was
the virtual level in case (3). The effective lifetime of this virtual level can be
estimated, as above, to be 2.5 x 10"12 s or 2.5 ps. This is approximately 7 times longer
than the previous case, resulting in an increased probability for the simultaneous
absorption of two photons by the atom. Actually, at this laser irradiance, the two-
photon transition has been saturated and ionization from the upper real level is
primarily through collisions with the discharge species. After this plateau, the OG
signal again becomes dependent on the laser irradiance. A probable reason for this
behavior was discussed by Curran et al [91]. From this terminal level of excitation,
the atom may undergo collisional ionization and/or photoionization. The rate of
formation of ions from this uppermost level, /, is a combination of the two processes
and can be given by
n -(*•♦**)».
(40)

Figure 42. Saturation curve for 599.24 nm absorption of U.

OG Signal (a.u.)
148
px(X 12) (W m 2 nm 1)

Figure 43. Log-log plot of Figure 42.

OG Signal (a.u.)
150
px(X12) (W m 2 nm 1)

151
where k/ and kac are the photoionization and collisional ionization rate constants,
respectively, and n, is the number density of atoms in the state /. Which of these two
ionization mechanisms predominates is dependent on the laser irradiance, collisional
environment and energy states available to the atom.
It has been postulated [92,93] and experimentally observed [94,95]
that the probability of photoionization is determined, in part, by the amount of
energy, provided to the excited atom, in excess of the ionization energy (i.e. the
energy overshoot, Eos). As £„ becomes smaller, k¡,p is expected to play a more
important role in ionization of the atoms, relative to collisional ionization.
Uranium has an ionization potential of 49035 cm'1 (6.08 eV). Absorption of
three photons at 599.24 nm, after correction for the index of refraction of air, imparts
an energy of 50049 cm'1 (6.20 eV) to the U atom. is therefore only 1015 cm'1
(0.12 eV). The slope of the final portion of the saturation curve (Figure 43) is
0.65 ±0.08. This dependence on the laser irradiance indicates that at such a low
value of E^, knp > ki{c, so that photoionization is the principal mechanism of U ion
formation. A diagram of this mechanism is given in Figure 44.
Neon OG Signal Dependence on Lamp Current
As discussed above, Ne metastable atoms play a central role in maintenance
of the discharge, and are therefore locked to the electrical characteristics of the
discharge. This becomes more important as the lamp is operated at lower currents.
Intuitively, one might expect that the closer the current is to the threshold current

Figure 44. Proposed excitation/ionization scheme for 599.24 nm absorption of U.

153
cm-1
49 035
33 366
i
2
a
a
CM
05
05
in
a
a
-«ii
CM
05
05
m
0
1

154
required for stable operation of the discharge, the greater would be the dependence
of the electrical properties of the discharge on perturbations of the Ne metastable
population. The relative laser-induced impedance change of the discharge can be
expressed as
A Rl Rl (laser on) - Rt (laser off)
Rl Rl (laser off)
(41)
Figure 45 is a plot of the laser-induced impedance change relative to the dc
operating current of the discharge. As can be seen, the relative impedance change
is maximum at the lower operating currents, exhibiting an exponential relation.
Double-resonance OG Effect of Ne
Many double resonance excitation schemes may be chosen for Ne (Figure 10).
One might therefore ask what criterion should be used to choose the "best" scheme(s)
for OG spectroscopy in the HCL. Physical intuition dictates that the greater the
probability of absorption of a photon by the Ne, the more sensitive the detector
would be for low light levels. Therefore, it is logical to assume that the transition
possessing the highest oscillator strength [96], /12, or absorption cross section,
a 12(^12), would lead to the greatest sensitivity. [Note: In the literature, the oscillator
strengths are often reported as gf values, where g is the degeneracy of the energy
level]. Also, from equation (16), a scheme should be chosen such that the energy of
the originating level of the first transition is low enough to ensure a high population

Figure 45. Plot of relative laser-induced impedance change vs lamp current.

AR, /R
156
Lamp current (A)

157
in the HCL. Ideally, one would like to use the ground state of Ne due to its
extremely strong oscillator strength and high number density in the discharge.
However, the wavelength of absorption of this transition lies in the far UV (~ 73
nm) and is therefore unsuitable for many reasons, the most important of which are
that this wavelength is effectively absorbed by air and that no tunable laser sources
are available in this region of the electromagnetic spectrum. The two transitions
used in this work were A,12 = 640.225 nm and X23 = 576.442 nm. The first transition
chosen is by far the strongest of any of the transitions originating from the first
excited electronic state of Ne. Ne metastables are excited from the 3P2(ls5) to the
3D3(2p9) state; the gf value is 2.211 [85], compared to the next strongest absorption,
with a gf value of 0.797. Also, as stated, this transition originates in a metastable
state of Ne, and is therefore expected to be critical in affecting discharge
characteristics. The second transition, 3D3(2p9) - > 4d4, promotes the atom to within
0.86 eV of the ionization potential of Ne, insuring that ionization from this level
occurs instantaneously by electron collision in the energetic discharge. This transition
is also the strongest excited state transition of Ne, with a gf value of 0.49.
Optimization of Boxcar Gate Position
The gate or observation window of the detection electronics must be
optimized prior to making any measurements. The two cases of single- and double¬
resonance OG effect must be considered separately. Also, the observation of the Ne
OG effect can be made using different schemes of gate position and width.

158
In the case of the OG effect of cathode material, positioning of the gate is
fairly straightforward. The OG signal induced by laser irradiation of atomic
transitions of the sputtered cathode atoms is always a fast, negative-going signal.
That is, an ionization rate enhancement is always a result of absorption of resonant
photons. Therefore, optimization of the gate is such that the maximum S/N is
obtained. This optimum position for a modified exponential signal waveform has
been calculated theoretically by Voigtman [97]. For optimal integration of the OG
signal, the gate width is set equal to the width of the signal peak at 0.369 of the peak
height.
In the case of the OG effect of Ne, the situation is much more involved as a
result of possible positive-going signals. Figure 46 is an oscilloscope trace of the
positive voltage change recorded for the 640.225 nm transition of Ne. As discussed
above, the signal consists of a fast voltage decrease, relative to steady state, followed
by a much slower positive voltage change. Depending on the positioning of the
boxcar gate, any combination of output signals may be observed. For example, if the
gate is set between points a and b, a negative voltage change will be observed, while
placement of the gate between points b and c will result in a positive signal.
Centering of the gate at point b will result in no signal being observed, since the
negative and positive signals will cancel and the net resultant voltage change will be
0. The Ne spectrum reported in Figure 33 was obtained by use of two boxcars with
two different gate positions; one for recording the negative voltage changes and
another for positive changes. Also, as discussed in the next section, alignment

Figure 46. Boxear gate position considerations.

160

161
of the laser beam(s) in the hollow cathode will affect the waveform of the voltage
change.
Alignment of Laser Beamfsl in the Hollow Cathode
The theory of the evolution of the OG effect has been largely postulated for
the formation of charges within the cathode dark space. It is in this region that the
entire applied voltage is dropped and the highest electric field exists. Charges are
formed by inelastic collision of electrons, accelerated toward the effective anode by
the electric field, and excited neon atoms. Formation of a charge in such an intense
field region results in the immediate "collection" of that charge. If on the other hand
the charge is created in the negative glow region of the discharge, then collection of
that charge is more ambiguous since the negative glow is essentially a field free
region of the discharge, as discussed above. In this region of the discharge, the main
ionization mechanism is by collision of neon metastables with thermal (slow, low
energy) electrons. The charges formed however are not subjected to an intense
electric field.
The energy of thermal electrons in the glow region range from 2 eV - 8 eV,
which is not adequate to ionize ground state neon atoms (IP=21.56 eV). If a
Maxwellian distribution of the electron energy is assumed, the fraction of electrons
with enough energy to ionize metastable neon atoms , A Ereq« 5 eV, is about 5 x 10'7.
If neon is excited to within 0.9 eV of the ionization limit, then the fraction of
electrons with enough energy to ionize the highly excited neon increases to 0.07.

162
Taking this into consideration along with the high number density of thermal
electrons in the glow region (n^ = 1010 cm'3), all neon atoms excited to within 1 eV
of the ionization limit are assumed to be instantaneously ionized by collision with
thermal electrons. The case is even more dramatic in the case of ionization within
the dark space since the electron energy distribution is shifted to much higher
energies by virtue of the energy input from the applied electric field.
Ionization Within the Negative Glow
If an electron is created within the negative glow, then the probability of an
electron escaping the potential barrier of the plasma, which has a small positive
voltage relative to the anode potential, is given by
P - exp
« kTe
(42)
where Vp is the potential of the plasma relative to the absolute value of the applied
potential, and Te is the electron temperature. Vp can be approximated by
kT
Vp - -Vf + —¿ In
\VU
(43)
where Vf is the potential applied across the electrodes, and ve and p¡ are the mean
square electron and ion velocities, respectively. Using equation (44) and the
parameters given in Table 4,

163
Table 4. Values used to calculate v¡ and ve in equation (42).
Variable
Magnitude
Unit
Te
4000
K
Ti
500
K
me
9.1 x 10'28
g
ntj
3.6 x IQ'23
g

164
v -
(44)
the mean square velocities can be calculated, yielding ve=3.4xl07 cm s'1 and
v¡=2.3xl04 cm s'1. Substituting these values back into equation (43) and for an
applied voltage of -100 V, Vp is calculated to be 2.5 V. Substituting this value for the
plasma potential back into equation (42), yields a probability of 7xlCT*. The net
result is that the electrons become trapped in the glow region, generally being
reflected at the interfaces with the electrode sheaths, including the sheath wall,
before eventually overcoming the anode barrier. The effective path length
(collection time) is thereby increased as necessary to maintain the electron and ion
densities by electron impact ionization. Intuitively, one would expect that the
absolute magnitude of the current density at the anode would be approximately the
same in both cases (ionization in the dark space and ionization in the glow region).
Because of the trapping of the low energy electrons within the glow region, the rate
of electron collection at the anode in the glow region ionization case will be much
more extended and delayed in time relative to the dark space ionization case. This
is indeed what was observed experimentally. When the laser is focussed into the
dark space, a fast, relatively sharp ionization signal is observed (Figure 47). If on the
other hand, the laser is focussed into the central portion of the glow region, the

Figure 47. One-step ionization signal observed in cathode dark space.

200 mV/d

167
ionization signal is longer (by approximately a factor of 3) and delayed in time by
approximately 20 ms. If the laser is not focussed and covers the entire discharge,
then the observed signal (Figure 48) is a convolution of the two extremes.
Ionization Within the Dark Space
In the case of ion production within the cathode dark space, the electrons are
given extra energy by the electric field to which they are exposed when formed and
therefore the probability of collection at the anode increases greatly since there is an
exponential dependence of the probability of collection on the energy of the
electrons. Actually, one might even expect a small current magnification factor from
any secondary ionization produced by the inelastic scattering of the high energy dark
space electrons with glow region species. The magnitude of this amplification factor
however, is not expected to be too great since the energy of the dark space electrons
is dependent on their initial position within the field and is most likely not equal to
the full field potential.
Two-step Enhancement of Ne OG Effect
As with other two-step excitation/ionization experiments, a large enhancement
in signal is observed when two lasers tuned to two successive transitions of an atom
are made temporally and spatially coincident in an atomic reservoir. This can readily
be seen in Figure 49 for the case of Ne in the HCL. Figure 49a is an oscilloscope
trace of the OG signal resulting from the resonant absorption of photons by Ne at

Figure 48. Convolution of ionization signals from cathode dark space and negative glow region.

p / sri 0S )
500 mV/d ¡ V
691

Figure 49. Two-step excitation enhancement of Ne OG effect in the HCL
a) Oscilloscope trace of one-step excitation OG signal of Ne (ground state).
b) Oscilloscope trace of one-step excitation OG signal of Ne (excited state).
c) Oscilloscope trace of two-step excitation enhancement of OG signal of Ne

200 mV/d!
i m e
( 50 ¡J,s/ d i V )

20 mV/d i

( A I P /sri 5 )
a uu i
2 0 0 mV/d ¡

174
640.2 nm. This transition originates in the metastable state of Ne. As expected, the
signal shows a fast negative going pulse, due to initial ionization enhancement,
followed by a much slower positive going pulse, resulting from depletion of the Ne
metastable population. The spectral energy density of the laser was 1.87 x 10'14 J m'3
Hz'1. This corresponds to approximately 1010 photons. The maximum negative
voltage change is 0.5 V. Figure 49b is the OG signal obtained by irradiating the
discharge with A. 23, with a spectral energy density of 1.94 x 10'11 J m'3 Hz'1. As can
be seen, the signal-to-noise is much worse than in the previous case. This decrease
in S/N is the result of two main factors. First, the transition originates in a much
higher energy state (2p9) of Ne than the previous one. Therefore, one can expect the
population density of this level to be much lower than that of the metastable level.
Second, this excited level does not play a central role in the maintenance of the
discharge, as discussed above; therefore one would not expect the electrical
characteristics of the discharge to be as sensitive to population changes in this energy
state. Figure 49c is the OG signal resulting from the simultaneous illumination of
the discharge by both lasers,tuned to the two transitions. The maximum voltage
change across the discharge observed in this case was 1.2 V, 2.5 times that observed
in the case of illumination of the discharge by the first laser beam alone. Also, in
the two-step case, while the spectral energy density of A 23 remained the same, the
energy density of A12 was decreased by 4 orders of magnitude relative to the
illumination by A12 alone. Therefore, a two-step enhancement of over 104 was
observed for this double resonance scheme of Ne over the single resonance case.

175
Evaluation of Ne OG in the HCL as a Sensitive Photon Detector
Comparison of a detector evaluated for transient signals (RID) to a detector
evaluated for steady-state signals (PMT) is not a straightforward matter. The former
are best evaluated in terms of absolute numbers of photons detectable, while the
latter is defined in terms of minimum detectable photon fluxes or rates of incident
photons. The main difficulty in the direct comparison lies in defining the response
bandwidth of the detector, to determine the bandwidth of the noise to which the
detector is sensitive. In the case of steady-state detection, the detection bandwidth,
A f ,is defined simply as the noise equivalent bandwidth and is taken to be 1 Hz. The
definition of A/ for a pulsed detector is somewhat more ambiguous. For example,
as relevant in this work, when dealing with signals times on the order of 10-8 s, a
boxcar integrator is most often chosen as the method of electronic detection. The
frequency bandwidth response of the boxcar is far from a simple function of the
length of the signal or the recording time of the electronics. In fact, as discussed by
Voigtman and Winefordner [98], the frequency bandwidth of the boxcar is a
complex function of the boxcar gate width, signal repetition rate, boxcar input filter
and signal frequency. Therefore, the only direct comparison that can be made
between the pulsed and steady-state detectors is that of the fundamental
characteristic response of the ionization process and photocathode efficiency,
respectively. The criterion decided upon in this work most suitable to describe the

176
performance characteristics of the Ne HCL RID was the quantum efficiency of the
detector. This quantity can also be used for characterizing PMTs and is a
characteristic function of the cathode material. The quantum efficiency, QE, is
defined as the ratio of the number of elementary events contributing to the detector
output to the number of incident photons.
Q.E.
# charges created
# photons incident
(45)
It gives a direct measure of the conversion efficiency of the detector in terms of
number of events measured per number of events occurring. In more commonly
measured quantities, the quantum efficiency can also be expressed as the radiant
cathodic sensitivity, s, in mA output per W of incident radiation. The maximum
radiant cathodic sensitivity for a common PMT (R955, Hamamatsu Corp.) is 60
mA/W. The photocathode quantum efficiency can be calculated from this to be 0.11
e'/ph.
In the RID, the number of charges (i.e. electrons) created during the laser
pulse is readily calculated from knowledge of the area under the signal produced by
a single laser pulse (V s) and the lamp impedance by using equation (32).
If the photon energy of k 12 is distributed over a larger frequency range than
that accepted by the detector, then a correction must be made for the number of
incident photons that are not absorbed by the Ne. In our case, the linewidth, £A.12,
of the laser whose energy is being measured is broader than the absorption linewidth

177
of the Ne in the HCL, that are transmitted through the HCL. We define the effective quantum efficiency,
h’i,
# charges created
# photons absorbed
# charges created
#. photons incident
1 - exp ( -ofA.)*/^ )]'*
(46)
where, as discussed above, the factor [1 - exp(-a (A. )nl)] is simply the fraction of the
incident photons absorbed, a.
hi - QE. [ 1 - exp ( -o/i/^)]’1
Q.E.
(47)
a
A simple absorption experiment was performed to determine the magnitude
of the correction factor. A typical trace obtained in this part of the experiment in
shown in Figure 50. The intensity of the laser at A. 12 transmitted through the hollow
cathode and the OG signal intensity were monitored simultaneously. As expected,
the transmitted intensity of the laser beam is a minimum when the optogalvanic
activity is a maximum. Averaging the results from 11 such scans and knowing the

Figure 50.
Scan showing simultaneous reading of absorption of A,12 and OG signal for determination of

Transmittance
640.10 640.18 640.25 640.33 640.40 640.48
\c
Wavelength (nm)
(E—3)
OG signal (V)

180
laser linewidth to be 2 x 10‘n m, a was found to be 0.187. So, 18.7 % of the incident
photons at this wavelength were within the 5Xabs of Ne in the HCL.
A calibration curve obtained for the Ne two-step excitation under study is
given in Figure 51. The slope of this curve gives the quantum efficiency of the
detector. From Figure 51 a slope of 0.90 (±0.12) e/ph is obtained. Therefore, at
least under the operating assumptions of this work, unity photon detection efficiency
has been obtained. A log-log plot of this curve is given in Figure 52. The linear
dynamic range (LDR) for the detector is approximately 3 orders of magnitude. From
n ’ the radiant sensitivity (at 640.225 nm) is calculated to be 463 mA/W.
To summarize so far, the Ne OG effect in the HCL is capable of single¬
photon detection efficiency and its spectral response is linear over 3 orders of
magnitude. Fundamentally, the RID is approximately 8 times more sensitive than the
PMT. Of more practical consideration is the minimum number of electrons that our
system can measure. That is, what is the limiting noise to the number of electrons
that we can measure and correspondingly, what is the minimum number of photons
of light energy that the detector could measure.
If an OG effect experiment is properly set-up, then the limiting noise results
from the statistical fluctuations in the dc current supplied to the lamp [71,99]. Figure
53 shows the RMS voltage measured across the discharge at different operating
currents. These data were obtained both with and without illumination of the
discharge by the second laser. No significant difference was observed between the
two sets of data. The theoretical shot noise, Vtheo(rms), that can be expected in this

Figure 51. Calibration curve for Ne RID in the HCL.

10
10
10
10
10
)!
10'
107
10
B
10’
00
N)
| photons absorbed

Figure 52. Log-log plot of Figure 51.

Log (# electrons produced)
8.00
7.40 -
6.80 -
6.20 -
5.60 -
5.00 L-1
5.5
6.1
6.7
Log (# photons
i i i i i i i i i i
7.3 7.9 8.5
absorbed)
2

Figure 53. Plot of experimental and theoretical V(rms) vs lamp current.

rms) (V)
theor.
• laser 2
off
A laser 2
on
Lamp current (mA)

187
type of experimental arrangement can be calculated from equation 47
(ms) - Rl /!ííí4 (48)
where
B = detection frequency bandwidth response (Hz)
Rl = lamp impedance (n)
¿te = dc operating current of the lamp (A).
A plot of Vtheo(rms) vs. idc is also shown in Figure 53. The experimentally
obtained shot noise is approximately two orders of magnitude larger than the
theoretical shot noise. Experiences of other workers in this laboratory have shown
this difference to be of reasonable magnitude. A plot of the signal-to-noise as a
function of lamp operating current is given in Figure 54. As expected from the above
discussion, the highest S/N is observed at the lowest operating current. The final
evaluation of the Ne HCL RID was therefore performed at the lowest possible
operating current, 0.400 mA.
These results are consolidated in Figure 55, in which is shown a typical
calibration plot, along with the experimental limiting noise and the theoretical
limiting noise. From the graph, the experimentally achievable minimum detectable
number of photons and energy of 2 x 104 photons and 6 x 10'15 J, respectively, are
obtained. The theoretical limits are correspondingly, 4 x 102 photons and 1 x 10"16
J.

Figure 54. Plot of signal-to-noise of Ne RID vs lamp current.

Lamp current (A)
oo
VO

Figure 55. Summary figure of results showing the calibration curve along with the limiting experimental (dashed line)
and theoretical (dotted line) noises.

Laser Energy (J)
10~16 10"15 10'14 10‘13 10~12 10“11 10
191
(Ara) S90
paonpojd snoj^oap #
| photons absorbed

CHAPTER 8
FINAL COMMENTS
Summary
In the initial part of this work, it was demonstrated that the laser-induced
optogalvanic effect in commercial hollow cathode lamps is a sensitive method for the
study of optical processes in energetic environments. Both cathode sputtered atoms
and inert filler gas transitions were studied. Several single-step optical transitions of
Ne and U were studied in terms of possible excitation/ionization schemes and the
relative importance of photo- and collisional ionization. In this manner, a new
optical transition for Ne was observed at 598.80 nm. Also, the potential use of the
OG effect as a method for directly estimating fundamental ionization rate constants
and lifetimes of virtual levels has been shown.
Step-wise excitations of Na, Pb and Ne were also studied. The signal
enhancement due to step-wise excitation of Na in the hollow cathode discharge was
found to be approximately 10-fold, in accordance with the reports of other
researchers [81]. The step-wise excitation of Pb in the hollow cathode lamp was
observed for the first time. The enhancement in OG signal from the second laser
was approximately 3-fold.
192

193
The major portion of this work concentrated on the step-wise excitation of Ne
and its potential use as a sensitive photon detector. The optimum optical excitation
scheme yielded a signal enhancement from the second laser of over 4 orders of
magnitude. This type of detection scheme was shown to have a detection efficiency
of unity. The limiting noise of this detector was determined to be the shot noise on
the operating current of the hollow cathode lamp. This noise was evaluated both
experimentally and theoretically. The experimentally attainable minimum detectable
number of photons and laser energy were 2 x 104 and 6 x 10 '15 J, respectively. The
corresponding theoretical limits were 4 x 102 photons and 1 x 1016 J.
Future Work
The direction of future work should be towards the evaluation of different
kinds of hollow cathode and low-pressure discharges as possible resonance ionization
detectors. At present, the minimum detectable energy and number of photons is set
by the shot noise of the lamp. Three possible avenues are open to overcome these
problems: 1) increasing the volume of the detector illuminated by the laser beams
should result in an increased photon sensitivity, resulting in a lower minimum
detectable energy; 2) use of an obstructed glow discharge has shown to provide
signals some 400 times larger than a conventional hollow cathode discharge; and, 3)
hollow cathode discharges can be designed which can operate below even the
theoretical shot noise limit.

194
Also, the use of low-pressure cells of atomic vapors as reservoirs for the RID
hold potential promise. The low pressure would ensure Doppler broadened lines,
with the correspondingly high wavelength selectivity. In this case however, the atoms
would have to be photoionized or field ionized since the number density of collision
partners is relatively low and the atom environment is of relatively low energy.
Photoionization may proceed either by absorption of a photon whose energy is
greater than the energy deficit between the highest excited level and the ionization
continuum, or by promotion of the atom into an autoionizing level. An autoionizing
level is a real atomic level in the ionization continuum. An atom promoted into an
autoionizing level spontaneously decays to the ion. The absorption cross-sections for
autoionizing transitions are of the same order of magnitude as transitions between
bound atomic levels and 4-6 orders of magnitude greater than photoionization cross-
sections. Therefore, it is much easier to ensure saturation of an autoionization
transition than a photoionizing transition.
In field ionization, atoms excited to high-lying Rydberg levels of the atom are
ionized by application of a high intensity electric field between two plates. The
magnitude of this field is normally on the order of kV/cm. In the case of
autoionization of the atoms, auxiliary plates must be introduced into the cell to
collect the ions formed, whereas for field ionization, the ionizing plates may also
serve as the collection electrodes.
Unlike the electric discharge, a major advantage of the low vapor pressure cell
is that there is essentially no background ionization. Therefore, the potential for

195
single-photon detection is much higher. Unfortunately, for such a detector, an inert
gas could not be used as a detector element since there would not be a significant
population of the metastable state. This, however, may prove to be a minor
disadvantage when compared to the negligible background of the low-pressure cell.

196
REFERENCE LIST
1. G. Tolg, Analyst, 112, 365 (1987).
2. J.R. Davis, Jr., A. Rohatgi, R.H. Hopkins, P.D. Blais, P. Rai-Choudhury, J.R.
McCormick, and H.C. Mollenkopf, IEEE Trans. Electron Devices, ED-27, 677
(1980).
3. T.Y. Kometani, Anal Chem., 49, 2289 (1982).
4. Y.H. Pao, R.N. Zitter, and J.E. Griffiths, J. Opt. Soc. Am., 56, 1133 (1966).
5. Y.H. Pao and J.E. Griffiths,/. Chem. Phys., 46, 1671 (1967).
6. C.A. Morton, Appl. Opt., 7, 1 (1968).
7. M.L. Franklin, G. Horlick, and H.V. Malmstadt, Anal Chem., 41, 2 (1969).
8. Commission Internationale de l’Eclairage, "International Lighting Vocabulary,"
Publ. No. 17, CIE, Paris 1970.
9. W. Herschel, Phil. Trans. Roy. Soc., 36, 421 (1800).
10. L.Nobili and M.Melloni, Ann. Chim. Phys., 48, 187 (1831).
11. S.P. Langley, Nature, 25, 14 (1881).
12. W.N. Hartley, Phil Trans., 175, 325 (1884).
13. H. Hertz, Ann. Phys., 31, 421 (1887).
14. H. Hertz, Ann. Phys., 31, 983 (1887).
15. H. Hertz, Ann. Phys., 36, 769 (1889).
16. A. Righi, Phil. Mag., 25, 314 (1888).
17. J. Elster and H. Geitel, Ann. Phys., 41, 161 (1890).
18. L.R. Roller, J. Opt. Soc. Am., 19, 135 (1929).
19. L.R. Roller, Phys. Rev., 36, 1639 (1930).
J.A. Rajchman and R.L. Snyder, Electronics, 13, 20 (1940).
20.

197
21. V.K. Zworykin and E.G. Ramberg, "Photoelectricity and Its Applications",
Wiley and Sons, New York 1949.
22. R.W. Wood, Philos. Mag., 10, 513 (1905).
23. J.V. Sullivan and A. Walsh, AppL Opt., 7, 1271 (1968).
24. O.I. Matveev, N.B. Zorov, and Yu. Ya. Kuzyakov, Talanta, 29, 907 (1980).
25. E.F. Zalewski, R.A. Keller and C.T. Apel, AppL Opt., 20, 1584 (1981).
26. M.A. Nippoldt and R.B. Green, AppL Opt., 20, 3206 (1981).
27. L.E. Salsedo-Torres, N.B. Zorov, Yu. Ya. Kuzyakov,/. AppL Spectrosc. USSR,
37, 488 (1982).
28. H. Rinneberg, J. Neukammer, and U. Majewski, Phys. Rev. Lett., 51, 1546
(1983).
29. B. Bolger, Lect. Notes Phys., 43, 460, NY (1975).
30. J.A. Gelbwachs, C.F. Klein, and J.E. Wessel, IEEE J. Quantum Electron., QE-
14, 77 (1978).
31. J.A. Gelbwachs, C.F. Klein, and J.E. Wessel, IEEE J. Quantum Electron., QE-
16, 137 (1980).
32. "Lasers in Chemical Analysis", G.M. Hieftje, J.C. Travis and F.E. Lytle, eds.
The Humana Press, Clifton, NJ (1981).
33. V.S. Letokhov, "Laser Photoionization Spectroscopy", Academic Press,
Orlando, FL (1987).
34. Ove Axner,"Laser Enhanced Ionization Spectroscopy", Chalmers Press,
Gotenberg, Holland (1987).
35. V.S. Letokhov in 'Tunable Lasers and Applications", T. Mooradian and P.
Stokseth, eds., Vol. 3, Springer-Veralg, Berlin (1976), p.122.
36. G.S. Hurst, M.H. Nayfeh and J.P. Young, AppL Phys. Lett. 30, 229 (1977).
37. G.S. Hurst, M.H. Nayfeh, and J.P. Young, Phys. Rev. A, 15, 2288 (1977).
G.I. Bekov, V.S. Letokhov, V.I. Mishin, and O.I. Matveev, Opt. Lett., 3, 159
(1978).
38.

198
39. 0.1. Matveev, N.B. Zorov, and Yu. Ya. Kuzyakov, J. AnaL Chem. USSR, 34,
654 (1979).
40. Yu. M. Milov, /. AppL Spectrosc. USSR, 44, 444 (1986).
41. O.I. Matveev, N.B. Zorov and Yu. Ya. Kuzyakov,/. AnaL Chem. USSR, 34,
846 (1979).
42. O.I. Matveev and V.A. Prybitkov,/. AppL Spectrosc. USSR, 46, 16 (1985).
43. T. Okada, H. Andou, Y. Moriyama and M. Maeda, Opt. Lett., 14(18), 987
(1989).
44. B.W. Smith, P.B. Farnsworth, J.D. Winefordner, and N. Omenetto, Opt. Lett.,
15, 823 (1990).
45. P.D. Foote, F.L. Mohler, Phys. Rev. 26, 195 (1925).
46. K.W. Meissner, W. Graffunder, Ann. d. Physik, 30, 109 (1927).
47. F.M. Penning, Physica, 8, 137 (1928).
48. R.B. Green, R.A. Keller, G.G. Luther, P.K. Schenck, J.C. Travis, AppL Phys.
Lett., 29, 727 (1976).
49. R.B. Green, R.A. Keller, G.G. Luther, P.K. Schenck, J.C. Travis, /. Am.
Chem. Soc., 98, 8517 (1976).
50. G.C. Turk, J.C. Travis, J.R. DeVoe, T.C. O’Haver, Anal. Chem., 50, 817
(1978).
51. R.B. Green, R.A. Keller, G.G. Luther, P.K. Schenck, J.C. Travis, IEEE J.
Quantum Electron., QE-13, 63 (1977).
52. D.S. Sing, P.K. Schenck, K.C. Smyth, J.C. Travis, AppL Opt., 16, 2617 (1977).
53. E. Nasser, "Fundamentals of Gaseous Ionization and Plasma Electronics",
Wiley Interscience, New York (1971).
54. B. Chapman, "Glow Discharge Processes: Sputtering and Plasma Etching",
John Wiley & Sons, New York (1980) p. 78.
55. M.G. Drouet, J.P. Novak, Phys. Lett., 34A, 199 (1979).
56. F.A. Sharpton, R.M. St. John, C.C. Lin, F.E. Fajen, Phys. Rev. A2, 1305 (1970)
and references therein.

199
57. D. Ton-That, M.R. Flannery ,/Viys. Rev., A15, 517 (1977) and references
therein.
58. E.W. McDaniel, "Collision phenomena in ionized gases", Wiley, New York ,
1964 p.35.
59. A.D. MacDonald, "Microwave breakdown in gases", Wiley, New York, (1966)
p.24.
60. N.H. Farhat, Proc. IEEE, 62, (1974) 279.
61. K.C. Smyth, R.A. Keller, F.F. Crim, Chem. Phys. Lett., 55, 473 (1978).
62. K.R. Hess, W.W. Harrisson, AnaL Chem., 60, 691 (1988).
63. E.M. van Veldhuizen, F.J. de Hoog, D.C. Schram, J. Appl Phys., 56, 2047
(1984).
64. E. Miron, I. Smilanski, J. Liran, S. Lavi, G. Erez, IEEE J. Quantum Electron.,
QE-15, 194 (1979).
65. A.J. Palmer, J. Wm. McGowan, J. Appl. Phys., 43, 4084 (1972).
66. D.A. Haner, C.R. Webster, P.H. Flamant, I.S. McDermid, Chem. Phys. Lett.,
96, 302 (1983).
67. C.T. Rettner, C.R. Webster, R.N. Zare, J. Phys. Chem., 85, 1105 (1981).
68. S. Fujimaki, Y. Adachi, C. Hirose, Appl Spec., 41, 567 (1987).
69. P.A. Fleitz, CJ. Seliskar, H.B. Fannin, Appl Spec., 41, 1405 (1987).
70. B.R. Reddy, P. Venkateswarlu, M.C. George, Opt. Comm., 75, 267 (1989).
71. R.A. Keller, E.F. Zalewski, Appl. Opt., 19, 3301 (1980).
72. G. Erez, S. Lavi, E. Miron, IEEE J. Quantum Electron., QE-15, 1328 (1979).
73. A. Ben-Amar, G. Erez, and R. Schuker, J. Appl. Phys., 54, 3688 (1983).
74. M. Broglia, F. Cantoni, A. Montone, P. Zampetti, Phys. Rev. A, 36, 705
(1987).
75. R.A. Keller, B.E. Warner, E.F. Zalewski, P.Dyer, R. Engleman, Jr., and B.A.
Palmer, J. Phys. (Paris), CJ 23 (1983).
76. R.A. Keller and E.F. Zalewski, Appl. Opt., 21, 3392 (1982).

200
77. K.C. Smyth, P.K. Schenck, Chem. Phys. Lett., 55, 466 (1978).
78. G.S. Hurst, M.G. Payne, S.D. Kramer, and J.P. Young, Rev. Mod. Phys. 51,
767 (1979).
79. B.B. Rossi and H.H. Staub, Ionization Chambers and Counters, McGraw-Hill,
New York, 1949 pp.20-71.
80. C.R. Vidal, Opt. Lett., 5, 158 (1980).
81. R.Engleman, Jr., R.A. Keller, Opt. Lett., 5, 465 (1980).
82. H.O. Behrens, G.H. Guthohrlein, A. Kasper, /. Phys. (Paris), Cl 239 (1983).
83. G.C. Turk, J.R. DeVoe, and J.C. Travis, AnaL Chem., 54, 643 (1982).
84. N. Omenetto, B.W. Smith, and L.P. Hart, Fresenius Z. AnaL Chem., 324, 683
(1986).
85. N. Omenetto, J.D. Winefordner, Prog. AnaL At. Spectrosc., 2, 1 (1979).
86. R.A. Keller, R. Engleman, Jr. E.F. Zalewski, J. Opt. Soc. Am., 69, 738 (1979).
87. F.A. Sharpton, R.M. St. John, C.C. Lin, F.E. Fajen, Phys. Rev., A2, 1305
(1970) and references therein.
88. C. Th. J. Alkemade, Spectrochim. Acta, 40B, 1831 (1985).
89. National Bureau of Standards (now NIST), "Atomic Energy Levels", Circular
467, Vol. I (1948).
90. F.A. Moscatelli, Am. J. Phys., 54, 52 (1986).
91. F.M. Curran, K.C. Lin, G.E. Leroi, P.M. Hunt, and S.R. Crouch, AnaL Chem.,
55, 2382 (1983).
92. W. Heitler, "The Quantum Theory of Radiation", 3rd ed., Clarendon Press,
Oxford (1970); pp. 204-9.
93. M. Stobbe, Ann. Phys. (Paris), 7, 661 (1930).
94. M. Aymar, E. Luc-Koenig, F.C. Farnoux, J. Phys. B, 9, 4279 (1976).
95. A. Msezane ans S.T. Manson, Phys. Rev. Lett., 35, 364 (1975).
R.C. Hilborn, Am. J. Phys., 50 982 (1982).
96.

201
97. E. Voigtman, Appl Spec., Feb. (1991) in press.
98. E. Voigtman and J.D. Winefordner, Prog. AnaL Atom. Spectrosc., 9, 7 (1986).
99. J.E. Lawler, A.I. Ferguson, J.E.M. Goldsmith, D.H. Jackson, and A.L.
Schawlow, Phys. Rev. Lett., 42, 1046 (1979).

BIOGRAPHICAL SKETCH
Giuseppe Antonio Petrucci was born in Faicchio (BN), Italy, on October 11,
1963. In June, 1981, he graduated from Notre Dame High School in West Haven,
Ct. In May, 1985, he graduated from the University of Toronto in Ontario, Canada,
with a Bachelor of Science degree, Specialist in Chemistry. In June, 1987, he
received a Master of Science degree in analytical chemistry from the University of
Toronto. In August, 1987, he entered the Graduate School at the University of
Florida in Gainesville, Florida.
He is a member of the American Academy for the Advancement of Science,
the American Chemical Society and the Society for Applied Spectroscopy.
202

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
James D. Winefordner, Chairman
Graduate Research Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
x Richard A. Yost
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Anna Brajter-Toth
Associate Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Ik
A VU. w (,|Q
Vaneica Young/
Associate Professor of Chemistry
I certify that 1 have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Eric Allen
Professor of Environmental
Engineering Sciences

This dissertation was submitted to the Graduate Faculty in the College of
Liberal Arts and Sciences and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
December, 1990
Dean, Graduate School

,T,iy£^!71 0F FLORIDA
3 4 ¿i a x ATri1"11,11 ""i mi I
1262 08556 9506



xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EFY2YEQDP_5IG1EQ INGEST_TIME 2011-10-06T21:00:40Z PACKAGE AA00004769_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES