Copyright by Michael Anthony Gully-Santiago 2015

Copyright by Michael Anthony Gully-Santiago 2015 The Dissertation Committee for Michael Anthony Gully-Santiago certiﬁes that this is the approved version of the following dissertation:

Innovative Technologies for and Observational Studies of Star and Planet Formation

Committee:

Daniel Jaﬀe, Supervisor

John Lacy

Neal Evans

Adam Kraus

Alycia Weinberger Innovative Technologies for and Observational Studies of Star and Planet Formation

Michael Anthony Gully-Santiago, B.A. ASTRO. & PHYS.

DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulﬁllment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

THE UNIVERSITY OF TEXAS AT AUSTIN May 2015 Dedicated to all my teachers. Acknowledgments

This work would not have been possible without the mentorship of my collaborators Katelyn Allers and Alycia Weinberger, for which I am deeply indebted. I acknowledge the mentorship and patience of my former student colleagues Dr. Jasmina Marsh and Dr. Casey Deen. I am grateful for the efforts of my junior colleagues Jared Rand, Amanda Turbyfill, and Carleen Boyer for their contributions to the Silicon Diffractive Optics Group. Engineers Weisong Wang and Cindy Brooks contributed substantially to the Si diffractive optics fabrication. I am indebted to my NASA GRSP mentor Daniel Wilson, with whom it was a pleasure to work. I am thankful for the supervision of Richard Muller and Victor White at the Microdevices Laboratory. Sungho Lee, Hyeonju Jeong, Taylor Chonis, Mike Pavel, Michelle Grigas, Neal Evans, John Lacy, and Adam Kraus, Rachel Walker, and Gordon Orris made this work possible.

I am delighted to acknowledge support from the NASA Graduate Stu- dent Research Program (GSRP) Fellowship, grant NNX10AK82H. Portions of this research were supported by NASA APRA grant NNX10AC68G, NASA ACT grant NNX12AC31G, NSF ATI grant AST-0705064, and NASA Origins grant number NNX07AI83G. MGS acknowledges support from the Univer- sity of Texas in the form of the Graduate Dean’s Prestigious Fellowship and

v from the Department of Astronomy in the form of the David Benﬁeld Memo- rial Fellowship in Astronomy. Funding from the McDonald Observatory and the Department of Astronomy’s Cox graduate student excellence funds have helped to support travel and other aspects of this research. Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Ad- ministration. Some of the work was carried out at the University of Texas under a contract from the University of Arizona. The development work for the grisms was supported in part by NASA (grant number NNX07AV15H). The authors wish to thank Gary Poczulp and the National Optical Astronomy Observatory for assistance in producing some interferograms of early grating prototypes. Thank you to David Hogg, Dan Foreman-Mackey, Jonathan Sick, Jake Vanderplas, and the participants and organizers of the Astro Data Hack Week (2014). This dissertation includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile.

I was lucky to be part of such a talented and creative group of incoming graduate students- Chris, John, Chalence, JJ, Julie, Manuel, Erik, Paul, and Manos. I look forward to following their promising careers, and crossing paths indeﬁnitely. Joi Ito and Datri Bean enhanced my creativity. Thank you to my supportive family members Diana, Tony, Erika, and Vanessa who gave me mettle. Thank you to Carol for bringing Chelsey into the world, to Alese for introducing us, and to Chelsey for being exceptionally supportive. Thanks to Mr. Emerson who got me started in astronomy. Thanks to all my friends.

vi I acknowledge the kindness of the Wolchover family, who have always been outstanding in their ﬁeld.

A very special thank you is reserved for my advisor, Daniel Jaﬀe, for contributing so deeply to my professional growth. In particular I acknowledge his patient editing of the prose in this document.

vii Innovative Technologies for and Observational Studies of Star and Planet Formation

Publication No.

Michael Anthony Gully-Santiago, Ph.D. The University of Texas at Austin, 2015

Supervisor: Daniel Jaﬀe

I summarize the optical design, fabrication, and performance of silicon diffractive optics for astronomical spectrographs. The first set of optical devices includes diffraction-limited, high-throughput silicon grisms for JWST- NIRCam. These grisms served as pathfinders to Silicon immersion gratings, which offer size and cost savings for high-resolution near-infrared spectrographs. I demonstrate the production and optical evaluation of the immersion grating that enabled IGRINS at the McDonald Observatory. This grating provides spectral resolution R = 40, 000 over the H− and K− near-infrared band atmospheric windows (1.5−2.5 µm). Electron-beam lithography offers much higher precision over contact mask photolithography for the production of Si immersion gratings. Electron-beam patterned prototypes are stepping-stones to monolithic Si gratings for iSHELL and GMTNIRS. The monolithic design

viii of Si immersion gratings presents a limitation for scaling up the grating size, since existing fabrication equipment cannot handle monolithic silicon pucks. The size limitation can be overcome by direct-bonding Si substrates to optical prisms. I demonstrate a technique to measure interfacial gaps as small as 14 nm between the bonding interfaces, which produce 0.2% transmission loss. These technologies will enable the direct measurement of the atmospheric properties of extrasolar planets in the next decade. IGRINS is now measuring fundamental properties of young T-Tauri stars; low mass young brown dwarfs are below the sensitivity limit of existing high spectral resolution near-IR spectrographs. My approach to the discovery and characterization of young brown dwarfs therefore employs low resolution (R ∼ 2000) near-IR spectroscopy. I conﬁrm and characterize 17 candidate young stars and brown dwarfs reported by Allers and collaborators. All 17 sources have circumstellar disks.

Using deep optical, near-infrared, and mid-infrared photometry, I search an oﬀ-core region towards the nearby ∼ 1 Myr Ophiuchus star forming cluster for candidate young stars and brown dwarfs. Multi-object I−band spectroscopy of 419 candidates reveals 12 new members. Ten of these have no evidence for mid-IR excess emission from 3.6 to 8.0 µm. The disk fraction for spectral types M4 and later towards this region of Ophiuchus is 5/15. Two of the disk sources have edge-on disks, pointing to a high edge-on disk fraction. I discuss possible sources of contamination in the survey.

ix Table of Contents

Acknowledgments v

Abstract viii

List of Tables xv

List of Figures xvii

Chapter 1. Introduction 1 1.1 Innovative Technologies for Star and Planet Formation . . .1 1.2 Observational Studies of Star and Planet Formation . . . . .8 1.3 Summary ...... 15

Chapter 2. High Performance Silicon Grisms for 1.2-8.0 µm: Detailed Results from the JWST-NIRCam Devices 16 2.1 Introduction ...... 16 2.2 Discussion of Loss Mechanisms ...... 18 2.2.1 Surface Flatness ...... 18 2.2.2 Groove Geometry ...... 20 2.2.3 Microscopic Surface Roughness ...... 21 2.2.4 Fresnel Losses ...... 21 2.3 Results of Anti-Reﬂection Coating ...... 22 2.4 Conclusions ...... 28

Chapter 3. Near infrared metrology of high performance silicon immersion gratings 30 3.1 Introduction ...... 30 3.2 Overview ...... 31 3.3 Eﬃciency ...... 34

x 3.4 Refractive index dependence ...... 38 3.5 Periodic errors, ghosts, and large scale performance . . . . . 41 3.6 Measurement setup description ...... 44

Chapter 4. High Performance Si Immersion Gratings Patterned with Electron Beam Lithography 46 4.1 INTRODUCTION ...... 46 4.2 On-sky performance of Si immersion grating ...... 48 4.3 Motivations for direct writing Si immersion gratings . . . . . 49 4.3.1 Motivation #1: Higher precision than contact lithography ...... 50 4.3.2 Motivation #2: Finer groove pitch capability . . . . 51 4.4 e-beam patterning strategies ...... 51 4.4.1 e-beam patterning scale size hierarchy ...... 52 4.4.1.1 e-beam step size and spot size ...... 54 4.4.1.2 Subfield deflector ...... 55 4.4.1.3 Field deflector ...... 56 4.4.1.4 Interplay of hierarchy at boundaries and design rules ...... 56 4.4.2 Predicting the ghost level associated with field positioning errors ...... 59 4.4.3 Employ multiple field sizes rather than one field size 61 4.4.4 Strategies for mitigating facet position errors attributable to large scale stage drift ...... 63 4.4.5 Characterization of e-beam stage drift ...... 63 4.5 Results: Test gratings produced with e-beam patterning . . 65 4.5.1 Measurement of ghost levels for a variety of writing strategies ...... 65 4.5.2 Improvement in wavefront performance from drift correction ...... 67 4.6 Limitations of direct writing Si immersion gratings . . . . . 67 4.6.1 Serial write process yields long write times ...... 67 4.6.2 Large per-part investment cost yields heightened process risk ...... 70 4.6.3 Experiments with negative resist ...... 70 4.7 Conclusions ...... 71

xi Chapter 5. Optical characterization of gaps in directly bonded Si compound optics using infrared spectroscopy 73 5.1 Introduction ...... 73 5.2 Si−Si Fabry Pèrotmeasurement theory ...... 78 5.2.1 The Si−Si interface gap is a low finesse Fabry-Pèrot etalon ...... 78 5.2.2 Predicted transmission spectrum for bonded Si with finite interface gap ...... 82 5.3 Laboratory demonstration: Embedding gaps of known sizes . 85 5.3.1 IR bubble imaging and limitations ...... 89 5.4 Measurement technique and correlated measurement errors . 90 5.5 Results of infrared spectroscopy of directly bonded Si . . . . 92 5.5.1 Spectra of direct bonded Si with known gap sizes . . 95 5.5.2 Spatially resolved measurements with Sample Trans- port Accessory ...... 96 5.5.3 What is the smallest gap this technique can detect? . 101 5.6 Discussion ...... 103 5.7 Conclusions ...... 106 5.8 Incoherent Multiple Reflections Transfer Matrix Method . . 107

Chapter 6. Conﬁrmation and characterization of young disk- bearing brown dwarfs and sub-brown dwarfs 112 6.1 Introduction ...... 112 6.2 Spectral Typing ...... 113 6.3 Luminosities ...... 115 6.4 Conﬁrmation of Youth ...... 115

Chapter 7. Evolved disk population of young brown dwarfs towards Ophiuchus 120 7.1 Introduction ...... 120 7.1.1 Young brown dwarfs for the study of low mass sources 121 7.1.2 Mass estimation ...... 122 7.1.3 Previous surveys of young brown dwarfs in nearby star forming regions- Diﬃculties in identiﬁcation and biases therefrom ...... 122

xii 7.1.4 Motivation for this project ...... 124 7.2 Input catalog and candidate selection ...... 128 7.2.1 Photometry ...... 128 7.2.1.1 c2deep from Harvey et al...... 130 7.2.1.2 W − filter ...... 130 7.2.2 ISPI JH Catalog (∼ 3.3 magnitudes deeper than 2MASS)132 7.2.3 2MASS JH Catalog ...... 134 7.2.4 Candidate selection ...... 135 7.2.4.1 Near-IR photometric selection ...... 136 7.2.4.2 Mid-IR excess (disk) selection criterion . . 142 7.2.4.3 W − filter selection criterion ...... 145 7.2.4.4 H − [3.6] color selection criterion ...... 147 7.2.5 Ranking the combinations of selection criteria . . . . 148 7.2.6 Whittling down from 54373 to ∼500 ...... 151 7.3 Spectroscopic observations ...... 154 7.3.1 IMACS observations ...... 154 7.3.1.1 Observing Dates and conditions ...... 154 7.3.1.2 Instrumental setup- special note on filters . 154 7.3.2 IMACS Multi-slit exposure 2D spectral extraction . 155 7.3.2.1 Multi-object spectroscopy data reduction . 155 7.3.2.2 Performance of spectral type standards compared to literature ...... 156 7.4 Spectral and photometric analysis ...... 158 7.4.1 Spectral classification with The Hammer ...... 158 7.4.2 Whittling down from 505 spectra to 71 late-type sources159 7.4.3 Extinction ...... 160 7.4.4 Second pass spectral type ...... 161 7.4.5 Spectral comparison sample ...... 161 7.4.6 Gravity sensitive indices ...... 163 7.4.7 Hα emission ...... 165 7.4.8 Effective Temperatures ...... 165 7.4.9 Luminosities ...... 166

xiii 7.4.10 Extinction and position in the HR Diagram . . . . . 166 7.4.11 Spectral Energy Distributions ...... 170 7.5 Results ...... 171 7.5.1 Whittling down from 71 to 16 ...... 171 7.5.2 Discussion of individual sources ...... 175 7.5.3 Edge-on disks ...... 181 7.5.4 Mid-IR colors of diskless members ...... 181 7.6 Analysis ...... 184 7.6.1 Have we found diskless YBDs? ...... 184 7.6.2 What would we have selected if we had used selection criteria similar to other authors? ...... 185 7.6.3 Performance of the W − ﬁlter ...... 186 7.6.4 What is the range of model-derived masses of all of the sources? ...... 187 7.6.5 What can we say, if anything, about the IMF? . . . 188 7.6.6 Is there a higher incidence of edge-on disks in BDs? . 189 7.6.7 Are any of these sources from Upper Sco? ...... 189 7.7 Conclusions ...... 190

Bibliography 195

Vita 242

xiv List of Tables

3.1 CA1 grating and substrate properties ...... 31

4.1 D07 and E12 e-beam pattern details...... 53

4.2 Wafer TJ04 pattern details...... 66

5.1 UTexas Si bonding experiments ...... 88

5.2 Patterned gap properties ...... 88

5.3 Summary of Cary 5000 Measurement parameters ...... 93

5.4 Inferred Gap sizes and ﬁll factors ...... 96

6.1 Derived extinction, spectral type, and luminosity for Allers et al. 2006 sources ...... 116

7.1 Photometry in this study ...... 133

7.2 Binary selection criteria ...... 136

7.3 Selection-priority scoring system ...... 151

7.4 IMACS F/2 multi-object slit masks ...... 153

7.5 Photometry from this work ...... 168

7.6 Mid-IR Photometry from this work ...... 169

xv 7.7 Spectral classiﬁcation and derived properties of our sample . . 174

xvi List of Figures

2.1 JWST grism pictures ...... 18

2.2 A7-I interferogram ...... 19

2.3 JWST grism transmission ...... 23

2.4 Transmission of single side AR coated silicon wafer witness . . 25

2.5 JWST grism transmission ...... 26

2.6 Trial part groove interferogram ...... 28

3.1 Photo and design drawing of the IGRINS immersion grating . 32

3.2 CA1a SEM ...... 35

3.3 CA1a Eﬃciency ...... 37

3.4 CA1a Diﬀraction ...... 39

3.5 Optical interferometry of the IGRINS immersion grating . . . 40

3.6 Immersion grating interferogram PSF ...... 43

3.7 Schematic of the CROWBAR: Custom Robotic Order, Wave- length, and Blaze Angle Recorder ...... 45

4.1 e-beam Hierarchy ...... 52

xvii 4.2 TJ04 under Zeiss ...... 57

4.3 Field Stitching Error Cartoon ...... 60

4.4 Drift amplitude ...... 64

4.5 Ghost level measurements ...... 68

4.6 Interferometry reveals dramatic improvement in performance of e-beam produced immersion gratings ...... 69

5.1 Si refractive index and Finesse as a function of wavelength . . 79

5.2 Direct measurement of Si absorption as a function of wavelength 81

5.3 Predicted eﬀect size of transmission loss as a function of Si gap axial extent ...... 84

5.4 Lab measurement of synthetic gap extent with precision optical proﬁlometry ...... 87

5.5 IR image of direct bonded Si wafers demonstrating interfacial gaps ...... 90

5.6 MCMC corner plot and ﬁtted spectrum for gap size parameters for a large 4 µm interfacial gap ...... 97

5.7 MCMC corner plot and ﬁtted spectrum for gap size parameters when the gap ﬁlls only a small fraction of the measurement beam 98

5.8 Spatially resolved near-IR spectroscopy of direct bonded Si optics- measurements consistent with prediction band ...... 100

xviii 5.9 We can constain interfacial gap axial extents to <14 nm . . . 102

6.1 Spectral classiﬁcation with spectral type standards and spectra of dwarfs and giants ...... 117

6.2 Gravity dependence of the Na I line ...... 118

7.1 Map of the region of Ophiuchus targeted in our survey . . . . 129

7.2 Photometric selection color-color cuts in I − J vs J − H ... 140

7.3 Photometric selection color-color cuts in I − J vs J − K ... 141

7.4 H−band magnitude selection criterion ...... 143

7.5 Mid-infrared color selection ...... 144

7.6 W −ﬁlter selection method ...... 146

7.7 Mid-infrared photospheric emission selection ...... 148

7.8 Comparison of IMACS spectroscopy to a previously published spectrum of the same source ...... 157

7.9 Eﬀect of reddening on spectral classiﬁcation ...... 162

7.10 Na I 8190 equivalent width as a function of spectral type from M0 to L5 ...... 164

7.11 Pre main sequence HR diagram with young very low mass stars and brown dwarfs ...... 170

7.12 Spectral energy distributions of nine members of Ophiuchus . 172

xix 7.13 Spectral energy distributions of seven members of Ophiuchus . 173

7.14 IMACS spectra of 10 very low mass YSOs or young brown dwarfs towards Ophiuchus with spectral types M5-M6 . . . . . 175

7.15 IMACS spectra of 5 young brown dwarfs with spectral types M6−M8.5 ...... 176

7.16 Images of an edge-on disk source with nearby source ...... 181

7.17 Mid-infrared slope as a function of spectral type ...... 183

7.18 Mid-IR colors as a function of spectral type for our sample . . 192

7.19 Performance of the W −ﬁlter Q value as a function of spectral type ...... 193

7.20 Luminosity distibution of this sample and background contaminants ...... 194

xx Chapter 1

Introduction

1.1 Innovative Technologies for Star and Planet Forma- tion

The James Webb Space Telescope (JWST) will be the ﬂagship NASA astrophysics mission of this decade. Its primary science goals include the detection of the ﬁrst galaxies after reionization, and characterization of exoplanetary atmospheres. These and other science goals required the development of new technologies, including microshutter arrays, lightweight cryogenic mirrors, infrared detectors, and high-precision wavefront sensing. In Chapter 2, I describe one of these technologies we have developed and tested at UT Austin, the silicon grism, destined for the NIRCam instrument [82] on the JWST.

These devices have exquisite optical characteristics: phase surfaces flat to λ/100 peak to valley at the blaze wavelength, diffraction-limited PSFs down to 10−5 of the peak, low scattered light levels, and large resolving-power slit- width products for their width and thickness. The one possible drawback to these devices is the large Fresnel loss caused by the large refractive index of Si. Chapter 2 reports on throughput and phase-surface measurements for a sample grating with a high performance antireflection coating on both the flat and grooved surfaces. These results indicate that we can achieve very high on-

1 blaze eﬃciencies. The high throughput should make Si grisms an attractive dispersive element for moderate resolution IR spectroscopy in both ground and space based instruments throughout the 1.2-8 µm spectral region.

The NIRCam Si grisms oﬀer a unique capability for spectroscopy of the atmospheres of extra-solar planets. The composition of the extrasolar planetary atmosphere can be ascertained from spectroscopy of the planet in- and out- of transit [193], when the planet passes in front of the star as viewed from Earth. The Si grisms can be used for slitless transit spectroscopy, which eliminates the ambiguity of slit-losses when disentangling the in- and out- of transit signals. The wavelength range 2.4−5.0 µm has numerous spectral feaures of interest for discriminating between planetary atmosphere models. For example, the 2.4−4.0 µm transit spectrum of GJ436b will be able to distinguish between models with and without non-equilibrium photochemical hydrocarbon products from insolation from GJ436 [216]. The JWST grism spectrum of GJ436b could have detectable signatures of CH4, HCN, C2H2,

CO, and CO2. NIRCam has recently (November 2014) completed its second cryogenic vacuum test, and is performing as expected.

Si grisms like those in Chapter 2 served as pathfinders for Si immersion echelle gratings. The precision fabrication of Si immersion gratings is more demanding than it is for Si grisms. The heightened precision demands for immersion gratings over grisms rises from two effects. First, grisms are operated in transmission, whereas echelles operate in reflection. Echelles therefore require 2n/(n − 1) = 2.8 times less wavefront error to meet the same optical

2 performance as Si grisms. Additionally, Si echelles operate at much steeper blaze angles than Si grisms do. For example, an R3 echelle will will be 8.8 times more sensitive to wavefront error than its grism counterpart with a blaze angle of 6.16◦. Taking the reﬂection and blaze angle eﬀects together, we see that Si immersion echelle gratings require 25 times more precision than Si grisms of the same aperture and design wavelength.

Despite their fabrication challenges, Silicon immersion gratings are attractive because they oﬀer size and cost savings for high-resolution near- infrared spectrographs. The Immersion GRating Infrared Spectrograph (IGRINS)

λ [176] achieves spectral resolution R = ∆λ = 40, 000 simultaneously over H and K near-infrared band atmospheric windows (1.5−2.5 µm).

In Chapter 3, I chronicle the metrology of the R3 silicon immersion echelle grating for IGRINS. The grating is 30 × 80 mm, etched into a monolithic silicon prism. Optical interferometry of the grating surface in reflection indicates high phase coherence (< λ/6 peak to valley surface error over a 25 mm beam at λ = 632 nm). Optical interferometry shows small periodic position errors of the grating grooves. These periodic errors manifest as spectroscopic ghosts. High dynamic range monochromatic spectral purity measurements reveal ghost levels relative to the main diffraction peak at 1.6 × 10−3 at λ = 632 nm in reflection, consistent with the interferometric results. Improved grating surfaces demonstrate reflection-measured ghosts at negligible levels of 10−4 of the main diffraction peak. Relative on-blaze efficiency is ∼75%. We investigate the immersion grating blaze efficiency performance over the entire

3 operational bandwidth 1500 < λ(nm) < 2500 at room temperature.

IGRINS has been in operation for over 1 year on the 2.7 m Harlan J. Smith Telescope at McDonald Observatory, with no performance limitation attributable to the immersion grating. Recently, Pyo et al. [186] have shown that 2MASS J06593158−0405277 shows a similar spectrum to outbursting FU Orionis objects. The wide spectral bandwidth and high resolution stand to revolutionize studies of protostars. The construction of a panchromatic spectral atlas of dwarfs, giants, and young stars is underway (IGRINS collaboration, in prep.). An especially intriguing possibility is to perform robust spectroscopic inference on hundreds or thousands of IGRINS spectra to construct semi-empirical stellar spectra with imperfect models [47]. The unique science capabilities of IGRINS rely upon the high performance of the silicon immersion grating.

Other astronomical instruments are using Si immersion gratings. The NASA Infrared Telescope Facility (IRTF) will soon commission iSHELL [188], which will reach spectral resolution R = 70, 000, with spectral range 1.15−5.4 µm. The performance demands for the iSHELL immersion grating are even higher than those for the IGRINS immersion grating, since the IRTF site, Mauna Kea, has lower median seeing conditions than McDonald, and iSHELL will reach shorter wavelengths than IGRINS. These two eﬀects conspire to make the fabrication of the iSHELL immersion grating more demanding than the IGRINS immersion grating. In Chapter 4, I describe my work to improve the precision of Si immersion grating production.

4 The grooves in Si gratings are made with semiconductor lithography techniques, to date almost entirely using contact mask photolithography. Planned near-infrared astronomical spectrographs like iSHELL require either finer groove pitches or higher positional accuracy than standard UV contact mask photolithography can reach. A collaboration between the University of Texas at Austin Silicon Diffractive Optics Group and the Jet Propulsion Laboratry Microdevices Laboratory has experimented with direct writing silicon immersion grating grooves with electron beam lithography. The patterning process involves depositing positive e-beam resist on 1 to 30 mm thick, 100 mm diameter monolithic crystalline silicon substrates. We then use the facility JEOL 9300FS e-beam writer at JPL to produce the linear pattern that defines the gratings.

There are three key challenges to produce high-performance e-beam written silicon immersion gratings. (1) E-beam field and subfield stitching boundaries cause periodic cross-hatch structures along the grating grooves. The structures manifest themselves as spectral and spatial dimension ghosts in the diffraction limited point spread function (PSF) of the diffraction grating. In Chapter 4, we show that the effects of e-beam field boundaries must be mitigated. We have significantly reduced ghost power with only minor increases in write time by using four or more field sizes of less than 500 µm. (2) The finite e-beam stage drift and run-out error cause large-scale structure in the wavefront error. We deal with this problem by applying a mark detection loop to check for and correct out minuscule stage drifts. We measure

5 the level and direction of stage drift and show that mark detection reduces peak-to-valley wavefront error by a factor of 5. (3) The serial write process for typical gratings yields write times of about 24 hours- this makes prototyping costly. We discuss work with negative e-beam resist to reduce the fill factor of exposure, and therefore limit the exposure time. We also discuss the trade- offs of long write-time serial write processes like e-beam with UV photomask lithography. We show the results of experiments on small pattern size prototypes on silicon wafers. Current prototypes now exceed 30 dB of suppression on spectral and spatial dimension ghosts compared to monochromatic spectral purity measurements of the backside of Si echelle gratings in reflection at 632 nm. We perform interferometry at 632 nm in reflection with a 25 mm circular beam on a grating with a blaze angle of 71.6◦. The measured wavefront error is 0.09 waves peak to valley.

The next generation of high precision near-IR spectrographs employing silicon immersion gratings will push further the demands on optical performance.

The Giant Magellan Telescope Near Infrared Spectrograph (GMTNIRS) will have 5 separate spectrograph channels, each with its own custom Si immersion grating and IR focal plane array [108]. The scientiﬁc requirements drive high spectral resolution (R ∼ 100, 000) for the long wavelength channels (3−5.4 µm). The design calls for a Si immersion grating between 150 and 200 mm in illuminated length- larger than our existing 100 mm immersion grating substrates. The substrates will also have to exceed 30 mm in thickness, which

6 is larger than what our existing fabrication equipment can handle.

In Chapter 5, I demonstrate a technique to directly bond Si wafers to optical Si prisms, alleviating the need for patterning and processing on monolithic Si substrates.

Silicon direct bonding offers flexibility in the design and development of Si optics by allowing manufacturers to combine subcomponents with a potentially lossless and mechanically stable interface. The bonding process presents challenges in meeting the requirements for optical performance because air gaps at the Si interface cause large Fresnel reflections. Even small (35 nm) gaps reduce transmission through a direct bonded Si compound optic by 4% at λ = 1.25 µm at normal incidence. Understanding the optical effects of such gaps and evaluation of various methods for preventing or eliminating them demands that we have a method for measuring not only the two-dimensional extent of the gaps but also their axial extent. Existing methods for studying gaps provide only poor measures of this axial extent. We describe a bond inspection method that makes use of precision slit spectroscopy. Using spectroscopy, we detect and measure gaps as small as 14 nm by measuring transmission as a function of wavelength. Our analysis involves modeling multiple incoherent reflections within the substrate interfaces with a wave transfer matrix, modified for intensities rather than complex amplitudes. We infer the gap axial extent and fill factor with Monte Carlo Markov Chain (MCMC) and a flexible Gaussian process noise model. We describe the measurement and analysis techniques and demonstrate the validity of the approach by measuring

7 bond gaps of known depths produced by microlithography.

The innovations in silicon immersion grating technology that I have pio- neered center around astronomical instruments like JWST NIRCam, IGRINS, iSHELL, and GMTNIRS. These technologies could also benefit the Earth Sci- ence community, in which remote sensing of trace gases in the Earth’s atmosphere is a major priority. In particular, a future space-based mission like the Orbiting Carbon Observatory will associate local sources and sinks of green- house gases. The scientific requirements of high spatial and spectral resolution drive a “pushbroom” spectrograph design, with near-IR capability to detect methane. This spectrograph design differs from those in astronomical applications because of its much larger angular slit length, and its higher groove frequency. The innovations in direct Si−Si bonding and metrology described in Chapter 5 will facilitate the transfer of technologies between the fields of astronomy and earth science.

1.2 Observational Studies of Star and Planet Formation

One outstanding question in star formation is “How do the properties of young stars affect the evolution of their circumstellar disks”. The effects of stellar mass, multiplicity, and radiative properties have been studied across the mass range from Herbig Ae-Be stars (2 − 8M ) to brown dwarfs (< 0.08M ) [242]. Extending studies further into the substellar regime is especially ap- pealing since brown dwarfs offer vastly different radiative environments and lower accretion rates [169, 97].

8 The current prevailing opinion is that most brown dwarfs form just like stars [33]. The existence of wide separation, similar mass binary brown dwarfs [131, 4, 36, 147] shows that at least some brown dwarfs form from direct gravitational collapse of a gas cloud, and could not have been formed from gravitational instability in the disk of a more massive star. Circumstellar disks are common around young (∼ 1 Myr) brown dwarfs [142, 6, 135, 13]. Large disks cannot survive a three-body interaction that would cause ejection from a stellar counterpart, while small protolunar disks could survive ejection [224]. These wimpy disks would be outwardly truncated at a semimajor axis of tens of AU [224]. These outwardly truncated disks would demonstrate an observational signature of dramatically suppressed mid-IR and far-IR excess emission. The abundance of disk-bearing young brown dwarfs is inconsistent with a large population of outwardly truncated disks, pointing towards formation like stars as the dominant formation pathway for brown dwarfs [135]. Additionally, recent interferometric ALMA continuum visibilities demonstrate that 3 Taurus brown dwarfs have large, ∼ 70AU disks [201]. See Chabrier et al. [33] for more lines of evidence, and a discussion of the IAU deﬁnition of brown dwarfs and giant planets.

Because they share a common formation pathway with stars, brown dwarfs must also share similar pre-main sequence evolution characteristics. Young stars go through a set of clear evolutionary stages that have distinc- tive appearances and physics. Brown dwarfs must form in exceptionally dense molecular cores, then proceed through an envelope phase, a disk-bearing phase,

9 and a dissipation phase. The observational signatures of these stages correspond to the observational classes 0, I, II, and III [1]. Stars have been observed in all of these stages [56] while brown dwarfs have been observed in classes I, II, and III. A few candidate class 0 proto-brown dwarfs exist[15, 185, 175], for example the source IC348-SMM2E is consistent with an envelope mass of merely ∼ 35MJup. The pre-main sequence classes are based on their Tbol [170], the spectral index in the mid-infrared [118] and, for class I-III on Hα equivalent widths (accretion rates). The dust in the disk is much easier to detect at mid-IR wavelengths, since dust has most of the opacity in the disk, despite having . 1% of the mass of the disk.

Strong H emission lines indicate mass accretion, and should be present in all observational classes, except possibly class III (e.g. weak-lined T-Tauri star analogs) [90]. Accretion is accompanied by outﬂows- spatially resolved collisionally excited lines like [OI] λ6300, 6363A˚ and [SII] λ6731A˚ [240] indicate shocked gas. Photometric variability, a hallmark of YSOs at all classes and all wavelengths [192, 37], is evidence for ongoing accretion, photospheric hot spots, and dynamic disk processes.

We assume that the majority of brown dwarfs form like stars, but that an unknown minority may have formed by ejection from a protoplanetary disk.

While you might expect accretion and outﬂows to be present among brown dwarfs, there are some diﬀerences from what we see in stellar mass objects of comparable age. The radiative environment will be much softer around brown dwarfs, since the accretion luminosity Lacc will scale down with

10 the low mass but large radii of young brown dwarfs, with observations indicating brown dwarfs have about 10−3 − 10−4 times the accretion luminosity of their T − T auri counterparts that have only 10 times the mass [172]. Young brown dwarf emission peaks at around 1 µm, almost twice that of their solar mass counter parts. Passively irradiated disk models [52] show that the sequence of Herbig Ae/Be to T-Tauri to young brown dwarf forms a continuum, with no significant variations in the turbulent mixing strength [165]. However many factors affect the appearance of the SED. Chief among the factors are grain growth and dust settling [35]. The key idea is that the central object temperature and luminosity controls the size of the dust-free cavity through photoevaporation [242]. The location in the disk where the equilibrium temperature of a dust grain is 1400 K is roughly equal to the dust inner rim radius, Rinner [54]. The detailed location of the dust inner rim depends on the grain size, composition, and local pressure [103], and presence or absense of disruptive planets [22, 177]. One main open question is “What happens to the dust inner rim when the brown dwarf photospheric temperature declines to equal the dust sublimation temperature?” Can dust survive all the way up to the stellar surface? The luminosity of the dust inner rim depends on both its equilibrium temperature and emitting area. Assuming a fixed (1400 K) dust inner rim temperature, the emitting area of the dust rim controls the luminosity of the disk compared to the luminosity of the star. The ratio of disk flux to photospheric flux at a given wavelength will therefore decrease as a function of photospheric temperature. This effect has been used to explain the

11 high frequency of objects with spectral energy distributions similar to those of transition disks without invoking a region in the inner disk where the temperatures reach the sublimation temperature but where dust is depleted [62], and is consistent with Herschel observations towards brown dwarfs in Ophiuchus [13].

The average steady state accretion rates scale as a function of mass with the scaling factor α in M˙ ∝ M α approximately equal to α ∼ 2 [72, 2, 173, 97]. The explanation for α ∼ 2 is unclear [92]. The ratio of stellar mass to stellar radius M/R scales with mass [32], so the energy of impact ∝ M/R should also scale with mass. Existing measures of accretion rate are noisy owing to the uncertainty in assigning mass accretion rates based on emission line strengths, and the intrinsic variability of accretion. Instruments with pan-chromatic UV- visible-near-IR spectroscopy [234, 204] are improving the accuracy of these methods. It has recently been suggested that the scaling factor could arise from selection eﬀects of brown dwarfs [155]. If true, this selection bias would mean there is an unobserved population of luminous brown dwarfs with mass

˙ −1 accretion rates log M/(M yr ) > −9 that has largely evaded detection.

Brown dwarfs will not follow a Henyey track [96]. Instead, brown dwarfs monotonically cool and dim for billions of years. For example, a 50 MJup brown dwarf will decrease in luminosity by a factor of about 2 over the . 5 Myr disk lifetime [19].

For low mass stars, the majority of mass accretion occurs in stages 0 and I, when the protostar is most embedded [158, 56]. The ubiquity of underlu-

12 minous class 0 YSOs indicates that most mass accretes in short-lived episodes [55]. Mass accretion rates are highly variable during this stage [236, 21, 17]. Speciﬁcally, the Spitzer legacy program “From molecular cores to planet- forming disks” [64, c2d] pointed out that a constant mass accretion rate of

−6 −1 10 M yr would form a solar mass star in 1 Myr, but that accretion lumi-

−8 −1 nosities corresponding to ∼ 10 M yr were observed. So protostars must accrete their mass in several very short bursts, with burst timescales consistent with FU Orionis events [56]. The presence of chemical species indicative of high disk temperatures also lends support to the episodic accretion paradigm [235]. Accretion history is predicted to have an observational consequence on the luminosities of very low mass stars and brown dwarfs [21, 225]. Specifically, episodic accretion onto a 50 MJup brown dwarf is predicted to demonstrate a luminosity spread equivalent to an age spread of ∼ 10 Myr. Sources that look young are young, while sources that look old, could still be young. The effect is greatest for the lowest mass sources, which can be understood because these sources are accreting a large fraction of their mass in these episodes. Young (1-10 Myr) brown dwarfs offer a unique laboratory to directly probe the evolutionary history of individual objects, since the appearance of a luminosity spread mimicking an age spread could indicate that episodic accretion has oc- curred. This indicator of episodic accretion would be complementary to the evidence for episodic accretion coming from the underluminosity problem in Class 0 protostars.

In Chapter 6, we conﬁrm and characterize, using R ∼ 2000 near-

13 infrared spectroscopy, 17 candidate young substellar objects in the Ophi- uchus, Lupus I, and Chamaeleon II star forming regions from the Allers et al. 2006 sample. The spectral types range from M2−L2.5, with extinctions of 0 < AV < 10. We assign youth based on the presence of mid-IR excess and gravity sensitive spectral indices, like the triangular H−band continuum shape and the Na I equivalent width. All but one source from the photometri- cally selected sample of 19 are confirmed as bona fide young late type objects, an exceptional confirmation rate for this type of study. Two of the sources are known wide-separation binaries. We explore the advantage of increased resolution over existing low resolution spectroscopy for six objects. The objects’ derived luminosities are in the range −3.3 < log L/L < −0.6, placing the lowest luminosity candidates comfortably in the substellar or even sub brown-dwarf mass regime.

Allers et al. [6] selected their sources for demonstrating the presence of mid-IR excess indicative of a circumstellar disk. In Chapter 7, I search the same region of Allers et al. [6] towards Ophiuchus for the presence of young brown dwarfs which do not exhibit mid-IR excess indicative of a circumstellar disk. A custom W −band ﬁlter centered on 1.4 µm is pivotal in distinguishing background contaminants from young brown dwarfs with intrinsic water absorption in their photospheres. Since this selection strategy is unbiased towards presence of mid-IR excess, we can pick out the diskless young brown dwarfs. These diskless young brown dwarfs are Class III analogs that have already undergone a phase of disk dispersal. The dominant mechanism of disk

14 dispersal is still unknown, though planet formation, binary companions, and photoevaporation may all play a role. Whatever the mechanism, it is clear that the timescale for disk clearing is short compared to the disk lifetime. Out of 15 sources towards this region we ﬁnd that only one source exhibits mid- infrared colors indicative of a transition disk. The small number of sources and possible contamination towards Upper Scorpius make it challenging to draw strong conclusions on the disk fraction towards this region. Our estimated disk fraction of 33% is lower than but consistent with estimates of other young star forming regions.

1.3 Summary

This work has developed the technology with which the next generation of astronomical discoveries will be made. At the same time I have used new selection strategies to discover a population of young low mass stars and brown dwarfs with evolved disks or no disks.

15 Chapter 2

High Performance Silicon Grisms for 1.2-8.0 µm: Detailed Results from the JWST-NIRCam Devices

2.1 Introduction

We have delivered a set of silicon grisms for use as dispersive elements in the long wavelength channel of the near-infrared camera (NIRCam)[101, 82] on the James Webb Space Telescope (JWST)[205]. The primary function of these grisms is to produce spectra for dispersed fringe sensing which will permit elimination of piston errors as the telescope is aligned to its design figure[218]. The NIRCam-based dispersive fringe sensing system, by virtue of its long operating wavelength, has a significantly larger capture range than the equivalent optical system. The grisms also offer the possibility of astronomical observations that can make use of NIRCam’s ability to conduct slitless spectroscopy at 3-5 µm over a large field. One important application is infrared spectroscopy of transiting planets where the absence of a slit eliminates the problem of time-variable slit losses[80]. Science operations in the NIRCam grism mode will be supported by the JWST data planning and data taking software.

The fabrication of silicon grisms was an eﬀective solution to the prob-

16 lems of maximizing resolving power in a predetermined and limited space and of providing optically efficient dispersers in a space-qualifiable material. Jaffe et al. (2008)[107] discuss the fabrication of the NIRCam devices and the optical quality of the grating surfaces. The performance significantly exceeds the requirements for diffraction-limited spectroscopy at 3-5 µm, as evinced by front-surface interferometry and monochromatic PSF measurements at optical wavelengths. Figure 1 shows a photograph of one of the six parts (four flight parts and two flight spares) delivered by the UT grating group. Each part has a diameter of 48 mm (usable diameter 42mm). Blazed at 5.75 degrees, these parts provide a resolving power R = λ/∆λ ∼ 1800. The flight grisms are blazed at 3.7 µm in first order and light at this wavelength is undeviated as it passes through the system. The interferometric measurements presented in our previous paper showed that the errors in the grating surface were extremely small, less than λ/100 peak to valley at the blaze wavelength, offering the promise of excellent throughput and superb spectral purity. These measurements do not, however, tell the whole performance story: The completed flight parts have flat entrance faces that can also contribute to phase errors. Etched silicon gratings have a groove vertex angle of 70 ◦ rather than the 90 ◦ that ruled gratings have. The manufacturing process produces small flat “dams” between each groove to serve as etch stops. The acute angle and/or these dams leave a portion of the grooved surface unusable. Small-scale surface roughness in the grooves themselves can lead to diffuse scattered light that is hard to measure directly. Finally, there are reflective losses at the vacuum/silicon in-

17 Figure 2.1 Photograph of flight grism “A6K” for JWST-NIRCam. The outer diameter is 48 mm and the part has an optically usable diameter of 42 mm. The forward-facing surface has grooves with a period of 15.36 µm. The opposite surface has been polished optically flat. The flats along the perimeter serve as mounting and orientation surfaces terfaces. In this paper, we give a more complete discussion of these sources of loss and of how they contribute to the measured performance of the devices.

2.2 Discussion of Loss Mechanisms 2.2.1 Surface Flatness

Because the parts are physically larger than the optically active area, it was possible to polish the ﬂat surfaces of the JWST grisms to very high accu-

18 Figure 2.2 Interferogram of the polished entrance surface of JWST trial grism “A7-I”. The interferogram was taken prior to the application of an antireflection coating. racy. The specification for the polishing vendor was that the surface be flat to λ/10 peak to valley at 633 nm. At 3.7 µm, this specification corresponds to a flatness of λ/60. The difference of 2.4 in the refractive indices inside and outside the grism imposes similar flatness criteria for a silicon transmission optic to those one would impose on a mirror. The achieved flatness of the entrance faces (Figure 2) did not always meet this optical specification but, in all cases, was very much better than required for diffraction-limited performance and these faces do not contribute to loss of performance in either throughput or resolution.

19 2.2.2 Groove Geometry

We form the grooves in the monolithic substrates from which we fabricate the grisms by taking advantage of the significantly different rates at which certain chemicals etch through the different planes in crystalline structure[152, 230]. In our process a solution of KOH etches approximately 60 times faster across the 100 plane than across the 111 plane and a suitably oriented mask of stripes will form triangular grooves at the intersection of 111 planes. The intersecting planes form an angle of 71 ◦. For blaze angles greater than 8 ◦, this acute angle will result in shadowing of one groove by another in transmission with the amount of shadowing a function of the blaze angle (see Figure 6 of Mar et al. (2006)[151]). For small prism opening angles, it is not the acute groove vertex but rather the small dams along the grating surface that lead to groove filling factors less than one. We need the dams to serve as etch stops between the grooves. For the JWST gratings, the grating constant was 15.36 µm and the final dam width was about 1.5 µm. At the 6.16 ◦ opening angle of the JWST prisms, the dams are responsible for the filling factor loss. The geometric blockage whether by the dams or by the lip of the neighboring acute groove leads to loss in two ways: direct blockage of the light and, via Babinet’s principle, diffraction of an equal amount of light into unwanted orders. For the geometric blockage of ∼ 10% in the JWST grisms, the maximum theoretical transmission is then 0.81.

20 2.2.3 Microscopic Surface Roughness

While the etching process results in remarkably flat grooves, point defects in the structure of the crystalline silicon grating substrates can lead to local pits and hillocks, that is, to roughness on various scales, as the anisotropic etching produces the blazed grooves. The consequences of this roughness are difficult to measure directly as the scattered light produced as a result of it is generally on large angular scales with low peak amplitudes. Instead, the best ways to evaluate this possible loss mechanism is to examine the roughness of the surfaces directly. We have done this for an earlier set of grating surfaces using atomic force microscopy[152] and concluded that the integrated diffuse scattered light due to small-scale roughness is 0.005% for a Si grism in operation at 3.7µm. We have also used interferometric metrology of roughness within individual grooves in the more demanding context of immersion grating production (see Wang et al. in this volume[238]) and find that the loss should be about 0.006% if such surfaces are used in transmission.

2.2.4 Fresnel Losses

The large refractive index (∼ 3.41 in the near-IR) that gives silicon grisms their large etendue also condemns them to substantial reflective (Fres- nel) losses at the vacuum/Si interface. For uncoated silicon, this loss is ∼ 30% per surface. When this loss is combined with the geometric loss, the maximum efficiency in the blaze order should be ∼ 0.41. Figure 3 shows the transmission versus wavelength curve for one of the NIRCam flight parts. The tight delivery

21 schedule for these parts did not allow us to measure the performance in first order, where the parts will be used in flight, but the on-blaze transmission of the uncoated gratings in modestly higher orders should be similar. The peak transmission in 3rd order is 43%, consistent to within the errors with the theoretical maximum. Even without an antireflection coating, the transmission of this grism is within the low end of the range of published efficiencies for near-IR grisms made from other materials and currently in use at ground-based telescopes, for example NSFCAM’s KRS5 grism[191] demonstrated efficiencies of 55%, 50%, 40% in orders 2, 3, and 4 which correspond to roughly the L, K, and H near-IR atmospheric bands.

2.3 Results of Anti-Reﬂection Coating

The initial plan for the JWST grisms was to coat only the ﬂat side of each grism with a broad-band antireﬂection (AR) coating. An ideal coating on this single face would result in a transmission of 0.57, a performance at the high end of the range of throughputs cited for grisms currently in use. Figure 4 shows the transmission of a thin silicon wafer witness with an AR coating applied to one air-Si interface. In the range of 2-5 µm, the transmission curve is consistent with Fresnel losses from only the uncoated surface, or in other words the AR coating transmits almost 100% of the incident light.

In a diffraction limited system, however, one needs to be concerned about whether the process control for a multilayer coating is sufficiently good to preserve the observed flatness of the entrance face. We were able to take

22 Figure 2.3 Measurement of throughput as a function of wavelength for JWST flight part “A6-I”. The combination of the geometric blockage by the groove dams and the Fresnel losses results in a theoretical maximum efficiency of ∼ 0.41 on the blaze. The plot shows the power in the fifth order and in adjacent orders.

23 interferograms of a geometrically similar test piece before and after a broad- band 2-5 µm antirection coating was applied. The large-scale phase coherence won in the polishing of this surface has not been degraded by the addition of the multi-layer dielectric AR coating.

The only way to improve the delivered throughput beyond that achieved with the single-side coating would be to coat the grism grooves as well with a broad-band AR coating. Such a procedure faces three potential problems: (1) The shape of the groove makes it hard to deposit even layers of controlled thickness that are the basis for the efficacy of any antireflection coating. (2) Even small-amplitude variations in the summed thickness of the coatings could diminish the superlative phase coherence of the grating on large scales. (3) Even if the coating preserves coherence on large scales, variations in the deposition thickness within each groove could produce a change in the blaze shape from perfectly flat to structured in a way that might divert power out of the blaze order.

In the course of the development work for the JWST grisms, we were able to test the viability of AR coatings on the grating grooves by putting test coatings onto a prototype. This prototype “trial” part (“A7-I”) had the same groove constant and same vertex angle as the flight parts and flight spares but has an 11 ◦ blaze angle, rather than the 5.75 ◦ angle shared by the other parts. The trial part functions well in the mid-infrared but differs from the flight parts in having its second-order rather than first-order blaze peak at the center of the band for the JWST long wavelength camera. The difference in

24 Figure 2.4 IR transmission of an optically flat thin silicon wafer witness that was AR coated on a single side. The wafer does not have grooves on it, and therefore does not have geometric losses. Since the uncoated air-Si interface suffers 30% Fresnel loss, the AR coated interface must exhibit close to 100% transmission between 2 and 5 µm. The AR coating is ineffective shortward of 2 µm, and Si does not transmit short of 1.15µm. Figure courtesy of II-VI Inc.

25 Figure 2.5 Transmission of trial part A7-I. The interferograms were taken with the surfaces (left) uncoated and (right) coated on both entrance and grating surfaces. The ineffectiveness of the AR coating shortward of 2.0 µm (cf. Figure 4) stifled a direct comparison of transmission at the same wavelengths before and after coating. The poor transmission below 2.0 µm is apparent in the right panel, since the 4th order curve is suppressed before it reaches its blaze peak near 1.8 µm. A similar measurement at 3.1-4.0 µm shows 75% peak efficiency for the double-side coated grism. the prism opening angle and groove blaze angle means that the wavelength at the peak of the blaze is not undeviated as it is for the flight parts. We coated this part with the same antireflection coating used for the flat surfaces of the flight parts, coating it first on the flat side and then, after measurement, on the grooved surfaces as well. Throughput measurements were carried out by our group at UT Austin with a scanning monochromator or by II-VI Infrared Inc with their spectrophotometer. The UT measurements were performed by measuring the ratio of the transmitted signal strength at the appropriate angle for the second-order beam to the signal from the monochromator incident on the detector with no intervening dispersive element.

The left panel of Figure 5 shows the performance of this part prior to

26 the application of the coating while the right panel shows the transmission after A7-I had been AR coated on both its entrance and exit surfaces. The right panel of Figure 5 does not reveal the peak on-blaze efficiency for two reasons- (1) the narrow wavelength range can only capture the 4th order blaze peak and (2) the AR coating is ineffective at wavelengths shorter than 2.0 µm, suppressing the peak near 1.8 µm. A coarse estimate for the blaze efficiency can be obtained by summing the power in orders 3 and 4 at a given wavelength, yielding an expected value for the peak efficiency of 80%, which would be consistent with the maximum 81% permitted by geometrical losses. Our group has also performed throughput measurements from 3.1 to 4.0 µm that indicate 75% efficiency at the 2nd order blaze peak at 3.7 µm (see figure in C. Deen et al. in preparation). The measurements at 2nd order also indicate negligible power in the adjacent orders at 3.7 µm. This observation is important because it means power was not diverted out of the blaze order after the AR coating was applied. The multi-layer coating must not have altered the shape of individual grooves- variations in the deposition thickness within each groove must be very small. This claim is also weakly supported by pre- and post- coating optical reflection measurements, which show similar ratios of power in the first and second brightest orders at 633 nm.

Figure 6 shows a comparison of the 633 nm Littrow interferogram of the grooved surface of the trial part before (left) and after (right) the application of the antireﬂection coating. While the images themselves appear quite dissimilar, the numbers at the bottom of the plot tell the true story. The peak

27 Figure 2.6 Optical interferograms at 633nm of the central 31 mm of the grooved surfaces of the trial part, A7-I. The left figure shows the grooved surface before AR coating. On the right is the interferogram of the grating surface after AR coating. The RMS and peak to valley wavefront errors are printed at the bottom of the figures- before: PV- 0.0308, RMS- 0.0061 waves; after: PV- 0.0557, RMS- 0.0120 waves. to valley deviation in the reflected phase front is virtually identical in the two cases and is extremely small (< λ/100 at the blaze wavelength).

2.4 Conclusions

In summary, we have completed a set of six high performance silicon grisms for the NIRCam instrument on JWST. The grisms are produced with precision photolithography and anisotropically etching the Si crystal plane. By enumerating the loss mechanisms we saw that geometric and Fresnel losses limit the throughput of silicon grisms to about 41%. When the entrance and grating surfaces are coated with a broad band anti-reﬂection coating, Fresnel

28 losses become negligibly small. Measurements of a sample double side AR coated grism indicate on blaze throughput of about 75%, marginally below the 81% expected for purely geometric losses. The grating performance was not significantly degraded by the multi-layer dielectric coating, as evinced by interferometry and optical reflection efficiency measurements.

29 Chapter 3

Near infrared metrology of high performance silicon immersion gratings

3.1 Introduction

Immersion gratings are diffraction gratings illuminated within a high refractive index optical material, which provides increased spectral resolving power compared to diffraction gratings of comparable size illuminated in air or vacuum. Scientific demands for high spectral resolving power combined with engineering demands for compact spectrographs make immersion gratings an attractive technology. This report chronicles the lab performance of CA1a, an immersion grating made of silicon (nSi ∼ 3.4). CA1a or its spare CA1b will serve as the primary dispersive optical element for the Immersion Grating Infrared Spectrometer, IGRINS[244]. We have reported on immersion grating design and fabrication elsewhere[152]. Wang et al. 2010[237] reported on the science requirements for, fabrication of, and optical testing results of CA1, the parent Si boule puck from which CA1a was cut. Since 2010 we have cut and polished two optical devices from CA1, and report here on their performance in immersion.

30 3.2 Overview

Figure 3.1a shows a photo of the final immersion grating CA1a after cutting, polishing, AR coating, and aluminization. The trapezoidal side profile is a relic from the shape of the parent substrate and our cutting strategy. The optically active volume is the prism shown above the dashed line in the photo in Figure 3.1a. We left on additional silicon to strengthen the thin end of the prism wedge. The front entrance face has a multi-layer dielectric antireflection (AR) coating, which, based on direct measurements off the CA1a entrance face, has a reflectivity < 1% across the 1.4−2.5 µm range. The grating grooves were aluminized with a conformal Al layer. Cryogenic testing of heritage gratings demonstrated that the conformal layer of Al is robust to typical cryogenic thermal cycling[152]. We have not yet cooled CA1a.

Table 3.1 CA1 grating and substrate properties

Property Value Pitch, σ (µm) 27.36 (l/mm) 36.55 Groove top, t (µm) 9.95 Blaze angle, δ (◦) 71.6±0.2 Apex angle, A (◦) 72.1±0.2 Material properties Material High resistivity ﬂoat zone Si Average Refractive index 3.44 Speciﬁc heat (Jg−1K−1) 0.71

We produce the grating grooves by photolithography and anisotropic chemical wet etching[152, 237]. This process has some special features. The

31 25 mm

(a) CA1a photo (b) CA1a drawing Figure 3.1 Photo and design drawing of the immersion grating CA1a in the lab in August 2011. The entrance face is on the right, with a light green color in the photo (color available in the digital manuscript), which is due to the AR coating. The grating surface is on the top with microscopic grating lines perpendicular to the long edge of the grating. In operation a 25 mm circular beam will be incident on the entrance face and will project into an ellipse on the grating surface as seen in the drawing. The dispersed light will reemerge from the entrance face. The units in the drawing are mm. The parent substrate and grating geometry are pictured in Figures 1, 3, and 4 in Wang et al. 2010[237]. Those ﬁgures reveal how the CA1a trapezoid shape and curved rear edge derive from the parent substrate shape.

32 wet etching process makes acute angle grooves, not 90◦ grooves, as illustrated in Figure 3.2. The groove apex angle A = 70.5◦ is the intersection of two 111 Si crystal planes. We anticipated an apex angle widened by 0.8◦ on both sides, for a net apex angle of about A = 72.1◦. A finite but small amount of etching accross the 111 crystal planes causes the small 0.8◦ angular correction[152, Figure 5]. The anisotropic correction similarly decreases the blaze angle δ by ∆δ = 0.8◦. This effect must be accounted for, first at the time of the initial x-ray orientation and cutting of the parent substrate and second at the time of cutting the immersion prism from the Si parent substrate. We verified the delivered blaze angle after wet etching but before cutting our immersion grating prism by measuring the relative intensity of eight diffracted orders in reflection in air at the air-Si grating interface. We made a simple scalar diffraction theory model and compared it to the observed intensity of the eight orders surrounding order 82, the brightest observed order at 632.8 nm in front-surface reflection. The measurements were performed in the Littrow configuration. The model predicted the effect of the blaze envelope as a function of incidence angle. We found δ = 71.63 ± 0.20◦, consistent within the uncertainty with δ = R3, so we cut the front face to R3. The apex and blaze angles are conspicuous in the SEM cross section (Figure 3.2). Importantly, the groove apex shows a sharp peaked tip with no evidence of a flat bottom, which can occur in incomplete wet etching. Flat bottoms cause a direct efficiency loss by diffract- ing light away from the blaze. In the right panel of Figure 3.2 the optically active facets are highlighted. The flat groove tops on the grating surface are

33 artifacts of the groove formation process. Speciﬁcally, nitride coated groove tops serve as anisotropic wet etch dams. It is clear from the annotated SEM micrograph that the groove tops are shadowed for light incident at or close to the blaze angle. The groove tops will be shadowed so long as the ratio of the grating top t to pitch σ ratio satisﬁes the condition:

t 1 < , σ tan(A) 1 + tan(δ)

For our grating, t/σ = 0.36 < 0.49, so the optically active groove facets fully shadow the groove tops as planned. The SEM micrographs are not sensitive enough to small (∼ 5 nm) scale groove position errors, so detailed optical and IR metrology is necessary to evaluate the performance.

3.3 Eﬃciency

For optimal performance immersion gratings should be as efficient as possible. The IGRINS specification for immersion grating efficiency is 65-70% peak on blaze[237]. We directly measured the AR-coated entrance face reflective loss at < 1% over the measured range 1500 − 2300 nm. From measurements of the microscopic surface roughness[237] we expect scattered light from microscopic surface roughness to be < 0.5%. We directly measured the immersion grating efficiency as a function of wavelength with a custom scanning monochromator setup in our lab, described in the Section 3.6. The reference mirror was aluminum on glass, so the absolute grating efficiency is about 3.5% lower than reported here, assuming aluminum reflectance of 95% in the near-

34 Aluminum

27.36 µm δ

β ~ α = δ = 71.56° Silicon n=3.4 Grating normal

Figure 3.2 Scanning electron micrograph (SEM) of a ∼100 µm cross section of a scrap portion of the immersion grating CA1. The left panel is the unaltered SEM. The right panel is a schematic illustrating the grating specifications and the geometry of incident and diffracted beams (thick black line with arrows). The beam is incident from the left, and diffracts at the facets at the silicon/aluminum interface. The incident angle α and diffracted beam β are measured from the grating normal (shown in blue). The blaze angle δ is set by the orientation of the crystal planes with respect to the grating surface. This angle was designed to be δ = 71.56◦, which is the angle whose tangent is 3. The optically active facets are highlighted as short red vertical lines (color online). The regions of the grating above the dashed line do not see the beam. In the IGRINS design and in our lab testing there is a small out of plane angle γ not shown here. The apparent hillock artifacts on the grating facets are a result of the cross-section preparation process, the measured[237] surface flatness is 1.7 nm.

35 IR. Recall that the grating grooves are aluminized, so the reported relative efficiency is a good indicator of how well the bulk of the immersion grating is performing. The measurement shown in figure 3.3 has 1 nm bandwidth, with 1nm sampling over the range 1500 − 2300 nm. The measured peak on-blaze efficiency is between 70% and 80% across all 43 orders, except for order 120 which has a peak efficiency of 68%. CA1a was measured with an out of plane angle [215], γ ∼ 2.6◦ in immersion. We only coarsely controlled the incidence angle α in our efficiency measurement, with α ∼ δ to within about 2◦. Accord- ingly, we measured some angularly dependent diffraction loss that one would expect if orders diffracted into the grating sidewalls. It is best to have α > δ so that the blaze envelope is centered at β < δ.

There are a few potential loss mechanisms which lead to the observed eﬃciency:

1. Fresnel loss from entrance through the front vacuum/Si interface

2. Loss from microscopic groove and entrance face surface roughness that goes into scattered light

3. Loss at the Si/Al interface due to dielectric eﬀects

4. Diﬀraction into other orders

5. Fresnel loss from exit through the front Si/vacuum interface

6. Systematic measurement error in beam alignment or collimation

36 Figure 3.3 Efficiency of CA1a as a function of wavelength. The measurements for 1500−2300 nm cover orders 120 to 78. The peak on-blaze efficiency is typically about 75% of an aluminum reference mirror, as shown by the horizontal dotted line at 75%. The vertical dashed lines at 1450 and 1900 nm demarcate the designed wavelength range of IGRINS H−band channel. Sim- ilarly, the vertical dash triple-dotted lines demarcate the K−band channel. The faint gray line in the background is the atmospheric transmission over Kitt Peak[99]. Measurements at λ > 2300 nm we not performed at the time of writing. The slightly suppressed efficiency at 1500 nm may result from visible light leakage in the reference mirror measurement from our 1450 nm low pass filter operated in uncollimated light, or perhaps from real polarization sensitive effects. See the notes on the next figure’s caption regarding the difference in measurements shortward and longward of 1870 nm.

37 3.4 Refractive index dependence

The refractive index of silicon is wavelength and temperature dependent, so the blaze pattern in Figure 3.3 will be different at the cryogenic operating temperature of an IR spectrograph. Precise measurements for crystalline Si are available for the CHARMS group at Goddard [70]. The right panel of figure 3.4 shows the refractive index as a function of wavelength for 296 K, 273 K, and 77K, using the Sellmeier equation from the Goddard group and assuming vacuum wavelengths. The index goes from about 3.483 to 3.445 in the wavelength range 1.5 to 2.3 µm, which is a change of about 1%. The index decreases by an average of 0.8% from room temperature to 77K. The index intimately controls both the diffraction angle β at the Si-Al grating interface via the grating equation, and the refraction angle θ at the Si-vacuum interface via Snell’s law. For example the wavelength λ = 2.290 µm at room temperature is diffracted to 78th order near the peak of the blaze. Reducing the temperature to 77K decreases the index of refraction by 0.8%. This puts λ = 2.290 µm into 77th order, which is at the edge of the blaze. The grating period σ also shrinks by a factor of the coefficient of thermal expansion (CTE) of Si, α ∼ 3 × 10−6/◦C. From room temperature to 77K the fractional shrinkage is about 0.06%, which is an order of magnitude less than the effect of the index of refraction. Furthermore, the CTE effect will have no effect at the Si-vacuum interface.

38 Figure 3.4 Measured and predicted diffraction angles for CA1a. The right panel is the index of refraction as a function of wavelength [70] for T = 296, 273, and 77 K. The left panel is the angular position of diffracted beams as a function of wavelength. The almost vertical lines are approximately 1 free spectral range of the observed 43 diffraction orders for 1500 < λ(nm) < 2300 in air at T = 296K. The order numbers for every fifth order, starting at 78th order are marked at the top. The black diamonds are the observed peaks of the blaze efficiency (cf. figure 3.3). The measurements longward and shortward of λ = 1870 nm have slightly different incidence α angles, which jogged the the blaze center positions. The red ∗, green square, and blue × demarcate the expected positions of beams from scalar optics diffraction and refraction theory assuming a Si refractive index at the temperatures of T=296, 273, and 77 K, respectively. The model corrects for α 6= δ measurements for λ < 1870 nm, causing a jog in the θ(λ) trend highlighted by the vertical black dashed lines. The temperature change shifts the position of diffracted beams by an entire order.

39 -0.05 0.00 0.05 -0.05 0.00 0.05 -0.02 0.00 0.02

Figure 3.5 Optical interferometry of CA1a in reflection off the back surface before cutting and aluminization. The color scales are in waves of surface error for 632 nm in reflection. Left: Interferogram measured in Littrow reflection at R3 over a 23.75 mm beam on the parent substrate CA1, in the vicinity where CA1a was later cut. The colorbars show the vertical scale in waves of surface distortion at λ = 632.8 nm. These optical measurements illuminate the back of the grating facets, they were taken before aluminization and should be a good proxy for immersion performance at 2.15 µm. Center: A fit to the large scale surface distortion using the first 200 Zernike polynomials in the Noll Sequence [174]. Right: The residual high spatial frequency surface error constructed from subtracting the fit from the measured surface error.

40 3.5 Periodic errors, ghosts, and large scale performance

Figure 3.5 shows the optical 632 nm interferogram of CA1 in reﬂection in air. The peak to valley surface error is 0.17 waves. These interferograms should be equivalent to 2.16 µm in immersion in a cryogenic environment. The shortest operational wavelength for the IGRINS instrument is 1.45 µm, at which the surface error is 0.25 waves. The surface structure can be broken into two components, the large scale surface aberration and and a periodic error of parallel stripes parallel to the grating grooves. Figure 3.5 shows the large scale surface aberration in the middle panel and the periodic error on the right panel. The vertical stripes are conspicuous in the right panel, while the center panel looks like a typical residual optical surface aberration possessing relatively low amplitude. The main power in the periodic error is in a single sine wave with 5 mm deprojected period and amplitude of 3.2 nm. There are other harmonic components with higher spatial frequency and comparable or lower amplitude.

The origin of the large scale surface aberration is a combination of the dozen or so processing steps that go into delivering the ﬁnal immersion grating. Chief among these is the UV contact photolithography step. The reactive ion etching, wet etching, and surface preparation steps may also contribute to the overall surface error. The periodic stripes arise in the UV photolithography process that transfers the pattern from the photomask to the underlying photoresist. Speciﬁcally the contacted mask and Si substrate pair repeatedly translate beneath a 1 cm wide UV slit to deliver the requisite UV dose. We

41 discovered that the translation stage had a periodic speed change which is equivalent to a periodic exposure time as a function of position on the photoresist. Prototype gratings made since CA1 have corrected for this problem and surface errors attributable to periodic errors have largely disappeared.

The major problem with periodic errors is that they cause symmetric ghosts surrounding the main diﬀraction peak. The intensity of the ghosts relative to the main peak is related to the periodic error amplitude by[152, 110, 237]:

I 2πn 2 ghost = ξ sin δ (3.1) Iline λ where ξ is the amplitude of the spacing error. Figure 3.6 shows a logarithmically scaled PSF from optical interferometry of CA1a in reﬂection from the aluminized surface in air at 632.8 nm over a 25 mm circular aperture. The

−4 measured intensity of the ghost relative to the main peak is Ig/I0 = 9 × 10 . Optical spectral purity lab measurements at 632.8 nm are higher by 20%. Measurements at 543 nm (comparable to 1.87 µm in immersion), show a level

−3 of Ig/I0 = 1.6×10 , which is 30% greater than one would expect from scaling interferometrically derived intensity at 632.8 nm. Extrapolating the interferometrically derived intensity to 1.45 µm in immersion, the ghosts in IGRINS will have a peak intensity of 0.2% of the main peak. Quantitative lab measurements at 1.523 µm in immersion were attempted but were not reliable due to nonlinear response at the requisite high dynamic ranges need to measure the low ghost levels.

42 20 100

10-1 10 10-2 ) 25

/D 0 10-3 632 h

y ( 10-4 Normalized Flux -10 10-5

-20 10-6 -20 -10 0 10 20 -20 -10 0 10 20 x (h632/D25) x (h632/D25) (a) 2D Zygo PSF (b) 1D Log PSF

Figure 3.6 Left: The 2-dimensional synthetic PSF from interferometric measurements of the air-aluminum reflective interface of CA1a at 632.8 nm at R3. The dispersion direction is x, the cross-dispersion or spatial dimension is y. The units on the axes are in terms of diffraction widths of λ = 632.8 nm and D = 25 mm, which were the conditions of the interferometry. The scale on the 2D image is linear, compare to the intensity levels shown on the right panel. Right: The 1D logarithmically scaled horizontal line profile of the PSF of CA1a under three conditions. The black is the synthetic interferometric PSF. The red is the lab-measured PSF in reflection at 632 nm with a 20 mm beam. This measurement is not diffraction limited. The green line is the measurement at 543 nm in reflection with a 20 mm beam.

43 3.6 Measurement setup description

The basic strategy of the custom efficiency measurement setup is to compare the chopped signal from the immersion grating to an aluminum mirror. The monochromator outputs 1 nm bandwidth and we sample at 1 nm steps. The basic layout is a light source, 1.45 µm long pass filter, Spectral Products DK480 scanning monochromator, a chopper, collimating and relay optics, a motorized swing arm, a single pixel PbS array, and a lock-in amplifier. The DK480, motorized swing arm, and lock-in amplifier are all computer controlled. Custom software predicts the diffraction angles of the immersion grating and fine scans the swing arm around the predicted angular order positions. Figure 3.7 shows a labelled photo of the measurement apparatus, with detailed description of the optical path in the figure caption.

44 Figure 3.7 View of the monochromator, periscope, and swing arm-camera system with the beam path highlighted. The beam exits the monochromator exit slit (8), where the optical chopper (9) is located. The beam is collimated by a 1 inch post-slit lens (10). The periscope system includes 3 mirrors (12, 13a, 13b), only two of which are active at any time. In the reflective arm of interest to this report, we use mirrors (12) and (13b). The beam travels about 1 meter (off the image) to an adjustable iris in double pass (14, 16) sandwiching a mirror (15) tilted about 10◦ from the z − y plane. The beam travels along the vector terminating on the center of the immersion grating (17). The immersion grating has its grooves vertical (parallel to the z−axis) so that the dispersion occurs in a the x − y plane. The camera lens (18) and single pixel detector (19) are mounted on a swinging arm which rotates in the x − y plane, with its center of rotation equal to the position of the immersion grating. The cartoon arrows demonstrate our angular sign convention which is positive counter clockwise, with zero along the optic axis. The grating normal is at about -70◦ with that convention. The lock-in amplifier electronics are marked with number (20).

45 Chapter 4

High Performance Si Immersion Gratings Patterned with Electron Beam Lithography

4.1 INTRODUCTION

At the 2012 SPIE Astronomical Telescopes and Instrumentation meeting (volume 8450) we described the detailed performance of the immersion grating (part number CA-1a [85]) for the high resolution infrared spectrograph IGRINS [244]. IGRINS saw first light at McDonald Observatory in March 2014. Papers describing its performance appear in the current volume[176, 29]. The technical readiness of the immersion grating now rests on firm footing, and our group has now moved on to pushing the performance and design limitations of silicon diffractive optics. The key limitation is phase coherence. Phase coherence for a diffraction grating is the accuracy to which repeated grating facets are positioned to an integer multiple of σ, the groove constant (the desired constant spacing from groove to groove). Specifically, the position, x of the nth facet in a sequence of N total facets is distributed as:

xn = nσ + n (4.1)

where n is the position error for facet n. Discussion of the phase

46 performance can be broadly separated by the correlations of errors, n, and their impact on the monochromatic spectral purity.

There are large scale, smooth correlations:

n = n(x, y) (4.2)

These errors manifest as low order optical aberrations and degrade the PSF and Strehl. Operationally these smooth errors correspond to the ﬁrst M Zernike polynomials in an orthonormal expansion of the wavefront, where M < 200. There is the especially pernicious repetitive error:

2πnσ = A sin − φ (4.3) n P where nσ is the desired position of the nth groove, A is the amplitude of the error (e.g. in nm), and P is the period of the error (e.g. in mm). These errors manifest as sidelobes of the PSF called Rowland ghosts. Although we have listed a single harmonic periodic error, any periodic structure can be broken into its Fourier components, so each of these Fourier components will be aﬃliated with a sidelobe Rowland ghost. Lastly there are small scale random errors:

n ∼ N(0, c) (4.4) where ∼ N(0, c) denotes that the error is normally distributed with mean zero and standard deviation c. This last type of error produces so-called spectral grass[152], which is scattered light ﬁlling the blaze.

47 4.2 On-sky performance of Si immersion grating

With the commissioning of IGRINS [244], we have demonstrated that the immersion grating performance measured in the laboratory translates into performance in a real world instrument in the ﬁeld. IGRINS is a high resolution near-infrared astronomical spectrograph. It employs an immersion grating as its primary dispersive element, and two cryogenic VPH gratings for cross- dispersion. The instrument covers a wavelength range of 1.5−2.5 µm in two channels. The design and early performance of IGRINS is described in this volume [talk 9147-48][176]. The immersion grating for IGRINS is internal part number CA-1a. Its lab-measured performance is summarized in Gully- Santiago et al. 2012[85].

IGRINS has no measured performance limitation attributable to the immersion grating. CA-1a is diffraction limited. CA-1a has been thermally cycled > 10 times at the time of writing, with no perceptible degradation in performance. We expect no degradation from thermal cycling. We have previously constrained the CA-1a blaze angle to δ = 71.5 ± 0.2◦. The overall instrument throughput is consistent with the expected throughput including the laboratory-measured diffraction efficiency of CA-1a.

One major open question is whether CA-1a meets its spectral ghost level speciﬁcation. Spectral ghosts are secondary images that arise from periodic facet positioning errors[109]. The ghosts in CA-1a where introduced from a cyclically varying position-dependent exposure dose in the UV photolithography patterning step. The processing error causing the ghosts has since been

48 eliminated. As a result our most recent immersion grating prototypes show a dramatic reduction in high frequency spectral ghosts [this volume, talk number 9151-35][29]. The ghost level depends on the amplitude of the error (cf. Equation 14 of Marsh et al. 2007[152]): I 2πn g = [ A sin δ]2 (4.5) I0 λ where Ig/I0 is the ghost level relative to the main peak, λ/n is the wavelength scaled in the refractive index, and A is deﬁned in Equation 4.3. We predicted

−3 an in-immersion ghost level of Ig/I0 ∼ 2×10 at 1.5 µm based on visible laser metrology[85]. At the time of writing the IGRINS commissioning team has

−2 constrained ghost levels at λ = 1.5 µm to Ig/I0 < 1 × 10 . The limitation of a direct ghost level measurement is the need to deconvolve the slit diﬀraction ringing from the spectral point spread function.

4.3 Motivations for direct writing Si immersion gratings

We have determined experimentally that the lithographic transfer step is the most important determinant of the optical quality of Si immersion gratings. The prior steps: orienting, polishing, passivating and resist-coating the monolithic substrates is now routine and our process control for these steps is sufficient to limit their contribution to the error budget to the point where they have no effect on the quality of the final gratings[152, 29]. The subsequent steps: development of the resist, reactive ion etching of the passivation layer, and anisotropic etching of the V-grooves similarly contribute little to the

49 overall errors. We therefore concentrate our efforts on finding more effective and accurate ways to carry out the transfer or patterning step.

The JPL Microdevices Laboratory has an advanced electron beam writer (a JEOL model 9300FS) and has made an extensive eﬀort to understand the nuances of using this device for precision patterning of small features over large spatial scales. For the large-area immersion grating exposures we use the JEOL 9300FS at 100 kV accelerating voltage with 60 nA current, a spot size ∼ 100 − 150 nm and spot step spacing of 50 nm. Our typical groove frequency for echelle grating prototypes is 40 - 12.5 grooves/mm (25-80 µm groove spacing) but groove frequencies higher than 1000 grooves/mm are possible. Experimental pattern sizes are up to 100 mm × 40 mm, but could be as large as 200 mm diameter.

4.3.1 Motivation #1: Higher precision than contact lithography

Electron beam lithography is more precise than contact lithography. One ﬁgure of merit for precision in e-beam lithography is the spot size, the typical diameter of the Gaussian e-beam current distribution at the location of the e-beam sensitive resist on the substrate surface. E-beam spot sizes on the JEOL 9300FS tool can be as low as 4 nm at low currents (less than 1 nA). To expose the required immersion spectrometer grating areas in reasonable times (∼50 hours), tens of nA of current are needed, and ∼ 100 − 150 nm spot sizes are typical. The ﬁnal precision is a small fraction of the spot size, since many adjacent spots are convolved together. In later sections we directly compare

50 the performance of immersion gratings produced with e-beam and contact lithography to show evidence that we have achieved much higher precision in e-beam lithography.

4.3.2 Motivation #2: Finer groove pitch capability

Owing to its small achievable spot size, electron beam lithography can reach finer groove spacings than contact photolithography can. Fine pitches are required for high dispersion in low order. Our group is currently designing a fine pitch (σ ∼ 2 µm, line frequency ∼ 500 lines/mm) pattern immersion grating for the NASA Earth Science Technology Office (ESTO) Advanced Component Technologies (ACT) program. The ACT mission concept requires high spectral resolution at low order (∼ 1 − 10). The desired first and second order gratings cannot be made with contact lithography. Higher order devices can be made with contact lithography, but suffer from order overlap and reduced bandwidth.

4.4 e-beam patterning strategies

E-beam patterning takes place within a hierarchy of increasing scale- sizes. The relationships of these pattern scale sizes aﬀect the relative power distributed among spectral and spatial scales in the delivered monochromatic PSF.

51 Figure 4.1 Hierarchy of e-beam pattern scale sizes- in the left panel the grooves are black and the ﬁelds are thin blue lines, the middle inset shows subﬁelds, and the right inset shows spots at a regular step spacing, though the spots are not to scale. Spot sizes are typically about 2-3 times their spacing.

4.4.1 e-beam patterning scale size hierarchy

There are a five key pattern scale sizes in e-beam lithography. These scales are typical among e-beam tools, though we focus our discussion to the scales relevant to the JEOL 9300FS. The scale sizes in order of small to large scales are 1) step size, 2) spot size, 3) subfield deflector size, 4) field deflector size, and 5) stage range of motion. Figure 4.1 shows a cartoon of the hierarchy from left to right- field, subfields, and steps.

Table 4.1 lists the pattern size scales for two immersion grating prototypes, parts D07 and E12. These prototypes are examples of successful pattern designs. D07 and E12 were both patterned on 10 mm thick Si pucks. A 10 mm thickness is sufficient for the piece to maintain its flatness after anisotropic etching of the grooves so that interferometric measurements will reflect accurately the effectiveness of the patterning step.

52 Table 4.1 D07 and E12 e-beam pattern details. D07 E12 substrate bias angle (◦) 6.1 71.5 pattern size (mm) 39.0 x 39.664 29.696 x 84.816 pitch (µm) 7.8 27.36 line frequency (lines/mm) 128.2 36.55 top width (µm) 0.4 9.96 line width (µm) 7.4 17.40 step size (nm) 50 50 steps per linewidth 148 348 subfield size (µm) 3.7 2.9 subfields per linewidth 2 6 steps per subfield 74 58 63: 491.4 17: 465.12 grooves per x−field and 61: 475.8 15: 410.4 x−field sizes (µm) 59: 460.2 13: 355.68 55: 429.0 11: 300.96 134: 495.8 subfields per y−field and 133: 492.1 y−field sizes (µm) 131: 484.7 160: 464.0 127: 469.9

53 4.4.1.1 e-beam step size and spot size

The e-beam step size is the center-to-center separation of the e-beam spots, controlled by the beam-deﬂection electronics of the writer. Step sizes can range from roughly 2 to 100 nanometers. We adopted a 50 nm step size for our immersion grating patterns. The rationale for the step size depends on understanding the e-beam spot size.

The spot size controls the smallest achievable feature size. Our spot size of ∼ 100 − 150 nm is determined by operational properties of the electron gun and focusing column. The spot size can be decreased by preferentially removing those electrons with large velocity components perpendicular to the bulk direction of motion. This preferential removal of fast electrons is achieved with a grounded conductive circular aperture in the beam path prior to the spot formation. The aperture is constricted to reduce the spot size. The net current (e−/s) consequently decreases, since the aperture has effectively thrown away electrons. So there is a tradeoff between current and spot size. This tradeoff is important in deciding optimal patterning strategies and sizes. The economical need to limit the expensive e-beam write time necessitated a high current and hence the resulting large spot size.

The conductive aperture setting coarsely selects the range of spot size achievable, while the detailed spot size depends on ﬁne adjustments made to the e-beam column before an exposure. These adjustments are familiar for those who have used scanning electron microscopy- astigmatism, wobble, and focus, for example. Poor calibration might deliver an elliptical, asymmetric

54 spot shape. In practice, a slightly asymmetric spot shape does not aﬀect the performance of immersion gratings.

A key idea is that the step size (50 nm) is much smaller than the spot size so that adjacent steps convolve to form a fairly uniform exposure area. Another key assumption is that the e-beam spot does not change signiﬁcantly over the course of an exposure. We expect that the e-beam spot is unchanged, so long as the e-beam column is unperturbed.

4.4.1.2 Subﬁeld deﬂector

The subfield deflector is a component of the e-beam gun that directs the e-beam spot within a box of up to 4 µm × 4 µm, centered around a mean position set by the main field deflector. For example we chose subfield sizes of 3.7 and 2.9 µm for D07 and E12, respectively. For recent work on fine pitch (∼ 2 µm) gratings we have experimented with smaller subfield sizes. The reason for these choices of subfield sizes of D07 and E12 is that these field sizes result in an integer number of subfield per linewidth, which avoids fractional e-beam spots at the boundaries. Subfield boundaries are perceptible in the intentionally underexposed e-beam resist of sample TJ04, depicted in Figure 4.2. In general we have found subfield stitching boundaries do not cause measurable ghosts unless the choice of subfield size results in fractional spots at the subfield/field boundaries.

55 4.4.1.3 Field deﬂector

The field deflector, also sometimes called the main-field deflector, coarsely redirects the electron beam over a square up to 500 µm in size. The main-field deflector positions the center of the subfields. For example, the choice of a 500 µm square field size and 4 µm square subfield size would result in 125 × 125 subfields.

The fields are stitched together by the interferometrically controlled stage that steps between them once each field’s pattern has been written. The stage move speed is typically much slower than the field and subfield deflector speed, so small field sizes are inefficient in time-on-target compared to wall-clock time. Even though the JEOL 9300FS dynamically corrects for beam position distortion (e.g. pincushion) and spot focus and astigmatism, the writing performance degrades slightly with distance from the center of the field. So there is a tradeoff between write speed and performance.

The choice of ﬁeld size is multifaceted. Field size choice is one of the key strategies for mitigation of ghosts (see Section 4.4.2).

4.4.1.4 Interplay of hierarchy at boundaries and design rules

Undesirable repetitive patterns that can cause ghosts arise when there are discontinuities as one steps up the field hierarchy. The e-beam spots, subfields, and fields must match up at the boundaries. We learned many subtle design rules unique to high performance immersion gratings. The main theme in all of the design rules is to avoid fractional steps in the writing process. The

56 Groove Pitch, σ Field boundary

Subfield size

Linewidth, L

Groove top, t

Figure 4.2 Subfield and field boundaries directly perceptible in optical microscopy of the e-beam resist on an intentionally underexposed sample, TJ04. The groove pitch for this sample is 100 µm, with a 75 µm written linewidth. The blue area is the linewidth portion of the grating which has e-beam resist already exposed to e-beam. The orange line is the groove top, where the e- beam resist was unexposed and would have served as the wet etch dam, had the linewidth actually developed out. The minute color differences within the exposed linewidth are attributable to tiny thickness differences of the resist, which originate from tiny differences in delivered e-beam dose. The cylin- drically symmetric color difference of teal to dark blue is attributable to the proximity effect as described elsewhere[243]. The tiny boxes are subfields, which are only perceptible due to subtle subfield stitching errors. Some subfields are more errant than others. The thick horizontal stripe is a portion of a much larger field boundary, perceptible only because of main-field deflector stitching boundaries as discussed in the text.

57 JEOL pattern generation software inserts patterns of spaces and spots when it reaches a command for a fractional step. The speciﬁc design rules below are probably unique to the JEOL pattern generation software. Other e-beam tool software is likely to have diﬀerent design rules, but the general principle is the same.

1. Subﬁelds must be an integer number of steps

2. Fields should be an integer number of subﬁelds.

3. Linewidth should be an integer number of subﬁelds.

4. Field sizes and linewidths can be non-integer number of subfields only if the remainder fractional subfield plus one subfield divided by two is an integer number of step sizes.

These rules ensure that all e-beam spots are equidistant. Figure 4.1 shows the JEOL shot shape display of a pattern that broke rules 2 and 4. Metrology of a grating prototype that broke rules 2 and 4 resulted in cross- dispersion grating ghosts > 10−3. The line-edge of contiguous spots lacked a solitary spot near the subﬁeld boundary. Such a periodic dearth in exposure manifested as a periodic divot along the length of the groove. The detailed impact on optical phase depends on the relative step size, e-beam sensitive resist contrast, and sundry subsequent processing steps. Rather than risk a performance degradation it is best practice to avoid the formation of subﬁeld

58 blips in the first place. The main concern for a final application is probably scattered light, and not efficiency loss.

4.4.2 Predicting the ghost level associated with ﬁeld positioning errors

The field size is only a few times larger than our typical coarse echelle grating groove constants. Figure 4.3 shows an exaggerated cartoon of the field size relative to grooves. In a hypothetically perfect e-beam field stitch, the line positions are exactly as desired. In reality there is some finite distortion, which is repeated each time the field is written into the e-beam resist. We define the ratio, G, as the field size, F , divided by the groove pitch size, σ. For example, there will be G = 500/100 = 5 grooves per field for σ = 100 µm and F = 500 µm. The omnipresent field deformations will be imprinted into each field, repeating every 5 grooves. The cyclically varying facet positions manifest as ghosts with G-fold symmetry. We expect G − 1 inter-order ghosts, separated by a fraction 1/G of the inter-order separation.

In principle it is possible to predict the ghost levels relative to the main diffraction peak, given some information about the magnitude and shape of the field distortion. As the amplitude of the field distortion is dialed up, the grating ghost level increases approximately as Equation 4.5. In practice, we have not directly mapped the field distortion, which we expect to be a function of both x and y.

59 Perfect field Perfect field stitching calibration

Field distortion, Field distortion and field stitching errors exaggerated

Figure 4.3 An exaggerated cartoon to demonstrate the repetitive nature of field stitching. A typical field size is about 300-500 µm on a side, and typical groove periods, σ, are about 20-100 µm (50-10 lines/mm groove frequencies). Here we show 5 grooves per field. The distortion shown in the cartoon is highly exaggerated, and in reality the calibration is much, much better than depicted. The center positions in the distorted fields are distributed around the target, demonstrating field stitching errors. The actual morphology of the distortion is not well characterized and should be mostly corrected by the 9300FS dynamic distortion correction system. We have depicted a pincushion shape, though the realized morphology could be more like barrel distortion or a parallelogram. The fields could also be perfectly square and simply misplaced in their center positions, still causing errors. The details of the morphology give rise to differing relative levels of harmonics, in a Fourier sense. To put the scale in perspective, we coarsely estimate the repetitive position error amplitude A (cf. eq. 4.3) as about 5-50 nm from experiments on e-beam wafers. Compare this minuscule position error with the ∼ 500 µm field size, to see that the fractional position error is 1 part in 104 or better.

60 4.4.3 Employ multiple ﬁeld sizes rather than one ﬁeld size

There are two strategies for mitigating ghosts. One is to reduce the overall power in ghosts, using a single field size. The other is to redistribute the power into different spatial scales, by using a variety of field sizes. The strategies can be combined.

We redistribute the field power into several different spatial scales following the method described in Wilson et al. 2005[243]. Rather than use a single field size, say 500 µm, we break up the field into several fields, say 500, 450, 400, and 350 µm. We array the fields on the pattern in the following way. We divide up the overall grating pattern, for example 30 mm × 85 mm, into eight long thin stripes of 3.75 mm × 85 mm. We then array the long thin stripes on top of each other, cycling through the patterns twice. So if we have patterns A, B, C, D, with unique field sizes, we cycle through from top to bottom: A, B, C, D, A, B, C, D. The reason for this periodic boundary condition is to make sure that the circular beam samples the patterns in roughly equal proportions. Specifically, if we had simply written four arrays of dimension 7.5 mm × 30 mm, indexed as A, B, C, D, then the circular beam would underfill patterns A and D at the bottom and top. The optimal strategy would probably be to randomly array fields, but in practice randomly arraying is non-trivial in existing software.

One way to reduce the overall power in a single field size is to select a small field size, say F = 200 µm. We know that the e-beam field performance is better in the center, and deviates towards the edge of the field. The tradeoff

61 with this strategy is that the stage move time is long compared to the e- beam field deflector time, so the write duration increases. Another strategy for reducing the power in ghosts attributable to a single field size is to improve the intra-field calibration. We could remove, for example, the minute pincushion or barrel distortion familiar from cathode ray tube computer monitors. In practice it is tricky to measure, and therefore correct for, these minuscule distortions. The absolute best way to eliminate inter-order ghosts is to use a field size equal to the pitch. The choice of F = σ is generally cost prohibitive for σ < 100. If long, inefficient write times can be tolerated, then in principle there is no limit to this strategy. It is conceivable that driving the stage so much would make the stage fail over time.

Another strategy for reducing the overall power in spatial distortions of e-beam fields is to experimentally determine the optimal height offset for the e-beam focus. For an unknown reason, the JEOL 9300FS selects a default writing height which is offset from the optimal height. We experimentally verified an offset which reduces the overall distortion in the fields.

Lastly, there are some slightly obscure JEOL e-beam commands relevant to ghost mitigation. These are the “overlay”, “gather”, and other af- filiated commands. The main idea behind these writing strategies is to re- write over a patch of grating so that it sees different portions of the field, and therefore the field distortions average down. We experimented with these techniques but found that they roughly double the write times with negligible performance benefit.

62 4.4.4 Strategies for mitigating facet position errors attributable to large scale stage drift

The largest scale in the e-beam writing hierarchy is the stage motion. Multiple tests have never revealed signiﬁcant wander or runout error in the interferometrically controlled stage. Secular drift of the e-beam stage, however, can cause large-scale facet position errors which manifest as optical aberrations.

4.4.5 Characterization of e-beam stage drift

We characterized the e-beam stage drift with built-in JEOL commands. Speciﬁcally, we used the DRIFT and CURRENT commands. The DRIFT command checks the position of the stage by scanning a precision gold cross mark mounted to the stage. The process ties the actual position to the predicted position to the precision of the stage mark’s centroid, which is a small fraction of the spot size. We measured a precision of about 15 nm in the centroid process. Having determined the amplitude and direction of the drift, the DRIFT command subtracts out the oﬀset and continues writing with its updated coordinates.

The centroiding DRIFT process can be automatically repeated on a desired frequency. We set a frequency of 10 minutes. For a typical 20 hour write we achieve 120 drift corrections. The JEOL software logs these corrections, so we can reconstruct the path of the drift, had we not taken action to correct it. Figure 4.4 shows one of these reconstructions for sample E12.

63 Figure 4.4 The reconstructed drift of the JEOL 9300FS e-beam stage during the patterning of sample E12. The write time was 20.9 hours, with drift samples every 10 minutes. The x and y components are separated and plotted as a function of time. The top curve is the y drift. The curves begin at 0 at time zero, and show a range of motion of ∆x = 206 nm and ∆y = 341 nm. This amplitude of drift would have been catastrophic for a grating which has line edge specifications of λ/10 ∼ 60 nm for diffraction limited performance in J− band. The JEOL9300FS command DRIFT automatically corrects out this drift, so the maximum realized drift is merely the minuscule difference that occurs over the 10 minute interval between corrections. Figures 4.6a and 4.6b show a direct comparison of prototype gratings patterned with and without drift correction.

The amplitude of the drift is ∆x = 206 nm and ∆y = 341 nm. This amplitude is much larger than we can tolerate for diﬀraction limited performance in immersion the near-IR.

A possible explanation for the beam drift is that there is thermal expansion attributable to heat conduction from the warm Si puck and holder unit into the stage. Speciﬁcally, there is some evidence that the drift rate is largest at the beginning of the writing, perhaps while thermal equilibration is

64 still happening. The thermal probes on the stage lend some credibility to this idea, since the probes asymptote to constant value after a few hours. Owing to this possibility, we recommend delaying the start of a write until the sample and holder have come into thermal equilibrium with the stage. Beyond this thermal explanation, there are many conceivable reasons why there could be drift. At some level we do not care, as long as we can correct it out suﬃciently well. The cost of correction is merely a hit in extended write time for the same written area, i.e. a decrease in eﬃciency. We found roughly a 10% overhead associated with drift checking.

4.5 Results: Test gratings produced with e-beam patterning 4.5.1 Measurement of ghost levels for a variety of writing strategies

In Figure 4.5 we show measurements of inter order ghosts for different trial runs of the writing process with internal designations TJ03 and TJ04. Each grating received a different treatment for e-beam field and/or subfield sizes. The grating pattern details are listed in Table 4.2. The first thing to notice is that virtually all ghosts are below 10−3 of the main peak. Some ghosts were expected but not detected (denoted ND in the plot legend). The non-detections are probably related to instrumental limitations, though upper limits are not available.

65 Table 4.2 Wafer TJ04 pattern details. Grating Area Size Scale Unit A B C D E F G H I J (x) mm 15 Pattern length (y) mm 10 66 Pitch µm 100 25 Linewidth µm 75 22.5 (x) µm 100 200 200 200 500 Multi 100 200 500 Multi Field (y) µm 500 500 100 250 500 500 500 500 500 500 Subﬁeld µm 2.5 2.5 4.0 4.0 2.5 2.5 2.5 2.5 2.5 2.5 Spot nm ∼ 300 Step nm 50 4.5.2 Improvement in wavefront performance from drift correction

In Figures 4.6b and 4.6a we show the dramatic impact of drift correction on the performance of our Si gratings. The stark difference in final wavefront error of the complete grating with drift correction and without drift correction is the “smoking gun” that the e-beam must have drift correction enabled to achieve high performance diffraction limited performance. At the time of writing we have produced and tested another grating, G07, with even higher performance than E12. Specifically, we perform interferometry at 632 nm in reflection with a 25 mm circular beam on a grating with a blaze angle of 71.6◦. The measured wavefront error is < 0.10 waves peak to valley for G07.

4.6 Limitations of direct writing Si immersion gratings

Electron beam lithography outperforms UV contact mask photolithography, at least in terms of the important metric of large scale phase coherence. There are tradeoﬀs in pursuing e-beam lithography over UV contact mask photolithography. We highlight some of these tradeoﬀs here.

4.6.1 Serial write process yields long write times

One key tradeoﬀ is that e-beam lithography is a serial write process, whereas UV contact mask photolithography is a parallel write process. A contact mask exposure takes about 1-2 minutes, whereas a e-beam exposure takes about 20 hours, for 30 mm × 80 mm patterns. The problem is even worse if you scale to larger areas, for the next generation immersion gratings. The

67 0.00 TJ03C TJ03B TJ03A -1.00 TJ04B TJ04A ) TJ04D

peak -2.00 TJ04E

/ L TJ04G

ghost ghost TJ03G

-3.00 TJ03D: ND TJ03E: ND Log ( L ( Log TJ03F: ND TJ03H: ND -4.00 TJ04C: ND TJ04F: ND TJ04H -5.00 TJ04I 0 0.2 0.4 0.6 0.8 1 TJ04J x (fraction of order)

Figure 4.5 Measurements of the levels of inter-order ghosts for different trial runs of the writing process with internal designations TJ03 and TJ04. The levels are normalized to the brightest order. A full order is shown, with the x−axis units normalized to an order spacing. The grating sub-areas of TJ04 are described in Table 4.2. Some ghosts are not detected, noted as ND. The non- detections are due to instrumental limitations or genuine absence of ghosts. The key idea here is that field size choice determines the number of- and to some extent the intensity of- inter order ghosts. The absolute best patterning strategy is to set your x−field size equal to your groove pitch σ, as in TJ04A, which has no inter order ghosts. All other patterns have a finite, albeit low, intensity ghost.

68 -0.30 0.00 0.30 -0.30 0.00 0.30 -0.10 0.00 0.10

(a) E12 Interferogram

-0.30 0.00 0.30 -0.30 0.00 0.30 -0.10 0.00 0.10

(b) E09 Interferogram Figure 4.6 Comparison of immersion grating surfaces on samples E09 and E12 measured with λ = 632.8 nm interferometry. These are both e-beam produced immersion grating surface prototypes. The color scale is reported in fractions of waves of surface deviation. The patterns on E09 and E12 are identical: σ = 27.36 µm. The groove top is not shadowed in these measurements which are taken in reflection in air. The interferometry is performed with a 25 mm circular beam, which is projected over an 80 mm × 25 mm ellipse at the R3 echelle blaze angle, δ = 71.5◦. The left panel is the measured interferometry. The middle panel is a decomposition into the first ∼ 80 Zernike terms. The right panel is the residual. The only difference between the samples is that E12 was written with DRIFT and CURRENT check protocols with the JEOL e-beam writing software. E09 was written without DRIFT and CURRENT check protocols. The outcome is dramatic- E12 has ∼ 4 times lower surface deformation than E09. Note that the vertical color bars are on the same scale to ease visual comparison.

69 high hourly expense of e-beam time makes the writing process the dominant expense over all other preparation steps, despite the high per-part cost of the large precision-oriented and optically polished monolithic Si pucks.

4.6.2 Large per-part investment cost yields heightened process risk

In reality, the expensive e-beam writing process is not more expensive than procuring a custom high precision vendor-provided photomask. E-beam lithography simply has a higher per-part risk than UV contact mask photolithography. Processes after the e-beam step better be low-risk. Specifically, the processes after exposure include: discharge layer removal, development, plasma etching, wet etching, and shaping. We find that plasma etching re- sponds differently to thick samples, probably due to the large difference in strike height and dielectric differences between vacuum and Si. In one case, an overactive plasma etch burned away all the e-beam resist on a 30 mm thick Si sample.

4.6.3 Experiments with negative resist

There is an steep tradeoﬀ in precision and write time. There is not much way around this tradeoﬀ except for one recent idea of replacing positive tone resist with negative tone resist. Recently we have experimented with low order Si immersion gratings with groove pitches on the order of 2 µm (groove frequency ∼ 500 lines/mm), and and groove tops on the order of 100 nm. The small pitch and groove top require a small spot size, and therefore a small step

70 size. We decreased our step size from 50 nm to 10 nm. This change alone drives up the write time by a factor of 25. To counteract the otherwise impossibly high write time, we have experimented with negative tone resist. Negative resist is cleared where the resist is unexposed, and remains only where the resist is exposed. Since the ﬁll factor of written to unwritten is a factor of 20, the negative resist makes possible the e-beam lithography of these ﬁne pitch patterns.

In principle these gains from negative resist could be extended to immersion echelles. Speciﬁcally our typically modus operandi has been to clear about 65% of the open area for an R3 echelle, in order to avoid groove top shadowing in immersion [85]. However we could write an exceptionally thin line in negative resist, so long as the line is thick enough to survive wet etching without disintegration. We estimate that this threshold is about 5% of the groove pitch.

4.7 Conclusions

Electron beam lithography is now the highest precision technique for producing diffraction limited silicon immersion gratings. The one performance disadvantage is the high level Rowland ghosts attributable to field stitching. These errors have been mitigated by breaking up the field sizes into several different field sizes, distributing the power among more inter-order ghosts of lower individual power. We can achieve 10−3 suppression with this multi-field technique. Ultimately science requirements will have to drive the performance

71 demand of immersion gratings to inform how low to push the inter-order ghost level. The optimal sizes for e-beam ﬁelds, subﬁelds, spots, and steps are nuanced- we lay out rules that avoid repetitive errors. One key innovation is the e-beam stage drift characterization and compensation. The correction of stage drift resulted in a > 4× reduction in peak to valley wavefront error in an R3 immersion echelle grating. Future experiments with negative tone resists will probably decrease write time and increase performance.

72 Chapter 5

Optical characterization of gaps in directly bonded Si compound optics using infrared spectroscopy

5.1 Introduction

Crystalline silicon is an excellent optical material for the infrared. Si has a high refractive index (3.55 − 3.45 from λ = 1150 − 2500 nm at room temperature) and superb transmission from slightly longer than the equivalent wavelength of its band gap (∼1.15 µm) to about 6.5 µm [223, 65] and in the far- IR [184]. It has adequate transmission (α ∼ 1 cm−1) for many purposes in the 18-30 µm region as well [184]. There is an extensive industrial infrastructure for the production of ultrapure Si and for polishing and lithographic patterning and etching of optical parts.

As with a number of glasses and crystalline optical materials, it is possible to form strong physical bonds between two planar or conformal silicon surfaces. One advantage of this direct Si−Si bonding of macroscopic optical parts is that it facilitates the manufacture of complex optical subsystems, for example double-convex aspheres, combinations of lenses, prisms, and transmission gratings, and pairs of gratings oriented at right angles [233, 83]. A second important advantage is that a suﬃciently close bond is optically lossless, an

73 important consideration not only for its effect on throughput but also because it can eliminate concerns about optical ghosts. The remaining advantages of bonding stem from various difficulties encountered in antireflection coating a high index material in the near and mid-infrared: There is a limited choice of index-matching materials, in particular at longer wavelengths. Systems often are used at cryogenic temperatures and considerations of differential thermal expansion, brittleness and hygroscopic properties can restrict the choice of coatings even further. It is hard to get good antireflection performance across broad spectral ranges and at a range of incidence angles.

There are several good reviews of Si bonding that include accounts of the history of the ﬁeld and a description of process alternatives, metrology, and problems [75, 154]. The foundation paper on Si bonding came in 1986 [219]. After that, there was a sequence of papers that used IR imaging to look for evidence of defects in the bond. Stengl et al. (1988) and G¨oeseleet al. (1995) [227, 77] directly monitored the bond propagation with time-lapse IR imaging. Lehman et al. 1989 and Goesele et al. [123, 77] demonstrated gap-free bonding in a microcleanroom, in which the bonding process occurs immediately after a rinse-spin-vacuum cycle inside of a vacuum enclosure. Other authors investigated the growth of bubbles at bond interfaces with time and the elimination of some or all of these bubbles after annealing bonded parts at temperatures of 800 − 1100 ◦C [100, 154].

The chemistry of the bonding interface began to be understood with infrared absorption spectroscopy and multiple internal reﬂection spectroscopy[66],

74 which lent credibility to the idea of distinct temperature phases and evidence for Si−H bonds[195]. These results ultimately helped to flesh out a robust picture of the chemistry as a function of anneal temperature[196, 75]. Other variables potentially affecting bond strength were studied, for example surface roughness[229], surface topography [79], surface preparation[228], annealing time [89], ambient pressure and substrate thickness [76, 88], and moisture and defects [124]. Notably, [229] found that surface roughness above 1.3 nm RMS results in poor bonding quality in their sample of wafers etched with Argon. Greco et al. examined the role of surface topography in determining the the bonding strength of thick optical surfaces. These authors showed that van der Waals interactions by themselves were consistent with their available experimental evidence, but they could not rule out other forces and phenomena. The dearth of measurements of the mean separation between contacted surfaces hindered the unambiguous identification of the forces at play in bonded, rough surfaces [79].

If Si−Si bonds are to be a useful part of the optical designer’s toolbox, the bonds must have transmission losses similar to or lower than the concate- nated losses of two antireflection coated surfaces over the operating wavelength (typically < 4%). For Si-air gaps, where the full Fresnel loss is ∼ 30% per interface this requirement translates to physical gaps or bubbles having an axial extent of < 35 nm. If the optical layout does not eliminate pupil ghosts from the flat Si surfaces, there are additional requirements on the reflectivity of individual bubbles in the bond. While completely bonded Si parts will be

75 completely lossless at the interface, problems on different scales with different physical origins can lead to less-than-perfect bonds. On the smallest scales, imperfect cleaning can leave small voids where particulates hold the bonding planes apart [160] or where hydrocarbons can serve as catalysts for gap formation. Even in the best of cleanrooms, particles at the optically significant 10 − 20 nm scale can be present in relatively high abundance. Figure 5 of Cooper 1986 [38] shows the surface flux (particles cm2 s−1) vs. particle size (µm). There will be roughly 104 times more 10 nm sized particles than 1 µm sized particles. Another possible source of gaps at the bond is inherent roughness in the initial surfaces that leads to a failure to conform [79]. On larger scales, gaseous hydrogen, which is a byproduct of the hydrophilic bonding process, can migrate into the bond and form local bubbles [154].

Most of the bonding literature concerns itself with wafer bonding, as opposed to thicker optical substrates. In bonding wafers to each other or to thicker optically polished Si disks, one or both of the partners can conform as the bonding front propagates. In optics, however, both of the bonding partners will likely be thicker and more mechanically rigid. When bonding two thick substrates, diﬀerences in the shapes of the polished surfaces can potentially lead to topological inconsistencies that prohibit some areas from bonding. Most of our thick substrates are optically polished to less than 60 nm peak to valley over the 75 to 100 mm diameter clear aperture. We assume that, if enough pressure is placed on the substrates during bonding, then the surfaces will come in contact and zipper up. Subsequent annealing will strengthen the

76 bond.

Veriﬁcation that an optical bond meets its requirements and diagnosis of possible problems in the bonding technique require an accurate assessment of the geometry and lateral and axial dimensions of any defects. Since silicon is opaque in the optical, the most straightforward technique for detecting defects in the bond is to image it in the infrared. Fresnel losses will cause unbonded regions to appear darker than regions where the bond is perfect. In cases where the axial extent of the gap is a half-wavelength or more, Newton rings appear in the image of the gap. X-ray topography [160] exploits the change in optical density along lines of sight to allow precise high spatial resolution measurements of the spatial extent of gaps with axial dimensions as small as a few nanometers but not of the axial extent itself. In ultrasound microscopy, the density change at the gap interface produces reﬂections of sound waves and enables mapping the lateral gap dimensions but also produces only limited information about the axial dimension [78].

We describe here a new technique for measuring the axial extent of small gaps, founded upon the ability to measure transmission as a function of wavelength with high accuracy. A recent generation of stock near-infrared spectrophotometers like the Cary5000 from Agilent oﬀer 0.2 % precision and good repeatability. We use the wavelength dependence of the transmission and a model of the gap as a closely-spaced Fabry-Perot to measure axial gaps down to a few tens of nanometers in size. In order to verify the applicability and accuracy of the technique, we have used microlithography to create small

77 artiﬁcial gaps of known size in wafers that we then bond and measure.

For all types of gaps and bubbles, our technique needs to provide an accurate assessment of the transmission loss at the operating wavelength. For ﬁnite-sized bubbles, measurement of the axial dimension helps us to assess the eﬀects of high-temperature annealing [100, 154] on removal of hydrogen bubbles. A wavelength-dependent transmission variation can also indicate the presence of large numbers of gaps that are too small to resolve spatially, as one might expect if there are many very small contaminants present along the interface. Our technique must be able to characterize gaps with losses of a few percent at the operating wavelength. A 2 % loss at 1.25 µm corresponds to a gap of > 25 nm at normal incidence and the gap size for a loss of this magnitude scales linearly with wavelength. We therefore need to be able to measure transmission as a function of wavelength to a fraction of a percent, including all systematic errors, for devices operating near 1 µm and to a somewhat looser standard for devices operating at longer wavelengths.

5.2 Si−Si Fabry Pèrotmeasurement theory 5.2.1 The Si−Si interface gap is a low finesse Fabry-Pèrotetalon

Our measurement technique exploits the large Fresnel reﬂection [95] at the Si−vacuum interface. The refractive index of silicon is one of the highest of any commonly used optical material. Figure 5.1 shows the refractive index at room temperature [70], which we assume through this article. The Fresnel reﬂection is about 30 % per surface, much larger than the 4 − 7 % per surface

78 of the many optical materials with refractive indices in the range 1.5 − 1.7.

Si Refractive Index Coefficient of Finesse 3.60 2.7 T= 295 K 77 K 3.55 2.6 n 3.50 F

2.5 3.45

3.40 2.4 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 λ (nm) λ (nm)

Figure 5.1 Plot of refractive index, n, and coeﬃcient of ﬁnesse, F , as a function of wavelength, λ. We computed the temperature dependent refractive index from the tabulations of [70].

We can treat a small Si−Si interface gap between two almost-bonded silicon parts as a low-Finesse Fabry-Pèrotetalon[207]. The key property of an etalon is that it has a cavity enclosed between two smooth and parallel reflective surfaces where the requirements for smoothness and parallelism depend on the reflective finesse of the cavity. For the narrow air gaps we consider here and for the modest reflectivity of a Si-vacuum interface, most gaps at Si−Si bonds will form effective etalons over most of their area. The transmission through a Fabry-Pèrotdepends on the wavelength of light, the reflectivity of the etalon sidewalls, and the size of the gap. We compute the reflectivity for an Si−vacuum interface, which is a modest function of wavelength through the refractive index of Silicon, n(λ, T ) [70], as shown in Figure 5.1. We drop

79 the subscripts on the refractive index n(λ, T ) → n and the coeﬃcient of ﬁnesse F (λ, T ) → F for clarity. The computation is simply Fresnel’s law at normal incidence:

(n − 1)2 R = (5.1) (n + 1)2 4R F ≡ (5.2) (1 − R)2

We define the coefficient of finesse[207], F (Equation 5.2), in the cus- tomary way to encapsulate the Fabry-Pèrotetalon’s dependence on reflectivity. The right panel of Figure 5.1 shows the coefficient of finesse as a function of wavelength. In this work, we assume transmission is at normal incidence and the refractive index of the gap is 1.0. Si absorbs negligibly longward of λ = 1250 nm, which we verified by comparing the transmission of Si reference samples of different thicknesses (Figure 5.2). We measured the ratio of transmissions of a 0.5 mm thick double side polished Si wafer and a 3.0 mm Si puck. Figure 5.2 verifies a key assumption that we make when comparing the transmission of scrap Si of different provenance and thickness. Specifically, double side polished 3 mm thick Si pucks and 0.5 mm thick Si wafers have indistinguishable transmission at the < 0.2% level long-ward of 1250 nm. The Si refractive index is indistinguishable from sample to sample for the wavelength ranges we care about- the non-absorbing wavelengths greater than about 1250 nm. [70] cites the wide variety of values for refractive index from the literature as evidence that batch-specific Si should be used as a reference for cases in which

80 absolute accuracy greater than ±5 × 10−3 is desired. An absolute deviation of ±5 × 10−3 in refractive index corresponds to a Fresnel transmission diﬀerence of about 0.2%, which is comparable to our measurement uncertainty. In the next subsection we work out the wavelength dependent transmission for the air etalon1

Typical drift error

1.04 Typical random error

1.02 Transmission ratio

1.00

0.98 1000 1200 1400 1600 1800 2000 2200 2400 h (nm)

Figure 5.2 Ratio of transmission of a 0.5 mm thick Si wafer to that of a 3.0 mm thick Si puck. We detect Si absorption shortward of λ = 1250 nm. The individual measurements have correlated uncertainties attributable to lamp drift at the level of 0.2%. The random uncertainties are typically about 0.02% per sample, though some wavelength regions (e.g. 1700-1900 nm) demonstrate much greater per sample uncertainties. Absorption longward of 1250 nm (vertical dashed line) is negligible.

1A note on nomenclature- we use the term gap for the physical structure, and etalon for the model of that structure.

81 5.2.2 Predicted transmission spectrum for bonded Si with ﬁnite interface gap

A pair of bonded silicon wafers or pucks with a small gap forms three coupled cavities with the air gap as the the central cavity. The outer cavities, those within the Si, however, were not produced with coherence in mind. Their sides are not necessarily flat and parallel to the required level and the specifics of their deviation from perfect etalons are usually not known to the level necessary to treat them as coherent structures in the analysis. The multiple internal reflections within the Si therefore present a hurdle to an analysis of the air gaps. In the air gap, however, the gap size is small enough that the cavity it forms can always be treated as a coherent structure. Treatments for multiple coherent reflections have been described in detail in the optics literature [207]. The wave transfer matrix technique treats each dielectric interface as a matrix with elements relating the pre- and post- interface complex amplitudes in the left and right directions. We adapted the wave transfer technique for incoherent interactions [114] to deal with the cavities within the thick Si substrates. Specifically we constructed an incoherent wave transfer matrix whose elements relate the intensities (and not complex amplitudes) before and after an interface. The details appear in Appendix 5.8. We computed the transmission for two scenarios: first a double side polished (DSP) Si sample with no gap, and second a pair of bonded Si samples with a gap thickness d. The DSP Si sample with no air gap has a transmission equal to:

82 2n T = (5.3) DSP 1 + n2

which has an average value of about 53%. Note that this transmission

2 is above a na¨ıve value of TDSP = (1 − R ), which does not take into account multiple incoherent reflections, and is therefore an underestimate. The top line in the upper panel of Figure 5.3 shows the value derived from Equation 5.3 in the wavelength range 1200 − 2500 nm. If the Si substrate thickness is less than the coherence length for the given spectral bandwidth, and if its surface roughness is much smaller than the wavelength, our assumptions break down and the multiple reflections would interfere coherently, and the outer Si cavities would behave as a Fabry-Pèrotetalon. We do not treat this case here since our focus is on thick substrates with small gaps between the interfaces.

Consider a pair of bonded Si samples with a gap thickness d. We derive the absolute transmission of bonded Si substrates with a gap in Equation 5.23 in the Appendix. We normalize the absolute transmission by the transmission of a double-sided Si structure with no gap to isolate the eﬀect of the gap. We call this normalized transmission the gap transmission Tg.

n2 + 1 T = (5.4) g 2 d 2 2nF sin (2π λ ) + n + 1

In the limit limd→0 Tg → TDSP and the gap approaches 100% transmission. Figure 5.3 shows a plot of Equation 5.4 for gap sizes, d, of 0, 20, 35,

83 0.56 No Gap 0.55 20 nm gap 35 nm gap 0.54 60 nm gap

0.53

0.52

Absolute Transmission 0.51

0.50

1.00

0.98

0.96

0.94 Gap Transmission 0.92

0.90

1.0

0.8

0.6

0.4 No Gap

Gap Transmission 60 nm gap 0.2 350 nm gap 3500 nm gap 0.0 1200 1400 1600 1800 2000 2200 2400 λ (nm)

Figure 5.3 The family of normal-incidence curves for transmission as a function of wavelength for various gap sizes in bonded Si optics. Top panel: Absolute transmission through a Si substrate with no gap (top denim-blue solid curve), and small gaps of axial extent 20 nm (green dashed curve), 35 nm (red dash- dotted curve), and 60 nm (purple dotted curve). The absolute transmission through Si depends on wavelength since the refractive index depends minutely on wavelength. The curves assume that multiple reflections within the Si substrates add incoherently as discussed in detail in Appendix 5.8. Middle panel: The “Gap Transmission”, defined as the Absolute transmission through a sample normalized by the absolute transmission through a gapless sample. The gap sizes and colors are the same as in the top panel. Bottom panel: “Gap Transmission” for larger gaps, spanning 0-3500 nm. The 3500 nm sized gap (cyan solid line), demonstrates characteristic Fabry-Pèrotetalon fringes. 84 60, 350, and 3500 nm. The bottom two panels show the “gap” transmission based on Equation 5.4, the value of the throughput with the losses from the outer Si cavities divided out. For the very largest gap, large fringes appear as the cavity resonance of the air gap modulates the transmission. Below a λ/2 gap size, the gap manifests itself as a wavelength-dependent diminution of the transmission. For the smallest (35 − 60 nm) gaps, there is a 2 − 6% decrease in gap transmission from 2400 nm down to 1250 nm. It is the magnitude and wavelength dependence of this transmission spectrum that provides information about the axial extent of the gap.

5.3 Laboratory demonstration: Embedding gaps of known sizes

We evaluated our metrology method by embedding gaps of known sizes in the interface between two bonded Si substrates and measuring the eﬀects of these gaps on IR transmission. The substrate thicknesses ranged from 0.5 to 3.3 mm. We denote substrates with thicknesses larger than 1 mm as “pucks” and substrates with thickness less than 1.0 mm thick as “wafers”. We distinguish the two classes of substrate thickness based on the anticipation that thin substrates will conform more easily to their bonding partner substrates. There is also evidence that bond front propagation is slower in thick pucks [88] than in wafers. Our ultimate goal is to bond optics with thicknesses as large as 30 mm.

The three important characteristics of gaps are their axial extent, their

85 lateral areal extent, and the areal ﬁll factor of ensembles of such gaps. To fabricate our test samples, we used photoresist lithography to pattern Si substrates, and we bored holes with inductively coupled plasma etching. We used two diﬀerent gases with low and high etch rates, CHF3 on Si exhibited about

0.3 nm/second etch rate, SF6 exhibited about 1 µm/minute to produce gaps with small and large depths. Tables 5.1 and 5.2 give information about the hole patterns and depths, as measured with Veeco NT9100 Optical Proﬁler for the small depth, and Dektak stylus proﬁlometry for the large depth.

The fill factor is the pattern area covered by gaps relative to the total pattern area. We achieved gap sizes of 14−95 nm on four substrates with three meshes with coarse, medium, and fine boxes, each with 50% fill factors. We did not verify the delivered fill factor, but since high precision lithography is very reliable, we assign no uncertainty to the difference between the delivered fill factor and the designed fill factor. For measurements taken with the Veeco NT9100 Optical Profiler, uncertainties were constructed by inspecting the histogram of topology, as shown in Figure 5.4. The large-scale distortions were removed from the topology by masking and flattening to ensure that the uncertainties accurately reflect the distribution of measured heights. The stylus profilometry measured values were assigned an uncertainty of 5%, our expe- rience with other etched parts. Table 5.1 lists part numbers and descriptions for our bonded substrates.

We cleaned the surfaces before bonding to minimize the interfacial particle density. The surface roughness was typically about 2 nm, as measured

86 Figure 5.4 Veeco optical profiler surface plot and histogram for part VS20-21 in the fine pattern section. The 100 mm diameter VS20-21 is comprised of two thick silicon wafers. We patterned three meshes with coarse, medium, and fine boxes, each with 50% fill factors. The depth was 95 ± 5 nm as indicated by the well-separated peaks in the Veeco profilometry histogram. The fill factor for this and all mesh patterns was 50%. The purpose for these patterns was to have gaps of known axial extent against which we could test the optical metrology technique we describe in this article.

87 Table 5.1 UTexas Si bonding experiments

Name Diameter Thickness Pattern Pattern Depth - mm mm - nm VG02 100 3.3 × 2 None - VG03 100 3.3 × 2 Hole & Petal 4000±200 VG09-12 75 1 × 2 Mesh C 49 ±6 VS20-21 100 0.8 × 2 Mesh C, M, F 95 ±5

Table 5.2 Patterned gap properties

Pattern Fill Factor feature size bulk description -% µm - Hole 100 - 25 mm diameter hole Petal ∼ 5 ∼2000 2 mm wide lines Mesh F 50 40 100 µm square holes, Fig. 5.4 Mesh M 50 200 500 µm square holes Mesh C 50 620 1500 µm square holes

with a Veeco NT9100 Optical Profiler. We also measured the large scale surface flatness of the pucks. The Fisba2 interferometer used for these measurements has a 50 mm diameter beam at λ = 632.8 nm. We found a typical peak to valley surface flatness of 2 waves over the central 50 mm diameter. We prepared the substrates with standard cleaning procedures of solvents in a megasonic. We then applied MHz frequency oxygen plasma ashing. We soaked the wafers in DI water then dried with N2. We pressed the Si substrates together from the center to the outside.

88 5.3.1 IR bubble imaging and limitations

We first looked for large gaps in our bonded substrate pairs detectable as “IR bubbles” [162], with IR imaging. The detector was an IR Vista αNIR infrared focal plane array, with 312 × 252 pixels, with 30 µm square pixels. We used a 50 mm F/2 lens, with a fiber optic white light illumination source. The combination of the absorption of Si, the lamp spectrum and the detector responsivity led to an effective bandpass from approximately 1.15 − 1.6 µm. The field of view was smaller than the 100 mm diameter wafers, so we dithered the sample. Figure 5.5 shows an IR image of bonded sample VS20-21. For this image, we coarsely flat-fielded the detector by observing a homogeneously illuminated white screen. Despite the flat-fielding, detector non-uniformities and vignetting are perceptible in our image as vertical stripes. Mosaic-stitching errors are also perceptible. It was easy to detect IR bubbles despite detector artifacts since the bubbles translate with the sample when we dither its position.

We also used IR imaging to inspect VG09-12 and VG15-13. We detected IR bubbles in all 3 of these bonded Si samples. The observable bubble areal density varied from about 4 per 100 mm diameter bonded wafer pair to over 20 per bonded wafer pair. The individual IR bubble areas were as small as a few square millimeters up to 400 mm2. The IR bubbles had various morphologies. The structure within some of the images of IR bubbles showed Newton’s rings, exposing the presence of gaps larger than about λ/2 up to ∼ 15λ. As expected, the unbonded DSP wafers show no such IR bubbles.

89 No attempt at quantitative measurement was made on the IR images due to evidence of a non-linear detector response. The bulk morphologies were clear regardless of the detector response. When IR imaging was available, it was leveraged to target IR spectroscopy in locations demonstrating presence or absense of IR bubbles, as desired. In other cases when IR imaging was not available or ignored, spectra were taken at random positions on the wafer.

Figure 5.5 IR image of part VS20-21. Three rectangular mesh areas are apparent (Table 5.2). The coarsest mesh, C, shows substructure, while the medium and ﬁne meshes are indistinguishable at the low resolution of the image. The three dark spots are gaps at the interface of the direct bonded Si samples.

5.4 Measurement technique and correlated measurement errors

We used the test pieces with known gaps to validate our measurement and analysis techniques. We took transmission spectra of the bonded Si wafers and pucks, and the double side polished Si reference wafers using an Agilent

90 Cary 5000 UV-Vis-NIR spectrophotometer. Table 5.3 lists the typical measurement settings and tool performance. The tool has a double monochromator, which reduces scattered light. The vendor reported linearity exceeds 40 dB.

The Cary 5000 has four operation modes: single front, single back, double, and double reverse. Double mode takes a reference spectrum simultaneously with the target spectrum. We experimented with single front and double modes. In principle double beam mode is even more precise than single beam mode. In practice we found that souble beam mode showed evidence for lamp-jump artifacts attributable to polarization diﬀerences between the two arms. So in this article we focus our results to those obtained in single beam mode. In both single and double mode, the spectrometer takes a baseline scan with no sample in the measurement holder. We automatically divide sample spectra by this baseline spectrum. In single beam mode, we must repeat the baseline measurements about every 10-30 minutes for post-process division.

We estimated the uncertainty and measurement repeatability experimentally. We computed the RMS error and measurement repeatability in a single measurement by computing the standard deviation of a spectrum taken immediately after a baseline scan with no sample present. We found that the mean value in single mode drifted by about 0.2% over several measurements. The standard deviation of the featureless spectrum was typically 0.02% from point to point, with some portions of the spectrum demonstrating increased variance. Table 5.3 summarizes the amplitudes of the drifts and individual

91 measurement errors. Correlated errors dominate the measurement uncertainty of our transmission spectra. The measurement uncertainty correlations are apparent in Figure 5.2. In some parts of the spectrum, the mean drift is about ten times larger than the local standard deviation of the spectrum.

The spectral sampling ranged from 2.0 to 10.0 nm. We set the spectrometer slit width to produce a spectral resolution of 5.0 nm. We expect smoothly varying spectral features for all conceivable interface gaps in Si bonded wafers. Speciﬁcally, Fabry-P`erotfringes attributable to interfacial gaps in bonded Si will be well-sampled with 5 nm spectral resolution, so long as the interface gap is less than ∼100 µm. This maximum gap limitation brings our technique to the point where it overlaps in capability with other techniques since the axial extents of such large gaps would be easily measurable by other means, like IR imaging and fringe-counting.

We also veriﬁed the linearity of the detector response my measuring the transmission through stacks of ﬁlters. We constrained the linearity to at least > 24 dB. The vendor reports linearity exceeding 40 dB, which is consistent with our measurement.

5.5 Results of infrared spectroscopy of directly bonded Si

The gaps in our test pairs should be a combination of the deliberately induced gaps and any inadvertent additional spaces caused by imperfections in the bonds. We infer the axial extent of gaps in our samples with etched holes

92 Table 5.3 Summary of Cary 5000 Measurement parameters

Parameter (Units) Value Spectral sampling interval (nm) 2.0,10.0 Spectral resolution (nm) 5 Time per sample (s) 0.1 Typical measurement range (nm) 1200-2500 Typical Single mode mean drift (%) 0.20 Typical Single mode standard deviation (%) 0.02 Beam size (mm × mm) 2 × 8 Directly measured linearity range (dB) > 24

from their measured transmission spectra. We use a Bayesian inference technique in our analysis. First we deﬁne a mixture model in which the observed normalized gap spectrum Tobs is composed of a sum of a spectrum through a gap of axial extent d, and a spectrum through a perfect bond:

Tmix = f Tg + (1 − f) (5.5)

where f is the areal fill factor of the region exhibiting a finite gap size, and 1 − f is therefore the areal fill factor of the perfectly bonded area. Tg is defined in Equation 5.4. The only free parameters in Equation 5.5 are d and f. Both of these parameters are fixed in our direct bonded Si wafers with synthetic gaps, and are listed in Table 5.2. These synthetic imbedded gaps therefore offer an excellent test of our ability to recover the gap axial extent d and areal fill factor f (Section 5.5.1).

Equipped with an observed spectrum and our mixture model, we con-

93 structed the likelihood function [104]. The measurement errors are strongly correlated as discussed in Section 5.4. To handle the correlated measurement errors we use Gaussian process regression [187, 69]. The Gaussian process takes into account the unknown but ﬁnite covariance structure by introducing a covariance matrix, C whose elements represent the correlations of each sample i with every other sample j. We parameterize the covariance matrix elements in the following way:

(λ − λ )2 C = σ2δ + a2 exp (− i j ) (5.6) ij i ij 2s2

where δij is the Kronecker delta, and σi are the independent measurement uncertainties on the ith data point. The parameter s controls the cor- relation length, and a controls the amplitude of the correlated noise. We experimented with different values for σi. When repeated double side polished reference sample measurements were available, we estimated the σi from the dispersion around mean-subtracted, detrended transmission spectra. We do not know a nor s and they are, in general, different for each measurement– they are nuisance parameters, and are ultimately marginalized out. They arise from the uninteresting properties of the spectrometer, and their interpretation is immaterial. The value of a should be close to the mean drift reported in Table 5.3. The value of s could be small (tens of nm) to capture local variation attributable to atmospheric air absorption, or large (hundreds or thousands of nm) to capture global features attributable to lamp drift. We allow both a and s to be free parameters in our fitting procedure.

94 We set our prior probability distribution functions [104], ln p(d, f, a, s) as uniform over a wide range of values for ln a, ln s, d, and f, consistent with visual inspection of each spectrum. The ﬁnal un-normalized posterior probability function, expressed as a natural logarithm is:

1 1 ln p(d, f, a, s|λ, T , σ ) ∝ ln p(d, f, a, s) − r|C−1r − ln det C (5.7) obs i 2 2

where the residual vector r is the data Tobs minus the model Tmix. We produce posterior samples with Markov Chain Monte Carlo (MCMC). Speciﬁcally, we implemented emcee2[68], with 32 walkers, hundreds of burn-in samples, and 600-1000 iterations. We initialized the walkers in the vicinity of our best guess for parameters based on visual inspection of the spectra. Figures 5.6, 5.7, and 5.8 show examples of posterior samples including corner plots of the interesting physical parameters d and f.

5.5.1 Spectra of direct bonded Si with known gap sizes

Figure 5.6 shows a parameter determination for the measurement of a bond over a deep (4000 ± 200 nm) 100% fill factor gap in part VG03. The analysis yields a best fit consistent with 100% fill factor, and a depth of 3960 ± 2 nm, well within the uncertainty of the physical measurement (Ta- ble 5.1). The spectrum in this region shows characteristic Fabry-Pèrotfringes of constructive and destructive interference. The only tunable parameters of

2https://github.com/dfm/emcee

95 the model are the gap axial extent, d and fill factor f. No scaling has been applied to the curves in Figure 5.6. Figure 5.7 shows a fit for a region of the same bonded pair where a nominally 4000 nm deep, 2 mm wide trench crosses the field scanned by the Cary 5000. Analysis of this transmission curve gave a best fit depth of 4094 ± 4 nm and a pattern fill factor of 4.6 ± 0.1 %, both consistent with the part geometry. These two results show that the formalism performs as expected on resonant gaps several wavelengths deep.

Table 5.4 Inferred Gap sizes and ﬁll factors

Name Region Predicted d Measured d f - - nm nm - +8 +0.456 DSP - 0.0 3−2 0.260−0.230 +21 +0.46 VG09-12 Oﬀ-Mesh 0.0 11−7 0.25−0.22 +2 +0.001 VG03 Hole 4000 ± 200 3960−2 0.999−0.002 +4 +0.001 VG03 Petal 4000 ± 200 4094−4 0.046−0.001

5.5.2 Spatially resolved measurements with Sample Transport Ac- cessory

We acquired spatially resolved measurements of the pair of bonded parts VG09-12, (Tables 5.1 and 5.2) with the Cary 5000 sample transport accessory 3. This accessory translates the sample through the measurement beam and takes a transmission spectrum at each position. We chose a 2 mm step size, which is slightly larger than the ∼ 1 mm beam width. We sampled

3http://www.chem.agilent.com/en-US/products-services/ instruments-systems/molecular-spectroscopy/sample-transport-accessory/

96 1.000

0.996

f 0.992

0.988

0.984

3956 3960 3964 0.984 0.988 0.992 0.996 1.000 d f

(a) Fitted gap size d and ﬁll factor f for VG03 hole region

1.0

0.8

0.6 p a g T 0.4

Measurement 0.2 Model with d =3960 nm, f =0.999 Draws from GP 0.0 1200 1400 1600 1800 2000 2200 2400 λ (nm) (b) Measured spectrum and fit of VG03 hole region Figure 5.6 Top panel: Corner plot of MCMC samples in our non-linear model fit of the transmission spectrum of Si optic part # VG03. The physical parameters of the model are the axial extent of the gap d, and the areal fill factor f of the gap over the measurement region. The MCMC model fit also includes nuisance parameters a and s (not shown) for the Gaussian process covariance model. Bottom panel:Transmission through bonded Si sample VG03, normalized by the transmission of a DSP Si wafer. See the text for details on the sample, setup, and analysis. The measured spectrum is the black stepped line. The red dashed line shows the best model fit with d = 3960 ± 2 nm, consistent with 100% fill factor. The blue band shows the collective locations of 60 random draws from the Gaussian process model. Wavelengths short-ward of 1250 nm (gray band) were not included in the fit, since Si is absorptive there. 97 0.0480

0.0465 f

0.0450

0.0435

4080 4088 4096 4104 0.0435 0.0450 0.0465 0.0480 d f

(a) Fitted gap size d and ﬁll factor f for VG03 petal region

1.00

0.98 p a

g 0.96 T

0.94 Measurement 0.92 Model with d =4094 nm, f =0.046 Draws from GP 0.90 1200 1400 1600 1800 2000 2200 2400 λ (nm) (b) Measured spectrum and ﬁt of VG03 petal region Figure 5.7 Same as Figure 5.6, but the measurement was in a region where < 5% of the area exhibited the ∼ 4 µm gap. The measured spectrum in this region shows subdued fringes. The model derived axial extent is 4094 ± 5 nm covering a ﬁll factor of 4.58 ± 0.06%.

98 50 mm across the mesh pattern and into the oﬀ-mesh pattern (Figure 5.8a). The large number of consecutive measurements prevented the requisite near- contemporaneous baseline measurements for normalization. We ﬁt a line to before-and-after baseline measurements to infer the mean-level drift, which we divided out of each spectrum. We measured over a wavelength range from 1250 to 1775 nm.

The colored dots in the position marked in Figure 5.8a match the color of the spectra in Figure 5.8b. The approximate size of the measurement beam is shown for scale. The conspicuous mesh pattern has a depth of 49 ± 6 nm, as measured with an optical profiler, and global fill factor of 50%. However, since the beam size is comparable to mesh grid size, the fill factor for any given measurement can vary from about 30% to 75%. The gray band in Figure 5.8b represents the allowable range of predictions, taking into account both the uncertainty in the mesh depth and fill factor. If the mesh pattern were perfectly bonded, we would expect all the spectra to fall inside the color swath in Figure 5.8b. We see excellent consistency between prediction and measurement, with one measured spectrum hinting at a small gap (. 15) in one measurement position. Outside the mesh area, the bonding is excellent, as demonstrated by the off-mesh transmission with transmission consistent with 100% to within the measurement uncertainty of 0.2%.

A key result of these test measurements is to demonstrate that gaps of known dimensions are recovered in our spectroscopy, both for large and small gaps. Table 5.4 summarizes the outcome of some measurements in the areas

99 Translation path

Beam Size

VG09-12 (a) Illustration of VG09-12 sample transport accessory measurement positions.

1.02

1.00

0.98

0.96

p 0.94 a g T

0.92 On-mesh- 4 mm On-mesh- 6 mm 0.90 On-mesh- 8 mm On-mesh- 10 mm 0.88 On-mesh- 12 mm On-mesh- 14 mm Off-mesh- 18 mm 0.86 Model with d =49 6 nm, 0.3

1300 1400 1500 1600 1700 λ (nm) (b) Measured gap transmission spectra of VG09-12 on- and off- mesh Figure 5.8 Predictions and measurements of the coarse mesh region in sample VG09-12. We took 50 measurements across the face of VG09-12, including both on- and off- mesh regions. The measurements are consistent with the predicted transmission, shown as the gray band. The off-mesh regions demonstrate near-perfect bonding.

100 with known gaps and ﬁll factors. The table lists the median sample and 68% conﬁdence intervals. The results from the scans shown in Figure 5.8 further support our conclusion.

5.5.3 What is the smallest gap this technique can detect?

We devised two experiments to approach the question, “What is the smallest gap this technique can detect?”. We applied our MCMC model fitting formalism to an unbonded DSP wafer. The measured transmission spectrum was normalized by a transmission spectrum of the same sample taken only a few minutes earlier. Any difference of this normalized transmission from unity is attributable entirely to measurement uncertainty, and represents the smallest possible signal one could extract. We also measured bonded sample VG09-12 in a region away from the intentionally implanted gap. This spectrum was processed in the same way as the spectra of the VG09-12 mesh area, exhibiting a mean value of 0.9998 and a standard deviation σ = 0.0008. This spectrum is consistent with no gap. We applied our MCMC formalism to further constrain the range of gap sizes consistent with the spectrum. Table 5.4 summarizes the sizes of gaps. The well-calibrated DSP noise spectrum rules out (at > 3σ) gap sizes larger than about 9.0 nm over > 80% of the measurement area. Similarly, the VG09-12 off-mesh spectrum rules out gaps greater than 14 nm over > 80% of the measurement area. Figure 5.8 shows the corner plots and spectra for the off-mesh region in VG09-12.

Figure 5.9a shows that there is a degeneracy between the axial extent

101 1.0

0.8

0.6 f

0.4

0.2

0.0

0 20 40 60 80 1000.0 0.2 0.4 0.6 0.8 1.0

d f

(a) Fitted gap size d and ﬁll factor f for VG09- 12 oﬀ-mesh

1.01

1.00 p a

g 0.99 T

0.98 Measurement 0.97 Model with d =14 nm, f =1.00 Draws from GP 0.96 1200 1300 1400 1500 1600 1700 1800 1900 λ (nm)

(b) Measured spectrum of VG09-12 Figure 5.9 Similar to Figure 5.6 and 5.7, but for sample VG09-12 in the oﬀ- mesh region. The measured spectrum in this region shows no appreciable deﬁcit of transmission from a DSP reference sample.

102 of a gap and its fractional ﬁll factor over the measurement beam; a larger gap can be hidden if it covers only a small fraction of the measured area. The red dashed line shows the normalized transmission spectrum of a 14 nm gap over 100% of the measurement area. Gaps larger than 60 nm would have to cover less than 10% of the measurement area in order to be consistent with the measurement.

5.6 Discussion

The experiments and measurements in Section 5.5 demonstrate that we can detect and measure the axial extent of gaps down to 14 nm. The technique is non-destructive and can be implemented with an oﬀ-the-shelf commercial product, namely the Cary 5000 or equivalent, or any existing high precision spectrograph. The spectrograph need not be high resolution– our 5 nm spectral resolution was not a limiting factor. The limiting factor is spectrophotometric accuracy and precision. In this Section we question the assumptions of our technique, identify its limitations, and mention some opportunities.

More complex underlying gap size distributions- One key assumption of our gap-as-etalon modeling strategy is that the distribution of gap sizes over the measurement area is bimodal- a gap of size d or zero gap. This choice was simply a matter of computational simplicity, and any more complicated gap size distribution could easily be dropped in as additional terms in Equa- tion 5.5. For example, if there is a gradient across the bond, the emergent transmission spectrum will be an admixture of many gaps with various areal

103 coverage fractions. The full solution becomes an areal integral of Equation 5.4 normalized by the total measurement area. Solving for the relative distributions of gaps is highly degenerate, in the same way as we saw in the 2-parameter corner plots of gap depth and fill factor. We experimented with by-eye fitting parametric distributions of gap sizes, characterized by a maximum and minimum gap size, and a monotonic slope of the distribution. We found that measurements of very large (> 10λ) gaps with a large gradient offered surprisingly strong constraints on the maximum gap size, because of the conspicuous high frequency Fabry-Pèrotfringes. For sub-wavelength gaps, the gap size distribution is too degenerate to derive much useful insight on the slope of the distribution. Specifically, for dmax < λ/4, our simple mixture model will converge on the spectrum of the average gap size, even if the True distribution is more complex. Reducing the measurement area could break some of these degeneracies, if more precision is desired.

The benefit of the Gaussian process- We chose to estimate the gap size with a Gaussian process regression, but this is not necessary. Any model fitting strategy, like least squares or over-plotting a model to data by-hand, will yield an estimate for a gap size. We tested the benefit of Gaussian process regression by generating synthetic data spectra with known gap size and fill factor, and known covariance structure. We applied ordinary least squares regression to the synthetic spectra and derived values for d and f that were biased by up to 20σ or more. Applying Gaussian process regression recovered the input values to within 1σ.

104 Normal incidence- We have assumed that the transmission measurement is performed at normal incidence. If the measurement beam forms a non-zero angle with the entrance face, bond interface, or exit face, several things happen to make this technique invalid. Notably, the polarization effects, Fresnel reﬂection losses, and the incoherent multiple reﬂections change the emergent transmission spectrum in non-trivial ways.

DSP vs AR coated front faces- We have assumed that the Si−air interfaces are approximated by Fresnel reflection losses. If the entrance and exit faces of the bonded samples are AR coated, the incoherent multiple reflection model will have to be modified. AR coated front and exit faces will result in a larger interface loss for a given gap size than the interface loss computed here.

How far can this technique go? The spectrophotometric precision of our instrument flows down directly to limit the smallest measureable gap size. This limitation will vary from instrument to instrument. Our instrument can achieve 10 times better accuracy and precision in double beam mode. How- ever, the slightly different polarization sensitivity in the different beams caused systematic jumps at the lamp/grating change-over wavelengths. Agilent offers an adapter to reduce the polarization sensitivity, which mitigates these lamp jumps. If precisions of 0.02% could be achieved, gaps < 4 nm could be reliably measured. This level begins to be comparable to the effect of interesting physics, like surface roughness and refractive index. In fact, the van der Waals bond energy could be constrained from these types of measurements [79].

Can this technique be applied to imaging? The analysis performed in

105 this article informs smart strategies for using IR imaging for gap detection in bonded Si optics. First, Equation 5.4 shows that short wavelengths have the most discerning power for detecting small gaps. So an IR imaging approach should use the shortest possible wavelength without getting close to the Si absorption cutoff. This work recommends a 1250−1300 nm filter. Images can then be normalized to the transmission through a DSP sample under identical, nearly collimated lighting conditions. Lastly, any deficits in flux of a bonded sample can be converted to a gap size d, using Equation 5.4. IR imaging will lack the spectral information available in the spectra shown in this article. The imaging will require exceptional quality of flat-fielding or dithering of the images to reach the precision achieved here with relative ease.

5.7 Conclusions

We have described a measurement technique and laid out an analysis formalism for the detection and measurement of sub-wavelength gaps at Si−Si interfaces. Experimental measurements show that we can precisely recover the extent of wavelength-scale gaps of known size, account for the presence of small gaps, and capture results consistent with no gap when measuring a monolithic part.

The technique and formalism we describe here can detect and measure the axial extent of gaps in Si−Si optical bonds down to a level of ∼ 14 nm. It makes use of widely available oﬀ-the-shelf metrology equipment and simple to implement analysis. Armed with this technique, optical fabricators have a

106 new diagnostic tool to assess the quality of Si−Si bonds.

5.8 Incoherent Multiple Reﬂections Transfer Matrix Method

Saleh and Teich (see Chapter 7 “Fundamentals of Photonics” [207]) describe the wave transfer matrix method. Their technique is to assemble a 2×2 scattering matrix S which has the elements:

t r S = 12 21 (5.8) r12 t21

Where t and r stand for transmission and reﬂection respectively. The order of subscripts is the order of origin and destination of the wave with respect to the interface, so we know the origin and direction of the wave. The S matrix encapsulates all information about how light waves interact with the interface. The power of the technique comes from the wave transfer matrix, M. The matrix M has the convenient property that its output can be used as the input for another matrix. In other words, the input vector to M is made of the left and right moving components directly before the interface; the outputs are the left and right moving components directly after the interface:

(+) ! (+) ! U2 U1 (−) = S (−) (5.9) U1 U2 (+) ! (+) ! U2 U1 (−) = M (−) (5.10) U2 U1

The elements of S and M are related to each other by geometric transformations[207]. In thin ﬁlms, the wavelength is comparable to the size of

107 the dielectric layer and the vector components Ui represent the complex amplitudes of the electromagnetic waves. The polarization state can be encapsulated in scattering matrix components[207]. The intensities of the emergent spectrum can be computed from the absolute square of the complex amplitudes. For thick ﬁlms, the vector components are the intensities of the emergent spectrum, since waves are incoherent. [114] work out the general transfer-matrix method for optical multilayer systems with incoherent interference. The key idea for the incoherent transfer matrix method approach is to populate a scattering matrix with elements equal to the (wavelength dependent) transmitted

Ti and reﬂected Ri intensities of an interface or set of interfaces that act together. Then, use the geometric transformations to construct the M matrix.

The matrix for the silicon air gap is calculated in the following way. We treat the air gap as a Fabry-P`erotetalon. We do not need to consider the microscopic coherent interactions with the etalon transmission, all of that information is encapsulated in these equations for a Fabry-P`erotetalon model for the gap:

2π δ = 2d (5.11) λ 4R F ≡ (5.12) (1 − R)2 1 T = (5.13) g 1 + F sin2(δ/2)

with λ the vacuum wavelength, R the Fresnel reflection of silicon, and F the coefficient of finesse. The coefficient of finesse F and the phase δ are

108 the two parameters of the Fabry-Pèrotetalon. The coefficient of Finesse encapsulates the Fresnel reflection and depends only on the Si refractive index which has only a small wavelength (and temperature) dependence. The phase δ (Equation 5.13) depends on the wavelength λ and d the air gap spacing. We assume the gap is lossless, i.e. Tg + Rg = 1. So the incoherent scattering and transfer matrices for the gap are:

1 1 F sin2(δ/2) S = g 1 + F sin2 δ/2 F sin2(δ/2) 1

1 − F sin2(δ/2) F sin2(δ/2) M = (5.14) g −F sin2(δ/2) 1 + F sin2(δ/2)

We assembled the matrix for the Air-Si Fresnel interface at the exterior of the bonded Si parts in the following way. First it is important to note that the matrix is the same whether the transmission is from Si to air or air to Si. This reciprocity is not necessarily true for the complex amplitudes matrix, but our approach employs intensities not complex amplitudes. The Fresnel interface is lossless. The transmission and reﬂection are given by the Fresnel equation for normal incidence:

4nSi Tn = 2 (5.15) (nSi + 1) 2 (nSi − 1) Rn = 2 (5.16) (nSi + 1)

For clarity I will drop the subscripts from nSi, since we have already set nair = 1 and there are no other dielectric interfaces to think about. So the scattering

109 and transfer matrices for the air-Si Fresnel boundary are:

1 4n (n − 1)2 S = n (n + 1)2 (n − 1)2 4n

1 −n2 + 6n − 1 (n − 1)2 M = (5.17) n 4n −(n − 1)2 (n + 1)2

Finally, we cascade the matrices together to compute the net transmission through the stack of abstractions. The result is a 2 × 2 transfer matrix:

Mnet = MnMgMn (5.18)

From the matrix transformation equations [207] we know M22 = 1/T .

Taking the inverse of the bottom right element of Mnet, we get the transmission Tnet through the net optical device:

2n T = (5.19) net 1 + 2nF sin2(δ/2) + n2

Compare equations 5.19 and 5.13. The revised transmission has picked up a few factors of 2 and n. While we are at it, let’s compute the matrix for the scenario with no intermediate gap: there are simply two Fresnel interfaces with which light interacts incoherently. This scenario is the model for a single

DSP reference sample. The revised matrix multiplication is simply MDSP =

MnMn. Taking the inverse of the M22 element, we ﬁnd:

110 2n T = (5.20) DSP n2 + 1

which is identical to the result obtained by directly summing the intensities from multiple reﬂections:

N 2 X 2i TDSP = T R (5.21) i=0

It is informative to isolate the eﬀect of the gap by dividing the measured bonded wafer transmission by the transmission of a reference DSP Si part. We call this normalized transmission the gap transmission Tg:

Tg = Tnet/TDSP (5.22) n2 + 1 T = (5.23) g 2nF sin2(δ/2) + n2 + 1

111 Chapter 6

Conﬁrmation and characterization of young disk-bearing brown dwarfs and sub-brown dwarfs

6.1 Introduction

Star and planet and formation theories predict the formation of substellar mass objects down to near the opacity limit fragmentation mass, with an abundance of brown dwarfs and sub brown dwarfs ejected from multiple systems [24, 23]. Observations of these failed stars are important probes for the study of star and planet formation, and may be the best method for directly observing planetary mass objects with current technology. Current moderate resolution (R ∼ 2000) spectrographic instrumentation on large telescopes is capable of detecting both young massive planets ejected from their stellar hosts and the lowest mass young free-ﬂoating products of the star formation process [143]. These objects still represent a challenge to identify and characterize given the low source luminosities, relatively large distances (& 100 pc) to the nearest young star forming regions, presence of variable extinction

(0 < AV < 35), and the high level of confusion with background and foreground sources. Allers et al. [6] published a list of 19 candidate young very low mass stars, brown dwarfs, and sub brown dwarfs (i.e. free ﬂoating plane-

112 tary mass objects) in portions of the Ophiuchus, Lupus I, and Chamaeleon II star forming regions with extinction AV < 7.5. Allers et al. selected sources based on near- and mid- IR colors indicative of disk bearing young objects with M and L spectral types. Allers et al. [8] present R = 300 near-IR spectroscopy of six objects from the Allers et al. [6] list, confirming the youth and cool temperatures of all six. Here we present near-IR (λ = 1.0 − 2.5 µm) spectroscopy on 17/19 sources observed with SpeX on NASA’s IRTF [189, 45, 232] in SXD mode (0.8−2.4 µm) with R ∼ 1200 and GNIRS [60, 61] in cross dispersed mode on Gemini with R ∼ 1700. The spectra confirm the low surface gravity (and therefore youth) and the M−L spectral types of these young objects for all but one source which appears to be extra-galactic [111]. The now confirmed sample is an important tool to extend the study of star formation and disk evolution down to near planetary masses. Additionally, this exceptionally low contamination fraction lends credibility to the selection criteria. Here we restrict our focus to the characterization of the objects through their near-IR spectra. In future work, we will present a detailed analysis of the objects and their disks, and the implications for disks around the lowest mass sub-stellar objects.

6.2 Spectral Typing

We determine the spectral types for our sources using the H-band index that quantiﬁes the spectral slope of the H2O absorption feature in the broad wavelength range 1.492-1.560 µm and is calibrated using optically spec-

113 tral typed objects of M5-L5 [8]. As a consistency check, we also employ the Slesnick et al. [221] J-band index which captures the increasing strength of the temperature-sensitive water absorption feature at 1.34 µm; the index is deﬁned for types M0-T0. Both indices are insensitive to surface gravity [221, 8] insofar as the indices reproduce the spectral types for standard dwarfs and giants over the spectral type ranges for which they are deﬁned.

The Allers et al. [8] H−band index requires dereddened spectra, since increased extinction will steepen the slope that the index attempts to quantify. We employ an iterative technique to derive the extinction and spectral type, speciﬁcally using the J− and H− band photometry and spectroscopy. Our ﬁrst step is to estimate the extinction from the observed (J − H) color, the intrinsic (J − H)0 [180], and the reddening law of Fitzpatrick [67]. We assume

(J − H)0=0.6, which is accurate for types M5-M9, rising to ∼ 1.08 at L2 [180]. Next, we derive the spectral type from the Allers et al. [8] index, having coarsely dereddened the spectra. We then reﬁne the estimate for (J − H)0 with our improved estimate for the spectral type. We typically iterate this procedure two times, by which the process converges. Table 1 lists the calculated spectral types from both the J− and H− band indices, and the derived spectral type. It is instructive to note that the J− and H−band indices have a reciprocal dependence on reddening: an underestimation of the extinction would make one conclude a later spectral type with the H− index, but an earlier type for the J−band index. Because of the reciprocal dependence on reddening of our two spectral typing indices, we are conﬁdent that our derived

114 spectral types are robust against reddening. For sources with types earlier than M5, the H− band index is undefined, and so we adopt only the J− band index. For other sources we derive the spectral type as the average of the J−band index and H−band index (when both are available), weighted to the value with higher confidence. The errors in the spectral types are reported from visual comparison of our dereddened spectra to standards with known spectral types: a typical spectrum is firmly sandwiched between two standards of ±1 spectral sub class, based on the overall shape in J−, H−, and K− bands.

6.3 Luminosities

To compute the luminosities of our sources, we apply a bolometric correction (BCJ ) to their dereddened J-band magnitudes. We converted BCK to BCJ for M1–L3 ﬁeld dwarfs in [74] using K-band (MKO system) photometry reported therein and J-band photometry from the 2MASS PSC. The spectral

1 2 type vs. BCJ relation is : BCJ = 1.60 + 0.10 × SpT − 0.007 × SpT with small (∼0.08 mag) dispersion about the second order ﬁt.

1SpT is the numerical translation of SpT: M1–M9=1–9 and L0–L3=10–13

115 Source AV SpT from A07 SpT s SpT a Derived SpT log L/L # mag 1 2.2 ± 0.5 9 11.4 12 11.5 ±1 -3.3 2 10.2 ± 0.4 6 5.9 6 6 ±1 -1.3 4 4.2 ± 0.3 2.1 - 2 ±1 -0.8 5 2.8 ± 0.5 11 13.3 8.3 11 ±2 -3.2 6 4.3 ± 0.3 4.8 - 5 ±1 -1.2 7 2.3 ± 0.4 6.7 5.7 6 ±1 -1.9 8 2.8 ± 0.4 2.8 - 3 ±1 -1.2 9 6.6 ± 0.4 5.2 5.9 5.5 ±1 -1.4 10 4.7 ± 0.3 3.1 - 3 ±1 -0.6 11n 0.4 ± 0.6 7 5.2 7 7 ±1 -2.5 11s 0.2 ± 0.7 8 9.7 9.2 9 ±1 -2.8 13 3.3 ± 0.3 6.1 6.2 6 ±1 -1.8 14 6.1 ± 0.4 7 - 8.1 8 ±1 -2.3 15 10.2 ± 0.4 2.3 - 2 ±1 -1.1 16n 3.7 ± 0.5 3 5.2 3 ±1 -0.8 16s 3.7 ± 0.5 3.9 5.1 4 ±1 -0.9 17 0 ± 0.4 12.1 13.2 12.5 ±2 -3.3 18 0.2 ± 0.5 6.1 7.5 7 ±1 -2.4 19 0 ± 0.3 4.3 5.5 4.5 ±1 -1.7

Table 6.1 Derived extinction, spectral type, and luminosity. Source # is the number from Tables 3 − 6 in Allers et al. [6], SpT from A07 is the spectral type reported in Allers et al. [8], SpT s and SpT a are the spectral types derived here using the prescription of Slesnick et al. [221] and Allers et al. [8], respectively. The derived spectral type is an average of the two types when possible, weighted to the value of higher conﬁdence. For source #16 n and s, we adopt only the Slesnick et al. [221] index. The uncertainties of the extinction are propagated from the uncertainty in (J −H)0, and an uncertainty of 1 spectral subclass in the spectral type.

116 Figure 6.1 Left- Spectral typing comparison for source 13 (derived SpT= M6), with spectral type comparison objects from the SpeX archive [190, 46]: Gl51 (M5V), and Gl644C (M7V). Right- Detail of the Na I line for source 13, with surface gravity comparison objects with identical spectral types, also from the SpeX archive: Gl406 (M6V) and HD196610 (M6 III). Source 13 is intermediate in surface gravity as demonstrated by the gravity sensitive index Na I.

6.4 Conﬁrmation of Youth

Once the sources were established as cool stars or sub-stellar objects, their youth was probable based on the presence of mid-IR excess [6] indicative

117 Figure 6.2 Gravity dependence of the Na I line. Dwarfs and giants from the SpeX spectral atlas are shown as red diamonds and green triangles respectively. The blue squares show the sources from this work. Compare to figure 35 of Rayner et al. [190]. of circumstellar disks. We improved the case for youth by quantifying gravity sensitive spectral lines. The Na I λ = 1.14 µm equivalent width is sensitive to surface gravity [190], showing a clear dichotomy in the spectra of dwarfs and giants after about M4, specifically with the dwarfs demonstrating increasing equivalent widths up to 15 A˚, while the giants exhibit equivalent widths of about 1 A˚. The right panel of figure 1 shows a detail of the Na I line and

118 Figure 2 shows the NaI equivalent width as a function of spectral type, with the independently measured equivalent widths of dwarfs and giants from the SpeX spectral atlas [190, 46], and the intermediate widths of young substellar objects in this sample. The increased resolution over the Allers et al. [8] study was critical for measuring the equivalent widths of lines since, for example, Allers et al. [8] employed a ﬂux ratio index to quantify the degree of Na I absorption because the line blending is too severe at R ∼300. With R ∼ 1200, one can isolate the Na I line well enough to notice that its strength is intermediate to dwarfs and giants, and not merely less than dwarfs. For future studies targeting diskless young sources, spectra at resolution similar to this study will be best for identifying weak gravity sensitive lines like Mg I, Al I, and Na I [190] for the purpose of assigning youth to the sources.

119 Chapter 7

Evolved disk population of young brown dwarfs towards Ophiuchus

7.1 Introduction

How do the circumstellar disks around young brown dwarfs differ from those around their higher mass T-Tauri star counterparts? One emerging an- swer to this question is that the disk frequency and lifetime may be a function of stellar mass and star forming region. At an age of ∼1 Myr, 40% of the brown dwarfs in the Taurus region have disks, which is lower than the disk fraction for Taurus stars [133]. While that might suggest that fewer brown dwarfs are born with disks, samples in the older, ∼2−3 Myr, Chamaeleon and IC 348 regions complicate the story. Luhman et al. [144] find that ∼50% of those brown dwarfs have disks, slightly higher than the fraction for stars. Riaz and Gizis [198] showed that 3/5 brown dwarfs in the TW Hydrae Association retained their primordial disks, whereas only 6/25 of their higher-mass counterparts in the same cluster showed any evidence for disks. It is conceivable that the initial disk fraction around brown dwarfs and stars is similar, but brown dwarf disks have longer lifetimes because they accrete more slowly [7]. Small sample sizes have made it difficult to say whether brown dwarf disks really do last longer than disks around stars. The reported uncertainties in disk fractions

120 are typically 10−20% [200]. Scholz et al. [210] and Riaz et al. [199] report disk fractions in discord at > 2σ for distinct subsamples of brown dwarf members of Upper Scorpius. Larger samples of brown dwarfs, with and without disks will be helpful for settling the role of stellar mass on disk lifetime.

7.1.1 Young brown dwarfs for the study of low mass sources

Firm members of young star forming clusters are especially valuable because we know the age of the clusters, so we can directly test substellar interior and substellar atmosphere models. There are not enough class III objects against which to test these models across a broad range of surface gravity. A collection of young, diskless brown dwarfs is needed. As brown dwarfs monotonically cool and contract, they exhibit M, L, and T spectral types [58]. Studies of the solar neighborhoood have succeeded at ﬁnding ∼Gyr populations of L, T, and Y dwarfs from their large proper motions and colors [116]. L-type and T-type objects now number in the hundreds [209, 116]. Meanwhile, studies of nearby young moving groups reveal “juvenile” brown dwarfs [5], with ages ∼ 20 − 100 Myr. Juvenile brown dwarfs serve as analogs to directly imaged exoplanets, which exhibit similar spectral types to brown dwarfs [34]. Young brown dwarfs discovered as companions to Herbig AeBe stars are analogous to lower mass planets forming in a disk around lower mass stars. The youngest brown dwarfs in nearby star forming clusters complete this picture of brown dwarf evolution across the time and mass domain.

121 7.1.2 Mass estimation

There is a minimum mass below which brown dwarfs cannot form directly from gravitational collapse of a gas cloud. Rees [194] showed that this minimum mass is about 2 MJup. Though several candidate <2 MJup free ﬂoat- ing objects have been found [181], only one has withstood spectroscopic follow up [153]. Their low luminosity and intrinsic rarity hinder observations.

We do not yet have dynamical mass measurements of young brown dwarfs in nearby star forming regions. Instead, the usual strategy for assigning masses to young stars is by placing individual objects on an HR diagram, and comparing their locations to stellar evolutionary model tracks. There are several flaws with this strategy, especially at low masses. Specifically, bolometric corrections and effective temperatures are highly uncertain for spectral types later than M5 [182], not to mention that the evolutionary model tracks differ by factors of 2 on the mass at a given place on the HR diagram [49, 18]. There are additional systematic uncertainties that go into assigning an effective temperature based solely on a spectral type. For example, correcting for chromospheric activity can affect masses by ∼ 3 − 100% [226].

7.1.3 Previous surveys of young brown dwarfs in nearby star forming regions- Diﬃculties in identiﬁcation and biases therefrom

To understand brown dwarfs, we need a large, complete, unbiased sample. Barring that, we at least need representative examples of brown dwarf/disk systems. Detection techniques for brown dwarfs have been “success-

122 −3 oriented”. Low luminosity (. 10 L ) brown dwarfs are hard to ﬁnd among copious reddened background stars and galaxies.

There have been dozens, if not hundreds, of searches for brown dwarfs in nearby star forming clusters (see Luhman [135] for a recent review). Some representative examples include [130, 12, 168]. The approaches in these searches all differ in their details, but the main theme is to construct a color magnitude diagram, and select sources that are brighter and redder than some threshold. This strategy relies on the fact that there are very few luminous red sources in the foreground, since the star forming regions are relatively close by (∼ 150 pc). This strategy works fine for stellar sources, which are much more luminous than the background objects. Brown dwarfs on the other hand exhibit optical and near-IR colors and magnitudes comparable to reddened distant background objects. At the same time, the intrinsic number density of brown dwarfs is decreasing, so the problem is like searching for a needle- in-a-haystack. The contamination becomes so unmanageable that additional selection methods become necessary in order to cull the large number of photometric candidates to a number of candidates that is amenable to follow up spectroscopy. These additional selection methods vary. One main strategy is simply to select sources that exhibit mid-IR excess [6]. This choice has the virtue of offering a high likelihood of success- 18/19 of the Allers et al. [6] sample were confirmed as bona fide young late-type sources [86]. Further, the availability of deep mid-IR imaging from c2d (and to a lesser depth WISE), makes it feasible to carry out this strategy.

123 Selection methods demanding the presence of mid-IR excess cannot discover sources without mid-IR excess. Evolved disks therefore go undis- covered. These evolved disks include debris disks and Class III analogs that have already undergone a phase of primodial disk clearing (perhaps by planet formation). This tautological bias means that brown dwarfs with disks are probably over-represented in our counts of young brown dwarfs. It is hard to say to what extent the number of diskless brown dwarfs is under-estimated. It is conceivable that diskless brown dwarfs are rare, because the disk dispersal timescale is longer in brown dwarfs [198]. Or it could be that disks that have already evolved went through a period of vigorous accretion that caused the sources to appear underluminous for their age [21], further hindering their unambiguous selection and detection. In the latter case, diskless brown dwarfs, and therefore brown dwarfs altogether, would be more common, raising the question- “What else is there?”. For example, are there pure photosphere sources or more extreme transition disks? Are we over-estimating accretion rates by selecting for strong disks? Are we missing objects hidden behind their disks by viewing angle? What are the diﬀerent modes of evolution? Again, to fully understand the YSO phase of BDs, we need to have examples of the full range of source types.

7.1.4 Motivation for this project

In order to trace the lifetimes of brown dwarf disks, statistically significant samples must be assembled for clusters of ages 1−10 Myr and searched

124 for infrared excesses. What is lacking is a sample of brown dwarfs that is unbiased by selection techniques based on infrared excess. This work assembles a sample of young brown dwarfs both with and without mid-infrared excess.

One of the main ideas of this work is that we take a more catholic approach to ﬁnding objects but with a sure way to verify them. We are sensitive to class III analogs. We investigate the properties of a broader population of young brown dwarfs to provide a better framework for the early evolution of these objects.

We introduce a custom filter centered at 1.4 µm, and demonstrate how measurements with this filter can facilitate selection of young brown dwarfs. We can therefore select hundreds of candidates that show intrinsic photospheric water absorption. Most of these objects will be old field M dwarfs. But some of them will be young brown dwarfs. We therefore use multi-object spectroscopy to identify the rare young objects from their more numerous old field counterparts.

Ancilary information alone, like the W −filter, variability, X-rays, or proper motion, cannot establish membership in a young cluster. Spectroscopy offers a method for assigning an effective temperature, which when combined with the bolometric luminosity, can be used to assign a position on an HR diagram. The HR diagram can then be used to coarsely assign masses and ages, about which we have already mentioned shortcomings. Still, the HR diagram is an exceptionally powerful vehicle for understanding the aggregate properties of a cluster, and the coarse properties of individual sources. Above all the

125 HR diagram lends strong evidence in favor of−or against−cluster membership of individual objects. Spectroscopy therefore drives all observational choices, because of its leading role in conﬁrmation.

The lowest mass young brown dwarfs in nearby star forming clusters are at the sensitivity limit of existing astronomical spectrographs. Futhermore, spectral resolution, spectral bandwidth, and number of targets all compete for the same spectrograph detector real estate. The wavelength and sensitivity requirements drive the choice of a large optical/near-IR spectrograph on a 6−10 meter class telescope. The instrument needs a wide field-of-view to cover a large enough portion of nearby star forming regions, which occupy degrees on the sky. The sensitivity and wide-field requirements drive the instrument choice to the largest product of collecting area A and solid angle Ω. Few existing instruments have a wide-enough AΩ to be feasible. The IMACS spectrograph has one of the largest AΩ products, and offers a multi-object mode in which ∼ 100 sources can be observed in parallel. The optical wavelength range of IMACS facilitates spectral classification which has historical been performed in the red visual portion of the spectrum.

We chose Ophiuchus because it is one of the closest clusters of very young YSOs [125]. We elected to focus on an oﬀ-core region since it oﬀers lines of sight of extinction low enough (AV . 10) to make I−band spectroscopy possible, but high enough to ensure an embedded population [126]. Deep near-IR and optical photometric data exist throughout the wavelength range of interest from Allers et al. [6]. The existing Allers et al. [6] photom-

126 etry includes about 0.7 square degrees of I−band through MIPS [24]. The photometric depths are suﬃcient to detect a 2 MJup source in all except the IRAC [5.8] and [8.0] bands. Additionally, we use about 0.5 square degrees of deep Spitzer IRAC [5.8] and [8.0] photometry made available by Harvey et al.

[93], making portions of our catalog sensitive to the photospheres of 2 MJup objects. This region has been searched previously for young brown dwarfs. Allers et al. [6] used deep near-IR photometry and c2d mid-IR photometry to identify 19 candidates with mid-IR excess. Gully-Santiago et al. [86] spectrally classiﬁed all but two of these candidates, ﬁnding a spectral type range M2−L2.5. Slesnick et al. [222] combined R− and I− band photometry with 2MASS, and optical spectroscopy to identify 30 likely new brown dwarf members for the Upper Scorpius OB association (Upper Sco). Finally, Harvey et al. [93] leveraged deep Spitzer observations to report 18 new candidates selected for their position on color-magnitude diagrams and their evidence for photospheric W −band absorption. In total our chosen region contains 7 sources from Allers et al. [6] and 3 sources from Slesnick et al. [222] in addition to the candidates from Harvey et al. [93].

Our approach is to apply a broad set of strategies for identifying targets to conﬁrm with spectroscopy. We select for sources that are bright enough to observe in I−band with IMACS on Magellan. The selection strategies include looking for evidence of disk, intrinsic water absorption, and red optical − near- IR colors. We place ﬁelds to include the largest number of best sources, and other, less promising candidates that the instrument properties allow us to

127 observe along with these sources. We follow up and conﬁrm a large number of candidates with multi-object I− band spectroscopy. We characterize and spectral type sources with I−band spectroscopy. We combine several lines of evidence for youth from the spectra, from the mid-IR photometry, and from the position on an HR diagram. At the end we summarize our sample, and use it to derive insights about the parent population of brown dwarfs. We can ultimately assess how well the selection methods work.

7.2 Input catalog and candidate selection 7.2.1 Photometry

Figure 7.1 shows the survey region, which is centered on—but larger than—the region of Allers et al. [6] for the Ophiuchus portion of their survey of Ophiuchus, Chamaeleon, and Lupus. Our photometric survey extends the spatial coverage of the Allers et al. [6] survey towards the core of Ophiuchus. Figure 7.1 shows the 2MASS extinction map [126] from the COMPLETE project [203] with lighter regions having higher extinctions. We use the same I and K photometry as Allers et al. [6], and the same JH photometry, except for the additional photometry towards the core, which is reduced identically to Allers et al. [6]. The JHK photometry is from ISPI at CTIO, and is about 3.3 magnitudes deeper than 2MASS [6]. The JH photometry has over twice as much spatial coverage as the K− band photometry. Figure 7.1 shows the footprint for the ISPI JH survey region, demarcated by the solid blue border extending towards the Ophiuchus core. The green border shows the footprint

128 for the K−band photometry. The positions of known brown dwarfs are shown as blue diamonds [6], red and green triangles [13], and yellow squares [222]. Table 7.1 lists the photometric depths and number of detections in bands I, J, W , H, K, IRAC [3.6], [4.5], [5.8], [8.0], and MIPS [24].

7.2.1.1 c2deep from Harvey et al.

We acquired a catalog of deep [5.8] and [8.0] photometry from Harvey et al. [93]. This region is shown as the red solid line in Figure 7.1. This region overlaps the region with the most pan-chromatic photometry available (K, green; W , yellow; I, magenta), and extends north of the region in which JH ISPI data is available (blue solid line). The Harvey et al. [93] photometry is 1.1−2.4 magnitudes deeper than c2d, which enables detection of disks of 2 Jupiter mass objects in Ophiuchus [6]. The cyan circles in Figure 7.1 are the 18 candidates from Harvey et al. [93].

7.2.1.2 W − ﬁlter

Allers et al. (in prep) designed and implemented a custom filter centered at 1.4 µm, intermediate between the J− and H− atmospheric windows. This filter is about 0.2 µm wide, cutting on near the long end of J and cutting off near the short end of H. This photometric band was designed to distinguish between the photospheric emission of late M and L spectral types and that of reddened FGK and early M spectral types. Cool stars and brown dwarfs with late M spectral types demonstrate intrinsic water absorption in their photo-

129 -23°00'00.0" 10.5

9.0

30'00.0" 7.5

6.0

-24°00'00.0" V A

Dec (J2000) 4.5

3.0 30'00.0"

1.5

-25°00'00.0" 0.0

28m00.00s 26m00.00s 24m00.00s 22m00.00s 20m00.00s 16h18m00.00s RA (J2000)

Figure 7.1 Map of the region targeted by our survey. The background grayscale image is the 2MASS NICER extinction map [126] from the COMPLETE project [203]. The solid line boundaries outline our regions of custom photometry with the following color scheme: blue solid lines for the ISPI JH catalog, green for ISPI K−band, red for c2deep, magenta for I−band, and yellow for the custom W −band. The large blue dashed box deﬁnes our 2MASS JH catalog. The yellow squares concentrated toward the right side of the image are from previous surveys of Upper Scorpius [222]. Ophiuchus members are concentrated around the high extinction core to the left of the image. All known brown dwarfs detected by Herschel are shown as green upward pointing triangles, while brown dwarfs not detected by Herschel are red downward pointing triangles, [13]. Cyan circles are from Harvey et al. [93], and blue diamonds are from Allers et al. [6].

130 spheres. There is a strong water absorption band centered around 1.4 µm. The filter can also distinguish high−z galaxies, which will not demonstrate intrinsic photospheric water absorption as brown dwarfs do. The broad-band IJHK colors for FGK and early M sources are indistinguishable, while the W −filter band photometry shows a deficit in M-type spectra (Allers et al. in prep).

One potential pitfall with the W −band is that this wavelength region has high and variable telluric water absorption. Telluric water absorption is problematic for two reasons. First, the absolute transmission through the ﬁl- ter will be low. Second, the variability of the telluric water absorption will manifest as shifting wavelength-dependent zero-points. To ameliorate these problems we observed from the high, dry site Mauna Kea, where the telluric water absorption is much lower than other sites. Ideally the W −band photometry should be taken contemporaneously with J− and H− bands, in order to overcome intrinsic source variability, which is especially acute for late type young brown dwarfs that demonstrate accretion variability and star spots [10, 37].

Despite the telluric absorption challenge, the W − filter works- it has already been successfully applied to select brown dwarfs with over 90% confirmation rate (K. Allers, priv. comm.). The W − filter has been successful at recovering known objects, and has been checked in the Ophiuchus core region, IC348, and NGC1333.

One main potential advantage of the W −band ﬁlter is its reddening

131 insensitivity. Allers et al. (in prep.) derive a Q−parameter from J, W , and H bands, following the form of Najita et al. [171]. The Q value is the depth of the W −band normalized by the J− and H−bands, and can be tuned for particular lines of sight to mitigate the eﬀect of reddening (Allers et al., in prep.). A ﬂat spectrum source would exhibit Q = 0, whereas a source with strong photospheric water absorption indicative of a late M spectral type would have a value of Q in the vicinity of −1. Najita et al. [171] have shown that the Q values scales with spectral types in the range M0−M9, for both sources in young clusters and standard stars.

The W − band photometry in this work was observed with the Uni- versity of Hawaii 88” telescope with the ULBCAM imager. The individual photometric frames were dark subtracted, divided by a normalized ﬂat, and median combined following the procedure of [6]. We use the Source Extractor [26] to perform aperture photometry on the W −band photometry. The yellow outline in Figure 7.1 shows the region for which W −band photometry exists.

7.2.2 ISPI JH Catalog (∼ 3.3 magnitudes deeper than 2MASS)

We established a source catalog based on the ISPI JH photometry, which had the most spatial coverage. Membership to the catalog requires 5 σ detection in both J and H bands. A total of 54373 sources met this criterion. This catalog is demarcated by the solid blue line in Figure 7.1. We refer to this catalog as the “ISPI JH Catalog”. We justiﬁed the JH detection requirement because these are the bands in which young brown dwarfs peak in

132 Table 7.1. Photometry in this study

Band N 3σ Detections 10σ mag Source Ref.

ISPI JH Catalog I 34467 23.0 MOSAIC/CTIO 4m 1 J 54373 19.4 ISPI/CTIO 1 W 31205 19.1 ULBCAM/U. Hawaii 88” 1 H 54373 18.8 ISPI/CTIO 1 K 20470 18.0 ISPI/CTIO 1 [5.8] 9135 15.7 c2deep 2 [8.0] 1948 14.9 c2deep 2 [3.6] 37423 16.1 c2d 3 [4.5] 30345 15.5 c2d 3 [5.8] 11542 15.7 c2d 3 [8.0] 2878 12.5 c2d 3 [24]a 145 ∼ 7.9 c2d 3 2MASS JH Catalog I 6939 22.9 MOSAIC/CTIO 4m 1 J 27208 16.1 2MASS 4 W 11226 16.3 ULBCAM/U. Hawaii 88” 1 H 27618 15.3 2MASS 4 K 25254 14.5 2MASS 4 [5.8] 4891 15.5 c2deep 2 [8.0] 2173 14.8 c2deep 2 [3.6] 18716 15.3 c2d 3 [4.5] 18604 15.4 c2d 3 [5.8] 12859 13.2 c2d 3 [8.0] 5973 12.4 c2d 3 [24]a 452 ∼ 7.9 c2d 3

aThe reported depth is for 8 σ.

References. — (1) Allers et al. [6] (2) [93] (3) c2d, [64] (4) 2MASS, [220]

133 ﬂux. Sources below our 5 σ detection limits in J− and H− bands would stand little chance of follow up near-IR spectroscopy with existing instrumentation. Further, sources with red optical minus IR colors—an expectation for late-type reddened young brown dwarfs—would stand even less of a chance of optical spectroscopic follow up.

The astrometric solution for the catalog comes from the ISPI astrometry, which is pegged to 2MASS (see Allers et al. [6] for details).

We cross-match the 54373 JH selected source catalog with each of the other photometric catalogs of K, W , [3.6], [4.5], [5.8] from c2d, [5.8] from c2deep, [8.0] from c2d, [8.0] from c2deep, and MIPS [24]. In cross matching, any source within a small angular separation of a JH catalog member is matched to the JH member, with angular separations typically between 0.5 and 1.5” depending on the quality of the WCS solution in the imaging frames. We do not attempt to calculate an upper limit for undetected sources.

Table 7.1 lists the number of > 3σ detections in each band, and the typical 10 σ magnitude, which was computed as the median ﬂux of sources with signal noise ratio between 9.5 and 10.7 σ.

7.2.3 2MASS JH Catalog

We also made a shallow catalog constructed with 2MASS JH photometry instead of the deeper ISPI JH photometry. This catalog had the virtue that its spatial coverage included all of the auxiliary imaging bands that extended past the footprint of the ISPI imaging. In particular, several candidates

134 reported in Harvey et al. [93] did not appear in the ISPI JH Catalog since they were outside the ISPI imaging region, but inside the c2deep imaging region.

We selected all sources in 2MASS with in a region with right ascension between 16h19m30s and 16h26m, and declinations between −25◦ and −23◦ (blue dashed line in Figure 7.1). This selection resulted in 28092 sources. We followed the same procedure as we did above for performing catalog matching. Table 7.1 lists the properties for the 2MASS JH catalog.

7.2.4 Candidate selection

Equipped with our photometric catalogs, we were prepared to select candidates for spectroscopic follow up. The IMACS spectrograph on Magellan can measure hundreds of sources, but not tens of thousands. We had to reduce the number of follow up sources from 54373 (deep JH) and 28092 (shallow JH) to about 300 candidates, a down-select factor of about 0.5%.

We first considered the sensitivity of the instrument to set the limiting magnitude for I− band spectroscopic follow up. Our 10 σ photometric depth in I− band is 23.0. We set a limit of I = 21.6 for follow up spectroscopy. We estimated that this threshold could provide sufficient signal-to-noise ratio for at least coarse spectral classification- “Is the source late type or not?”, though higher signal to noise or auxiliary information would be needed to assign youth and therefore membership to the source. Only two thirds of catalog had I−band measurements available, due to the smaller spatial coverage of the I−band imaging. Of those sources with I−band detections, only 38% had

135 Table 7.2. Binary selection criteria

Score Criterion IDs N meet N eligible % catalog % eligible

8 IJHK NIR 3680 34469 6.8 10.7 4 H − [3.6], K − [3.6] [3.6] 23112 42268 43.5 54.6 2 W − band W 1180 31348 2.2 3.8 1 Mid-IR excess Disk 1407 14095 2.6 10.0

Note. — The number of catalog members eligible to meet a criterion diﬀers from the length of the catalog (54373) due to missing data in the form of non-detections or non-observation.

I > 21.6. We assigned a proxy limiting magnitude of J > 17.4 for sources undetected at I−band.

We devised four physically motivated selection criteria. Each criterion incorporated a different aspect of known or expected physics. The criteria are broadly IJHK colors, H − [3.6], custom W −filter, and mid-IR excess. The criteria are binary– the candidate met the criterion or it did not. In this section we describe the motivation and justification for the details of these four selection criteria. In the next subsection we describe the method we used for combining the various combinations of these 4 criteria to issue an observation priority for each candidate. Table 7.2 summarizes the four criteria.

136 7.2.4.1 Near-IR photometric selection

For those sources where we had I− band available, we set a selection criterion based on optical minus near-IR. The main point of this criterion was to select sources with colors indicative of—or at least consistent with—late M spectral types. Known young brown dwarfs at 1 Myr have spectral types later than about M6 [135]. The full range of colors for young brown dwarfs is not known. Our approach was to compile examples of colors of known young brown dwarfs and design criteria that would recover these objects. The ﬁnal criterion is composed of three color cuts, and one magnitude cut.

The color cuts rely heavily on I−band photometry, owing to this band’s discriminatory power of separating red optical colors indicative of young brown dwarfs from bluer optical colors indicative of unreddened or minimally reddened stars. The lack of I−band measurements for some sources was because of the limited spatial coverage of the I−band mosaics, not because of sensitivity limits (our I− band photometry is exceptionally deep). Because of our heavy reliance on I−band, sources without I−band photometry were ineligi- ble to meet the near-IR photometric selection criterion. A total of 34469 out of 54373 sources had I−band measurements. This cut reduced the number of sources from 100% to 63.4%.

As mentioned above, one of the clearest signatures of brown dwarfs is their red optical color, since optical (R−,I−, z− band; λ ∼ 0.8 µm) is short of the peak transmission of the cool (T (K) < 2900; λ ∼ 1.0-2.0 µm) substellar photospheres of brown dwarfs. However the large optical minus

137 infrared color is a hallmark of both brown dwarfs and high-z galaxies, and can be mimicked by the eﬀect of high reddening. The I − J color of brown dwarfs with spectral types later than ∼M6 is typically greater than ∼ 2.85 [6]. Reddening would only act to make this value larger. So we required

I − J + σI−J > 2.85, where σI−J is the measurement uncertainty of I− and J− bands added in quadrature. The measurement uncertainty in I− and J− bands are the statistical uncertainties in the measurement and do not include calibration uncertainties. The statistical uncertainty is evaluated for each source, and ranges from 0.001 to 0.1 for H−, and I− bands.

The eﬀect of including the uncertainty in this color cut is to include sources that are consistent with—albeit with values nominally below—our threshold. For example, a hypothetical candidate with I − J =2.80 and com-

p 2 2 bined measurement uncertainties in I− and J− bands σI−J = σI + σJ =0.07 would have I −J +σI−J = 2.87 and would therefore exceed our 2.85 threshold. This inclusive selection strategy is perceptible in Figure 7.2. The motivation for setting an inclusive boundary was to avoid cutting out interesting albeit low signal-to-noise ratio sources at the margin.

The I − J color cut was met by 12548/54373 (23.1%) of the total catalog members, or 12548/34469 (35.4%) of those sources possessing I−band measurements

Our next color cut is to select for blue intrinsic J − H colors. The motivation for this color cut is that observed young brown dwarfs demonstrate a tight range in intrinsic J − H (0.58-0.71 for M5−M9 [148]), so we could

138 eliminate contamination by setting the threshold redward of the largest J − H we could expect. We set that threshold at 0.84156, on the MKO scale1.A large extinction could pull the observed value past the 0.84156 threshold. So we constructed a reddening line that related the observed I −J with the observed

J − H through the selective extinction ratios A(λ)/AV compiled from the

Asiago Database of Photometric Systems (ADPS) [164] with RV = 3.1. The

AI −AJ color cut is: I−J+σI−J > 2.85+[(J−H)−0.84156+σJ−H ] . Where σI−J AJ −AH is the uncertainty in the I− and J− bands added in quadrature, and σJ−H is the photmetric uncertainty in J− and H− bands added in quadrature, using the same methodology as already discussed. The ratio AI −AJ is equal to 3.33, AJ −AH and takes into account the selective extinction. Figure 7.2 shows this color cut as the diagonal line. The upper left portion of the plot meets both color cuts discussed so far. The upper right corner has red I − J color, but has J − H color that is too red for an M9 (which has the largest J − H for any M spectral type) to be explained by reddening alone. This color cut was met by 8105/54373 sources (14.9%). At this point, 3967 sources (7.3% of the catalog) met all the previous color cuts.

We leveraged the K−band photometry when it was available to make another color cut. Like the I−band data, the K− band had incomplete spatial coverage– only 38% of sources had a K−band measurement available. Our strategy here was similar to the color cut above selecting for blue intrinsic J−H

1When performing candidate selection on the 2MASS JH Catalog, we altered our color- cut thresholds to the 2MASS photometric system.

139 6

J 3 − I

0 0.0 0.5 1.0 1.5 2.0 2.5 J H −

Figure 7.2 Color-color cuts in I −J vs J −H. The horizontal dashed line shows I−J = 2.85. The tilted dotted line demonstrates the selection for intrinsic blue J − H colors (< 0.84156), allowing for reddening. The grayscale Hess diagram in the background shows the density of points in each color bin, constructed from 34469 sources with I−band detections. The points in the upper left quadrant of the diagram meet the color cuts 2 and 3 from the list in Section 7.2.4.1. Sources that meet the color cut are illustrated with black circles with white outlines. Some of the sources that meet the selection lie outside the thresholds shown as the red dotted and red dashed lines. The magenta circles are sources from Allers et al. [6] that have spectral types between M6 and L2 [86]. color, except now we are selecting for intrinsic blue J − K color. We assumed a maximum J − K for brown dwarfs of 1.37662 in the MKO system. We then built a reddening relationship between I −J and J −K that takes into account the selective extinction from ADPS, as above. Lastly, we removed sources that were redder than this curve, removing only sources that had K−band available. The sources we removed satisﬁed this criterion: I − J + σI−J <

140 AI −AJ 2.85+[(J −K)−1.37662−σJ−K ] , where σI−J is the same as it is above, AJ −AK and σJ−K is the photometric measurement uncertainty in J− and K− bands added in quadrature. We removed 11020/54373 sources, which means that the complement, 43353 passed on. Combining this criterion with the previous color cuts brings the passage rate from 7.3% from the previous cuts to 6.8%.

J 3 − I

0 0.0 0.5 1.0 1.5 2.0 2.5 J K −

Figure 7.3 Color-color cuts in I − J vs J − K. The horizontal dashed line shows I − J = 2.85. The tilted dotted line demonstrates the selection for intrinsic blue J − K colors (< 1.37662), allowing for reddening. The grayscale Hess diagram in the background shows the density of points in each color bin, constructed from 19733 sources with both I− and K−band detections. The points in the upper left quadrant of the diagram meet the color cuts 2 and 4 from the list in Section 7.2.4.1. The square boxes plotted are sources from Allers et al. [6] which have spectral types between M6 and L2 [86].

Lastly, we applied a K− magnitude cut, with the intention of ﬁnding the faintest and therefore lowest luminosity young brown dwarfs. For a given cluster age, the lowest luminosity young brown dwarfs are also likely to be the

141 lowest mass. We deemed these lowest mass sources to be most scientiﬁcally interesting. Following Allers et al. [6], we assumed an absolute K−band magnitude of 8.01 for a young M9, and a distance modulus µ = 5.48, for a K−band apparent magnitude cut of K +σK > 13.49, where σK is the photometric measurement uncertainty in the K−band. Since K−band data was unavailable for many sources, we also removed sources consistent with H−band apparent magnitudes less than 8.51 plus the distance modulus, keeping sources with:

H + σH > 13.99. Figure 7.4 shows the number density Hess diagram of all 54373 sources in the H− versus J − H diagram. The large magenta circles are sources from Allers et al. [6] towards Ophiuchus. The only Allers et al. [6] sources fainter than our H > 13.99 threshold are the latest type sources known in that region. Again, we sought sources fainter than this limit since we were most interested in low luminosity, low mass brown dwarfs. This criterion is likely to cut sources with spectral types earlier than M9, as demonstrated in Figure 7.4. We do not plot the K−magitude cut plot, but it looks similar to Figure 7.4.

This magnitude cut removed 1105 sources out of the 54373 source catalog. When combined with the previous color cuts above, this magnitude cut removed 14 sources: OPH 675, OPH 672, OPH 679, OPH 678, OPH 673, OPH 674, OPH 12081, OPH 12079, OPH 3054, OPH 5413, OPH 12961, OPH 13049, OPH 19613, and OPH 956.

142 10

14 H

20 0.0 0.5 1.0 1.5 2.0 2.5 J H −

Figure 7.4 H−band Magnitude cut. The horizontal dashed line shows H = 13.99. The grayscale Hess diagram in the background shows the density of points in each color-magnitude bin, constructed from the entire 54373 point ISPI deep JH source catalog. The circles are sources from Allers et al. [6] towards Ophiuchus. The two Allers et al. [6] sources with H > 13.99 have M8 spectral types, while the others are M6 or earlier [86].

7.2.4.2 Mid-IR excess (disk) selection criterion

Sources detected at 24 µm with greater than 3 σ conﬁdence were automatically considered disk sources, since we assumed [24] could not detect photospheric emission for our low luminosity sources. The 3 σ depth for 24 µm is ∼ 9.8 magnitudes, so given the assumed distance modulus to Ophi- uchus of 5.48, the absolute magnitude of the photosphere would have to be 4.3, which is brighter than we expect for young brown dwarfs without disks. Only 200 sources had > 3 σ detection at [24].

143 We required a 2 σ detection in [3.6] and a 2 σ detection in any one of [5.8], [8.0], or [24]. Only 14095 sources met this cut.

Sources had to demonstrate a 2 σ excess above both the photospheric [3.6] − [5.8] color and [3.6] − [8.0] color. We deﬁned the photospheric mid-IR colors of [3.6] − [5.8] = 0.08 and [3.6] − [8.0] = 0.21 [179]. Figure 7.5 shows this color cut. In total, 1558 sources met this color cut.

Note that the mid-IR excess threshold as deﬁned above is fairly liberal- sources marginally above the assumed photospheric emission threshold would be counted as mid-IR excess. This minuscule degree of excess could be consistent with no disk whatsoever and unusually red mid-IR colors. Our choice to set this liberal threshold was that the deep Spitzer imaging could detect exceptionally weak mid-IR excess. We would expect diskless young sources to be clustered around the intersection of the dashed and dotted lines in Figure 7.5. Anemic disks would occupy the region of color-color space between the diskless sources and the colored circles representing the Allers et al. [6] sources. Altogether 1407 sources met all of the above criteria consistent with mid-IR excess.

7.2.4.3 W − ﬁlter selection criterion

We used W −ﬁlter photometry to construct a selection for late-type objects. The extent of water absorption depends on the eﬀective temperature

Teﬀ . We quantiﬁed the degree of intrinsic water absorption with a Q parameter from the trio of J−, W −, and H− magnitudes (Allers et al. in prep.).

144 6

2 ] 0 . 8 [ − ] 6 . 3 [ 0

4 4 3 2 1 0 1 2 3 4 [3.6] [5.8] −

Figure 7.5 [3.6] − [5.8] vs [3.6] − [8.0] color plot, demonstrating the mid-IR excess selection criterion. The colored 2D histogram (Hess diagram) shows the density of 14095 sources in our sample possessing a 2 σ detection in [3.6] and a 2σ detection in at least one of [5.8], [8.0], or [24]. The horizontal dashed line is [3.6] − [8.0] = 0.21, the vertical line is [3.6] − [8.0] = 0.08 [179]. Sources meeting the criteria described in Section 7.2.4.2 are primarily in the upper right quadrant. Some sources with 3σ [24] detections in the other quadrants met our disk selection criteria based solely on their [24] detection. The large colored circles are all sources from Allers et al. [6].

The Q parameter is zero for no evidence of water absorption, and negative when water absorption is present. The water absorption is stronger for cooler photospheres- M6 has a Q value of about -0.5, and L0 has a Q value of about -1.0.

A total of 31348 sources (57.6% of the catalog) had W −band photometry. Since all sources in our catalog had J− and H− band photometry, all 31348 sources with a W −band measurement were issued a Q value. Figure

145 7.6 shows the histogram of the Q values.

We designed our W −band selection criterion around the value of the Q parameter. Sources met the W −band criterion if they were within the boundary −0.5 < Q < −2.5. Based on preliminary trials of the W − filter, we expected this range in Q values to correspond to roughly M6 to early L spectral types (Allers et al. in prep.). There were few sources with measurements of Q < −2.5, a number so low that we did not expect it to originate from photospheric absorption alone. Most of these were extremely low Q−value sources were attributable to noise. We required a 2 σ measurement of Q inside those bounds, where σ is the uncertainty in the Q value propagated from the photometric and calibration uncertainties in the W −band. A total of 1180 sources met the W −filter selection criterion. The number 1180 is 2.1% of the entire catalog, or 3.7% of those sources possessing a W −band detection. Figure 7.6 shows the selection boundaries as vertical lines in the histogram, with the fraction of sources meeting the criterion highlighted in a different shade.

7.2.4.4 H − [3.6] color selection criterion

We required the H − [3.6] color to appear redward of the assumed photospheric colors. We assumed photospheric colors from Patten et al. [179]. The motivation for this color cut was that extinction and mid-IR excess emission both act to increase H−[3.6]. In principle [3.6] can exhibit ﬁnite disk excess, as is seen in T − T auri stars. However, we expect brown dwarfs to exhibit negli-

146 104

103

N 10

101

100 6 4 2 0 2 4 6 Q

Figure 7.6 Histogram of the Q value derived from W −band photometry. The vertical dashed lines represent the boundaries of the selection method. The dark colored region region interior to the boundaries indicates the 4% of sources that were both detected in W −band and met the selection criteria. The measured Q−values had to be at least 2 σ within the boundaries on either side, excluding some low-signal to noise ratio sources with nominal values between the boundaries and causing the blue shaded histogram to be below the light shaded parent population histogram. gible excess at [3.6], based on radiative transfer models that show brown dwarf mid-IR excess detaches from the photosphere at wavelengths > 4 micron [62]. Our selection criterion required a [3.6] measurement, albeit at any signal-to- noise ratio. We required H − [3.6] + σ > 0.8, where σ is the photometric measurement uncertainty in H− and [3.6] bands added in quadrature. For objects with existing K− band photometry we further required K − [3.6] − σ > 0.49, where σ is the photometric measurement uncertainty in K− and [3.6] bands added in quadrature. All combined, 23112/54373 sources passed this crite-

147 rion. Note that we did not apply a signal-to-noise ratio cut on [3.6], which is evinced in Figure 7.7- sources with large measurement uncertainty still meet our criterion. Notice also that the K − [3.6] color cut is more stringent than the H − [3.6] color cut; the K − [3.6] demands a 1σ excess over 0.49, whereas the H − [3.6] can be merely consistent with 0.8.

10000 10000

8000 8000

6000 6000 N

4000 4000

2000 2000

0 0 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 H [3.6] K [3.6] − − Figure 7.7 H − [3.6] and K − [3.6] color cuts that comprise the “mid-IR photosphere” criterion. Left panel- The gray histrograms show the distribution of the 42268 sources in the catalog with a [3.6] measurement, while the colored histogram shows the distribution of sources with H − [3.6] consistent with 0.8 (dashed vertical line) or greater. The right panel shows an additional and more restrictive color cut applied only to the 18420 sources detected in both K− band and [3.6]: these sources had to have K − [3.6] exceed 0.49 (vertical dashed line) by 1 σ. The ﬁnal “mid-IR photosphere criterion” is the union of the color cuts in the left and right panels if K−band exists, otherwise it is just the sources satisfying the left panel.

Table 7.2 summarizes the four selection criteria and assigns the criteria abbreviated identiﬁcations (NIR, [3.6], W , and Disk) that will be used throughout the rest of the text. The Table lists the number of sources that

148 met each criterion, and the number of sources that were eligible to meet the criterion based on the availability of photometry. The last two columns list the fraction of the 54373-member source catalog meeting the criterion, and the fraction of sources that were eligible to meet the criterion, and did meet it.

7.2.5 Ranking the combinations of selection criteria

We carried out the I−band spectroscopy with IMACS [53] on the Baade 6.5 meter Magellan Telescope [217] at the Las Campanas Observatory. IMACS is an imager and multi-object specrograph that uses high-precision laser-cut slit masks to acquire optical spectroscopy over a 27.5 arcminute field of view. Six IMACS fields cover our photometric region (Figure 7.1), but we can only select . 100 slits per field. We therefore need to assign slits to sources based on a combination of our selection cuts and non-interference of spectra on the detector.

Table 7.3 shows our scoring system for translating combinations of our four selection criteria into priority for observation. There are 16 unique combinations of subsets of selection criteria; sources could meet all four criteria, three criteria (4 combinations), two criteria (6 combinations), only one criterion (4 combinations), or no criteria. The column Scores in Table 7.3 lists the combinations of criteria for 10 diﬀerent combinations of selection methods. The rank ordering of these combinations is the Priority column with 1 being the highest priorty for observation, and 10 being the lowest priority for obser-

149 vation. The Net Score column is the sum of the individual score values, and distinguishes the 16 possible combinations. Column IDs repeats the identiﬁers associated with each score, vis-`a-vis Table 7.2. The last two columns list the number of sources satisfying the combination of selection criteria.

For example, consider priority 2 sources. These sources satisﬁed the NIR, [3.6], and W criteria (scores 8, 4, and 2, respectively), but did not satisfy our disk selection criterion (score 1). The net score is 14. Twenty-seven sources satisfy this combination of selection criteria. We interpret these sources as diskless young brown dwarf candidates. Since they lack mid-IR excess indicative of a disk, they could also be foreground dwarfs or background dwarfs or giants. The higher possibility of contamination in this priority compared to priority 1 leads us to assign a lower rank than priority 1. We rank them above all the rest of the priority groups because the prospect of discovering diskless young brown dwarfs directly addressed our science question of whether or not disks around young brown dwarfs are longer lived than their T-Tauri star counterparts [198].

For another example, consider priority 3 sources. These sources sat- isfied the NIR, [3.6], and disk criteria (scores 8, 4, and 1, respectively), but did not satisfy our W −band selection criterion (score 2). The net score is 13. Seventeen sources satisfy this combination of selection criteria. Since these sources do not satisfy the W − filter selection method, they are ranked lower than those sources that meet all four selection methods (priority 1). They are also ranked lower than sources that meet the W − filter selection criterion, but

150 Table 7.3. Selection-priority scoring system

Priority Scores Net Score IDs N I < 21.6 N I > 21.6

1 1,2,4,8 15 Disk, W , [3.6], NIR 7 5 2 2,4,8 14 W , [3.6], NIR 27 138 3 1,4,8 13 Disk, [3.6], NIR 17 30 4 1,2,8 11 Disk, W , NIR 1 0 5 1,2,4 7 Disk, W , [3.6] 15 12 6 1,2 3 Disk, W 10 5 7 2,8 10 W , NIR 11 109 8 1,8 9 Disk, NIR 10 20 9 2,4 6 W , [3.6] 103 158 10 2 2 W 282 297 other - - - 53116 not the disk selection criterion.

In total, 483 sources had a top 10 observing priority. The other 6 combinations of criteria (net scores 0, 1, 4, 5, 8, and 12) were assigned priority 100, ten times lower priority than our priority 10 sources. These are listed in Table 7.3 as “other”.

7.2.6 Whittling down from 54373 to ∼500

Equipped with a prioritized list of candidates, we designed multi-object slit masks for IMACS. The MaskGen software2 takes a prioritized list of sources and optimizes the placement of slits for the highest number of high priority

2See http://code.obs.carnegiescience.edu/maskgen

151 sources. Our science goal required a wavelength range of ∼ 650 − 900 nm for broad-band spectral typing and Hα equivalent width measurement. Mea- surement of spectrally narrow gravity-sensitive features indicative of youth [127, 39, 43] was a top level requirement. This requirement imposed spectral resolution R ∼ 1000.

Availability of bright stars needed by the telescope active optics system for real-time primary mirror control constrained the available center positions and rotations of the masks. We settled on center positions that included the most priority 1’s, 2’s, and 3’s. Table 7.4 lists the slit masks used in this study.

152 Table 7.4. IMACS F/2 multi-object slit masks

Name N slits Obs. Dates Net Exp. time Filter Center RA & Dec. - # YYYYMMDD hours - J2000

153 nc200 75 76 20100617 2.50 spectroscopic-2 16:21:25 -23:26:42.5 southwes 72 20100617 2.00 spectrosopic-2 16:21:44.8 -24:08:45.5 southeas 45 20110707 2.25 5694-9819 16:22:36 -23:54:27 nc 2011 104 20110707 4.66 5694-9819 16:21:25 -23:26:42.5 sw 2011 101 20120513 3.58 WB6300-9500 16:21:44.8 -24:08:45.5 ophwes 25 20120513 0.76 WB6300-9500 16:21:29.3 -23:48:38.2 ophne 107 20120513, 20120514 4.38 WB6300-9500 16:21:58.1 -23:17:54.7 7.3 Spectroscopic observations 7.3.1 IMACS observations 7.3.1.1 Observing Dates and conditions

We acquired 530 spectra on six diﬀerent slitmasks over three years. Table 7.4 lists the observation dates and on-sky exposure time for all six of the masks.

7.3.1.2 Instrumental setup- special note on ﬁlters

We computed spectral response corrections by observing A0V stars and White Dwarfs. We normalized the spectra for the observed White Dwarfs LTT7987 and LTT3218 by their counterpart model spectra from Moehler et al. [163]. The A0V stars were normalized by a synthetic model. The normalized spectral response correction is dominated by a smoothly varying component (ﬁlters, grating blaze, etc) and sharp features (telluric atmosphere).

We used three different filters- “Spectroscopic 2”, “5694-9819”, and “WB6300-9500” (Table 7.4). The “Spectroscopic 2” filter had a short wavelength cutoff < 4000A,˚ which resulted in second order overlap for wavelengths longer than 8000A.˚ For our intrinsically red sources, this choice does not affect the spectra. However, the telluric A0V and White Dwarf calibrators are very blue, causing strong second order overlap. For the observations with this filter, we generated a synthetic spectral response correction. We computed an average spectral response from the 2012 observing season, observed through the “WB6300-9500” filter, which has a short wavelength cutoff of 6300 A˚ and

154 was therefore unaffected by second order overlap. We divided out the published filter response and multiplied back by the Spectroscopic-2 filter curve. We then applied this synthetic spectral response to the affected 2010 and 2011 spectra.

7.3.2 IMACS Multi-slit exposure 2D spectral extraction 7.3.2.1 Multi-object spectroscopy data reduction

We reduced the multi-object spectroscopy with the facility data reduction package Cosmos, version 2-163 [53], which includes an algorithm for optimal sky subtraction [115]. Cosmos maps each spectrum from the multi-slit exposure, beginning with the coarse optics model of the instrument. Cosmos iteratively refines the mapping solution to produce flat-fielded, sky-subtracted, rectified, 2D spectra for each slit. We wrote custom IDL scripts4 to automatically run through the Cosmos cookbook for all of the multi-slit exposures. Mapping solutions should be accurate to one-tenth of a pixel [53], we found mapping solutions were typically < 0.3 pixels.

The main challenge to extract 1D spectra from 2D spectra was to automatically identify low signal to noise ratio traces or handle traces distorted from poor 2D mapping. The spectral trace delivered by the Cosmos 2D spectral mapping is characterized by the pixel position of the center, and a rotation from the pixel x − y basis. The lowest signal to noise ratio traces were as-

3See http://code.obs.carnegiescience.edu/cosmos 4All of the code used for this paper is available on GitHub: https://github.com/ BrownDwarf/BAADE

155 signed the average center positions and rotations of the brightest traces, which worked fairly well at matching the visually identiﬁed traces for low signal to noise ratio spectra.

7.3.2.2 Performance of spectral type standards compared to literature

We observed several spectral type standards to demonstrate that we can reproduce the observed spectra of known late type sources. We observed an L2 dwarf, 2MASS J11553952-3727350 [197]; an M9 dwarf, 2MASS J15101685- 0241078 [197]; an L0pec, J00100009-2031122 [42]; and two young M7.75 members of Chamaeleon I, ChaHα1 and ChaHα7 [130]. We also observed the pair of low-mass wide binary brown dwarfs OPH1622-2405 a and b [4, 145]. Figure 7.8 overplots our observation of OPH1622-2405a with the spectrum provided by K. Luhman from Luhman et al. [145], with comparable spectral resolution of about 18 A.˚ We overplotted our spectra with published spectra. The spectra are virtually indistinguishable, except that the spectra from Luhman was not telluric corrected, whereas our spectra were telluric corrected. The vertical gray bands indicate regions of known atmospheric absorption. The other standard star spectra show comparable levels of agreement between their existing published spectra and our observations. In a few cases the spectral slopes disagreed slightly, pointing to wavelength-dependent slit losses either in the published spectra or ours. Based on the excellent accord in our spectra and published spectra, we are conﬁdent in all of the spectral response corrections and extraction strategies we applied.

156 this work Luhman et al. 2007 2 t n a t s n o c

+ 1 λ F

0 6500 7000 7500 8000 8500 9000 λ ( )

Figure 7.8 Direct comparison spectra of the M7.25 young brown dwarf OPH1622-2405a, observed with IMACS from this work (solid blue line), and provided by K. Luhman (dotted black line, Luhman et al. [145]). The regions of telluric atmospheric absorption are indicated with light gray vertical bands.

Single pixel defects were also conspicuous in some of our comparison spectra. These defects are mostly uncorrected cosmic rays. Prominent in low signal-to-noise ratio spectra, the cosmic rays are about 10 to 20 times the typical pixel-to-pixel variance. It is easy to identify these as cosmic rays during visual comparison. However, automated spectral analysis like equivalent width measurements and continuum estimation can be aﬀected by these large outliers. We employ robust algorithms (e.g. median instead of mean) when available, and manually ﬂag pixels when needed.

157 Of the 530 slits on the seven slit masks (Table 7.4), 505 spectra passed through spectral reduction with Cosmos. The other 25 were not reduced mostly because they fell on chip gaps or were irretrievable.

7.4 Spectral and photometric analysis 7.4.1 Spectral classiﬁcation with The Hammer

We visually inspected the IMACS I−band spectra for evidence of broad- band molecular absorption in the region 6500 < λ(A)˚ < 9000. The broad FeH, VO, and TiO bands are characteristic of late M spectral types, and are conspicuous even in low resolution (R ∼ 100) low signal-to-noise ratio (S/N > 5) spectra. To accelerate the process of visually classifying hundreds of spectra, we employed Version 1.2.5 of The Hammer spectral typing code [39, 239]. The Hammer first computes a machine spectral type based on several spectral type sensitive indices. Then The Hammer overlays user-selectable comparison spectra, which can be visually matched to the overall spectral shape. The Hammer does not have a mechanism for tuning the extent of wavelength-dependent extinction, so since some of our sources are reddened, matches to the observed spectra may lead us to overestimate the spectral type. This overestimate is okay, since we only use this first pass as a coarse filter for both signal-to-noise ratio (S/N > 5), and overall spectral shape (consistent with M0 or later). If the spectral shape is inconsistent with an M or L spectral type, we discard the spectrum from our follow up sample. If there is evidence for an M or L spectral shape, we assign a coarse spectral type that we will later use to coarsely

158 estimate the extinction.

7.4.2 Whittling down from 505 spectra to 71 late-type sources

The 505 reduced spectra covered 416 unique targets. The redundant observations came from the target reappearing on different masks in different years, since the slit mask fields occasionally overlapped. In total, 337 were observed only once, 69 were observed twice, and 10 were observed three times. None were observed more than three times. We elected not to coadd these spectra since many duplicate observations had one spectrum that was much higher signal to noise ratio than the other and repeats allowed us to look at variability (e.g Hα) from year-to-year. The duplicates allowed us to quantify repeatability and variance in our spectral estimators.

We reduced the number of observed spectra from 505 to 92 by rejecting spectra that do not show evidence of an M or L spectral classiﬁcation. We matched the 92 M or L spectra with their 71 unique targets and picked the best spectrum. These 71 sources deﬁne the follow up sample.

More than half of the spectra that were rejected had S/N < 8. About 5 of these rejects were due to the most egregious cases of instrumental artifacts in the MOS spectral mapping. In those cases, we went back to visually inspect the 2D trace to convince ourselves that the traces were inconsistent with M or L spectral types. Slitmask ophwes (Table 7.4) exhibited a large fraction of unusable spectra since since it only received ∼ 45 minutes of on- sky observing time due to a weather closure. The lion’s share of the rejects

159 were spectra consistent with FGK stars (evinced by calcium triplet lines), or unknown interlopers.

7.4.3 Extinction

Reddening most likely leads us to conclude a spectral type 1 to 3 subtypes later than we ought to [11], assuming an AV . 10. We assign an intrinsic J −H for each of the 71 follow up sources based on their first pass coarse spectral type from The Hammer. We use J − H, since some sources were missing I− band measurements. We calculated the median and standard deviation of the intrinsic J − H as a function of spectral subtype from M0−L5 using data from field dwarfs [239, 58]. We converted between 2MASS and MKO photometric systems where appropriate. The spread in intrinsic J − H is fairly large (∼ 0.1), which propagates into our uncertainty in the reddening estimate. Sources with J − H bluer than field dwarfs for their spectral type were assigned zero extinction. Otherwise, an AJ was estimated from the E(J − H).

AJ was converted to AV assuming an RV = 3.1. The range in AV is about

0−7, which is consistent with the AV spread observed towards this region with

2MASS [126]. The typical uncertainties were about σAV ∼ 1.0 which includes the contribution from the uncertainty in the intrinsic J − H and photometric uncertainties.

We revised our extinction estimate for the sources identiﬁed as members. For these sources we de-redden to J − H as a function of spectral type reported in Pecaut and Mamajek [182]. We interpolated between points in

160 cases of non-integer spectral subtypes.

7.4.4 Second pass spectral type

We dereddened all spectra by their estimated extinctions. The dereddened spectra were once again visually classiﬁed with The Hammer. Figure 7.9 shows the visual spectral type assigned before and after de-reddening. The dashed line shows the 1-to-1 line obeyed by spectra of modest or no reddening. A small 0.1 subtype jitter has been added to see the overlapping plot markers. Sources with AV > 3 initially show as high as 3 spectral subtype misclassiﬁcation based on the de-reddened spectra.

For most sources, the second pass spectral type is the ﬁnal spectral type we assign. Since the J − H value to which we deredden is fairly constant from M4−M9, there is little to gain by re-estimating the extinction from the revised spectral type.

7.4.5 Spectral comparison sample

We assembled a spectral comparison sample to quantify the gravity- sensitivity of spectral diagnostics as a function of spectral type. The spectra of dwarfs, giants, and young stars show differences because of their different surface gravities [208]. A sufficiently large comparison sample will allow the quantification of the spread in spectral indices as a function of spectral type (proxy for temperature) and surface gravity (proxy for age). The scatter in the spectral indices is important to assign uncertainties in our final age and

161 14 6.4

12 5.6

4.8 10

4.0 8

3.2 V A 6 2.4

Observed Spectral Type (M0=0) 1.6

2 0.8 1:1 +2 offset 0 0.0 0 2 4 6 8 10 12 14 Dereddened Spectral Type (M0=0)

Figure 7.9 Comparison of first- and second- pass visual spectral classification of the 92 spectra with evidence of M or L spectral classification. The one-to-one line is shown in long dashes. Jitter has been added to the spectral subtypes to ease comparison of multiple overlapping sources. The color bar indicates the amount by which each spectrum was de-reddened. membership classifications.

We constructed the spectral comparison sample from the RIZzo database [44], which includes 803 sources- 135 giants, 29 intermediate gravity sources [43], and 639 other sources which are mostly old ﬁeld brown dwarfs or very low mass stars, but contains a few other interlopers and peculiar spectra. Since the vast majority of the 639 other sources are ﬁeld brown dwarfs, we treat all of

162 them as such. We crossmatched the RIZzo sample with Simbad to verify their spectral classiﬁcations. A minuscule fraction of the sources had spectral types discordant by more than 1 subtype. We made no attempt to remove these sources, since we are only using the aggregate properties of the comparison sample.

7.4.6 Gravity sensitive indices

The gravity sensitive Na I line at 8200 A˚ is one indicator of whether our candidate young brown dwarfs are indeed young [127, 39, 43]. Figure 7.10 shows the spectral type versus pseudo equivalent width of the Na I line. The continuum is ill-deﬁned at low spectral resolution in our heavily line-blanketed spectra in the wavelength region of interest. Nevertheless, the index clearly distinguishes between dwarfs and giants taken from the RIZzo comparison sample. The dwarfs (red circles in Figure 7.10) demonstrate a pseudo equivalent width of about 6 A˚ by M8 spectral type, while giants (blue circles in Figure 7.10) reach values of about -2 A˚ at M8. The low spectral resolution and choice of feature indices yield negative Na I pseudo equivalent widths for the giants for spectral types later than M4.

Based on the observed Na I index alone, thirty-one sources (green boxes)in our survey are consistent with low surface gravity suggestive of youth. We adopted the continuum and feature indices deﬁned by Schlieder et al. [208], a central wavelength λc = 8190A˚ and measurement window δλ = 22A.˚ We assigned an uncertainty σEW to the equivalent width by adding in quadrature

163 8

4 ) (

W 2 E

a N 0 Dwarfs Giants 2 Int. Gravity BPMG Na I young 4 Na I old

0 2 4 6 8 10 12 14 Spectral Type (M0=0, L0=10)

Figure 7.10 Na I 8190 equivalent width as a function of spectral type from M0 to L5. The sequence shows a clear bifurcation, splitting into groups of relatively high surface gravity (dwarfs, red points at the top), and low surface gravity (giants, blue points at the bottom). Objects classified as intermediate gravity [43] are shown as purple circles. Young 10−20 Myr sources in the Beta Pictoris moving group (BPMG, Schlieder et al. [208]) are shown as large orange circles. The dotted black line shows the median of the field dwarfs in Rizzo. The solid black line excludes 90% of the field objects, and defines our criterion for Na I EW indicative of youth. The green squares are young brown dwarf candidates from this work that meet the youth criterion. The brown triangles are sources that do not meet the criterion for youth. the uncertainty in the mean of the feature and continuum values. We defined a Na I youth detection as 3σEW below the bottom 10% of Na I equivalent width values of RIZzo dwarfs for a given spectral type. The 10% boundary is shown as a solid line in Figure 7.10. We also overplot the Na I EWs of Beta Pic moving group members tabulated in Schlieder et al. [208]. Our Na I EW threshold cuts out some sources in the 10-20 Myr Beta Pic moving group [208] at spectral types M3 and earlier. Our spectra demonstrated a range of spectral

164 types from M0 to L0. The Na I EW is ineﬀective at distinguishing gravity for M0 to M3 at our spectral resolution. We also compared the Na I EWs for our sample to those for members of Upper Scorpius [222]. We converted the ratio computed in their Table 1 to an equivalent width, and found a range of about 0.6−4.2 A˚ for spectral types M5 to M8, comparable to the range we see.

7.4.7 Hα emission

We computed the Hα equivalent width using a 22 A˚ width centered on 6563 A,˚ with continuum indices from 6530−6540 and 6570−6580 A.˚ We assigned an uncertainty to the equivalent width in the same way as we did for Na I- adding the uncertainty in the means of feature and continua values in quadrature. We report the measured Hα equivalent width in Table 7.7. The presence of Hα alone is not enough to establish a source as young, since > 40 % of ﬁeld M dwarfs later than M4 exhibit Hα emission indicative of activity, with the fraction active approaching 80% by spectral type M9 [239].

7.4.8 Eﬀective Temperatures

We use the [141] eﬀective temperature scale for spectral types M1-M9.

For M0 we assume Teﬀ = 3770 [182]. We ignore sources with spectral types earlier than M0. For sources with non-integer spectral substypes, we linearly interpolate between adjacent integer subtypes. We assign an uncertainty in temperature of 150 K which is the uncertainty of the spectral classiﬁcation (±1 subtype). The systematic uncertainty in the temperature scale is even

165 larger, as noted by Pecaut and Mamajek [182] and Rice et al. [202].

7.4.9 Luminosities

We computed luminosities for all 71 sources with late M or L spectral types. We computed absolute magnitudes assuming a distance of 125 pc [125], and using the apparent J− magnitudes corrected for extinction and J−band bolometric corrections. For spectral types M5 or earlier we used BCJ reported by [182]. For spectral types M5.5 and later we used the mean BCJ per spectral type bin reported in Dahn et al. [48]. We linearly interpolated between data points for fractional spectral subtypes not reported in either Dahn et al. [48] or Pecaut and Mamajek [182].

7.4.10 Extinction and position in the HR Diagram

Equipped with derived eﬀective temperatures and luminosities, we placed all 71 late type sources on an HR diagram. Figure 7.11 shows the HR diagram with the pre-main sequence (PMS) evolutionary model tracks of [18, 19]. The dotted lines are logarithmically spaced model isochrones from 1 Myr to 1 Gyr.

The solid black lines show the evolutionary track for sources down to 20 MJup. The key idea from this Figure is that our sample is split into two populations- those below the main sequence and those above the main sequence. Below the main sequence, sources are likely to be more distant background dwarfs. Alternatively, a source can have a position in the HR diagram below the main sequence if it has a nearly edge-on disk. These sources would have evidence

166 for a mid-IR excess. Sources OPH 349 and OPH 2 are potential edge-on disk sources. Sources above the main sequence could also possibly be in the foreground, so membership assignment also requires evidence of low surface gravity from the optical spectroscopy. We define 16 sources define as members, based on a holistic review of each object in terms of its position on the HR diagram, indication of extinction, evidence of strong Hα emission, previous character- izations from the literature, presence of mid-IR excess emission indicative of a disk, and presence of weak Na I EW. The holistic approach means that all pieces of available evidence were considered together, and membership was decided taking into account missing or noisy data. Tables 7.5 and 7.6 list the near-IR photometry and mid-IR photometry for the 16 sources that we define as members. Table 7.7 lists their derived properties.

167 Table 7.5. Photometry from this work

Name RA DEC Alt. Names Ref. QIJHK

2mx 10919 245.45202 -23.67426 2M J16214848−2340273, (1,2) -0.91±0.15 17.50±0.01 13.59±0.03 12.34±0.03 11.69±0.02 [AKC2006] 9, [EDJ2009] 740 2mx 12644 245.56067 -23.78650 ...... -0.27±0.07 16.19±0.01 12.85±0.03 11.89±0.02 11.41±0.03 2mx 14856 245.68725 -23.28707 2M J16224494-2317134, (1,2,6) . . . 17.07±0.01 13.68±0.03 12.74±0.02 12.25±0.03 [AKC2006] 13, [EDJ2009] 748 2mx 10360 245.41609 -23.19431 ...... -0.85±0.05 15.75±0.01 12.50±0.03 11.57±0.02 11.12±0.02 OPH 673 245.42743 -23.60256 ...... -0.91±0.07 19.68±0.01 15.04±0.01 13.97±0.01 13.25±0.01 OPH 674 245.59602 -24.11968 ...... -0.67±0.01 18.96±0.01 14.80±0.01 13.83±0.01 13.18±0.01 168 OPH 678 245.31862 -24.29600 ...... -0.69±0.01 18.42±0.01 14.81±0.01 13.96±0.01 . . . OPH 675 245.31889 -23.60123 ...... -0.86±0.07 17.35±0.01 13.77±0.01 12.94±0.01 . . . 2mx 8891 245.32603 -23.18708 ...... -1.09±0.05 15.33±0.01 12.25±0.03 11.43±0.02 10.96±0.02 2mx 14049 245.64313 -23.38955 ...... 16.02±0.01 12.45±0.02 11.64±0.02 11.23±0.02 OPH 679 245.25929 -23.97774 2M J16210222−2358395 (3) -0.73±0.01 18.27±0.01 14.63±0.01 13.79±0.01 13.25±0.01 OPH 681 245.81346 -23.78497 ...... -1.09±0.06 . . . 15.10±0.01 14.21±0.01 13.56±0.01 OPH 349 245.49823 -23.26736 [JJK2008] (4) -0.58±0.02 19.25±0.01 16.32±0.01 15.67±0.01 15.36±0.01 J162159.55−231602.5 OPH 12081 245.39963 -23.91767 2M J16213591−2355035, (5) -1.06±0.01 17.10±0.01 13.79±0.01 13.16±0.01 12.72±0.01 [SCH2006] J16213591- 23550341 OPH 2 245.56548 -23.50553 ...... -1.01±0.12 20.66±0.07 17.63±0.02 17.09±0.02 16.90±0.04 OPH 672 245.56064 -23.95042 ...... -1.03±0.03 18.48±0.01 14.62±0.01 13.91±0.01 13.36±0.01

Note. — Q is the degree of water absorption in the W −ﬁlter band. The source names containing “2mx” are from the 2MASS JH catalog. The sources with “OPH” are from the ISPI JH catalog.

References. — (1) Allers et al. [6] (2) Evans et al. [64] (3) Luhman and Mamajek [136] (4) Jørgensen et al. [113] (5) Slesnick et al. [222] (6) Harvey et al. [94] Table 7.6. Mid-IR Photometry from this work

Name [3.6] [4.5] [5.8] [8.0] [24]

2mx 10919 10.89±0.05 10.44±0.05 10.02±0.01 9.13±0.01 4.88±0.10 2mx 12644 10.95±0.05 10.84±0.05 10.71±0.01 10.66±0.01 10.35±0.83 2mx 14856 11.58±0.05 11.26±0.05 11.02±0.01 10.35±0.01 7.83±0.11 2mx 10360 10.74±0.05 10.64±0.05 10.55±0.01 10.47±0.05 10.07±0.44 OPH 673 12.53±0.05 12.39±0.05 12.18±0.01 12.19±0.01 . . . 169 OPH 674 12.54±0.06 12.40±0.05 12.26±0.01 12.26±0.01 . . . OPH 678 12.81±0.05 12.74±0.06 12.57±0.07 12.45±0.01 <8.5 OPH 675 11.87±0.05 11.71±0.05 11.61±0.01 11.59±0.01 9.94±0.49 2mx 8891 10.54±0.05 10.44±0.05 10.32±0.05 10.28±0.05 10.49±0.88 2mx 14049 10.80±0.06 10.67±0.05 10.63±0.02 10.53±0.01 10.10±0.59 OPH 679 12.65±0.05 12.52±0.05 12.37±0.01 12.36±0.01 <9.6 OPH 681 12.95±0.05 12.73±0.05 12.52±0.02 12.47±0.02 10.55±0.91 OPH 349 14.96±0.06 13.85±0.06 12.53±0.01 11.96±0.01 7.17±0.10 OPH 12081 12.20±0.05 12.12±0.05 11.94±0.01 11.89±0.01 10.25±0.75 OPH 2 16.05±0.08 15.07±0.08 13.85±0.02 12.25±0.02 8.88±0.20 OPH 672 12.72±0.05 12.65±0.06 12.51±0.01 12.44±0.01 <8.1 10-1 0.09 non-members 0.08 members 0.0750.0720.07 0.06 0.055 0.05 0.04 10-2 0.03 ¯

L 0.02 / L

10-3

10-4 3400 3200 3000 2800 2600 2400

Teff(K)

Figure 7.11 Pre main sequence HR diagram indicating membership of young very low mass stars and brown dwarfs to Ophiuchus. The green circles are members based in part on their position in this diagram. The red squares are sources without evidence for membership, or evidence of non-membership. Sources OPH 349 and OPH 2 are edge-on disks, based on the presence of mid- IR excess, suppressed near-IR and optical colors, and their apparent position below the main sequence in this diagram.

7.4.11 Spectral Energy Distributions

We explored the diversity of mid-IR excess emission properties by con- structing spectral energy distributions (SEDs). Figures 7.12 and 7.13 show the SEDs for the 16 members in our sample. Many of the sources identiﬁed as young, low-mass objects do not appear to have mid-IR excess, despite meeting the disk criterion for selection. Often, such sources met the selection criterion because they were detected at 24 µm. When designing the survey, we targeted the lowest luminosity young brown dwarfs, which should not have detectable

170 photospheres at 24 µm at the distance of Ophiuchus. The sources we detected are typically warmer and more luminous than our prediction for M8 sources, so we can detect photospheric 24 µm emission in some of them.

7.5 Results 7.5.1 Whittling down from 71 to 16

We adopted a holistic approach to assigning membership to the 71 targets with late-type spectra to arrive at 16 sources with confident evidence for membership. An additional 3 sources are consistent with membership, but have spectral types M4 or earlier, which makes their Na I equivalent widths difficult to distinguish between dwarfs and YSOs. The remainder of targets have evidence for high gravity features and/or are below the main sequence line and are therefore deemed dwarf contaminants. Table 7.7 lists the derived properties for the final sample of 16 members.

171 2mx_10360 2mx_12644 2mx_10919 Teff = 3130 K Teff = 3130 K Teff = 3130 K 100

10-1

10-2 d

n 2mx_8891 OPH_675 2mx_14049 a

b Teff = 3060 K Teff = 3060 K Teff = 3060 K −

H 0

10 t a

d e z i l -1

a 10 m r o N

ν -2

F 10

2mx_14856 OPH_678 OPH_349 Teff = 3020 K Teff = 3020 K Teff = 2990 K 100

10-1

10-2 100 101 100 101 100 101 λ(µm) λ(µm) λ(µm)

Figure 7.12 Spectral energy distributions of 9 members with spectral types M5−M6. The gray circles show the observed photometry. The green squares show the photometry corrected for the extinction value derived from the first- pass spectral typing. Both the observed and extinction-corrected photometric data have been normalized by the extinction-corrected H−band measurement. The red dotted line shows the blackbody with temperature equal to Teff for each source. The observed photometry is sometimes below the blackbody photosphere, since the photospheric spectra for the cool sources differ substantially from blackbody sue to molecular species in their atmospheres.

172 OPH_2 OPH_679 OPH_674 Teff = 2990 K Teff = 2940 K Teff = 2880 K 100

10-1

10-2 d

n OPH_12081 OPH_672 OPH_673 a

b Teff = 2880 K Teff = 2630 K Teff = 2560 K −

H 0

10 t a

d e z i l -1

a 10 m r o N

ν -2

F 10 100 101 100 101 OPH_681 λ(µm) λ(µm) Teff = 2560 K 100

10-1

10-2 100 101 λ(µm)

Figure 7.13 Spectral energy distributions of 7 members with spectral types M6−M8.5. The plots have the same symbols and scaling as in Figure 7.12.

173 Table 7.7. Spectral classiﬁcation and derived properties of our sample

Name Priority Sp. Type AV Teﬀ log L/L Hα EW Na I EW SED Class Night K A˚ A˚ YYYYMMDD

2mx 10919 1 M5 7.1 3130 -1.4 -126.8 22.0±0.3 II 20120513 2mx 12644 8 M5 4.1 3130 -1.4 -7.9 2.1±0.1 III 20120513 2mx 14856 3 M5.75 4.0 3020 -1.8 -8.3 2.4±0.1 II 20120513-4 2mx 10360 7 M5 3.8 3130 -1.3 -6.5 2.8±0.1 III 20120513-4 OPH 673 5 M8.5 4.1 2560 -2.3 -13.9 4.3±0.1 III 20120513 OPH 674 5 M7 4.4 2880 -2.2 -13.2 3.5±0.1 III 20100617

174 OPH 678 5 M5.75 3.6 3020 -2.3 -4.8 3.5±0.1 III 20120514 OPH 675 5 M5.5 3.4 3060 -1.9 -7.2 2.8±0.1 III 20120514 2mx 8891 7 M5.5 2.9 3060 -1.3 -6.1 2.2±0.1 III 20120513-4 2mx 14049 8 M5.5 2.8 3060 -1.4 -6.7 2.3±0.1 III 20120513-4 OPH 679 5 M6.5 3.2 2940 -2.2 -7.4 3.6±0.2 III 20120513 OPH 681 5 M8.5 2.3 2560 -2.5 -6.5 1.0±0.2 III 20110707 OPH 349 4 M6 1.5 2990 -3.1 -8.6 2.1±0.1 EO 20100617 OPH 12081 6 M7 1.0 2880 -2.1 -7.9 2.8±0.1 III 20110707 OPH 2 1 M6 0.4 2990 -3.7 -44.5 1.7±0.1 EO 20120514 OPH 672 5 M8.25 0.9 2630 -2.5 -16.6 1.9±0.2 III 20110707

Note. — Typical uncertainties are about 0.2 in AV , 150 K in Teﬀ , 0.2 dex in luminosity, and 0.1 A˚ in EW. The SED Class refers to the mid-IR slope, with “EO” indicating edge-on disks. 7.5.2 Discussion of individual sources

10 OPH_2 M6

9 OPH_349 M6

8 OPH_678 M5.75

7 2mx_14856 M5.75

t 6 n 2mx_14049 a t

s M5.5 n o c

λ 5 F OPH_675 M5.5

4 2mx_8891 M5.5

3 2mx_10919 M5

2 2mx_12644 M5

1 2mx_10360 M5

0 6500 7000 7500 8000 8500 9000 λ ( )

Figure 7.14 IMACS spectra of 10 very low mass YSOs or young brown dwarfs towards Ophiuchus with spectral types M5-M6.

Figures 7.14 and 7.15 show the spectra of the M5−M6 and M6−M8.5 sources consistent with membership to Ophiuchus.

175 8

6 OPH_681 M8.5

5 OPH_673 M8.5 t n a t s n

o 4

c OPH_672

M8.25 λ F

3 OPH_12081 M7

2 OPH_674 M7

1 OPH_679 M6.5

0 6500 7000 7500 8000 8500 9000 λ ( )

Figure 7.15 IMACS spectra of 5 young brown dwarfs with spectral types M6−M8.5. Same scaling as in Figure 7.14.

2mx 12644 shows a spectral shape comparable to the 2 Myr M5 source T50 [130], with comparably weak Na I absorption. It has modest Hα, although

176 not substantially more than active M dwarfs [239].

2mx 10919 was discovered in Allers et al. [6] (their source 9), and was given a spectral type of M5.5 by Gully-Santiago et al. [86]. Its IMACS spectrum is unluckily missing the portion of spectrum surrounding the 8200 A˚ Na I line, but its youth and membership are ﬁrm based on the presence of mid-IR excess and signiﬁcant Hα emission, as well as the NIR spectrum from Gully- Santiago et al. [86]. We issue 2mx 10919 a spectral type of M5, based on its similarities with T50. 2mx 10919 also has the largest estimated extinction of any source, supporting our interpretation that it is a member of Ophiuchus.

2mx 10360 has spectral features very similar to T50, so we assign an M5 spectral type, and membership to Ophiuchus based on its weak Na I absorption.

2mx 8891 has a spectrum most similar to chxr84, an M5.5 member of Chamaeleon I [130], with comparable Na I. Its Na I is much weaker than the M5.5 dwarf 2MASS J11245327+1322533 [41].

OPH 675 has an M5.5 spectral type based on comparison to the same comparison sources as 2mx 8891. OPH 675 has a slightly deeper appearance of the Na I line than chxr84 does, but still much less than 2MASS J11245327+1322533, so we assign it youth and therefore membership. Un- corrected telluric absorption in the comparison spectra could contribute to the slightly deeper appearance of Na I in our spectra versus those of Luhman and RIZzo.

177 2mx 14049 looks almost identical to OPH 675.

OPH 678 looks most similar to ChaHα6 [130], an M5.75. OPH 678 has slightly deeper Na I than ChaHα6 does, but much shallower than ﬁeld M5.5 2MASS J11245327+1322533.

2mx 14856 was discovered by Allers et al. [6] (their source 13), with spectral type M6 from Gully-Santiago et al. [86]. It has mid-IR excess indicative of a disk. Further, its weak Na I and moderate Hα support its youth. Its IMACS spectral type is most similar to ChaHα6, so we assign it spectral type M5.75.

OPH 679 has a low signal-to-noise ratio spectrum. Its spectrum is comparable to the Cha I M6.5, iso138 [130], with much less Na I absorption than 2MASS J14450627+4409393 [41]. OPH 679 is listed as an M5.25 Upper Sco member, source 2MASS J16210222−2358395 in Luhman and Mamajek [136], though no spectrum for it has been published.

OPH 673 also has a low signal-to-noise ratio spectrum. Its spectral shape and Na I absorption are comparable to the M8.5 KPNO06 [27, 141]. At this late spectral type, the dwarf comparison spectra exhibit Na I comparable to their young counterparts, so assigning youth is more challenging. Still, the Na I line strength in OPH 673 and KPNO06 is noticeably shallower than M8.5 dwarf 2MASS J16141557+8211327 [42]. We tentatively assign it as a member.

OPH 674 resembles Cha I M7 11123099-7653342 [130]. The Na I line is suﬁciently weaker than 2MASS J04365019-1803262 [42], so we assign OPH 674

178 as amember.

The spectrum of OPH 681 is most similar to M8.5 KPNO06 [27, 141], and ﬁrmly weaker than M8.5 V 2MASS J13235206+3014340 [42].

OPH 1 and OPH 3 were not above the main sequence for their derived Teﬀ and Lbol, but exhibited apparent mid-IR excess in IRAC band 4. We examined the IRAC band 4 imaging and found that the IRAC4 detections were consistent with spurious structure from cloud nebulosity. OPH 3 exhibits strong Na I and K I absorption for its M3 spectral type. The Na I absorption cannot be reliably distinguished between OPH 1 and dwarfs of the same spectral type. Nevertheless, their underluminosity and refuted evidence for a disk lead us to mark these sources as background objects (given their extinction).

OPH 2 has dramatically rising mid-IR excess emission. The low signal- to-noise ratio spectrum of OPH 2 is most similar to that of Cha I M6 chsm1982 [130], and has a clear indication of youth from its weak Na I line. The moderate Hα supports its youth. Its apparent position below the main sequence leads us to demarcate OPH 2 as an edge-on disk, and therefore a member.

By the same logic applied to OPH 2, OPH 349 is also an edge-on disk. Speciﬁcally, its prominent mid-IR excess and apparent position below the main sequence are strong evidence for being edge-on disks. The spectrum is consistent with an M6 spectral type classiﬁcation, with Na I comparable to that of CHSM1982. The Hα is weak in this source.

OPH 12081 was identiﬁed as a M6 member of Upper Scorpius by Slesnick

179 et al. [222]. We assign it a spectral type of M7 based on its similarity to Cha I M7 11123099-7653342 [130].

OPH 672 is most similar to M8.25 KPNO 7 [27, 141], with a similar amount of Na I absorption.

Sources 2mx 10500, 2mx 10966, and 2mx 9647 have spectral types M4 or earlier. We leave these sources out of our member list since they are more likely low mass stars than brown dwarfs.

2mx 9647 is the earliest spectral type source that meets either of our youth criteria. It is consistent with a spectral type earlier than M1. We assign it an M0 spectral type, though it could be a late K type. There is no evidence of accretion, and the source does not have evidence for mid-IR excess. The source is above the main sequence and demonstrates an AV of 3.8, so we reject the interpretation that it is a foreground object. Still, we cannot conﬁdently assign evidence of youth based on the spectrum, so we mark this source as a candidate.

2mx 10966 has an M4 spectral type with modest Hα emission. The Na I equivalent width is weak- more similar to Hn17 [130], than 2M J05102396- 2800539 [42], but only marginally so. We mark this source as a candidate.

The youth of 2mx 10500 is ﬁrm based on mid-IR excess, its weak Na I equivalent width, and its AV ∼ 2.7 and position above the HR diagram. Its moderate Hα lends support to its youth and therefore membership. Its Na I is weaker than M4V 2MASS J02193311+1416327 [41], and comparable to the

180 2 Myr M4 Hn17 [130].

7.5.3 Edge-on disks

Figures 7.12 and 7.13 include the conspicuously rising SEDs of sources OPH 349 and OPH 2. These sources demonstrate mid-IR flux increasing with wavelength from 3.6 to 24 µm. The sources fall below the main sequence in the HR diagram, indicating that these sources are most likely heavily- extincted edge-on disks with near-IR colors determined by a mixture of scattering and extinction. The IMACS spectrum of OPH 2 shows strong Hα emission. OPH 349 is separated by 4” from OPH26571. Figure 7.16 shows the postage stamp images of the pair in different bands. [113] identified OPH 349 during their search for deeply embedded YSOs. This source is included in their list of candidate edge-on disks, since it exhibited very red mid-IR colors but no associated SCUBA flux.

Figure 7.16 Images of OPH 349 with the nearby OPH 26571. Images are from left to right: MOSAIC I−band, [3.6], [8.0].

181 7.5.4 Mid-IR colors of diskless members

We looked at the distributions of the mid-IR slope of our sample to distinguish between the diskless and disk-bearing members. We include in our analysis the mid-IR data of 187 Class I, II, and III Taurus members with spectral types later than M0 [148]. The large number of Taurus members allows us to construct a kernel density estimate in a plot of [3.6] − [8.0] versus spectral type, shown in Figure 7.17. The marginal distribution of [3.6] − [8.0] reveals two populations: a presumably diskless group of sources with [3.6] − [8.0] ∼ 0 and disk-bearing sources with [3.6] − [8.0] ∼ 1.5. The valley in- between the disk-bearing and diskless sources can be understood as evidence for a short-lived phase of disk-clearing [64]. All of the Allers et al. [6] sources (black circles in Figure 7.17) were selected for evidence of mid-IR excess, they appear in the upper branch with [3.6]−[8.0] ∼ 1.5. Most of our sources (white squares in Figure 7.17) appear in the lower branch with [3.6] − [8.0] ∼ 0. The source 2MASS J16214199−2313432, an M3 [86], has [3.6] − [8.0] = 0.79 ± 0.2 placing it in the valley between the two clusters of disk bearing and diskless objects. This source might be the only “transition disk” out of the Allers et al. [6] sample and our sample. Despite being sensitive to them, we ﬁnd no sources in this valley, a feature that extends into the sub-stellar regime. We take this observation as evidence that whatever the mechanism for disk-clearing is, it proceeds similarly in the sub-stellar regime as it does for stellar objects.

We used the class III analogs in our sample to construct mid-IR photospheric colors of late-type sources. Luhman et al. [148] construct the pho-

182 4 OPH_2 this work Allers et al. 2006, (Ophiuchus) 3 OPH_349

] 2 0 . 8 [ − ] 6 . 3 [ 1

1 0 2 4 6 8 10 Spectral Type (M0 = 0)

Figure 7.17 Distribution of [3.6]− [8.0] as a function of spectral type for young stellar and substellar objects in this work (white squares with black edges). The distribution of 187 Class I, II, and III Taurus members with spectral types later than M0 [148] is shown as the kernel density estimate contours in the background. The black circles with white edges are the 8 sources towards Ophiuchus from Allers et al. [6] with spectral types from Gully-Santiago et al. [86]. The white dashed line is constructed from Class III young stellar and substellar objects in η Cha, Cha, and TWA [148], and represents the photospheric colors of young objects. The two edge-on disks OPH 2 and OPH 349 are outliers in this plot. The two disk-bearing sources are 2mx 10919 and 2mx 14856. The other 12 members are diskless sources. tospheric colors of young objects as a function of spectral type with evolved class III objects in η Cha, Cha, and TWA5. We extend the relationship of Luhman et al. [148] with more late-type sources by combining our sam-

5The original table with these values contains an error, see the erratum in [149]

183 ple with theirs. The Luhman et al. [149] sample includes 7 Class III sources with spectral type later than M8: J04272799+2612052, J04274538+2357243, J04302365+2359129, J04354526+2737130, J04355143+2249119, J04373705+2331080, J04574903+3015195. This work adds 3 new Class III sources with spectral types later than M8. The colors are consistent with the Luhman et al. [149] sample, with a mean [3.6] − [8.0] = 0.3 for M8.5 spectral types. For comparison, M0−M2 sources have [3.6] − [8.0] < 0.1. Figure 7.18 shows a close-up on the mid-IR colors of old ﬁeld dwarfs [179], young Taurus members [148], and Ophiuchus members from [6] and this work. The increasing bifurcation between the background density of Taurus Class II and Class III sources as a function of wavelength can be understood as the mid-IR excess detaching from the photosphere.

7.6 Analysis 7.6.1 Have we found diskless YBDs?

One of the main results of this work is that we have found a large population of diskless young sources. Taken at face value, these discoveries could indicate that 1) disk fractions are probably lower for low-mass stars/brown dwarfs than was previously thought, and 2) brown dwarfs are slightly more common than was previously thought. We join our sample with the Allers et al. [6] Ophiuchus sample to construct a disk fraction for sources with spectral type later than M4. There are four sources from Allers et al. [6] with spectral type later than M4- their sources 9, 11, 13, and 14. Source 11 (OPH1622−405) was

184 identiﬁed as an Upper Sco member [145], so we leave it out of consideration. Sources 9 and 13 are common to our sample, and are our only disk-bearing sources, other than the edge-on disks. So the total number of disk bearing objects towards this region of Ophiuchus is 5. The rest of our sources, excluding the edge-on disks, are diskless. There are 12 diskless sources in our sample. Two of those were previously identiﬁed as Upper Sco members [222, 136], so we remove them from our comparison. So we have 10 diskless sources towards this region of Ophiuchus. That gives us a disk fraction of 5/15, or 33%.

The average disk fraction for spectral types later than M4 is about 40- 60% in Taurus (1 Myr), Chamaeleon I (2-3 Myr), and IC348 (2-3 Myr) [135]. Upper Scorpius (∼ 11 Myr) has a disk fraction of about 20 − 30% for spectral types later than M4. Our derived disk fraction 33% would be unusually low for Ophiuchus, if we assume all of the objects are members of Ophiuchus. It is conceivable that some of our objects are members of the older population of Upper Sco, which would explain the absence of disks around such a large fraction of our sources. However, not all of our diskless sources are likely to be members of Upper Sco, since the surface number density is too high for Upper Sco, and the Na I equivalent widths are comparable to young Taurus members. Allowing as many as three addtional sources to belong to Upper Sco would revise our disk fraction from 5/15 to 5/12, yielding a disk fraction of ∼ 40%, which is comparable to the ∼ 1 − 3 Myr Taurus, Chamaeleon, and IC348.

185 7.6.2 What would we have selected if we had used selection criteria similar to other authors?

The various surveys for young brown dwarfs use different combinations photometric systems, and different permutations of successive color cuts. It is difficult to reproduce the selection of other surveys with our available data, unless we restrict ourselves to large survey data (like WISE, 2MASS, c2d). Most of the sources in the spectroscopic sample that are not confirmed as members in our work are background sources, based on their apparent position below the main sequence. This makes sense, since the W − filter does not select based on youth, but only late spectral type.

The main diﬀerence between our result and others’ is that we ﬁnd a large fraction of diskless sources. Any survey that relies on mid-IR excess as a criterion for selection would miss a large fraction of our detections.

7.6.3 Performance of the W − ﬁlter

We use our derived spectral types to evaluate to what extent the W − filter Q value correlates, as intended, with spectral type. Figure 7.19 shows Q as a function of spectral type for both our confirmed young members (green squares) and late-type non-members. We fit a straight line to the members, which have higher precision on their spectral type classification than the non- members. The fit shows a trend in the right direction: later type sources have larger Q values on average. We do not use the uncertainty in the Q value in the straight-line fits. The trend is even stronger in the same direction, if the

186 measurement uncertainty is included in the fit. Still, the large number of non- members that disobey the fit point to the role of measurement uncertainty both in Q and in the coarse spectral typing of non-members with The Hammer. We find no late-type sources with Q > 0 (excluding a known wide binary brown dwarf 1622-2405, which has been omitted from the figure, since its W −band photometry is likely affected by its companion.) Most of the non-members and all but 1 of the members have Q < −0.5, which defined the lower boundary of our W −band selection method.

7.6.4 What is the range of model-derived masses of all of the sources?

Based on the position of the sources in the HR diagram in Figure 7.11 we can infer a mass and age for our sources. From inspection of the HR diagram we see that the objects range in inferred ages from 1−80 Myr, and inferred masses from 20-200 Jupiter masses. There are many perils associated with deriving ages and masses in this way. This strategy assumes the models are accurate, and that secondary effects like accretion history have not oc- cured. We also assume that chromospheric activity is negligible [226]. The uncertainties in spectral classification correspond to errors of ∼ 100 K, which can change masses by factors of 50% or more. The luminosities depend on the assumed distance, extinction, spectral-type dependent bolometric corrections, and the observed J− band photometry. The largest uncertainty from those four are the distance and extinction. We dereddened to the J − H values assumed for the first pass spectral type. There is a large intrinsic spread in

187 J − H. So based on this large uncertainty, the luminosities could change by 50% or more, changing the ages by factors of 3 or more.

7.6.5 What can we say, if anything, about the IMF?

Our survey was exceptionally sensitive to very low luminosity substellar objects and yet we did not find them. To demonstrate the survey depth, Figure 7.20 shows the distributions of derived luminosities for all 71 of the sources demonstrating M or L spectral types, overplotted with the distributions of the confirmed young objects. At face value this result would point to an intrinsic paucity of these sources, as expected from the decreasing number densisty with lower mass of the sub stellar initial mass function. However, as the IMF is decreasing, the number of contaminating sources is increasing as photometric depth increases. So the a-priori probability that any given source is a young brown dwarf goes down as a function of flux. We only searched 1% of the sources in our photometric catalog. It is conceivable that we have missed very low luminosity brown dwarfs. If we assume the peak of the IMF is around M5 for this off-core region of Ophiuchus, and assume a star to brown dwarf ratio of 4, and assume we have detected all 7 of the M5’s towards this region, we would expect zero L0 sources [135]. The non-discovery of young L-type sources is consistent with—though not necessarily evidence for—a steeply declining IMF. We do not find any sources with spectral types later than M8.5, despite our ability to detect them.

A true understanding of the stellar and substellar initial mass function

188 (IMF) requires careful consideration of biases and selection effects, so we make no attempt to derive a shape of the IMF from our sample. For example, survey selection methods that bias against detection of luminous or underluminous sources will directly flow down to an inaccurate derivation of the IMF. Since our selection methods involved many different factors, it is a bit tricky to disentangle how these effects might have biased the selections towards and away from the IMF.

7.6.6 Is there a higher incidence of edge-on disks in BDs?

One main result of this work is the discovery and identiﬁcation of two edge-on disks around low-mass sources, out of only 5 disk-bearing sources towards this region of Ophiuchus. Forty percent of the disks are edge-on. This fraction is higher than the incidence of edge-on disks around higher mass stars. We interpret this high fraction as tentative evidence that brown dwarf disks have a larger scale height for a given radial position. This interpretation is consistent with our intuition that the vertical component of gravity should be much lower for a given radial position, and that the disk inclination should be random on the sky. Of course, the achieved scale height also depends on the degree of turbulence in the disk, so a detailed analysis would have to consider the average temperature and diﬀusion timescales at a given location in the disk [165, 62]. However, on average, the systematic bias should tend towards higher gravitational scale height for brown dwarf disks, at a given radial distance.

189 7.6.7 Are any of these sources from Upper Sco?

One of the main potential uncertainties throughout all of this work is the question of whether the young sources belong to the younger Ophiuchus or the older Upper Scorpius. Our region sits between these two on the sky, so it’s conceivable that some of our detections include a mix of these two populations. By plotting the projected positions of known objects, we can get an estimate of the surface number density of low mass objects. Extrapolating roughly from Slesnick et al. [222], Luhman and Mamajek [136] we estimate that about 2−4 Upper Sco objects could be in our region. This number is consistent with the appearance of our HR diagram, in which 4 objects sit substantially lower than the 10 Myr isochrone, but above the 100 Myr isochrone. The slightly older and more distant population of Upper Sco would be expected to occupy a region in this vicinity. The fact that the disks are more evolved is consistent with an interpretation of an older, ∼ 5 − 11 Myr population. For example, the low-mass binary brown dwarf OPH1622-2405 discovered in this region as part of the Allers et al. [6] survey was shown by Luhman et al. [145] to have Na I line strengths more similar to members of Upper Scorpius than Taurus (∼1 Myr).

7.7 Conclusions

We have reported on a broad-band survey aimed at the discovery of young brown dwarfs and very low mass stars towards the Ophiuchus star forming region. We present the selection, spectral analysis, discovery, spectral

190 types, luminosities, and physical characterization of a population of 12 young members, and 3 candidates of an off-core region towards Ophiuchus. Five of the 12 members show disks, while the other 7 members and 3 candidates show photospheric mid-IR colors. All members show strong evidence for youth through their gravity-sensitive spectral features. Specifically the Na I lines are comparable to 1-3 Myr Taurus and Cha I members reported by Luhman and collaborators. We interpret the majority of these photospheric young sources towards Ophiuchus as Class III analogs- diskless young brown dwarfs that have already lost–or never had–disks. The prevalence of these sources is tantalizing evidence for a shorter-lived disk lifetime for very low mass stars and brown dwarfs than had been previously thought. This shorter disk lifetime for brown dwarfs would put brown dwarf disk lifetimes more in line with their higher mass T-Tauri star counterparts. We also take the prevalence of Class III analogs in this study compared to other studies as evidence for a possible bias in selection for sources with evidence for mid-IR excess. This bias would manifest as an underestimated brown dwarf to star number density ratio, and an over-estimated disk lifetime. Our key tool in avoiding this bias is the introduction of a custom filter that isolates late type sources from the large number of reddened contaminants. We caution that contamination from Upper Scorpius could decrease the effect size seen here, but anticipate changes of merely a few objects, based on the low surface number density of Upper Sco.

191 0.8 0.8

0.6 0.6 ] ] 5 8

. 0.4 0.4 . 4 5 [ [ − − ] ] 6 5 . .

3 0.2 0.2 4 [ [

0.0 0.0

0.2 0.2

0.8 0.8

0.6 0.6 ] ] 0 0

. 0.4 0.4 . 8 8 [ [ − − ] ] 8 6 . .

5 0.2 0.2 3 [ [

0.0 0.0

0.2 0.2 4 5 6 7 8 9 10 4 5 6 7 8 9 10 Spectral Type (M0 = 0) Spectral Type (M0 = 0)

Figure 7.18 Mid-IR colors as a function of spectral type for our sample. Young stellar and substellar objects in this work are white squares with black edges and error bars. The distribution of 187 Class I, II, and III Taurus members with spectral types later than M0 [148] is shown as the kernel density estimate contours in the background. The black circles with white edges are the 8 sources towards Ophiuchus from Allers et al. [6] with spectral types from Gully-Santiago et al. [86]. The white dashed line is constructed from Class III young stellar and substellar objects in η Cha, Cha, and TWA [148], and represents the photospheric colors of young objects. The photospheric colors of ﬁeld dwarfs from Patten et al. [179] are shown as blue diamonds. The increasing dichotomy between the background density of Taurus members as a function of wavelength can be understood as the mid-IR excess detaching from the photosphere. The Taurus members and Allers et al. [6] members have not been corrected for extinction. 192 1.0 Late-type non-members Late-type non-members Entire catalog Members 0.5

0.0

0.5 Q 1.0

1.5

2.0

2.5 p(Q) 0 2 4 6 8 10 Spectral Type (M0 = 0)

Figure 7.19 Performance of the W −filter Q value as a function of spectral classification. The blue squares are members, the green squares are late-type non-members. The left portion of the plot shows the probability density function for the parent catalog of 31348 sources with a W −filter measurement (red stepped histogram with fine binning centered at Q = 0.0). The probability density distribution of all the late-type non-members is shown as the blue stepped histogram with coarse binning. We have excluded the outlier 1622-2405, a known binary brown dwarf, from the figure. The spectral type positions have a small (∼ 0.1 spectral subtype jitter added to them to displace the points for legibility).

193 25 71 late-type spectra members 20

15 N

0 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Lbol/L ¯ Figure 7.20 Distributions of luminosities of all 71 sources demonstrating M or L spectral types, overplotted with the 16 conﬁrmed young stellar objects.

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241 Vita

Michael Gully-Santiago was born in Boston, and attended high school in Norwell Massachusetts. He matriculated at Boston University in 2003, where he earned a Bachelor of Arts in Astronomy & Physics in May 2007. Dur- ing his undergraduate years he worked at the McDonald Observatory in Fort Davis, Texas and the Clay Center Observatory in Brookline, Massachusetts, where he remained as a faculty member until 2008. He enrolled in the Uni- versity of Texas at Austin Department of Astronomy’s Graduate Program in August 2008. In 2010 he was awarded the NASA Graduate Student Research Program fellowship, which enabled him to work at the NASA JPL Microde- vices Laboratory in Pasadena, CA.

Permanent address: [email protected]

This dissertation was typeset with LATEX† by ‘the author’.

†LATEX is a document preparation system developed by Leslie Lamport as a special version of Donald Knuth’s TEX Program.

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