Daniel Wolf Savin

James F Babb

Paul M Bellan

Christopher J Fontes -Los

Sarah M Hörst -Johns

Joan P Reno

Paul Barklem

Christiaan Boersma

Julie Brisset

Steven R Federman

Sarah M Hörst

Jeffrey Kuhn

Timothy J Lee

Maurice A Leutenegger

Joan P Marler

Brett A Mcguire

Stefanie N Milam

Kenneth M Nollett -San

Ella M Sciamma

Phillip C Stancil

Frank Timmes

Glenn Wahlgren

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2019

). The spectra of many small molecules are incomplete, inaccurate, or completely unknown. Some of the important molecules include: H2, H2O, OH, HF, NH3, CH4, HCN, KOH, HCl, H2S, PH3, CO, SiO, CO2, C2S2, KCl, O3, SO2, TiO, and VO. Data are needed for pressureinduced line broadening parameters, continuum opacity due to collision-induced absorption, molecular opacities at high spectral resolution, photoabsorption cross sections for small molecules at high temperatures, and expanded public databases for atmospherically relevant chemical reactions. In addition, complex-refractive indices of condensed matter particles that contribute to the observed continuum in exoplanet atmospheres are needed. The laboratory spectra of analogs to exoplanetary aerosols can provide a first step in this direction. Meeting these astrophysical needs requires new advances in theoretical and experimental molecular physics methods.

Exoplanetary interiors: The discovery of accretion onto white dwarf stars of tidally disrupted rocky planets and asteroids has given us a unique and direct way to explore exoplanet interiors (Jura & Young 2014). In the strong gravities of white dwarfs, heavy elements quickly sink below the observable photosphere. So the heavy elements observed in these stars are from the continual accretion of tidally disrupted objects. The relative abundances of the heavy elements indicate the geological composition of the rocky planetary interiors. New time domain surveys like the Zwicky Transit Facility (ZTF) at Caltech are turning up more of these objects. This survey, started in 2017, will increase the sample from a handful of objects to thousands, giving us a window into the internal compositions of rocky planets and asteroids throughout the galaxy. Spectroscopy will be possible for this larger (and therefore fainter) sample through improved infrared sensitivity available with JWST and the next generation large telescopes. Our only window into the interior composition of rocky worlds for the next decade and beyond is likely to be spectroscopy of white dwarf atmospheres, which will require accurate spectroscopic data for those heavy elements forming the planetary interiors.

Solar wind interactions with planetary bodies: Charge exchange (CX) recombination of solar wind ions with neutrals atoms and molecules around comets, in planetary exospheres, and within the heliosphere can be a sensitive probe of both the solar wind and the neutral gas it interacts with (Dennerl et al. 2012). However, laboratory benchmarks have shown that many of the most common CX models are flawed (Betancourt-Martinez 2018). Using CX to probe solar system objects require further experiments and more advanced theoretical methods to better understand the CX process.

Atmosphereless Solar System Bodies (ASSBs) as exoplanet analogs: Reflected light is the primary means used to understand the chemical and physical properties of regolith on the surface of an ASSB. This light is the product of the interaction between the solar spectrum and the spectrally active species on the surface of the body and may be polarized. The spectral properties of the airless surface can also be altered by micrometeorite impacts, solar wind ion irradiation, photon stimulated desorption, and other processes that are collectively known as space weathering. Spectrophotometric measurements of ASSBs are interpreted by comparison to laboratory reflectance measurements of simulated regolith [START_REF] Nelson | [END_REF]) and simulated space weathering of regoliths (Domingue et al. 2014). Deepening our experimental and theoretical understanding into the physical and chemical nature of ASSB surfaces and the effects of space weathering in our own solar system will aid in the interpretation of exoplanet data.

Star and Planet Formation

Understanding the evolutionary pathway of baryonic matter from atoms in space to the formation of a planetary system around a host star lies at the forefront of current day astrophysical research. This pathway encompasses diffuse atomic and molecular clouds, dense molecular clouds, interstellar dust, prestellar cores, protostars, protoplanetary disks, interplanetary dust particles, comets, and meteorites. Unambiguously tracing out this evolutionary history will need new theoretical and experimental advances in various areas of laboratory astrophysics.

The molecular Universe: We have entered a new era of discovery, due to facilities such as the Atacama Large Millimeter/submillimeter Array (ALMA), the Stratospheric Observatory for Infrared Astronomy (SOFIA), and the upcoming JWST. Over 200 different molecules have been identified to date in the interstellar medium and in circumstellar media (McGuire 2018). However, the species responsible for the vast majority of the astronomically observed molecular spectral features remain unidentified (Cernicharo et al. 2013, McGuire et al. 2017). Many of these are thought to be associated with larger and more complex molecules such as polycyclic aromatic hydrocarbons (PAHs), which are abundant and ubiquitous in space (Tielens 2013). Theoretical methods have proven to be insufficiently accurate to correctly predict molecular spectra, notably when it concerns effects due to anharmonicity. Overall, lab spectra are the only reliable way at present to identify molecules in space, but many of the experiments are difficult and time consuming. As a result, new molecules are being identified in space at the rate of about 3.7 per year and it will take decades to catch up with existing observations. Unlocking the full mystery of the molecular Universe requires new AMO theoretical and experimental advances in molecular spectroscopy.

Molecular observations also reveal important gas-phase chemical processes driving the evolution of baryonic gas, such as inorganic chemistry forming dust (raw material for planets) and organic chemistry leading to the formation of aromatic molecules and other molecules necessary for life as we know it. The complexity of the multi-atom reaction systems challenges current quantum mechanical and experimental capabilities; most of the relevant gas-phase reaction rate coefficients can only be roughly estimated (O'Connor et al. 2015). Reliably modeling and interpreting the molecular properties of the Cosmos requires new AMO theoretical and experimental advances in inelastic and reactive scattering techniques.

The presence of complex organic molecules (COMs) is only easily explained by physicochemical processing in condensed matter environments driven by light and particle radiation (Linnartz et al. 2015, Oberg 2016). JWST promises a new era for observations of icy solids (for which high resolution COM spectra are needed), while ALMA will reveal the extent of gas-phase chemical complexity. Understanding the link between the gas and solid phases is essential. Addressing this issue necessitates advances in theoretical and experimental surface physics and chemistry.

Using chemistry to study star forming clouds: The transition from diffuse atomic to diffuse molecular clouds is studied using observations of molecules such as OH + , CF + , HCl + , and ArH + , while observations of the exoergically formed CH + and SH + are used to study the input of mechanical energy into the gas (Gerin et al. 2016). Interpreting the astrophysical properties of the observed clouds requires quantitatively understanding the scattering processes that control the observed molecular abundances, in particular dissociative recombination (DR), which destroys these molecules. Accurate DR calculations are challenging, as it is a many-body problem with multiple electrons and nuclei. Common theoretical approximations are usually inadequate, making a rigorous theoretical description of the problem quite challenging, thus requiring new theoretical advances. In the lab, the challenge is to measure DR on heavy cations with internal excitation levels of only about 10 to 100 K. Generating the required DR data will require state-of-the-art facilities such as the heavy ion Cryogenic Storage Ring (CSR) at the Max Planck Institute for Nuclear Physics (von Hahn et al. 2016).

Studies of star forming clouds use observations of ortho (o-) and para (p-) H2D + and D2H + to determine the age of the prestellar cores, follow their evolution, and infer the role that magnetic fields may play in the collapse of the cloud (Harju et al. 2017). Utilizing the observed ratios of o-H2D + /p-H2D + and o-D2H + /p-D2H + , combined with chemical models for the nuclear spin evolution of the gas, estimates can be made for the age of the cloud and compared to the gravitational free-fall time. The inferred ages can exceed that of the free-fall timescale, implying that magnetic fields may be slowing the collapse of the cloud (Kong et al. 2015). The reliability of these prestellar core studies is limited by existing uncertainties in the reaction o/p-H2 + o/p-H3 + → o/p-H2 + o/p-H3 + , and the deuterated isotopic variations, which challenge current quantum theoretical capabilities.

Protoplanetary disk chemistry: Protoplanetary disks are studied using deuterated molecules. These are powerful probes of cold astrophysical environments, yielding information about the temperature, density, chemistry, abundances, ionization level, evolutionary stage, and thermal history of the disk (Ceccarelli et al. 2014, Millar 2015). The diagnostic power of D-bearing molecules arises because the zero-point energy of deuterated molecules is lower than the normal isotope, typically by several hundred kelvin. Important species driving deuteration are H2D + , N2D + , CH2D + , C2HD + , and CH4D + (Millar 2015, Aikawa et al. 2018). The complexity of these reactive scattering systems requires advances in current quantum mechanical theory and challenges current experimental methods.

COMs in protoplanetary disks are the foundation from which biology may be built. Frost lines reveal the presence of the simple molecular precursors and their distribution within disks. Condense matter processing, solid-gas interactions and gas-phase processing contribute to the evolution of chemical complexity in these environments. For example (Chutjian et al. 2012), the presence of ferromagnesosilica (MgFeSiO) grains; coated with the relatively abundant CO2, NH3 and CH4 species; and bombarded by energetic H( 2 S) and O( 3 P) atoms; can be a scenario for synthesis of amino acids such as NH2CH2COOH (glycine) and NH2CHCH3COOH (alanine). Advances in theoretical and experimental surface science and AMO physics are necessary to fully understand these complex processes and their interplay.

Accretion processes: The fast accretion required to form stars and planets is necessarily accompanied by turbulence in the corresponding disks. Numerous turbulence generation mechanisms have been proposed, including magnetorotational instability (MRI) or nonlinear hydrodynamic turbulence. Few of them, if any, can be confirmed from observation. Numerical simulations have been the main research approach, but unrealistic assumptions have been necessary. Laboratory experiments, when well controlled and well diagnosed, serve a muchneeded complementary approach for the problems (Ji & Balbus, 2013). Advances in experimental and numerical research in the laboratory settings, using liquids, gases, and plasmas, to test and challenge the proposed concepts to generate and sustain turbulence and its consequences are necessary to confirm their existence and effectiveness for accretion in disks.

Dust in the interstellar medium (ISM):

Dust is ubiquitous throughout the cold ISM and plays an important role in the local chemistry, where grain surfaces serve as a catalyst for molecular formation (Tielens 2013). Dust grains are the building blocks out of which larger solid bodies form. The inferred grain sizes and shapes provide diagnostics for their local physical environment (pressure, temperature, etc.). The properties of the dust grains can be studied through the ISM absorption spectra from a variety of stellar objects (Gao et al. 2009), absorption that is impacted by the size, shape, and composition of the dust grains. Using ISM dust studies to advance our understanding of the presence, generation, and role of solid matter in the Universe will require laboratory experiments to quantify light absorption and scattering by dust.

Solid body formation in protoplanetary disks: Solid body formation in protoplanetary disks occurs as µm-sized grains grow into larger aggregates. Our understanding of these early stages of planetesimal formation is based on studies of our own Solar System. Hierarchical aggregate growth is expected to proceed through binary sticking collisions from µm to mm sizes. But this growth stalls as the aggregates start bouncing and fragmenting upon collision rather than sticking and growing, a phenomenon called the "bouncing barrier" (Zsom, et al. 2010). To overcome this barrier, aggregate growth is believed to proceed further through local concentrations in the gas, for example in streaming instabilities (Krapp et al. 2019), that collapse under their own weight. Laboratory experimental data on the coagulation of dust simulants have helped to advance our understanding of these early stages of planet formation by uncovering growth barriers (Schräpler et al., 2018). Understanding of dust growth and planet formation will require further experiments on the formation of aggregates at all growth stages using a variety of realistic analog materials.

Stars and Stellar Evolution

Stellar spectroscopy: Measurement of stellar properties such as chemical compositions, masses, and ages is a fundamental problem in astrophysics (Heiter et al. 2015). The problem has become even more relevant in the era of current and future large astrometric surveys such as the Sloan Digital Sky Survey (SDSS), Global Astrometric Interferometer for Astrophysics (GAIA), Large Synoptic Survey Telescope (LSST) and Skymapper, complimented by large, highresolution and high-signal-to-noise ratio spectroscopic surveys such as Sloan Extension for Galactic Understanding and Exploration (SEGUE), Apache Point Observatory Galactic Evolution Experiment (APOGEE), 4-meter Multi-Object Spectroscopic Telescope (4MOST), William Herschel Telescope Enhanced Area Velocity Explorer (WEAVE), GALactic Archaeology with HERMES (GALAH), and GAIA-ESO. While stellar spectral line strengths are now routinely measured at accuracies of 1% or better, AMO uncertainties dominate the interpretation, and the actual errors in derived properties, such as the abundance of a chemical element, are at least an order of magnitude larger. Advances in the accuracy of the interpretation of stellar spectra, and thus the accuracy of stellar chemical compositions and other properties, are needed to gain insight into many current problems in modern astrophysics, such as the formation of planets, stars, and galaxies (especially the Milky Way, so-called Galactic archeology) as well as studies into fundamental stellar physics, the origin and evolution of the chemical elements, and cosmology. Analysis of stellar spectra at the 1% accuracy level is a significant challenge, and requires atomic and molecular data, including wavelengths, transition probabilities (gfvalues), photoionization cross sections, line broadening parameters, and collisional cross sections, with a high level of accuracy and completeness (see Barklem 2016 for a recent overview). Advances in AMO theory and experiment, with interplay between theoretical atomic physics, laboratory spectroscopy, and astrophysical observations, are needed to generate the data with the required accuracy and completeness.

Solar physics: The recent launch of the Parker Solar Probe, the 2019 commissioning of the Daniel K. Inoyue Solar Telescope (DKIST), and the upcoming launch of the Interstellar Mapping and Acceleration Probe all herald a new era in solar physics. These facilities and missions will study the magnetohydrodynamics and dynamo processes of the Sun, flares and eruptive events that can affect life on Earth, the flow of mass and energy through the solar atmosphere, and the long-term behavior of the Sun. Analyzing DKIST spectra will require extensive new AMO data needs for maximum scientific return (Judge 2017). The DKIST spectral range will extend from the visible into the near-IR, the latter of which is largely unexplored spectroscopically. Line identifications, oscillator strengths, transition rates, and branching ratios will be needed for multi-electron systems. New magnetic field diagnostics in the IR will also become available using the Hanle and Zeeman effects, all of which will require the relevant atomic data. Lastly, the solar plasma is dynamic and not in equilibrium. The ionization states of abundant elements encode the thermal history of the plasma, but they can only be interpreted in terms of plasma heating processes if accurate ionization and recombination data are known. Advances in AMO theory and experiment are needed to generate all of the above required data.

Solar eruptions and flares: The underlying physics of solar eruptions and flares involves ideal MHD instabilities and magnetic reconnection. Despite the long history of observational efforts to study these processes, direct confirmation is still out of reach due to inaccessibility of the microscopic plasma processes. New progress is being made on these processes from laboratory experiments that are designed to study these phenomena in isolated environments much simpler than the complicated situations on the solar surface (Yamada et al. 2010, Ji & Daughton 2011, Myers et al. 2015). Further advances in plasma laboratory experiments, supported by numerical modeling, are needed to directly test the proposed concepts and in addition to predict solar eruptions.

Solar interior physics: Helioseismology has shown that our best models of the Sun are unable to reproduce the measured depth of its convection zone, although a 15% revision to the opacities at the base of the solar convection zone could resolve this difficulty. Recent measurements of iron at these conditions show that larger-than-expected opacities of iron could produce a 7% increase in the mean total opacity of solar material (Bailey et al. 2015). Measurements of other elements under solar convection zone conditions may revise this number further. Reliable astrophysical modeling of the Sun and other stars will require advances in modeling the opacities of heavy elements around the iron peak.

Formation and Evolution of Compact Objects

White dwarf stars: White dwarfs are the endpoint of the stellar life-cycle for more than 97% of all stars. White dwarfs are also the most accurate chronometers for determining the age and star-formation history of the galaxy and provide an independent constraint on the age of the universe. Their interiors ca provide information about crystallization in dense Coulomb plasmas. White Dwarfs are also thought to be the site of Type Ia supernovae, which are crucial for determining cosmological distances and understanding the increasing expansion rate of the Universe due to "dark energy". Such studies build on understanding the plasma conditions at their photospheres, which is critical to providing the boundary conditions for determining their global parameters. Developing new theoretical calculations appropriate to the surface conditions of white dwarfs will require a concerting theoretical and experimental effort to study laboratory plasmas under these conditions.

Accreting neutron stars, X-ray bursts, and the rp-process: X-ray bursts are some of the most energetic stellar events, believed to occur when a neutron star accretes matter from a companion main-sequence star. The bursts of X-rays emitted regularly, every few hours to days, have been observed by various X-ray missions, and the characteristic light curve has been well studied. Modeling the events, and interpreting the astronomical observations requires an accurate description of the nuclear reaction rates that drive the explosive hydrogen and helium burning.

In addition, understanding the nucleosynthesis during this rapid-proton capture process (rpprocess) is essential for predicting the element composition of the ashes that are deposited on the neutron star at the end of each burst. Much of the necessary nuclear input data is not accessible with current facilities using either direct or indirect techniques. Many of these data will become accessible with the Facility for Rare Isotope Beams (FRIB), currently under construction in the U.S., combined with state-of-the-art equipment such as the Separator for Capture Reactions (SECAR). Deeper understanding of X-ray burst events will require direct measurements of some of the most critical nuclear reaction rates using these next generation facilities.

5. Resolved stellar populations and their environment Nucleosynthesis in our Galaxy: Direct measurement of γ-rays from long-lived radionuclides have been observed by various γ-ray missions. Detecting isotopes such as 44 Ti, 26 Al, and 60 Fe provide unique signatures of active nucleosynthesis in our Galaxy. Combining the observations of the various isotopes provides insights into their production mechanisms and the astrophysical events themselves. However, to interpret the observations it is crucial to have a good understanding of the nuclear reaction chains that produce or destroy the relevant isotopes. Current radioactive beam facilities can measure only some of the needed nuclear data. Next generation facilities such as FRIB combined with SECAR are needed to measure currently inaccessible systems. Reliable nuclear reaction data are critically important for understanding the chemical evolution of our Galaxy.

6. Galaxy Evolution X-ray astrophysics: X-ray observations probe some of the most energetic events in the Cosmos. Observations of supernova remnants provide information on the physics of the explosion and the corresponding nucleosynthesis. Active galactic nuclei host supermassive black holes with masses of 10 6 to 10 9 MSun. Accretion onto the central black hole and the subsequent feedback sends energy into the galaxy and regulates star formation. Clusters of galaxies are the most massive gravitationally bound objects in the Universe and can be used to constrain various cosmological parameters. These are all extended objects and require studies with non-dispersive instruments with high spatial and spectral resolution, such as was provided by the X-ray microcalorimeter on the recently lost Hitomi mission, which observed the Perseus cluster of galaxies (Hitomi Collaboration 2016), and will be provided by the X-ray Imaging and Spectroscopy Mission (XRISM) planned for launch in 2021. Other important upcoming X-ray astrophysics missions include Lynx and the Advanced Telescope for High Energy Astrophysics (ATHENA). Interpreting the collected spectra requires an accurate understanding of the underlying atomic physics for elements with atomic number Z ≤ 30. Important data and processes include: transition wavelengths, rates, and branching ratios; electron impact excitation; innershell excitation and the corresponding Auger and fluorescence yields; electron impact ionization; the electron-ion recombination process known as dielectronic recombination and the corresponding emission line wavelengths and fluxes; and charge balance calculations. Though these processes have been studied for decades, shortcomings in our AMO understanding still limit our ability to reliably interpret astrophysical observations, often related to the underlying highly-correlated, multi-electron interactions inherent in heavy, highly-ionized species.

7. Cosmology and Fundamental Physics Fundamental constants: Astronomical spectra can be used to test for variations in fundamental constants as a function of redshift such as the fine structure constant α and the ratio of the electron-to-proton mass μ (Ubachs et al. 2016). These studies require highly accurate atomic and molecular structure data that will require new intellectual advances in AMO scientific capabilities.

Multi-Messenger Astronomy and Astrophysics

Nucleosynthesis by kilonovae: Merging neutron stars were found using gravitational waves. Nucleosynthesis during the neutron-star merger takes place via the rapid-neutron capture process (r-process). The nuclear physics properties that drive this process are still highly uncertain. Specifically, the properties needed are nuclear masses, decay properties, neutron-capture rates and fission properties. In addition, the kilonova itself is fueled by the radioactive decay of rprocess nuclei and their decay products. The next generation FRIB will give access to the majority of r-process nuclei. Advancing our knowledge into the physics of kilonovae and the accompanying nucleosynthesis will require improving our understanding r-process nucleosynthesis for numerous heavy nuclei that are currently experimentally inaccessible.

Kilonovae seem to match predictions that they are the formation site for most of the elements with atomic numbers Z ≥ 44. Optical and infrared spectra from the expanding remnants enable us to study the rapid neutron-capture nucleosynthesis processes that occur during the merger (Kasen et al. 2017). To this end, opacities are needed for low ionization stages of heavy elements, especially for the lanthanides and actinides. High-level atomic structure methods can provide reasonable atomic data for low resolutions spectral analysis, but it is only in combination with laboratory work and critical evaluations of the data that the needed high resolution spectral information can be generated. Significant advances are required in both AMO theoretical and experimental methods in order to maximize our scientific understanding of these newly discovered objects.

Gravitational waves: Squeezed light methods, combined with enhanced power in the interferometer detectors, are predicted to enhance gravitational wave detections at high frequencies (50 -5,000 Hz). These advances will double the spatial detection volume, provide better sky localization, enable better estimates for the tidal deformability parameters of the merging compact objects, open up the ability to study the post-merger phase, and constrain the neutron star equation of state. Continued advances in AMO techniques hold the promise of expanding our ability to use gravitational waves to open a new window into some of the most extreme conditions in the Cosmos.

Strategic Plan -Workforce, Funding, and Facilities Workforce: Compared to other areas in astronomy and astrophysics, there are very few laboratory astrophysics faculty working to address the needs of the astrophysics community. This is a major concern for the U.S., Europe, and Asia. The small number of laboratories is remarkable, as laboratory astrophysics studies provide the needed understanding that enables us to fully benefit from astronomical research. But these interdisciplinary studies typically fall outside of traditional academic departments and funding agency divisions. As a result, laboratory astrophysics does not get the robust level of support needed to advance our astrophysical understanding of the cosmos. For example, physics departments are currently interested in quantum, ultracold, and ultrafast AMO studies and point AMO laboratory astrophysicists to astronomy departments. On the other hand, astronomy departments are primarily interested in observational and astrophysical theoretical/modeling studies. So if one is studying molecules, astronomy departments will direct that person to chemistry departments. But chemistry departments are primarily focused on large molecules and biochemistry and are uninterested in astrophysically important molecules such as PAHs or C-and Si-based structures. Such "small" molecules, they say, are the realm of a physics department. But traditional AMO laboratories are designed primarily for the study of two-or three-atom molecules and are poorly equipped to study more complex systems. So AMO laboratory astrophysics lies at the interface of three academic departments, none of whom want to take ownership. In addition, the workforce issue begins early in the academic pipeline with junior scientists finding it difficult to get professional and financial support for their laboratory astrophysics work. Similar situations exist for plasma laboratory astrophysics, as they often fall in between physics, astronomy, and engineering departments. These issues raise the serious question: how will we train the next generation of laboratory astrophysicists? Mirroring this issue, it should be noted that laboratory astrophysics is not a research area that is currently represented in the National Academy of Sciences and hence lacks the robust leadership in this critical interdisciplinary area that is needed to advance the field.

Funding: It is extremely hard to get funding for laboratory astrophysics. One of the main reasons for this is that in the current era of restricted funding means, the review panels for the NSF Division of Physics, the NSF Division of Chemistry, and the DOE tend to move the responsibility for funding laboratory astrophysics proposals to other disciplines. The multidisciplinary aspect of laboratory astrophysics then turns out to become a real disadvantage. For example, one proposal submitted to the NSF Division of Physics Experimental AMO program was declined, in part, because "This work is more appropriately funded through the Foundation's Division of Astronomy [sic] or by NASA." Another NSF proposal submitted to the same program was declined, in part, because "There does not seem to be a pre-existing demand from theory for the measurements." These reviews are despite the fact that the complex AMO physics that describes the Cosmos is a largely unexplored frontier in physics and chemistry. But the NSF Divisions of Physics and Chemistry have moved in directions different from the AMO complexity studies needed for astrophysics. DOE support for AMO laboratory astrophysics research has dried up over the last few decades and does not appear likely to be resurrected. For plasmas experiments, the NSF Directorate for Engineering supports primarily specific applications to societal needs rather than astrophysics. Hence, it is clear that NASA and the NSF Division of Astronomical Sciences are going to have to increase their funding for the frontier laboratory astrophysics research needed by the astrophysics community.

Facilities: Laboratory astrophysics facilities range in scale from table top to national laboratory. Table-top devices, excellent for training students, are disappearing as laboratory astrophysics faculty retire and close their labs. These faculty are not being replaced. For the soft-money scientists who remain in the field, it is extremely hard to build a new lab without start-up funds. National laboratories can sometimes carry out critically needed studies. For example, the Linac Coherent Light Source -II (LCLS II) will have the wavelength stability to study the opacity of multiply ionized heavy elements needed for kilonova spectra. However, it is extremely hard to get beamtime os such a facility for a project unlikely to result in a Science, Nature, or Phys. Rev. Lett. publication. Supercomputer support and funding for modern code development are also critical for the advanced theoretical computations that are now needed.

Changes since 2010: Many of the above workforce, funding, and facilities issues were raised in the white paper entitled "Laboratory Astrophysics and the State of Astronomy and Astrophysics" (AAS WGLA et al. 2009) submitted to the 2010 Astronomy & Astrophysics Decadal Survey. We refer the reader to that white paper for additional discussion on the state of laboratory astrophysics as the situation has only deteriorated since then. It is true that a number of the white paper recommendations were incorporated into the report of the 2010 Decadal Survey (National Research Council 2010). Unfortunately the recommendations had little impact on the funding priorities of the major funding agencies. The issues have become even more urgent in the intervening decade and action is needed even more desperately to grow the laboratory astrophysics program in the U.S. back to the level needed to fully meet the needs of the astronomy & astrophysics community. These concerns are reinforced in the report from the 2018 NASA Laboratory Astrophysics Workshop (2019), which both prioritized laboratory astrophysics work for the next decade and addressed the needs of the community. Recommendations Laboratory astrophysics is the Rosetta stone that helps us to unlock the mysteries of the Cosmos. The next decade of astronomical exploration will require significant laboratory astrophysics advances into our understanding of the underlying complexity that drives much of the Universe. Major astrophysical advances will come from these studies, but no academic department has taken intellectual ownership for this field. Maximizing the scientific return from the next decade of astronomical exploration will require a rejuvenation of laboratory astrophysics faculty and a corresponding restoration of funding from NASA, NSF, and DOE for such studies.

We close by reiterating many of the recommendations made in AAS WGLA et al. ( 2009) that are even more urgently needed now:

• Increased and steady support for laboratory astrophysics among the various agencies is critical for future advances in astronomy and astrophysics.

• Explicit support for laboratory astrophysics by missions, facilities, and projects is essential to maximize their astronomical and astrophysical scientific return.

• Faculty development in laboratory astrophysics, possibly through federal agency programs, is necessary to ensure the health and vitality of laboratory astrophysics on university teaching faculties.

• Strong instrumentation, technology, and facilities development programs in laboratory astrophysics are needed to support the development, construction, and maintenance of state-of-the-art instrumentation and facilities.

• Adequate funding for critically evaluated databases needed by those analyzing astronomical measurements and modeling the associated environments.

Acknowledgements

The authors thank J. Berengut, P. Bernath, D. Helfand, D. Kipping, J. Kuhn, H. Linnartz, B. Metzger, T. Oka, Y. Ralchenko, and M. Tse for stimulating discussions.


C Mukherjee
email: chhandak.mukherjee@ims-bordeaux.fr

G G Fischer

F Marc

M Couret

T Zimmer

C Maneux

A Unified Aging Compact Model for Hot Carrier Degradation under Mixed-mode and Reverse E-B stress in Complementary SiGe HBTs

Keywords: Aging, compact model, complementary SiGe HBTs, hot-carrier degradation, safe operating area

This paper presents an accurate, comprehensive and physics-based aging compact model for stress-induced degradation due to hot-carrier generation and oxide trapping in advanced complementary NPN and PNP SiGe HBTs. The analytical model equations are derived from the solution of reaction-diffusion theory and Fick's law of diffusion combined with oxide trapping mechanism under accelerated stress conditions. The model accuracy has been validated against results from long-term aging tests performed close to the safe-operating-areas of an advanced complementary 0.25 µm BiCMOS technology. Degradation asymmetry observed between NPN and PNP devices is accurately captured by this unified aging compact model. This study highlights the challenges of predicting degradation of complementary circuits and thereby improving its functionalities by designing better-matched NPN and PNP HBTs.

Introduction 

Long-term reliability of modern SiGe heterojunction bipolar transistors (HBTs) is increasingly becoming a major concern for circuit designers. Continuous improvement of the maximum operating frequency leads to an increase of operating current density and a reduction of breakdown voltages [START_REF] Chevalier | Si/SiGe:C and InP/GaAsSb Heterojunction Bipolar Transistors for THz Applications[END_REF]. Moreover, advanced circuit applications require the transistors to operate closer and even beyond their classical safe-operating areas (SOA). Hence, reliability-aware circuit design has become a mandatory approach [START_REF] Mukherjee | Reliability-Aware Circuit Design Methodology for Beyond-5G Communication Systems[END_REF] employing accurate aging models [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF] to facilitate time and cost-effective circuit design. Complementary circuit functionalities employing both NPN and PNP bipolar transistors are of particular interest owing to their large variety of RF, analog and high speed digital applications [START_REF] Cressler | Circuits and Applications Using Silicon Heterostructure Devices[END_REF]. However, performance mismatch between the NPN and PNP devices, due to their different architectures and mode of technological integration, are particularly detrimental for both DC and AC operation of complementary circuits. Added to these concerns, reliability issues such as bias temperature instability are more severe for complementary circuits because of nonequivalent degradation in either type of devices. More precisely, as supported by experimental evidence [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF], hot carrier induced damage is more aggressive and accelerated in PNP devices over their NPN counterpart, which not only significantly impedes symmetric circuit operation, it also poses major challenges for high performance circuit design.

Only a few previous studies have illustrated the impact of bias-dependent mismatch on the aging of complementary devices [START_REF] Fischer | Comparative study of HBT ageing in a complementary SiGe:C BiCMOS technology[END_REF]. Investigation of degradation physics in complementary devices has also been studied using TCAD simulation [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF]. From the circuit designers' point of view, the major degradation mechanism that needs to be accurately incorporated in SPICE compact models is hot-carrier degradation (HCD) that predominantly limits the lifetimes of modern SiGe HBTs [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF][START_REF] Fischer | Comparative study of HBT ageing in a complementary SiGe:C BiCMOS technology[END_REF][START_REF] Fischer | Ageing and thermal recovery of advanced SiGe heterojunction bipolar transistors under long-term mixed-mode and reverse stress conditions[END_REF][START_REF] Fischer | Analysis and modeling of the long-term ageing rate of SiGe HBTs under mixed-mode stress[END_REF][START_REF] Jacquet | Reliability of high-speed SiGe: C HBT under electrical stress close to the SOA limit[END_REF][START_REF] Jeppson | Negative bias stress of MOS devices at high electric fields and degradation of MNOS devices[END_REF]. The principal physical degradation mechanism is the generation of hot carriers, through impact ionization under high field or current conditions at the collector base junction, which are accelerated toward the emitter-base (EB) spacer oxide interface where they create traps via Si-H bond-breaking. The formation of these traps can be identified by the degradation of nonideal base current [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF]. There have been many forms of the reaction-diffusion (R-D) formalism adapted for describing HCD physics in SiGe bipolar transistors [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF][START_REF] Jacquet | Reliability of high-speed SiGe: C HBT under electrical stress close to the SOA limit[END_REF][START_REF] Jeppson | Negative bias stress of MOS devices at high electric fields and degradation of MNOS devices[END_REF] each with their application specific limitations. One of the more versatile and unified closed form solutions has been proposed in [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF]. This model (HiCuM AL V1) has been further enhanced in an upgraded version, HiCuM AL V2, and a more accurate compact model implementation that also accounts for dynamic stress conditions, ensuring timeinvariance of the compact model [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF].

This paper aims to provide a detailed compact modeling approach for studying the aginginduced degradation asymmetry in advanced complementary SiGe HBT technologies under both mixed-mode and reverse E-B stress conditions, based on the aging compact model developed in [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF]. With the accuracy of the model in [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF] validated for a wide range of advanced industrial SiGe HBT technologies under diverse stress conditions close to their safe-operating areas, the aging compact model is adapted for analyzing the degradation behavior of a complementary BiCMOS technology from IHP Microelectronics [START_REF] Heinemann | High-performance BiCMOS technologies without epitaxially-buried subcollectors and deep trenches[END_REF]. Mixed-mode (MM) aging tests for the complementary NPN and PNP HBTs show the expected asymmetry in the degradation depicting more aggressive degradation in PNP devices. An additional component of degradation is observed in case of the PNP devices at higher stress bias that cannot be captured by R-D based HCD compact models such as the one in [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF]. While this component is not clearly visible in case of NPN HBTs under MM stress within the maximum of 1000h stress duration, both transistors exhibit this additional component under high E-B reverse stress conditions, confirming the presence of this component for both HBTs. The stress bias-dependence of this component, attributed to fast oxide trapping, is analyzed and modeled using HiCuM AL V3.1, which extends the previous aging compact model in [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF].

The rest of this paper is organized as follows: Section 2 illustrates the model formulation and the derivation of bias-dependence of aging model parameters along with model implementation; Section 3 describes the SiGe HBT technology under test and the stress bias conditions, the aging test results, model validation followed by the conclusion.

Aging Model Formulation: Premise and Derivation

To illustrate the electrical signature of the aforementioned additional oxide trapping mechanism, Fig. 1 shows the base current degradation for an NPN SG25H3P HBT from the complementary 0.25 µm BiCMOS technology developed by IHP Microelectronics [START_REF] Heinemann | High-performance BiCMOS technologies without epitaxially-buried subcollectors and deep trenches[END_REF] under mixed mode (1 (a)) and reverse emitter-base (1 (b)) stress conditions. While for the reverse E-B stress conditions it is much more significant, both stress conditions exhibit that at longer stress time, there exists an additional contribution to the base current degradation (even though it is not evident under MM stress unless compared with model simulations) that cannot be accurately captured by the previous version of our aging model HiCuM AL V2 [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF]. In contrast, the improved model formulation presented in this work, HiCuM AL V3.1 (detailed in the next section), can accurately capture this additional mechanism (Fig. 1). Considering that modern SiGe HBTs have thermally grown homogeneous SiO2 spacers free from external impurities, the possibility of two different interface traps (with two activation energies) is rather low in SiGe HBTs when a single polarity of hot carriers is considered (as [START_REF] Fischer | Comparative study of HBT ageing in a complementary SiGe:C BiCMOS technology[END_REF]). On the contrary, III-V HBTs with deposited nitride sidewalls, can result in two different types of interface traps [START_REF] Mukherjee | Reliability-Aware Circuit Design Methodology for Beyond-5G Communication Systems[END_REF]. In our present analysis, it was thus considered that the double hump (more clearly visible in Fig. 1(b)) observed in the base current degradation is the combined result of two independent mechanisms originating from interface and deep oxide traps that are responsible for the overall degradation. In effect, the oxide trapping mechanism is evidently more significant under reverse E-B stress, which can be explained by the fact that regardless of the presence of large electric fields, the origin of the hot carriers are somewhere in the E-B region under reverse E-B stress compared to that of the C-B junction under mixed-mode stress [START_REF] Fischer | Comparative study of HBT ageing in a complementary SiGe:C BiCMOS technology[END_REF]. While the hot carriers under E-B stress have a lower transport loss and smaller distance to cover (relative to the scattering length/mean free path) to reach the E-B spacer, more significant degradation can be observed in this case. In case of PNP transistors, as we will show later on, this effect is more pronounced even in mixedmode conditions. This additional effect can be attributed to the oxide trapping (OT) mechanism which appears to intensify at higher stress bias at long stress time. The dynamics of this mechanism is similar to the phenomenon of bulk trap generation in MOS transistors, responsible for its dielectric breakdown [START_REF] Mahapatra | A Comparative Study of Different Physics-Based NBTI Models[END_REF]. To the best of our knowledge, this is the first notable observation of this effect in modern SiGe HBTs. While the oxide trapping component starts to dominate at longer stress time, HiCuM AL V2 [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF] can accurately describe the degradation in the earlier stress time. For reverse E-B stress, on the other hand, specifically at a stress voltage of 4 V, the excess degradation component (OT) depicts a significant deviation from what the HiCuM AL V2 predicts. HiCuM AL V2 has been adapted to incorporate modeling of this effect in a newer version, HiCuM AL V3.1, where the OT mechanism has also been introduced.

HiCuM AL V2 has been developed principally based on the R-D theory [START_REF] Jeppson | Negative bias stress of MOS devices at high electric fields and degradation of MNOS devices[END_REF]. Hence the initial phase of modeling concerns the derivation of the analytical model equations governing the physics of hot-carrier degradation (HCD). In HCD, the rate of bond dissociation is governed by a chemical interaction between the carriers and the passivated Si-H bond through generation and annihilation of traps. The interface-trap density, NT (t), increases with the net rate of reaction described by the R-D model [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Jeppson | Negative bias stress of MOS devices at high electric fields and degradation of MNOS devices[END_REF][START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF] as,

𝑑𝑁 𝑇 𝑑𝑡 = 𝐾 𝐹 (𝑁 𝐹 -𝑁 𝑇 (𝑡)) -𝐾 𝑅 𝑁 𝑇 (𝑡)𝑁 𝐻 (0, 𝑡) = 𝑔 𝑇 (1)
Here, KF is the rate constant of the forward reaction, i.e., generation of traps, KR is the rate constant of trap annihilation by hydrogen atoms, 𝑁 𝐻 (𝑥, 𝑡) is the volumetric density of hydrogen at distance x of the Si/SiO2 interface and NF is the total number of available bonds that can break. The modeling of interface trap generation and recovery has been implemented in [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF] through the equivalent circuit representations shown in Figs. 2(a) and (b) where the latter employs an R-C ladder network for modeling hydrogen diffusion within the E-B spacer. In addition to this setup, HiCuM AL V3.1 employs an additional fictitious transistor node for the oxide trap generation through the total oxide trap density 𝑁 𝑂𝑋 (𝑡) which is governed by an exponential stress time dependence similar to the implementation of bulk trap in [START_REF] Mahapatra | A Comparative Study of Different Physics-Based NBTI Models[END_REF]. In our model the following differential form is incorporated in the compact model with two additional model parameters, 𝑁 𝑂𝑋𝑀𝐴𝑋 and 𝜏 𝑂𝑋 for the maximum oxide trap density and oxide time constant, respectively, as,

𝑑𝑁 𝑂𝑋 (𝑡) 𝑑𝑡 = 𝑁 𝑂𝑋𝑀𝐴𝑋 -𝑁 𝑂𝑋 (𝑡) 𝜏 𝑂𝑋 (2)
Eq. ( 2) is represented by a single pole network shown in Fig. 2(c), consisting of a resistor of value 𝜏 𝑂𝑋 and a capacitor of value 1F, along with a current source of magnitude 𝑁 𝑂𝑋𝑀𝐴𝑋 /𝜏 𝑂𝑋 . It is theorized that thicker oxides are more prone to exhibit the OT mechanism owing to their higher capacity of oxide trap generation, as indicated in [START_REF] Alam | A comprehensive model of PMOS NBTI degradation[END_REF]. This could also present a comparative perspective for the different topographies of spacer oxides integrated within their respective process flows of the SiGe HBT technologies [START_REF] Couret | Scaled formulation for trap generation near the EB spacer oxide interface in SiGe HBTs[END_REF]. In other words, this could explain the absence of this component in our earlier works [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF]. Interestingly though, the presence of this component can also be seen in case of previous aging tests performed on the same technology [Fig. 6, ref.

5], which was left unaddressed due to absence of sufficient data for analysis.

(A) and τOX (s) by τOX,I (s). While IF and IOX remain model parameters pertaining to the process, the parameters KF,I, KR,I and τOX,I are represented as function of the stress bias. This results in a revised model parameter set that can be efficiently exploited for analysis of circuit aging. Firstly, under mixed-mode stress the forward rate constant, KF,I, increases with VCB,stress following an exponential dependence while JE,stress is kept constant. On the other hand, while VCB,stress is kept constant, KF,I demonstrates a peak value before starting to roll off [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Fischer | Ageing and thermal recovery of advanced SiGe heterojunction bipolar transistors under long-term mixed-mode and reverse stress conditions[END_REF][START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF]. This has been explained by a decrease in the C-B electric field at the onset of the Kirk effect at such high stress current densities [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Jaoul | A compact formulation for avalanche multiplication in sige hbts at high injection levels[END_REF], resulting in a reduction in ΔIB. The decrease of the impact ionization mechanism at high current densities has been demonstrated in [START_REF] Jaoul | A compact formulation for avalanche multiplication in sige hbts at high injection levels[END_REF], which can be held responsible for the decline of the avalanche current density, JAVL, at large emitter stress current densities [START_REF] Jaoul | A compact formulation for avalanche multiplication in sige hbts at high injection levels[END_REF]. Taking this into account, the expression for KF,I under mixedmode stress has been simplified by introducing the JAVL parameter obtained using the new avalanche model [START_REF] Jaoul | A compact formulation for avalanche multiplication in sige hbts at high injection levels[END_REF]. For reverse E-B stress, however, KF,I is only an exponential function of the reverse E-B stress bias, VEB,stress. Additionally, an Arrhenius-like temperature dependence is added to the expressions of KF,I. The activation energy, E0, is identical (0.24 eV) to the values for previously reported SiGe HBT technologies [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF] which governs the temperature dependence of the rate constants. The expressions of KF,I under mixed mode and reverse E-B stress, respectively, can thus be written as,

𝐾 𝐹,𝐼 | 𝑀𝑀 = 𝑔 𝑟𝑎𝑡𝑒 𝐽 𝐴𝑉𝐿 exp(𝜇 𝐹 𝑉 𝐶𝐵,𝑠𝑡𝑟𝑒𝑠𝑠 ) exp [- 𝐸 0 𝑘 𝐵 𝑇 ] (3) 𝐾 𝐹,𝐼 | 𝐸𝐵 = 𝐾 𝐹,𝐼0 exp(𝜇 𝐹 𝑉 𝐸𝐵,𝑠𝑡𝑟𝑒𝑠𝑠 ) exp [- 𝐸 0 𝑘 𝐵 𝑇 ] (4)
Here, the new aging compact model parameters are 𝑔 𝑟𝑎𝑡𝑒 (µm 2 A -1 s -1 ), which is the fraction of the avalanche current density that reaches the spacer oxide interface [START_REF] Couret | Scaled formulation for trap generation near the EB spacer oxide interface in SiGe HBTs[END_REF] and 𝜇 𝐹 (V -1 ) which is the exponential factor that governs acceleration of hot carriers under the applied electric field. The use of JAVL instead of JE,stress simplifies the previous expression proposed in [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF].

On the other hand, the trap annihilation rate strongly depends on the junction temperature and follows an Arrhenius law. Additionally, the stress bias dependences are introduced similar to that of KF,I, although the bias-dependence is relatively weaker. The expressions of KR,I under mixed mode and reverse E-B stress, respectively, can thus be written as,

𝐾 𝑅,𝐼 | 𝑀𝑀 = 𝐾 𝑅0 exp(𝜇 𝑅 𝑉 𝐶𝐵,𝑠𝑡𝑟𝑒𝑠𝑠 ) exp [- 𝐸 0 𝑘 𝐵 𝑇 ]
(5)

𝐾 𝑅,𝐼 | 𝐸𝐵 = 𝐾 𝑅0 exp(𝜇 𝑅 𝑉 𝐸𝐵,𝑠𝑡𝑟𝑒𝑠𝑠 ) exp [- 𝐸 0 𝑘 𝐵 𝑇 ] (6)
Here, the new aging model parameters are 𝐾 𝑅0 , which is the magnitude of KR,I in cmA -1 s -1 , 𝜇 𝑅 is the exponential factor in V -1 . Finally, the temperature and stress bias-dependence of τOX,I was found to be of inverse nature as that of KF,I and KR,I. Hence, to maintain modular expressions, the following equations can be written for τOX,I under mixed mode and reverse E-B stress, respectively,

𝜏 𝑂𝑋,𝐼 | 𝑀𝑀 = 𝜏 𝑂𝑋0 exp(-𝜇 𝑂𝑋 𝑉 𝐶𝐵,𝑠𝑡𝑟𝑒𝑠𝑠 ) exp [ 𝐸 0 𝑘 𝐵 𝑇 ] (7) 𝜏 𝑂𝑋,𝐼 | 𝐸𝐵 = 𝜏 𝑂𝑋0 exp(-𝜇 𝑂𝑋 𝑉 𝐸𝐵,𝑠𝑡𝑟𝑒𝑠𝑠 ) exp [ 𝐸 0 𝑘 𝐵 𝑇 ] (8)
Here, the new aging model parameters are 𝜏 𝑂𝑋0 , which is the magnitude of τOX,I in s and 𝜇 𝑂𝑋 is the exponential factor inV -1 . Further analyses on the three aging model parameters are presented at the end of section 3 which demonstrate the validity of the equations (3-8) against experimental results. The temperature dependence of the H-diffusion coefficient, DH, is also governed by an Arrhenius law, for which the value of the activation energy EA used in our model is roughly 0.48 eV, which is consistent with the values reported in [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF]. Additionally, the temperature dependence of the H-diffusion R-C network directly stems from the temperature dependence of DH. The resistance R1, which is inversely linked to the velocity at which the Hdiffusion front diffuses, is the only temperature dependent quantity; whereas, C1 signifies the lateral incremental length of the subsequent cells of the R-C network and is only geometry dependent. Hence the equations governing these two quantities read,

𝐷 𝐻 = 𝐷 𝐻0 exp [- 𝐸 𝐴 𝑘 𝐵 𝑇 ] , 𝑅 1 = 𝐶 1 𝐷 𝐻 (9)
Here, the aging model parameters are 𝐷 𝐻0 and EA.

Model Validation

In this section, we test the validity of the model under various aging conditions, close to the SOA of the NPN and PNP HBTs from IHP's complementary 0.25 µm BiCMOS technology [START_REF] Heinemann | High-performance BiCMOS technologies without epitaxially-buried subcollectors and deep trenches[END_REF]. The mixed mode aging tests were performed up to 1000h of stress time, whereas the aging tests under reverse E-B stress were performed up to 10 5 s of stress time.

The aging compact model was validated on both NPN and PNP HBTs featuring transistors in BEC configuration with effective emitter areas of 0.3×0.92 and 0.22×0.84 µm 2 , respectively. Aging tests were performed at ambient temperatures (300K) under various mixed-mode stress conditions as illustrated on the output characteristics in Fig. 3 Classically, the BVCEO defines the stable operating region (SOR) whereas BVCBO defines the boundary of real degradation conditions in circuit operation and thus defines the safe operating area of modern transistors. So, beyond BVCBO the transistor is likely to have its degradations aggressively accelerated and is thus the maximum limit that can be used. Our stress conditions are chosen between these two limits.

In case of reverse E-B stress, degradation occurs under reverse biased E-B diode stress with a shorted CB junction (VCB = 0V). The stress conditions chosen in our study are highlighted in Fig. 3(b) for the two HBTs. Here, the junction tunneling current is the major source of the highly energetic carriers which are able to create traps at the E-B spacer oxide interface [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF]. Since the distance these carriers have to travel is much shorter than for MM stress [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF], an immediate and more pronounced increase of the non-ideal base current is expected in case of reverse E-B stress. For practical circuit operating conditions, however, these stress conditions are of minor importance as both the MM and EB stress conditions used in this work are quite harsh and may not have realistic applications.

The asymmetry of the degradation in the NPN and PNP HBTs is evident from the results of the evolution of the normalized excess base current (ΔIB/IB0) as a function of aging time, as demonstrated in Figs. 4 (a) and (b) for both HBTs under mixed-mode stress. Fig. 4 (a) depicts the results for different VCB,stress (3 -4.25 V) under constant JE,stress (4.5 mA/µm 2 ) for the NPN HBTs, while Fig. 4 (b) shows the results for the PNP HBTs under different VCB,stress (2.5 -3.75 V) with constant JE,stress (6.2 mA/µm 2 ). The different values of JE,stress are used to maintain similar junction temperature values for both NPN and PNP HBTs during aging. Matching junction temperatures were chosen to ensure the same accelerating conditions/factors, impact ionization and self-heating at the beginning of the degradation for both HBTs. This emulates realistic degradation scenarios where base current degradation is simultaneously governed by impact ionization due to hot carrier degradation and increase of junction temperature. The evolution of aging parameters, such as KF,I, governed by these factors are thus also different for the two HBTs in realistic scenarios. In fact, the effect of oxide trapping starts to dominate from a VCB,stress of 3.25V for the PNP HBTs whereas the oxide trapping effect is not at all prominent in case of the NPN HBTs under mixedmode stress, in the 1000h stress window. Since it is not feasible to stress the devices experimentally for longer stress duration, NPN HBTs were stressed under reverse E-B stress conditions to accelerate the degradation mechanisms. On the other hand, PNP HBTs, being more susceptible to degradation, exhibit this component even under MM stress within 1000h of aging. In fact, the presence of oxide trapping is universal for this technology as even new generations too show this component on an advanced 0.13 um SG13S technology. The fact that even the latest generations show this component indicates that it has not been observed or at least noticed in earlier works as the stress time (1000h) is not sufficient for it to manifest.

The principal reason that the PNP HBTs (Fig. 4 (b)) show much more pronounced oxide trapping compared to the NPN HBTs under MM stress is that there is more impact ionization in the PNP HBTs at high VCB due to its lower BVCBO compared to that of the NPN HBTs that depict more gradual degradation. Apart from the different generation rates of hot carriers in the two device types, the dynamics of hot carrier trapping depends on carrier types [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF]. While secondary hot holes are dominant carriers in NPN devices, the hot electrons are the major force behind the degradation in PNP HBTs that have superior scattering lengths and thus higher retention of energy V CB =0 [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF]. As demonstrated in [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF], the hot carrier generation rate has two peaks in PNP HBTs, one due to the proximity of the E-B spacer region compared to the NPN devices, and the other due to a lower activation energy, which result in significantly more trap formation in PNP devices. Added to this, the complexity of complementary device degradation increases due to the different activation energies associated to the E-B spacer traps with relevant polarities involved in the degradation. With lower activation energies in case of PNP transistors [START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF], the Si-H bonds are easier to break in these devices, making them more susceptible to degradation.

The oxide trapping mechanism occurs in the E-B spacer oxide where deep oxide trap level are created under accelerated stress conditions. The fact that the oxide trapping effect can be visible at longer stress time confirms that these traps are slow to respond compared to the interface traps. Due to the fact that the technology under test has a thicker spacer oxide compared to the other technologies we studied in our earlier works [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF][START_REF] Couret | Scaled formulation for trap generation near the EB spacer oxide interface in SiGe HBTs[END_REF][START_REF] Jaoul | A compact formulation for avalanche multiplication in sige hbts at high injection levels[END_REF], the oxide trapping effect could be observed in this case. We have however, neither seen any collector current degradation nor any recovery under normal conditions. On the other hand, we have not performed annealing measurements [START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF], as they fall within the future scope of this work.

The limits of the base current degradation, estimated following [START_REF] Mahapatra | A Comparative Study of Different Physics-Based NBTI Models[END_REF] and from the model V3.1, are also shown in Fig. 4 highlighting the cases what only the R-D model predicts and where both R-D model and oxide trapping effects govern the degradation. While for PNP HBTs, the R-D model limit has already been crossed, for NPN HBTs the base current degradation is still below the R-D limits and thus there are no significant oxide trapping effects. In both cases excellent accuracy is observed. As a validation, Gummel characteristics measured at different stress intervals under a VCB,stress of 3.75V and JE,stress of (a) 6.2 and (b) 4.5 mA/µm 2 for the PNP and NPN HBTs, respectively, are compared with model simulation, as shown in Fig. 5. Initial simulation is performed using a foundry-generated scalable model card followed by re-simulations using extracted HiCuM AL V3.1 aging model parameters, for different aging intervals. Excellent agreement between model and measurement is observed.

In contrast with the results obtained under MM stress, reverse E-B stress shows rather symmetric degradation for both NPN and PNP HBTs, owing to the proximity of hot carriers to the E-B spacer in both cases. Hot carriers generated under reverse E-B stress are quite close to the E-B spacer region compared to that of the C-B junction in mixed-mode stress, thus implying much shorter transit time of hot carriers in the former case. Thus, Figs. 6 (a) and (b) show rather equivalent evolution of the normalized excess base current (ΔIB/IB0) as a function of aging time for both NPN and PNP HBTs under different reverse E-B stress (3 -4.5 V), respectively. The limits of the base current degradation are shown here which indicates that in both cases the R-D limit is crossed for a stress voltage of 3.75V and eventually the limit due to R-D and oxide trapping is reached. In both cases good model accuracy is observed. The simulation of Gummel plots at different stress intervals under a VEB,stress of 4V for both HBTs are compared with measurements, as shown in Fig. 7.

Excellent agreement between model and measurement is also observed for all stress conditions. Finally, the accuracy of bias dependence captured in the aging model parameter equations [START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF][START_REF] Cressler | Circuits and Applications Using Silicon Heterostructure Devices[END_REF][START_REF] Raghunathan | Physical Differences in Hot Carrier Degradation of Oxide Interfaces in Complementary (n-p-n+p-n-p) SiGe HBTs[END_REF][START_REF] Fischer | Comparative study of HBT ageing in a complementary SiGe:C BiCMOS technology[END_REF][START_REF] Fischer | Ageing and thermal recovery of advanced SiGe heterojunction bipolar transistors under long-term mixed-mode and reverse stress conditions[END_REF][START_REF] Fischer | Analysis and modeling of the long-term ageing rate of SiGe HBTs under mixed-mode stress[END_REF] is validated through comparison between the extracted values (from experimental data) and model simulations for the generation (KF,I) and annihilation (KR,I) rate constants as well as the oxide trapping time constant (τOX,I), under different stress conditions studied in this work. It has to be noted that all of these three parameters are simultaneous functions of both stress bias and temperature. Similarly, Figs. 9 and 10 show the evolution of KR,I and τOX,I exhibiting similar dual dependence on bias and temperature. In all cases excellent model accuracy can be observed. Note that the trap annihilation rate, KR,I, shows a much weaker stress bias dependence under mixed-mode stress compared to under reverse E-B stress. This disparity is less evident in case of PNP transistors. However, the bias dependence of KR,I is weaker in all cases compared to that of KF,I and τOX,I and its evolution is principally governed by its junction temperature dependence. Interestingly, the magnitudes of KF,I and τOX,I, which basically signify generation rates of interface and oxide traps, respectively, are quite similar for both type of HBTs under reverse stress, even though they largely differ under mixed-mode stress. The elements of the H-diffusion R-C network, however, are only functions of temperature (R1) or geometry (C1) and show no evolution with stress bias.

The new parameter values EA, R10 are identical regardless of the HBT type and stress conditions. The new set of aging parameters are much more convenient for circuit aging simulations and reliability-aware circuit design.

Conclusion

In this work, we have presented a unified physical and accurate aging compact model implementation, compatible with existing circuit design framework, developed for modern SiGe HBT technologies based on the reaction-diffusion theory of hot-carrier degradation combined with oxide trapping mechanism and a differential form of Fick's law of diffusion. Significant oxide trapping has been observed under accelerated stress bias conditions, particularly under reverse E-B stress, which has been taken into account

K R [cmA -1 s -1 ] 1000/T [K -1 ] Reverse E-B PNP Model V EB [V] K R [cmA -1 s -1 ] Mixed-mode PNP V CB [V]

Fig. 1 :

 1 Fig. 1: Base current degradation of an NPN SG25H3P HBT under (a) mixed mode and (b) reverse emitter-base stress depicting the additional oxide trapping component at longer stress time.

Fig. 2 : 1 )

 21 Fig. 2: Organization of the (a) R-D, (b) Diffusion model[START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF] and (c) Oxide-trapping model implementations.Similar to the previous versions of the aging model, HiCuM-AL V1[START_REF] Mukherjee | Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model[END_REF], and HiCuM-AL V2[START_REF] Mukherjee | A Physical and Versatile Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating Conditions[END_REF], the base current degradation has been implemented in HiCuM compact model through the recombination current parameter in the periphery, IREpS. In the current version of the aging model (HiCuM-AL V3.1), the evolution of IREpS is translated from the combined evolution of the trap densities NT (t) and NOX (t). KF (s -1 ), KR (cm 3 s - 1 ) of (1) are represented by their corresponding compact model parameters KF,I (s -1 ), KR,I (cm.A -1. s -1 ), respectively, and NF by IF (A) which is the final value of ΔIREpS, (A). Similarly, for oxide trap generation related parameters in (2) NOXMAX is represented by IOX

  (a) for both type of HBTs. Base current degradation under mixed mode stress conditions is governed by the two accelerating factors of stress: VCB and JE, which are chosen around peak-fT, where most modern circuits operate, and the operating points are chosen above the open base breakdown voltages BVCEO, NPN = 2.2 V and BVCEO, PNP = 2.8 V. The open-emitter break-down voltages of these HBTs are BVCBO,PNP = 4.0 V and BVCBO,NPN = 6.0 V, which already indicates that the PNP HBT will be more prone to base current degradation under the same stress voltages.

Fig. 3 :

 3 Fig. 3: Aging test bias conditions for both NPN and PNP HBTs under (a) mixed-mode, (b) reverse E-B stress.

Fig. 4 :

 4 Fig. 4: Comparison between measurement and HiCuM-AL-V3.1 simulation: Evolution of excess base current at VBE= 0.7 V for (a)

Fig. 5 :

 5 Fig. 5: Comparison between measurement and HiCuM-AL-V3.1 simulation: Gummel plots at different aging intervals for (a) PNP HBTs under JE,stress of 6.2 mA/µm² and VCB,stress of 3.75V and (b) NPN HBTs under JE,stress of 4.5 mA/µm² and VCB,stress of 3.75V.

Fig. 6 :

 6 Fig. 6: Comparison between measurement and HiCuM-AL-V3.1 simulation: Evolution of excess base current extracted at VBE= 0.7 V for (a) NPN HBTs and (b) PNP HBTs under different VEB,stress (3 -4.5V).

Fig. 7 :

 7 Fig. 7: Comparison between measurement and HiCuM-AL-V3.1 simulation: Gummel plots at different aging intervals for (a) PNP HBTs and (b) NPN HBTs under VEB,stress of 4V.

Fig. 8 :

 8 Fig. 8: Evolution of KF,I as an explicit function of (a) inverse of junction temperature and (b) stress bias; Surface plot of KF,I as function of inverse junction temperature and stress bias, under (c) reverse E-B and (d) mixed mode stress. This dual dependence is shown for KF,I (based on the analytical eqs. (3) -(4)) in Figs. 8 (a) and (b) which depict the comparison between the measurement and model as explicit functions of (a) inverse of temperature and (b) stress bias, depicting good agreement. To further aid the visualization of the quantity, Figs. 8(c) and (d) show the 3D surface representation of KF,I as simultaneous functions of both the inverse of temperature and stress bias for an NPN HBT, under reverse E-B and mixed-mode stress conditions, respectively. The higher curvature of the surface in case of the reverse E-B stress highlights the difference between MM and reverse E-B stress, particularly observed for NPN HBTs.

Fig. 9 :

 9 Fig. 9: Evolution of KR,I as an explicit function of (a) inverse of junction temperature and (b) stress bias; Surface plot of KR,I as function of inverse junction temperature and stress bias, under (c) reverse E-B and (d) mixed mode stress.

Fig. 10 :

 10 Fig. 10: Evolution of τOX,I as an explicit function of (a) inverse of junction temperature and (b) stress bias; Surface plot of τOX,I as function of inverse junction temperature and stress bias, under (c) reverse E-B and (d) mixed mode stress.

Table I

 I

	lists
	the extracted aging model parameters for the rate
	constants depicted in equations (3) -(8). Significantly
	higher values of the trap generation rate for the PNP
	HBTs under mixed-mode stress further validates the
	degradation asymmetry between the two HBT types,
	owing to different breakdown voltages and the
	polarity of hot carriers.

TABLE I :

 I AGING PARAMETERS OF THE RATE CONSTANTS UNDER DIFFERENT STRESS CONDITIONS the current modeling framework. To the best of our knowledge, this is the first notable observation and systematic modeling of this effect in advanced SiGe HBTs. The model implementation is time-invariant and predictive. Moreover, the aging rate constants are implemented as function of stress bias conditions, enabling circuit aging simulation capabilities. The aging model has been validated against long-term aging tests on a complementary 0.25 µm SiGe BiCMOS technology from IHP, yielding very good agreement thus confirming its accuracy and versatility. Significant asymmetry in degradation behavior between NPN and PNP HBTs have been observed under mixed-mode stress conditions that are close to the realistic long-term degradation scenarios in contrast with the reverse E-B stress. The different dynamics of degradation can be attributed to the origin of the hot carriers in the two cases of stress conditions. The fundamental difference between the degradation in NPN and PNP transistors can be attributed to hot carrier polarity and trap activation energy pertaining to each case, demonstrating significantly faster degradation in PNP HBTs. This needs to be taken into account when evaluating the long-term performance of circuits sensitive to HBT mismatch. With its strong physical basis, the proposed aging compact model, HiCuM AL V3.1, is indispensable for ensuring stable circuit operation close to the SOA of the technology, through prediction of reliability-aware circuit architectures.

	HBT Type	Stress type	KF0 (s -1 )	µF (V -1 )	grate (µm 2 A -1 s -1 )	KR0 (cmA -1 s -1 )	µR (V -1 )	τOX0 (s)	µOX (V -1 )	E0 (eV)
	NPN	Mixed-mode	-	0.95	0.02	1.95×10 11	0.65	4.5×10 10	2.95	0.24
		Reverse E-B	9×10 -9	6.5	-	6.55×10 10	1.05	3×10 14	8.2	0.24
	PNP	Mixed-mode	-	1.3	0.28	2.5×10 11	0.45	3.1×10 10	3.95	0.19
		Reverse E-B	8×10 -8	5.6	-	1.4×10 11	1.08	9.2×10 12	6.5	0.19

in

Acknowledgement

This work was supported by European Commission through the H2020 ECSEL Project Taranto (No.

737454)

and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -Project No. 391631565.