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Generative Artificial Intelligence (GenAI) is becoming ubiquitous in our daily lives. The increase in computational power and data availability has led to a proliferation of both single- and multi-modal models. As the GenAI ecosystem matures, the need for extensible and model-agnostic risk identification frameworks is growing. To meet this need, we introduce the Python Risk Identification Toolkit (PyRIT), an open-source framework designed to enhance red teaming efforts in GenAI systems. PyRIT is a model- and platform-agnostic tool that enables red teamers to probe for and identify novel harms, risks, and jailbreaks in multimodal generative AI models. Its composable architecture facilitates the reuse of core building blocks and allows for extensibility to future models and modalities. This paper details the challenges specific to red teaming generative AI systems, the development and features of PyRIT, and its practical applications in real-world scenarios.

Cubic boron nitride (c-BN) is an ultrawide-bandgap semiconductor of significant interest for high-frequency and high-power electronics applications owing to its high saturation drift velocity and high electric breakdown field. Beyond transistors, devices exploiting the valley degree of freedom or negative differential resistance are of keen interest. While diamond has been found to have potential for these applications, c-BN has not been considered owing to a lack of knowledge of the relevant charge transport properties. Here, we report a study of the high-field transport and noise properties of c-BN using first-principles calculations. We find that c-BN exhibits an abrupt region of negative differential resistance (NDR) below 140 K, despite the lack of multi-valley band structure typically associated with NDR. This feature is found to arise from a strong energy dependence of the scattering rates associated with optical phonon emission. The high optical phonon energy also leads to an intervalley scattering time rivaling that of diamond. The negative differential resistance and long intervalley scattering time indicate the potential of c-BN for transferred-electron and valleytronic devices, respectively.

Recent innovations in language model training have demonstrated that it is possible to create highly performant models that are small enough to run on a smartphone. As these models are deployed in an increasing number of domains, it is critical to ensure that they are aligned with human preferences and safety considerations. In this report, we present our methodology for safety aligning the Phi-3 series of language models. We utilized a "break-fix" cycle, performing multiple rounds of dataset curation, safety post-training, benchmarking, red teaming, and vulnerability identification to cover a variety of harm areas in both single and multi-turn scenarios. Our results indicate that this approach iteratively improved the performance of the Phi-3 models across a wide range of responsible AI benchmarks. Finally, we include additional red teaming strategies and evaluations that were used to test the safety behavior of Phi-3.5-mini and Phi-3.5-MoE, which were optimized for multilingual capabilities.

On-chip photonic devices based on SiO$_2$ are of interest for applications such as microresonator gyroscopes and microwave sources. Although SiO$_2$ microdisk resonators have achieved quality factors exceeding one billion, this value remains an order of magnitude less than the intrinsic limit due to surface roughness scattering. Atomic layer etching (ALE) has potential to mitigate this scattering because of its ability to smooth surfaces to sub-nanometer length scales. While isotropic ALE processes for SiO$_2$ have been reported, they are not generally compatible with commercial reactors, and the effect on surface roughness has not been studied. Here, we report an ALE process for SiO$_2$ using sequential exposures of Al(CH$_3$)$_3$ (trimethylaluminum, TMA) and Ar/H$_2$/SF$_6$ plasma. We find that each process step is self-limiting, and that the overall process exhibits a synergy of 100%. We observe etch rates up to 0.58 \r{A} per cycle for thermally-grown SiO$_2$ and higher rates for ALD, PECVD, and sputtered SiO$_2$ up to 2.38 \r{A} per cycle. Furthermore, we observe a decrease in surface roughness by 62% on a roughened film. The residual concentration of Al and F is around 1-2%, which can be further decreased by O$_2$ plasma treatment. This process could find applications in smoothing of SiO$_2$ optical devices and thereby enabling device quality factors to approach limits set by intrinsic dissipation., Comment: 19 pages, 8 figures, 1 table

Quantum systems subject to random unitary evolution and measurements at random points in spacetime exhibit entanglement phase transitions which depend on the frequency of these measurements. Past work has experimentally observed entanglement phase transitions on near-term quantum computers, but the characterization approach using entanglement entropy is not scalable due to exponential overhead of quantum state tomography and post selection. Recently, an alternative protocol to detect entanglement phase transitions using linear cross-entropy was proposed which eliminates both bottlenecks. Here, we report the demonstration of this protocol in systems with one-dimensional and all-to-all connectivities on IBM's quantum hardware on up to 22 qubits, a regime which is presently inaccessible if post-selection is required. We demonstrate a collapse of the data into a scale-invariant form with critical exponents agreeing with theory within uncertainty. Our demonstration paves the way for studies of measurement-induced entanglement phase transitions and associated critical phenomena on larger near-term quantum systems., Comment: 23 pages, 15 figures

Lithium niobate (LiNbO$_3$, LN) is a ferroelectric crystal of interest for integrated photonics owing to its large second-order optical nonlinearity and the ability to impart periodic poling via an external electric field. However, on-chip device performance based on thin-film lithium niobate (TFLN) is presently limited by propagation losses arising from surface roughness and corrugations. Atomic layer etching (ALE) could potentially smooth these features and thereby increase photonic performance, but no ALE process has been reported for LN. Here, we report an isotropic ALE process for $x$-cut MgO-doped LN using sequential exposures of H$_2$ and SF$_6$/Ar plasmas. We observe an etch rate of $1.59 \pm 0.02$ nm/cycle with a synergy of $96.9$%. We also demonstrate ALE can be achieved with SF$_6$/O$_2$ or Cl$_2$/BCl$_3$ plasma exposures in place of the SF$_6$/Ar plasma step with synergies of $99.5$% and $91.5$% respectively. The process is found to decrease the sidewall surface roughness of TFLN waveguides etched by physical Ar$^+$ milling by 30% without additional wet processing. Our ALE process could be used to smooth sidewall surfaces of TFLN waveguides as a post-processing treatment, thereby increasing the performance of TFLN nanophotonic devices and enabling new integrated photonic device capabilities.

Ab-initio calculations of charge transport properties in materials without adjustable parameters have provided microscopic insights into electron-phonon interactions which govern charge transport properties. Other transport properties such as the diffusion coefficient provide additional microscopic information and are readily accessible experimentally, but few ab-initio calculations of these properties have been performed. Here, we report first-principles calculations of the hot electron diffusion coefficient in Si and its dependence on electric field over temperatures from 77 -- 300 K. While qualitative agreement in trends such as anisotropy at high electric fields is obtained, the quantitative agreement that is routinely achieved for low-field mobility is lacking. We examine whether the discrepancy can be attributed to an inaccurate description of f-type intervalley scattering by computing the microwave-frequency noise spectrum and piezoresistivity. These calculations indicate that any error in the strength of f-type scattering is insufficient to explain the diffusion coefficient discrepancies. Our findings suggest that the measured diffusion coefficient is influenced by factors such as space charge effects which are not included in ab-initio calculations, impacting the interpretation of this property in terms of charge transport processes.

Microwave loss in superconducting titanium nitride (TiN) films is attributed to two-level systems in various interfaces arising in part from oxidation and microfabrication-induced damage. Atomic layer etching (ALE) is an emerging subtractive fabrication method which is capable of etching with Angstrom-scale etch depth control and potentially less damage. However, while ALE processes for TiN have been reported, they either employ HF vapor, incurring practical complications; or the etch rate lacks the desired control. Further, the superconducting characteristics of the etched films have not been characterized. Here, we report an isotropic plasma-thermal TiN ALE process consisting of sequential exposures to molecular oxygen and an SF$_6$/H$_2$ plasma. For certain ratios of SF$_6$:H$_2$ flow rates, we observe selective etching of TiO$_2$ over TiN, enabling self-limiting etching within a cycle. Etch rates were measured to vary from 1.1 \r{A}/cycle at 150 $^\circ$C to 3.2 \r{A}/cycle at 350 $^\circ$C using ex-situ ellipsometry. We demonstrate that the superconducting critical temperature of the etched film does not decrease beyond that expected from the decrease in film thickness, highlighting the low-damage nature of the process. These findings have relevance for applications of TiN in microwave kinetic inductance detectors and superconducting qubits., Comment: 17 pages, 7 figures

The transport properties of hot holes in silicon at cryogenic temperatures exhibit several anomalous features, including the emergence of two distinct saturated drift velocity regimes and a non-monotonic trend of the current noise versus electric field at microwave frequencies. Despite prior investigations, these features lack generally accepted explanations. Here, we examine the microscopic origin of these phenomena by extending a recently developed ab-initio theory of high-field transport and noise in semiconductors. We find that the drift velocity anomaly may be attributed to scattering dominated by acoustic phonon emission, leading to an additional regime of drift velocity saturation at temperatures $\sim 40$ K for which the acoustic phonon occupation is negligible; while the non-monotonic trend in the current noise arises due to the decrease in momentum relaxation time with electric field. The former conclusion is consistent with the findings of prior work, but the latter distinctly differs from previous explanations. This work highlights the use of high-field transport and noise phenomena as sensitive probes of microscopic charge transport phenomena in semiconductors., Comment: 19 pages, 4 figures

The semiconductor BAs has drawn significant interest due to experimental reports of simultaneous high thermal conductivity and ambipolar charge mobility. The \textit{ab~initio} prediction of high electron and hole mobility assumed the dominance of charge carrier scattering by one phonon. Recently, higher-order electron-phonon scattering processes in polar and non-polar semiconductors have been reported to have a non-negligible impact on charge transport properties, suggesting they may play a role in BAs as well. Here, we report an \textit{ab~initio} study of two-phonon electron and hole scattering processes in BAs. We find that inclusion of these higher-order processes reduces the computed room temperature electron and hole mobility in BAs by around 40\% from the one-phonon value, resulting in an underestimate of experimental values by a similar percentage. We suggest an experimental approach to test these predictions using luminescence spectroscopy that is applicable to the defective samples which are presently available.

The deviations of cryogenic collector current-voltage characteristics of SiGe heterojunction bipolar transistors (HBTs) from ideal drift-diffusion theory have been a topic of investigation for many years. Recent work indicates that direct tunneling across the base contributes to the non-ideal current in highly-scaled devices. However, cryogenic discrepancies have been observed even in older-generation devices for which direct tunneling is negligible, suggesting another mechanism may also contribute. Although similar non-ideal current-voltage characteristics have been observed in Schottky junctions and were attributed to spatial inhomogeneities in the base-emitter junction potential, this explanation has not been considered for SiGe HBTs. Here, we experimentally investigate this hypothesis by characterizing the collector current ideality factor and built-in potential of a SiGe HBT versus temperature using a cryogenic probe station. The temperature-dependence of the ideality factor and the relation between the built-in potential as measured by capacitance-voltage and current-voltage characteristics are in good qualitative agreement with the predictions of a theory of electrical transport across a junction with a Gaussian distribution of potential barrier heights. These observations suggest that lateral inhomogeneities in the base-emitter junction potential may contribute to the cryogenic non-idealities. This work helps to identify the physical mechanisms limiting the cryogenic microwave noise performance of SiGe HBTs.

The quantum computation of molecular response properties on near-term quantum hardware is a topic of significant interest. While computing time-domain response properties is in principle straightforward due to the natural ability of quantum computers to simulate unitary time evolution, circuit depth limitations restrict the maximum time that can be simulated and hence the extraction of frequency-domain properties. Computing properties directly in the frequency domain is therefore desirable, but the circuits require large depth when the typical hardware gate set consisting of single- and two-qubit gates is used. Here, we report the experimental quantum computation of the response properties of diatomic molecules directly in the frequency domain using a three-qubit iToffoli gate, enabling a reduction in circuit depth by a factor of two. We show that the molecular properties obtained with the iToffoli gate exhibit comparable or better agreement with theory than those obtained with the native CZ gates. Our work is among the first demonstrations of the practical usage of a native multi-qubit gate in quantum simulation, with diverse potential applications to the simulation of quantum many-body systems on near-term digital quantum computers., Comment: 10 pages, 6 figures

Recent ab-initio studies of electron transport in GaAs have reported that electron-phonon (e-ph) interactions beyond the lowest order play a fundamental role in charge transport and noise phenomena. Inclusion of the next-leading-order process in which an electron scatters with two phonons was found to yield good agreement for the high-field drift velocity, but the characteristic non-monotonic trend of the power spectral density of current fluctuations (PSD) with electric field was not predicted. The high computational cost of the ab-initio approach necessitated various approximations to the two-phonon scattering term, which were suggested as possible origins of the discrepancy. Here, we report a semi-analytical transport model of two-phonon electron scattering via the Fr\"ohlich mechanism, allowing a number of the approximations in the ab-initio treatment to be lifted while retaining the accuracy to within a few percent. We compare the calculated and experimental transport and noise properties as well as scattering rates measured by photoluminescence experiments. We find quantitative agreement within 15% for the drift velocity and 25% for the $\Gamma$ valley scattering rates, and agreement with the $\Gamma-L$ intervalley scattering rates within a factor of two. Considering these results and prior studies of current noise in GaAs, we conclude that the most probable origin of the non-monotonic PSD trend versus electric field is the formation of space charge domains rather than intervalley scattering as has been assumed., Comment: 28 pages (including 5 pages appendix), 3 figures, submitted to Physical Review B

We report the on-wafer characterization of $S$-parameters and microwave noise temperature ($T_{50}$) of discrete metamorphic InGaAs high electron mobility transistors (mHEMTs) at 40 K and 300 K and over a range of drain-source voltages ($V_{DS}$). From these data, we extract a small-signal model and the drain (output) noise current power spectral density ($S_{id}$) at each bias and temperature. This procedure enables $S_{id}$ to be obtained while accounting for the variation of small-signal model, noise impedance match, and other parameters under the various conditions. We find that the thermal noise associated with the channel conductance can only account for a portion of the measured output noise. Considering the variation of output noise with physical temperature and bias and prior studies of microwave noise in quantum wells, we hypothesize that a hot electron noise source based on real-space transfer of electrons from the channel to the barrier could account for the remaining portion of $S_{id}$. We suggest further studies to gain insights into the physical mechanisms. Finally, we calculate that the minimum HEMT noise temperature could be reduced by up to $\sim 50$% and $\sim 30$% at cryogenic temperature and room temperature, respectively, if the hot electron noise could be suppressed., Comment: 7 pages, 5 figures

We report the isotropic plasma atomic layer etching (ALE) of aluminum nitride using sequential exposures of SF$_6$ plasma and trimethylaluminum (Al(CH$_3$)$_3$, TMA). ALE was observed at temperatures greater than 200 $^\circ$C, with a maximum etch rate of 1.9 \r{A}/cycle observed at 300 $^\circ$C as measured using ex-situ ellipsometry. After ALE, the etched surface was found to contain a lower concentration of oxygen compared to the original surface and exhibited a $\sim 35$% decrease in surface roughness. These findings have relevance for applications of AlN in nonlinear photonics and wide bandgap semiconductor devices.

The ab-initio theory of charge transport in semiconductors typically employs the lowest-order perturbation theory in which electrons interact with one phonon (1ph). This theory is accepted to be adequate to explain the low-field mobility of non-polar semiconductors but has not been tested extensively beyond the low-field regime. Here, we report first-principles calculations of the electric field-dependence of the electron mobility of Si as described by the warm electron coefficient, $\beta$. Although the 1ph theory overestimates the low-field mobility by only around 20%, it overestimates $\beta$ by over a factor of two over a range of temperatures and crystallographic axes. We show that the discrepancy in $\beta$ is reconciled by inclusion of on-shell iterated 2-phonon (2ph) scattering processes, indicating that scattering from higher-order electron-phonon interactions is non-negligible even in non-polar semiconductors. Further, a ~20% underestimate of the low-field mobility with 2ph scattering suggests that non-trivial cancellations may occur in the perturbative expansion of the electron-phonon interaction., Comment: 18 pages, 3 figures, submitted

The parameter-free computation of charge transport properties of semiconductors is now routine owing to advances in the ab-initio description of the electron-phonon interaction. Many studies focus on the low-field regime in which the carrier temperature equals the lattice temperature and the current power spectral density (PSD) is proportional to the mobility. The calculation of high-field transport and noise properties offers a stricter test of the theory as these relations no longer hold, yet few such calculations have been reported. Here, we compute the high-field mobility and PSD of hot holes in silicon from first principles at temperatures of 77 and 300 K and electric fields up to 20 kV cm$^{-1}$ along various crystallographic axes. We find that the calculations quantitatively reproduce experimental trends including the anisotropy and electric-field dependence of hole mobility and PSD. The experimentally observed rapid variation of energy relaxation time with electric field at cryogenic temperatures is also correctly predicted. However, as in low-field studies, absolute quantitative agreement is in general lacking, a discrepancy that has been attributed to inaccuracies in the calculated valence band structure. Our work highlights the use of high-field transport and noise properties as a rigorous test of the theory of electron-phonon interactions in semiconductors., Comment: 19 pages, 4 figures

The fundamental limits of the microwave noise performance of high electron mobility transistors (HEMTs) are of scientific and practical interest for applications in radio astronomy and quantum computing. Self-heating at cryogenic temperatures has been reported to be a limiting mechanism for the noise, but cryogenic cooling strategies to mitigate it, for instance using liquid cryogens, have not been evaluated. Here, we report microwave noise measurements of a packaged two-stage HEMT amplifier immersed in normal and superfluid $^4$He baths and in vacuum from 1.6 - 80 K. We find that these liquid cryogens are unable to mitigate the thermal noise associated with self-heating. Considering this finding, we examine the implications for the lower bounds of cryogenic noise performance in HEMTs. Our analysis supports the general design principle for cryogenic HEMTs of maximizing gain at the lowest possible power., Comment: 36 pages (including 15 SI pages), 9 figures (including 3 SI figures), 2 tables (including 2 SI tables)

Simulating complex molecules and materials is an anticipated application of quantum devices. With strong quantum advantage demonstrated in artificial tasks, we examine how such advantage translates into modeling physical problems of correlated electronic structure. We simulate static and dynamical electronic structure on a superconducting quantum processor derived from Google's Sycamore architecture for two representative correlated electron problems: the nitrogenase iron-sulfur molecular clusters, and $\alpha$-ruthenium trichloride, a proximate spin-liquid material. To do so, we simplify the electronic structure into low-energy spin models that fit on the device. With extensive error mitigation and assistance from classically simulated data, we achieve quantitatively meaningful results deploying about 1/5 of the gate resources used in artificial quantum advantage experiments on a similar architecture. This increases to over 1/2 of the gate resources when choosing a model that suits the hardware. Our work serves to convert artificial measures of quantum advantage into a physically relevant setting., Comment: 17 pages, 5 figures

Ergodic quantum many-body systems undergoing unitary dynamics evolve towards increasingly entangled states characterized by an extensive scaling of entanglement entropy with system volume. At the other extreme, quantum systems repeatedly measured may be stabilized in a measurement eigenstate, a phenomenon known as the quantum Zeno effect. Recently, the intermediate regime in which unitary evolution is interspersed with quantum measurements has become of interest. Numerical studies have reported the existence of distinct phases characterized by volume- and area-law entanglement entropy scaling for infrequent and frequent measurement rates, respectively, separated by a critical measurement rate. The experimental investigation of these dynamic quantum phases of matter on near-term quantum hardware is challenging due to the need for repeated high-fidelity mid-circuit measurements and fine control over the evolving unitaries. Here, we report the realization of a measurement-induced entanglement transition on superconducting quantum processors with mid-circuit readout capability. We directly observe extensive and sub-extensive scaling of entanglement entropy in the volume- and area-law phases, respectively, by varying the rate of projective measurements. We further demonstrate phenomenological critical behavior of the transition by performing a data collapse for different system sizes. Our work paves the way for the use of mid-circuit measurement as an effective resource for quantum simulation on near-term quantum computers, for instance by facilitating the study of dynamic and long-range entangled quantum phases., Comment: 10 pages, 4 figures; supplementary material 7 pages, 6 figures

High-field charge transport in semiconductors is of fundamental interest and practical importance. While the \textit{ab initio} treatment of low-field transport is well-developed, the treatment of high-field transport is much less so, particularly for multi-phonon processes that are reported to be relevant in GaAs. Here, we report a calculation of the high-field transport properties and current power spectral density (PSD) of hot electrons in GaAs from first principles including on-shell two-phonon (2ph) scattering. The on-shell 2ph scattering rates are found to qualitatively alter the high-field distribution function by increasing both the momentum and energy relaxation rates as well as contributing markedly to intervalley scattering. This finding reconciles a long-standing discrepancy regarding the strength of intervalley scattering in GaAs as inferred from transport and optical studies. The characteristic non-monotonic trend of PSD with electric field is not predicted at this level of theory. Our work shows how \textit{ab initio} calculations of high-field transport and noise may be used as a stringent test of the electron-phonon interaction in semiconductors., Comment: 34 pages, 6 figures, submitted to Physical Review B

The realization of novel phases of matter on quantum simulators is a topic of intense interest. Digital quantum computers offer a route to prepare topological phases with interactions that do not naturally arise in analog quantum simulators. Here, we report the realization of symmetry-protected topological (SPT) phases of a spin-{1/2} Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor. We observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string order parameters. Our work advances ongoing efforts to realize novel states of matter with exotic interactions on digital near-term quantum computers., Comment: 10 pages, 3 figures

The thermal transport properties of oriented polymers are of fundamental and practical interest. High thermal conductivities ($\gtrsim 50$ Wm$^{-1}$K$^{-1}$) have recently been reported in disentangled ultra-high molecular weight polyethylene (UHMWPE) films, considerably exceeding prior reported values for oriented films. However, conflicting explanations have been proposed for the microscopic origin of the high thermal conductivity. Here, we report a characterization of the thermal conductivity and mean free path accumulation function of disentangled UHMWPE films (draw ratio $\sim 200$) using cryogenic steady-state thermal conductivity measurements and transient grating spectroscopy. We observe a marked dependence of the thermal conductivity on grating period over temperatures from 30 - 300 K. Considering this observation, cryogenic bulk thermal conductivity measurements, and analysis using an anisotropic Debye model, we conclude that longitudinal atomic vibrations with mean free paths around 400 nanometers are the primary heat carriers and that the high thermal conductivity for draw ratio $\gtrsim 150$ arises from the enlargement of extended crystals with drawing. The mean free paths appear to remain limited by the extended crystal dimensions, suggesting that the upper limit of thermal conductivity of disentangled UHMWPE films has not yet been realized.

The study of pinnacle sets has been a recent area of interest in combinatorics. Given a permutation, its pinnacle set is the set of all values larger than the values on either side of it. Largely inspired by conjectures posed by Davis, Nelson, Petersen, and Tenner and also results proven recently by Fang, this paper aims to add to our understanding of pinnacle sets. In particular, we give a simpler and more combinatorial proof of a weighted sum formula previously proven by Fang. Additionally, we give a recursion for counting the admissible orderings of the elements of a potential pinnacle set. Finally, we give another way of viewing pinnacle sets that sheds light on their structure and also yields a recursion for counting the number of permutations with that pinnacle set.

High electron mobility transistors are widely used as microwave amplifiers owing to their low microwave noise figure. Electronic noise in these devices is typically modeled by noise sources at the gate and drain. While consensus exists regarding the origin of the gate noise, that of drain noise is a topic of debate. Here, we report a theory of drain noise as a type of partition noise arising from real-space transfer of hot electrons from the channel to the barrier. The theory accounts for the magnitude and dependencies of the drain temperature and suggests strategies to realize devices with lower noise figure.

Consider a permutation p to be any finite list of distinct positive integers. A statistic is a function St whose domain is all permutations. Let S(p,q) be the set of shuffles of two disjoint permutations p and q. We say that St is shuffle compatible if the distribution of St over S(p,q) depends only on St(p), St(q), and the lengths of p and q. This notion is implicit in Stanley's work on P-partitions and was first explicitly studied by Gessel and Zhuang. One of the places where shuffles are useful is in describing the product in the algebra of quasisymmetric functions. Recently Adin, Gessel, Reiner, and Roichman defined an algebra of cyclic quasisymmetric functions where a cyclic version of shuffling comes into play. The purpose of this paper is to define and study cyclic shuffle compatibility. In particular, we show how one can lift shuffle compatibility results for (linear) permutations to cyclic ones. We then apply this result to cyclic descents and cyclic peaks. We also discuss the problem of finding a cyclic analogue of the major index., Comment: 13 pages, the new version fixes some minor errors

Silicon-germanium heterojunction bipolar transistors (HBTs) are of interest as low-noise microwave amplifiers due to their competitive noise performance and low cost relative to III-V devices. The fundamental noise performance limits of HBTs are thus of interest, and several studies report that quasiballistic electron transport across the base is a mechanism leading to cryogenic non-ideal IV characteristics that affects these limits. However, this conclusion has not been rigorously tested against theoretical predictions because prior studies modeled electron transport with empirical approaches or approximate solutions of the Boltzmann equation. Here, we study non-diffusive transport in narrow-base SiGe HBTs using an exact, semi-analytic solution of the Boltzmann equation based on an asymptotic expansion approach. We find that the computed transport characteristics are inconsistent with experiment, implying that quasiballistic electron transport is unlikely to be the origin of cryogenic non-ideal IV characteristics. Our work helps to identify the mechanisms governing the lower limits of the microwave noise figure of cryogenic HBT amplifiers.

The study of pattern containment and avoidance for linear permutations is a well-established area of enumerative combinatorics. A cyclic permutation is the set of all rotations of a linear permutation. Callan initiated the study of permutation avoidance in cyclic permutations and characterized the avoidance classes for all single permutations of length 4. We continue this work. In particular, we establish a cyclic variant of the Erdos-Szekeres Theorem that any linear permutation of length mn+1 must contain either the increasing pattern of length m+1 or the decreasing pattern of length n+1. We then derive results about avoidance of multiple patterns of length 4. We also determine generating functions for the cyclic descent statistic on these classes. Finally, we end with various open questions and avenues for future research., Comment: 23 pages, 3 figures, 1 table