Understanding Edge-of-Stability Training Dynamics with a Minimalist Example

Recently, researchers observed that gradient descent for deep neural networks operates in an ``edge-of-stability'' (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) is often larger than stability threshold 2/$\eta$ (where $\eta$ is the step size). Despite this, the loss oscillates and converges in the long run, and the sharpness at the end is just slightly below $2/\eta$. While many other well-understood nonconvex objectives such as matrix factorization or two-layer networks can also converge despite large sharpness, there is often a larger gap between sharpness of the endpoint and $2/\eta$. In this paper, we study EoS phenomenon by constructing a simple function that has the same behavior. We give rigorous analysis for its training dynamics in a large local region and explain why the final converging point has sharpness close to $2/\eta$. Globally we observe that the training dynamics for our example has an interesting bifurcating behavior, which was also observed in the training of neural nets.Comment: 53 pages, 19 figure

Generating accurate negative samples for landslide susceptibility mapping: A combined self-organizing-map and one-class SVM method

The accuracy of data-driven landslide susceptibility mapping (LSM) is closely affected by the quality of non-landslide samples. This research proposes a method combining a self-organizing-map (SOM) and a one-class SVM (SOM-OCSVM) to generate more reasonable non-landslide samples. We designed two steps: first, a random selection, a SOM network, a one class SVM model, and a SOM-OCSVM model were used to generate non-landslide sample datasets. Second, four machine learning models (MLs)—namely logistic regression (LRG), multilayer perceptron (MLP), support vector machine (SVM), and random forest (RF)—were used to verify the effects of four non-landslide sample datasets on LSM. From the region along the Sichuan-Tibet Highway, we selected 11 conditioning factors and 1186 investigated landslides to perform the aforementioned experiments. The results show that the SOM-OCSVM method achieves the highest AUC (>0.94) and minimum standard deviation (<0.081) compared with other methods. Moreover, RF achieves the best performance in different datasets compared with other ML models. The aforementioned results prove that the proposed method can enhance the performance of ML models to produce more reliable LSM

High-efficiency ultrafast optical-to-electrical converters based on inas nanowire-plasmonic arrays

There has been a growing interest in developing high-efficiency ultrafast optical-to-electrical converters for advanced imaging and sensing applications. Here, we propose a three-dimensional (3D) plasmonic platform based on InAs nanowire arrays with self-assembled gold gratings, which converts a telecom-wavelength (1550 nm) optical beam to sub-picosecond current pulses with quantum efficiency up to 18.3%, while operating in photovoltaic mode, i.e., at zero bias. Using a comprehensive 3D photoresponse model, we reveal that the incident photons form tightly confined fields near the gratings at nanowire tips, and thus a majority of the photogenerated carriers are efficiently routed to the metal within a few tens of nanometers distance, resulting in ultrafast current pulses. In addition, we show that the amplitude of current pulses is robust to the nanowire surface quality and can be effectively tuned by varying the doping levels in nanowires. This work paves a way to realizing a low-power, highly compact, and low-cost device scheme for ultrafast pulse generation

Room-temperature midwavelength infrared InAsSb nanowire photodetector arrays with Al2O3 passivation

Developing uncooled photodetectors at midwavelength infrared (MWIR) is critical for various applications including remote sensing, heat seeking, spectroscopy, and more. In this study, we demonstrate room-temperature operation of nanowire-based photodetectors at MWIR composed of vertical selective-area InAsSb nanowire photoabsorber arrays on large bandgap InP substrate with nanoscale plasmonic gratings. We accomplish this by significantly suppressing the nonradiative recombination at the InAsSb nanowire surfaces by introducing ex situ conformal Al2O3 passivation shells. Transient simulations estimate an extremely low surface recombination velocity on the order of 103 cm/s. We further achieve room-temperature photoluminescence emission from InAsSb nanowires, spanning the entire MWIR regime from 3 to 5 μm. A dry-etching process is developed to expose only the top nanowire facets for metal contacts, with the sidewalls conformally covered by Al2O3 shells, allowing for a higher internal quantum efficiency. Based on these techniques, we fabricate nanowire photodetectors with an optimized pitch and diameter and demonstrate room-temperature spectral response with MWIR detection signatures up to 3.4 μm. The results of this work indicate that uncooled focal plane arrays at MWIR on low-cost InP substrates can be designed with nanostructured absorbers for highly compact and fully integrated detection platforms

Feasibility of achieving high detectivity at short- and mid-wavelength infrared using nanowire-plasmonic photodetectors with p-n heterojunctions

Photodetection at short- and mid-wavelength infrared (SWIR and MWIR) enables various sensing systems used in heat seeking, night vision, and spectroscopy. As a result, uncooled photodetection at these wavelengths is in high demand. However, these SWIR and MWIR photodetectors often suffer from high dark current, causing them to require bulky cooling accessories for operation. In this study, we argue for the feasibility of improving the room-temperature detectivity by significantly suppressing dark current. To realize this, we propose using (1) a nanowire-based platform to reduce the photoabsorber volume, which in turn reduces trap state population and hence G-R current, and (2) p-n heterojunctions to prevent minority carrier diffusion from the large bandgap substrate into the nanowire absorber. We prove these concepts by demonstrating a comprehensive 3-D photoresponse model to explore the level of detectivity offered by vertical InAs(Sb) nanowire photodetector arrays with self-assembled plasmonic gratings. The resultant electrical simulations show that the dark current can be reduced by three to four orders at room temperature, leading to a peak detectivity greater than 3.5×1010 cm Hz1/2W-1 within the wavelength regime of 2.0 – 3.4 μm, making it comparable to the best commercial and research InAs p-i-n homojunction photodiodes. In addition, we show that the plasmonic resonance peaks can be easily tuned by simply varying the exposed nanowire height. Finally, we investigate the impact of nanowire material properties, such as carrier mobility and carrier lifetime, on the nanowire photodetector detectivity. This work provides a roadmap for the electrical design of nanowire optoelectronic devices and stimulates further experimental validation for uncooled photodetectors at SWIR and MWIR

A three-dimensional insight into correlation between carrier lifetime and surface recombination velocity for nanowires

The performance of nanowire-based devices is predominantly affected by nonradiative recombination on their surfaces, or sidewalls, due to large surface-to-volume ratios. A common approach to quantitatively characterize surface recombination is to implement time-resolved photoluminescence to correlate surface recombination velocity with measured minority carrier lifetime by a conventional analytical equation. However, after using numerical simulations based on a three-dimensional (3D) transient model, we assert that the correlation between minority carrier lifetime and surface recombination velocity is dependent on a more complex combination of factors, including nanowire geometry, energy-band alignment, and spatial carrier diffusion in 3D. To demonstrate this assertion, we use three cases—GaAs nanowires, InGaAs nanowires, and InGaAs inserts embedded in GaAs nanowires—and numerically calculate the carrier lifetimes by varying the surface recombination velocities. Using this information, we then investigate the intrinsic carrier dynamics within those 3D structures. We argue that the conventional analytical approach to determining surface recombination in nanowires is of limited applicability, and that a comprehensive computation in 3D can provide more accurate analysis. Our study provides a solid theoretical foundation to further understand surface characteristics and carrier dynamics for 3D nanostructured materials

Uncooled photodetector at short-wavelength infrared using InAs nanowire photoabsorbers on InP with p-n heterojunctions

In this work, we demonstrate an InAs nanowire photodetector at short-wavelength infrared (SWIR) composed of vertically oriented selective-area InAs nanowire photoabsorber arrays on InP substrates, forming InAs–InP heterojunctions. We measure a rectification ratio greater than 300 at room temperature, which indicates a desirable diode performance. The dark current density, normalized to the area of nanowire heterojunctions, is 130 mA/cm2 at a temperature of 300 K and a reverse bias of 0.5 V, making it comparable to the state-of-the-art bulk InAs p-i-n photodiodes. An analysis of the Arrhenius plot of the dark current at reverse bias yields an activation energy of 175 meV from 190 to 300 K, suggesting that the Shockley–Read–Hall (SRH) nonradiative current is the primary contributor to the dark current. By using three-dimensional electrical simulations, we determine that the SRH nonradiative current originates from the acceptor-like surface traps at the nanowire-passivation heterointerfaces. The spectral response at room temperature is also measured, with a clear photodetection signature observed at wavelengths up to 2.5 μm. This study provides an understanding of dark current for small band gap selective-area nanowires and paves the way to integrate these improved nanostructured photoabsorbers on large band gap substrates for high-performance photodetectors at SWIR

Exploring time-resolved photoluminescence for nanowires using a three-dimensional computational transient model

Time-resolved photoluminescence (TRPL) has been implemented experimentally to measure the carrier lifetime of semiconductors for decades. For the characterization of nanowires, the rich information embedded in TRPL curves has not been fully interpreted and meaningfully mapped to the respective material properties. This is because their three-dimensional (3-D) geometries result in more complicated mechanisms of carrier recombination than those in thin films and analytical solutions cannot be found for those nanostructures. In this work, we extend the intrinsic power of TRPL by developing a full 3-D transient model, which accounts for different material properties and drift-diffusion, to simulate TRPL curves for nanowires. To show the capability of the model, we perform TRPL measurements on a set of GaAs nanowire arrays grown on silicon substrates and then fit the measured data by tuning various material properties, including carrier mobility, Shockley–Read–Hall recombination lifetime, and surface recombination velocity at the GaAs–Si heterointerface. From the resultant TRPL simulations, we numerically identify the lifetime characteristics of those material properties. In addition, we computationally map the spatial and temporal electron distributions in nanowire segments and reveal the underlying carrier dynamics. We believe this study provides a theoretical foundation for interpretation of TRPL measurements to unveil the complex carrier recombination mechanisms in 3-D nanostructured materials

InGaAs-GaAs nanowire avalanche photodiodes toward single-photon detection in free-running mode

Single-photon detection at near-infrared (NIR) wavelengths is critical for light detection and ranging (LiDAR) systems used in imaging technologies such as autonomous vehicle trackers and atmospheric remote sensing. Portable, high-performance LiDAR relies on silicon-based single-photon avalanche diodes (SPADs) because of their extremely low dark count rate (DCR) and afterpulsing probability, but their operation wavelengths are typically limited up to 905 nm. Although InGaAs-InP SPADs offer an alternative platform to extend the operation wavelengths to eye-safe ranges, their high DCR and afterpulsing severely limit their commercial applications. Here we propose a new separate absorption and multiplication avalanche photodiode (SAM-APD) platform composed of vertical InGaAs–GaAs nanowire arrays for single-photon detection. Among a total of 4400 nanowires constituting one photodiode, each avalanche event is confined in a single nanowire, which means that the avalanche volume and the number of filled traps can be drastically reduced in our approach. This leads to an extremely small afterpulsing probability compared with conventional InGaAs-based SPADs and enables operation in free-running mode. We show a DCR below 10 Hz, due to reduced fill factor, with photon count rates of 7.8 MHz and timing jitter less than 113 ps, which suggest that nanowire-based NIR focal plane arrays for single-photon detection can be designed without active quenching circuitry that severely restricts pixel density and portability in NIR commercial SPADs. Therefore, the proposed work based on vertical nanowires provides a new degree of freedom in designing avalanche photodetectors and could be a stepping stone for high-performance InGaAs SPADs