Physics-based Analytical Model Research Articles

Space Charge Redistribution in Epoxy Mold Compounds of High-Voltage ICs at Dry and Wet Conditions: Theory and Experiment

Space charge profile plays an important role in defining the charge transport and breakdown field of an insulator. Non-destructive experimental techniques (e.g., PEA measurement) have recently been used to track in-situ the time-evolution of space charge profiles within complex insulators, such as epoxy mold compounds. Unfortunately, the published results are often inconsistent (both positive and negative charge build-up have been reported), and the discrepancy remains unexplained. In this paper, we (i) derive a physics-based compact analytical model of homocharge injection, (ii) explain the time-and voltage-dependent redistribution of homo- and heterocharge, (iii) investigate experimentally and explain theoretically the importance of moisture ingress regarding space charge redistribution, and finally, (iv) summarize strategies to suppress space-charge related instability in modern ICs encapsulated by epoxy mold compounds.

Temperature dependency and linearity assessment of dual-metal gate stack junctionless accumulation-mode cylindrical surrounding gate (DMGS-JAM-CSG) MOSFET

A physics-based temperature-dependent analytical model for a Dual- Metal Gate Stack Junctionless Accumulation-Mode Cylindrical Surrounding Gate (DMGS-JAM-CSG) MOSFET has been presented in this paper by solving the 2D Poisson’s equation utilizing the suitable boundary conditions. The device performance is examined at various temperatures (T = 100K, 300K and 500K) by observing several parameters like potential, electric field, electron concentration and electron velocity. The obtained outcomes are also contrasted with the outcomes acquired after simulation. Further, the device is also analyzed for its analog performance. Lastly, to check the relevancy of the device for RFIC applications, linearity assessment is performed by evaluating its several figure of merits (FOMs) like second-order and third-order Voltage Intercept Points (VIP2, VIP3), third-order Intercept Input Power (IIP3), third-order Intermodulation Distortion (IMD3) and various higher order transconductances. The obtained results are contrasted with an analogous device and it is discovered that DMGS- JAM- CSG MOSFET device acquires better electrical and linearity characteristics. ATLAS 3D device simulator has been utilized to conduct the simulations.

Analytical breakdown voltage model for a partial SOI-LDMOS transistor with a buried oxide step structure

We have developed a simple physics-based two-dimensional analytical off-state breakdown voltage model of a partial buried oxide step structure (PBOSS) silicon-on-insulator laterally diffused metal oxide semiconductor (SOI-LDMOS) transistor. The analytical model includes the expressions of surface potential and electric field distributions in the drift region by solving the 2D Poisson equation. The electric field at the Si–SiO2 surface is modulated by additional electric field peaks developed due to the presence of the PBOSS structure. The uniformly distributed electric field results in improved breakdown voltage. Further, the breakdown voltage is analytically obtained by means of the critical electric field concept, to determine the breakdown characteristics. The model reveals the impact of the critical device design parameters such as thickness and length of the PBOSS structure, doping, and thickness of the drift region on the surface electric field and the breakdown voltage. The proposed model is verified by ATLAS two-dimensional simulations. The analytical model will be useful to design high-voltage SOI-LDMOS transistors for power switching applications.

Insights into unconventional behaviour of negative capacitance transistor through a physics-based analytical model

The present work investigates key attributes of metal–ferroelectric–metal–insulator–semiconductor (MFMIS) cylindrical nanowire (NW) transistor through a physics-based analytical model. The proposed NW MFMIS negative capacitance model is developed by solving the baseline short channel NW model coupled with one-dimensional Landau’s equation while considering the radial dependency of electric field in the ferroelectric, a key feature for NW architecture. Contrary to the expected behaviour of a short channel MOSFET, the analytical framework successfully captures the unconventional effects such as an increase in the threshold voltage, lowering of subthreshold swing, and a negative value of drain-induced barrier lowering with gate length downscaling in MFMIS cylindrical NW devices. Also, the impact of ferroelectric thickness, spacer induced polarization charge density, remnant polarization and coercive field on the unconventional short channel effects have been examined. The influence of different ferroelectric materials (Al–HfO2, Gd–HfO2, Y–HfO2, and HZO) on the extent of internal amplification has also been investigated. The developed model provides new insights into the functioning and optimization of NW MFMIS architecture for facilitating hysteresis-free high internal voltage amplification with sub-60 mV/decade swing.

Residual stress modeling considering microstructure evolution in metal additive manufacturing

Metal additive manufacturing (AM) process induces residual stress which can hinder the applicability of AM. Residual stress build-up causes part failure due to the crack initiation and growth, and also distortion during or after fabrication. Consequently, it is of great importance to accurately and rapidly predict residual stress within the AM parts. During the thermal loading, the grain size is altered at the subsurface through dynamic recrystallization (DRx) and subsequent recovery. The yield strength of the alloys is largely determined by the size of nucleated grains, and it has a substantial influence on residual stress build-up. In this work, a physics-based analytical model is proposed to predict the residual stress considering the microstructure of the additively manufactured part. The thermal signature of this process is predicted using a transient moving point heat source. Due to the high-temperature gradient innate in this process, material may experience high thermal stress which often exceeds the yield strength. The thermal stress is obtained from Green’s functions of stresses due to the point body load. The modified Johnson-Cook flow stress model is used to predict the yield surface. In this flow stress model, the yield strength parameter is modified to incorporate the effect of grain size using Hall-Petch equation. The dynamic recrystallization and the resultant grain size are predicted by utilizing the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model for IN718 alloy. Moreover, a grain refinement model is used to include the effect of the rapid solidification on grain size. Then, as a result of the cyclic heating and cooling and the fact that the material is yielded, the residual stress build-up is precited from incremental plasticity and kinematic hardening behavior of the metal according to the property of volume invariance in plastic deformation in coupling with equilibrium and compatibility conditions. Results from the analytical residual stress model showed good agreement with X-ray diffraction measurements used to determine the residual stresses in the IN718 specimens. Moreover, the phases present in the IN178 samples built via direct metal disposition (DMD) are evaluated using X-ray diffraction.

A Physics-Based Analytical Model for Current–Voltage Characteristics of Perovskite Solar Cells Incorporating Bulk Recombination

A physics-based compact analytical model for studying the current–voltage characteristics of perovskite solar cells has been proposed by considering the external voltage-dependent carrier transport, exponential photon absorption, and bulk charge carrier recombination. The explicit analytical expressions for both the forward dark and photocurrents in perovskite solar cells are derived. The current in the external circuit is calculated considering the actual solar spectrum. The mathematical models are verified and useful physical parameters are extracted by comparing the model calculations with the published experimental results on various perovskite solar cells. The proposed model shows excellent agreement with the experimental results. The power conversion efficiency can be improved further by enhancing the carrier transport in the perovskite layer. The improvement in charge carrier transport enhances the fill factor and hence the power conversion efficiency.

Mechanics Modeling of Residual Stress Considering Effect of Preheating in Laser Powder Bed Fusion

This study aimed at the investigation of the effect of substrate temperature on residual stress in laser powder bed fusion using a physics-based analytical model. In this study, an analytical model is proposed to predict the residual stress through the calculation of preheating affected temperature profile and thermal stress. The effect of preheating is super-positioned with initial temperature in the modeling of temperature profile using a moving heat source approach; the resultant temperature gradient is then employed to predict the thermal stress from a point body load approach. If the thermal stress exceeds the yield strength of the material, then the residual stress under cyclic heating and cooling will be calculated based on the incremental plasticity and kinematic hardening behavior of metal. IN718 is used as a material example to pursue this investigation. To validate the predicted residual stress, experimental measurements are conducted using X-ray diffraction on IN718 samples manufactured via laser powder bed fusion under different process conditions. Results showed that preheating of the substrate could reduce the residual stress in an additively manufactured part due to the reduction in temperature gradient and resultant shrinkage stresses. However, the excessive preheating could have an opposite impact on residual stress accumulation. Moreover, the results confirm that the proposed model is a valuable tool for the prediction of residual stress, eliminating the costly experiments and time-consuming finite element simulations.

Analytical Model for Two-Dimensional Electron Gas Charge Density in Recessed-Gate GaN High-Electron-Mobility Transistors

A physics-based analytical model for GaN high-electron-mobility transistors (HEMTs) with non-recessed- and recessed-gate structure is presented. Based on this model, the two-dimensional electron gas density (2DEG) and thereby the on-state resistance and breakdown voltage can be controlled by varying the barrier layer thickness and Al mole fraction in non-recessed depletion-mode GaN HEMTs. The analytical model indicates that the 2DEG charge density in the channel increases from 2.4 × 1012 cm−2 to 1.8 × 1013 cm−2 when increasing the Al mole fraction from x = 0.1 to 0.4 for an experimental non-recessed-gate GaN HEMT. In the recessed-gate GaN HEMT, in addition to these parameters, the recess height can also control the 2DEG to achieve high-performance power electronic devices. The model also calculates the critical recess height for which a normally-ON GaN switch becomes normally-OFF. This model shows good agreement with reported experimental results and promises to become a useful tool for advanced design of GaN HEMTS.

Analytical model for the inductive turn-off process of GCT with dynamic avalanche

Dynamic avalanche injection during the turn-off of the gate commutated thyristors (GCTs) can slow down the removal of the remaining carriers, thereby affecting the turn-off characteristics. In addition, it is also a key factor inducing the turn-off failure of the device. However, the analytical model for the turn-off process considering dynamic avalanche effect has been not developed so far. In this paper, the turn-off process is divided into two phases, without dynamic avalanche and with dynamic avalanche, to be analyzed while assuming the appearance of the electron current in the space charge region of the P base/N- drift junction as the initial condition of occurrence of dynamic avalanche. As a result, a one-dimensional (1-D) physics-based analytical model is derived based on the basic principles of semiconductor and it gives insight into the details of internal physical mechanisms of the GCTs when dynamic avalanche occurs. And the analytically calculated results obtain a good agreement with the numerical simulations on the whole. It is also revealed that the avalanche-generated current filament is the main reason causing the difference between the 1-D analytical model and the two-dimensional (2-D) numerical simulation.

A virtual sensing approach for monitoring melt-pool dimensions using high speed coaxial imaging during laser powder bed fusion of metals

Abstract Metal parts produced by Laser Powder Bed Fusion (L-PBF) are frequently used for demanding applications. To meet stringent safety and certification requirements, a better understanding of melt-pool behavior and stability during processing is desired. This work presents a novel, fast and economically feasible virtual sensing approach for accurate estimation of melt-pool depth and width during L-PBF of metals. In a first step, the melt-pool width is determined by GPU-based processing of images from a high-speed coaxial camera monitoring system. In a second step, a physics-based analytical model is used to calculate the melt-pool depth-to-width ratio from the processing conditions and material properties. In a third and last step, the results from the first two steps are combined to estimate the melt-pool depth. Experimental validation of these predicted melt-pool dimensions is performed on 316L SS single layer strips that are consecutively produced, cross-sectioned, polished and etched to reveal the actual melt-pool boundaries. The results indicate an average relative error on the predicted melt-pool depth of 9.9% and 2.8% for the full L-PBF parameter range and for the optimal parameter range respectively. This gives confidence in the predictive capabilities of a virtual sensing approach using coaxial camera images for the assessment of the melt-pool depth and process stability.

Compositional and entropy indirect noise generated in subsonic non-isentropic nozzles

Abstract

Modeling and Analysis of Double Channel GaN HEMTs Using a Physics-Based Analytical Model

In this work, we report the development of a new physics-based analytical model for current and charge characteristics of Double Channel (DC) Gallium Nitride High Electron Mobility Transistors (GaN-HEMTs). The model has at its core the self-consistent calculation of the charge densities, for both upper and lower channels, obtained from a solution of the Schrodinger and Poisson equations. Fermi-Dirac (FD) distribution together with 2D density of states is used for mobile carrier statistics in both the channels. Furthermore, drift-diffusion transport is used to compute the channel current using charge densities at channel extremities. Finally, the model is validated against TCAD simulation and experimental data for a DC-GaN-HEMT. The model, by virtue of its fully physics-based nature, precisely captures the charge screening effect in the lower channel without invoking any empirical clamping functions, unlike prior models, and also possesses the feature of being geometrically scalable.

Parasitic Capacitance Modeling of Copper-Foiled Medium-Voltage Filter Inductors Considering Fringe Electrical Field

This article characterizes three parasitic capacitances in copper-foiled medium-voltage inductors. It is found that the conventional modeling method overlooks the effect of the fringe field, which leads to inaccurate modeling of parasitic capacitances in copper-foiled inductors. To address this problem, the parasitic capacitances contributed by the fringe electrical field is identified first, and a physics-based analytical modeling method for the parasitic capacitances contributed by the fringe electrical field is proposed, which avoids using any empirical equations. The total parasitic capacitances are then derived for three different cases with three different core potentials, from which a three-terminal equivalent circuit is derived, and thus, the parasitic capacitances in copper-foiled inductors are explicitly identified. The calculated results show a close agreement with the measured capacitance by using an impedance analyzer. Two recommendations for reducing the parasitic capacitances in copper-foiled inductors are given in this article.

A Dynamic Self-Clamping Caused by Dynamic Avalanche During the Turn-Off of PT-IGBT

A dynamic self-clamping is found during overstress turn-off of the PT-insulated gate bipolar transistor (IGBT) with a higher carrier lifetime. Theoretical analysis and numerical device simulation reveal that it is caused by the remaining plasma that cannot be completely removed due to dynamic avalanche injection. A 1-D physics-based analytical model for the self-clamping is established, and analytical results indicate that clamped voltage is inversely proportional to the initial turn-off current density and the carrier lifetime. When the dc-link voltage is larger than the clamped voltage of the device at a certain turn-off current, both terminal voltage and terminal current will be clamped, causing the device to lose control of the gate. Simulations of the multicell structure demonstrate that the avalanche-generated current filament under the self-clamping is stationary and may exist for a longer time, which is extremely likely to lead to local overheat and device destruction.

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation

Residual stress (RS) is the most challenging problem in metal additive manufacturing (AM) since the build-up of high tensile RS may influence the fatigue life, corrosion resistance, crack initiation, and failure of the additively manufactured components. While tensile RS is inherent in all the AM processes, fast and accurate prediction of the stress state within the part is extremely valuable and results in optimization of the process parameters to achieve a desired RS and control of the build process. This paper proposes a physics-based analytical model to rapidly and accurately predict the RS within the additively manufactured part. In this model, a transient moving point heat source (HS) is utilized to determine the temperature field. Due to the high temperature gradient within the proximity of the melt pool area, the material experiences high thermal stress. Thermal stress is calculated by combining three sources of stresses known as stresses due to the body forces, normal tension, and hydrostatic stress in a homogeneous semi-infinite medium. The thermal stress determines the RS state within the part. Consequently, by taking the thermal stress history as an input, both the in-plane and out of plane RS distributions are found from the incremental plasticity and kinematic hardening behavior of the metal by considering volume conservation in plastic deformation in coupling with the equilibrium and compatibility conditions. In this modeling, material properties are temperature-sensitive since the steep temperature gradient varies the properties significantly. Moreover, the energy needed for the solid-state phase transition is reflected by modifying the specific heat employing the latent heat of fusion. Furthermore, the multi-layer and multi-scan aspects of metal AM are considered by including the temperature history from previous layers and scans. Results from the analytical RS model presented excellent agreement with XRD measurements employed to determine the RS in the Ti-6Al-4V specimens.

A charge-based capacitance model for double-gate hetero-gate-dielectric tunnel FET

In this paper, a charge-based capacitance model has been proposed for a double-gate (DG) hetero-gate-dielectric tunnel FET (HGD-TFET). By solving the Poisson equation, the surface potential model is developed. The developed potential model is then used for developing the terminal capacitance model and drain current model. The device is working under enhancement-mode as the channel region is considered to be n-type doped. For developing the charge model, accumulated charges and ionized impurity charges are included in the channel charge equation. The developed model can capture the impact of V G = 0 V and V D = 0 V. The model can also successfully capture the scaling issues and gate dielectric variation. To ensure the performance of the developed model, the results are validated with TCAD simulation results and a good agreement is achieved between them. Since, high-k gate dielectric and low-k gate dielectric are used in a single structure, it combines the merit of both and hence, results in the performance improvement. • Physics-based analytical model has been developed for Hetero-gate dielectric TFET. • Surface potential, capacitance and drain current for HGD-TFET are modeled. • The models include the impact of zero gate bias and zero drain bias. • Impact of scaling and dielectric variation can also be captured by the developed model.

A Comprehensive Physics-Based Current–Voltage SPICE Compact Model for 2-D-Material-Based Top-Contact Bottom-Gated Schottky-Barrier FETs

In this article, we report the development of a novel physics-based analytical model for explaining the current-voltage relationship in Schottky barrier (SB) 2-D-material field effect transistors (FETs). The model has at its core the calculation of the surface-potential (SP) which is accomplished by invoking 2-D density of states in conjunction with Fermi-Dirac (FD) distribution for electron and hole statistics. The explicit computation for the SP, carried out using the Lambert-W function together with Halley's method, is used to construct the SP-based band-diagram for realizing the transparency of the SBs. Thereafter, the ambipolar current is derived in terms of the electron and hole injection phenomena-the thermionic emission and Fowler-Nordheim tunneling mechanisms-at the SB contacts. Furthermore, drift-diffusion current is derived in terms of the SP and incorporated in the model to account for the scattering in the intrinsic 2-D channel. Finally, the Verilog-A model is validated against experimental I-V data reported in the literature for two different 2-D-material systems. This is the first demonstration of an explicit SP-based SPICE model for ambipolar SB-2-D-FETs that is simultaneously built on tunneling-emission and drift-diffusion formalisms.

Modeling of High-Q Conical Inductors and MOM Capacitors for Millimeter- Wave Applications

Conical inductors and metal-oxide-metal (MOM) capacitors are shown to have higher qualityfactor (Q) characteristics at millimeter wave (mm-wave) frequencies over conventional inductors and nitride MIM capacitors. In this work, Physics-basedanalytical models are developed for conical inductors and MOM capacitors usable at mmwave frequencies. The linear voltage profile along the turns of the conical inductor is taken into account for capacitance calculation which is critical in accurately predicting Q-values. Two RL networks coupled by capacitors are proposed to capture the frequency-dependent characteristics of the MOM capacitor. The lumped elements in both these device models are frequency independent and can be calculated using layout and process parameters. The proposed models for conical inductors and MOM capacitors are verified with electromagnetic (EM) simulations till 100 GHz. A prototype 60-GHz bandpass filter (BPF) is fabricated using 0.18 μm RF-silicon on insulator (SOI) technology to validate the accuracy of the developed compact models. BPF simulation results using the proposed models are shown to be in excellent agreement with those produced with EM simulations and silicon measurements.

Analytical Modeling of Current and Quantum Capacitance of Single-Electron Transistor with Island Made of Armchair WSe2 Nanoribbon

Single-electron transistors (SETs), which operate by quantum-mechanically controlled coulomb blockade and the single-electron tunneling effect, are promising candidate future nanoelectronic devices. A physics-based analytical model is developed to study the current and quantum capacitance of a SET with an island made of monolayer tungsten diselenide (WSe2) nanoribbon in an armchair pattern. It is noteworthy that the SET current is not degraded much in the coulomb blockade region, whereas outside this region, the SET current decreases with varying width of the nanoribbon, presumably due to the greater width of the potential well in the island that lowers the tunneling rate. Since atomically thin nanoribbon possesses quantum capacitance, which might cause further degradation in the SET performance, its influences are also studied. A three-band nearest-neighbor tight-binding model is applied to assimilate the details and information of the energy band formation into the quantum capacitance estimation.

Combining learned and analytical models for predicting action effects from sensory data

One of the most basic skills a robot should possess is predicting the effect of physical interactions with objects in the environment. This enables optimal action selection to reach a certain goal state. Traditionally, dynamics are approximated by physics-based analytical models. These models rely on specific state representations that may be hard to obtain from raw sensory data, especially if no knowledge of the object shape is assumed. More recently, we have seen learning approaches that can predict the effect of complex physical interactions directly from sensory input. It is, however, an open question how far these models generalize beyond their training data. In this work, we investigate the advantages and limitations of neural-network-based learning approaches for predicting the effects of actions based on sensory input and show how analytical and learned models can be combined to leverage the best of both worlds. As physical interaction task, we use planar pushing, for which there exists a well-known analytical model and a large real-world dataset. We propose the use of a convolutional neural network to convert raw depth images or organized point clouds into a suitable representation for the analytical model and compare this approach with using neural networks for both, perception and prediction. A systematic evaluation of the proposed approach on a very large real-world dataset shows two main advantages of the hybrid architecture. Compared with a pure neural network, it significantly (i) reduces required training data and (ii) improves generalization to novel physical interaction.